/************************************/
/*                                  */
/*           Mathsteroids           */
/*                                  */
/************************************/
/* This code was written            */
/*               by Matthew Scroggs */
/*    mscroggs.co.uk/mathsteroids   */
/* github.com/mscroggs/mathsteroids */
/************************************/
/* This code is licensed under      */
/*                   an MIT license */
/************************************/

// inputs
var quitPressed  = false;
var upPressed    = false;
var firePressed  = false;
var leftPressed  = false;
var rightPressed = false;
var selectPressed = false;
var selectDone = false;
var mutePressed = false
var mute = false
var titlescreen = true

if(game_config("sound")){
    var sound_fire = new Audio(game_config("sound-dir") + '/fire.wav');
    var sound_thrust = new Audio(game_config("sound-dir") + '/thrust.wav');
    sound_thrust.loop = true
    var sound_bang_large = new Audio(game_config("sound-dir") + '/bangLarge.wav');
    var sound_bang_medium = new Audio(game_config("sound-dir") + '/bangMedium.wav');
    var sound_bang_small = new Audio(game_config("sound-dir") + '/bangSmall.wav');
    var sound_level_up = new Audio(game_config("sound-dir") + '/levelUp.wav');
    var sound_next = new Audio(game_config("sound-dir") + '/next.wav');
    var sound_start = new Audio(game_config("sound-dir") + '/start.wav');

    var sounds = [sound_fire, sound_thrust, sound_bang_large, sound_bang_medium,
                  sound_bang_small, sound_level_up, sound_next, sound_start]
    // force load
    for(var i = 0; i < sounds.length; i++){
        var a = sounds[i].cloneNode()
        a.volume = 0
        a.play()
    }
}

// titlescreen
var leftTimer=0
var rightTimer=0
var game_n = 0
var game_title = ""

// high score
var entered_name = ""
var entered_available_letters = "abcdefghijklmnopqrstuvwxyz !$"
var entered_letter = 0

// Global variables
var nscores = 5
var games = [
    // Sphere levels
    ["sphere (mercator projection)","sphere","Mercator"],
    ["sphere (isometric)","sphere","isometric"],
    ["sphere (stereographic projection)","sphere","stereographic"],
    ["sphere (gall-peters projection)","sphere","Gall"],
    ["sphere (craig retroazimuthal projection)","sphere","Craig"],
    ["sphere (azimuthal projection)","sphere","azim"],
    ["sphere (robinson projection)","sphere","Robinson"],
    ["sphere (sinusoidal projection)","sphere","sinusoidal"],
    ["sphere (mollweide projection)","sphere","Mollweide"],
    ["sphere (goode homolosine projection)","sphere","Goode"],
    ["sphere (van der grinten projection)","sphere","van der Grinten"],
    ["sphere (plate carée projection)","sphere","plate caree"],
    ["sphere (dymaxion map)","sphere","dymaxion"],
    ["sphere (tetrahedron net)","sphere","tetrahedron"],
    ["sphere (cube net)","sphere","cube"],
    ["sphere (octahedron net)","sphere","octahedron"],
    ["sphere (dodecahedron net)","sphere","dodecahedron"],
    ["sphere (icosahedron net)","sphere","icosahedron"],

    // Flat levels
    ["(flat) cylinder","flatcylinder","flat"],
    ["(flat) möbius strip","flatmobius","flat"],
    ["(flat) torus","flattorus","flat"],
    ["(flat) klein bottle","flatKlein","flat"],
    ["(flat) real projective plane","flatreal-pp","flat"],
    ["unbounded 2d space","flatunbounded", "unbounded"],
    ["loop (elliptical pool table)","pool","loop"],

    // Torus levels
    ["torus (top view)","torus","top_v"],
    ["torus (projected)","torus","projected"],

    // Hyperbolic levels
    ["hyperbolic circle (poincaré disk)","hyperbolic","Poincare"],
    ["hyperbolic circle (beltrami-klein)","hyperbolic","Beltrami-Klein"],
    ["hyperbolic circle (poincaré half-plane)","hyperbolic","Poincare HP"],
    ["hyperbolic circle (hyperboloid)","hyperbolic","hyperboloid"],
    ["hyperbolic circle (gans)","hyperbolic","gans"],
    ["hyperbolic circle (band)","hyperbolic","band"],
    ["unbounded hyperbolic (poincaré disk)","hyperbolicunbounded","Poincare"],
    ["unbounded hyperbolic (beltrami-klein)","hyperbolicunbounded","Beltrami-Klein"],
]

var projections = []
for(var i=0;i<games.length;i++){
    if(games[i][1]=="sphere"){
        projections[projections.length] = [games[i][2], i, games[i][0]]
    }
}

var options = {"surface":"sphere","projection":"Mercator"}
var mouse = "";
var WIDTH=800
var HEIGHT=450

var RADIUS = 2
var TRADIUS = [2,1]
var LOOPSIZE = [380,200]
var LOOPFOCUS = Math.sqrt(Math.pow(LOOPSIZE[0],2)-Math.pow(LOOPSIZE[1],2))
var MOBIUSY = 50
var Craig_zeroang = -0.3
var HYPER_RADIUS = 2

var score = 0
var lives = 3
var timestarted = 0
var timeleft = 60000
var asterN = 1

var fired = 0;
var fires = Array()
var spaceship = {"hangle":0,"vangle":0,"rotation":0,"speed":0,"direction":0}

var asteroids = Array()
var explode = Array()

var front_points = Array()
var back_points = Array()


function pass(){}
var interval = setInterval(pass, 10000)

// Game functions
function start_game(){
    reset()
    tick()
    clearInterval(interval)
    interval = setInterval(tick,1000/60);
}

function reset(){
    spaceship = {"hangle":0,"vangle":0,"rotation":0,"speed":0,"direction":0}
    if(options["surface"].substring(0,4)=="flat"){
        spaceship["hangle"] = WIDTH/2
        spaceship["vangle"] = HEIGHT/2
    } else if(options["surface"]=="sphere"){
        if(options["projection"]=="Mercator" || options["projection"]=="Gall"
        || options["projection"]=="Craig" || options["projection"]=="Robinson"
        || options["projection"] == "sinusoidal" || options["projection"]=="Mollweide"
        || options["projection"] == "Goode" || options["projection"] == "van der Grinten"
        || options["projection"] == "plate caree"){
            spaceship["hangle"] = Math.PI
        }
        if(options["projection"]=="stereographic"){
            spaceship["vangle"] = Math.PI/2
        }
        if(options["projection"]=="azim"){
            spaceship["vangle"] = Math.PI/2
        }
        if(options["projection"]=="octahedron"){
            spaceship["hangle"] = Math.PI/4
        }
        if(options["projection"]=="dodecahedron"){
            spaceship["hangle"] = 1.35*Math.PI
        }
        if(options["projection"]=="dymaxion"){
            spaceship["hangle"] = 1.8*Math.PI
            spaceship["vangle"] = 0.3*Math.PI
            spaceship["rotation"] = 7*Math.PI/6
        }
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        spaceship["hangle"] = 0
        spaceship["vangle"] = 0
    } else if(options["surface"]=="torus"){
        if(options["projection"] == "projected"){
            spaceship["hangle"] = Math.PI
            spaceship["vangle"] = Math.PI
        } else {
            spaceship["hangle"] = 3*Math.PI/2
            spaceship["vangle"] = Math.PI/2
        }
    } else if(options["projection"]=="loop"){
        spaceship["hangle"] = WIDTH/2 - LOOPFOCUS
        spaceship["vangle"] = HEIGHT/2
    }
    score = 0
    lives = 3
    var d = new Date()
    timestarted = d.getTime()
    fired = 0
    fires = Array()
    explode = Array()
    asterN = 2
    asteroids = make_new_asteroids(asterN)
    titlescreen = false
}

function make_new_asteroids(n){
    var out = Array()

    for(var i=0;i<n;i++){
        new_a = {"hangle":spaceship["hangle"],"vangle":spaceship["vangle"],
                 "rotation":Math.random()*Math.PI*2,"direction":Math.random()*Math.PI*2,
                 "size":4,"sides":2,
                 "radius":1,"speed":1}
        if(options["surface"].substring(0,4) == "flat"){
            new_a["speed"] = 0.5+Math.random()*0.5
            new_a["radius"] = 0.1
        } else if(options["surface"]=="sphere"){
            new_a["speed"] = 0.005+Math.random()*0.005
            new_a["radius"] = 0.01
        } else if(options["surface"].substr(0,10)=="hyperbolic"){
            new_a["speed"] = 0.001+Math.random()*0.001
            new_a["radius"] = 0.004
        } else if(options["surface"]=="torus"){
            new_a["speed"] = 0.005+Math.random()*0.005
            new_a["radius"] = 0.01
        }
        if(options["surface"] == "pool"){
            new_a["speed"] = 0.5+Math.random()*0.5
            new_a["radius"] = 0.1
        }
        while(too_close(new_a,spaceship)){
            if(options["surface"].substring(0,4) == "flat"){
                new_a["hangle"] = Math.random()*WIDTH
                if(options["surface"]=="flatmobius" || options["surface"]=="flatcylinder"){
                    new_a["vangle"] = Math.random()*(HEIGHT-2*MOBIUSY) + MOBIUSY
                } else {
                    new_a["vangle"] = Math.random()*HEIGHT
                }
            } else if(options["surface"]=="sphere"){
                new_a["hangle"] = Math.random()*Math.PI*2
                new_a["vangle"] = Math.random()*Math.PI-Math.PI/2
            } else if(options["surface"].substr(0,10)=="hyperbolic"){
                var ang = Math.random() * 2 * Math.PI
                var dist = Math.random() * HYPER_RADIUS
                var pt = hyper_add(0, 0, Math.random() * 2 * Math.PI, Math.random() * HYPER_RADIUS)
                new_a["hangle"] = pt[0]
                new_a["vangle"] = pt[1]
            } else if(options["surface"]=="torus"){
                new_a["hangle"] = Math.random()*Math.PI*2
                new_a["vangle"] = Math.random()*Math.PI*2
            } else if(options["projection"] == "loop"){
                var angle = Math.random()*Math.PI*2
                var rad = Math.random()
                new_a["hangle"] = WIDTH/2+rad*LOOPSIZE[0]*Math.cos(angle)
                new_a["vangle"] = HEIGHT/2+rad*LOOPSIZE[1]*Math.sin(angle)
            }
        }
        var as = get_a_s(new_a)
        new_a["radius"] = as["radius"]
        new_a["sides"] = as["sides"]

        out[i] = new_a
    }
    return out
}

function too_close(p,q){
    var d = 0
    var x1 = 0
    var x2 = 0
    var y1 = 0
    var y2 = 0
    var z1 = 0
    var z2 = 0
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        d = 80
        x1 = p["hangle"]
        x2 = q["hangle"]
        y1 = p["vangle"]
        y2 = q["vangle"]
        z1 = 0
        z2 = 0
    } else if(options["surface"]=="sphere"){
        d = 0.15
        x1 = Math.cos(p["hangle"])*Math.cos(p["vangle"])
        x2 = Math.cos(q["hangle"])*Math.cos(q["vangle"])
        y1 = Math.cos(p["hangle"])*Math.sin(p["vangle"])
        y2 = Math.cos(q["hangle"])*Math.sin(q["vangle"])
        z1 = Math.sin(p["vangle"])
        z2 = Math.sin(q["vangle"])
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        d = 0.15
        z1 = hyper_compute_distance(p["hangle"], p["vangle"], q["hangle"], q["vangle"])
    } else if(options["surface"]=="torus"){
        d = 0.2
        x1 = Math.cos(p["hangle"])*(TRADIUS[0]+TRADIUS[1]*Math.cos(p["vangle"]))
        x2 = Math.cos(q["hangle"])*(TRADIUS[0]+TRADIUS[1]*Math.cos(q["vangle"]))
        y1 = Math.sin(p["hangle"])*(TRADIUS[0]+TRADIUS[1]*Math.cos(p["vangle"]))
        y2 = Math.sin(q["hangle"])*(TRADIUS[0]+TRADIUS[1]*Math.cos(q["vangle"]))
        z1 = TRADIUS[1]*Math.sin(p["vangle"])
        z2 = TRADIUS[1]*Math.sin(q["vangle"])
    }
    if(Math.abs(x1-x2)<d && Math.abs(y1-y2)<d && Math.abs(z1-z2)<d){
        return true
    }
    return false
}

function toggle_mute(){
    if(game_config("sound")){
        if (mute) {
            mute = false
            sound_start.cloneNode().play()
        } else {
            mute = true
        }
    }
    if(titlescreen){
        redraw_menu()
    }
}
function tick(){
    if(quitPressed){
        show_menu()
        return
    }
    if(upPressed){
        if(game_config("sound") && !mute){ sound_thrust.play() }
        increase_speed()
    } else {
        if(game_config("sound") && !mute){ sound_thrust.pause() }
        decrease_speed()
    }
    if(leftPressed){
        rotate_left()
    }
    if(rightPressed){
        rotate_right()
    }
    if(selectPressed && options["surface"] == "sphere" && !selectDone){
        selectDone = true
        var pre_proj = options["projection"]
        while(pre_proj == options["projection"]){
            new_p = projections[Math.floor(Math.random() * projections.length)]
            options["projection"] = new_p[0]
            game_n = new_p[1]
            game_title = new_p[2]
        }
    }
    move_ship()
    move_fire()
    move_explodes()
    move_asteroids()

    if(game_config("game-mode") == "time") {
        var d = new Date()
        timeleft = timestarted + 60000 - d.getTime()
    }


    var canvas = document.getElementById("mathsteroids");
    var ctx = canvas.getContext("2d");
    ctx.fillStyle = "#000000";
    ctx.fillRect(0,0,WIDTH,HEIGHT);

    ctx.strokeStyle = "#FFFFFF"
    ctx.lineWidth = 2;
    ctx.beginPath()
    add_scaled_text(ctx,""+score,20,38,0.6)
    draw_lives(ctx)
    draw_mute(ctx)
    ctx.stroke();

    front_points = Array()
    back_points = Array()

    draw_shape()
    draw_fire()
    draw_asteroids()
    draw_explodes()
    draw_ship()

    ctx.beginPath()
    ctx.strokeStyle = "#444444"
    for(var i=0;i<back_points.length;i++){
        draw_line(ctx,back_points[i][0],back_points[i][1],back_points[i][2],back_points[i][3])
    }
    ctx.stroke()

    ctx.beginPath()
    ctx.strokeStyle = "#FFFFFF"
    for(var i=0;i<front_points.length;i++){
        draw_line(ctx,front_points[i][0],front_points[i][1],front_points[i][2],front_points[i][3])
    }
    ctx.stroke()

    if(lives<=0){highscore()}
    if(timeleft <= 0){highscore()}
}

function load_scores() {
    if(!game_config("high-scores")){ return }
    var score_file = "scores-" + options["surface"]
    var data = localStorage.getItem(score_file)
    var scores = []
    if (data != null){
        scores = JSON.parse(data)
    }
    return scores
}

function save_scores(scores) {
    if(!game_config("high-scores")){ return }
    var score_file = "scores-" + options["surface"]
    localStorage.setItem(score_file, JSON.stringify(scores))
}

function highscore() {
    clearInterval(interval)
    if(game_config("sound") && !mute){ sound_thrust.pause() }

    var canvas = document.getElementById("mathsteroids");
    var ctx = canvas.getContext("2d");
    ctx.fillStyle = "#000000";
    ctx.fillRect((WIDTH-270)/2,(HEIGHT-50)/2,270,50);

    ctx.strokeStyle = "#FFFFFF"
    ctx.lineWidth = 2;
    ctx.beginPath()
    add_text(ctx, "game over", (WIDTH-270)/2+10, (HEIGHT-50)/2+40)
    ctx.stroke();

    if(game_config("high-scores")){
        var scores = load_scores()
        if (score > 0 && (scores.length < nscores || score > scores[nscores-1][0])){
            setTimeout(enter_name,1000)
        } else {
            setTimeout(gameoveron,1000)
        }
    } else {
        setTimeout(gameoveron,1000)
    }
}

function enter_name()
{
    if(!game_config("high-scores")){ return }
    entered_name = ""
    entered_letter = 0

    name_tick()
    clearInterval(interval)
    interval = setInterval(name_tick,1000/60);
}

function show_enter_name()
{
    if(!game_config("high-scores")){ return }
    var canvas = document.getElementById("mathsteroids");
    var ctx = canvas.getContext("2d");
    ctx.fillStyle = "#000000";
    ctx.fillRect(0, 0, WIDTH, HEIGHT);
    ctx.strokeStyle = "#FFFFFF"
    ctx.lineWidth = 2;
    ctx.beginPath()
    add_text(ctx, "high score", (WIDTH-300)/2+10, (HEIGHT-50)/2-100)
    add_text(ctx, "enter your name", (WIDTH-440)/2+10, (HEIGHT-50)/2-50)
    add_text(ctx, entered_name, (WIDTH-100)/2+10, (HEIGHT-50)/2 + 20)
    add_text(ctx, "<< " + entered_available_letters[entered_letter] + " >>", (WIDTH-150)/2+15, (HEIGHT-50)/2 + 70)
    ctx.stroke();
}

function name_tick(){
    if(!game_config("high-scores")){ return }
    if(leftPressed){
        if(leftTimer==0){
            entered_letter--
            if (entered_letter < 0)
            {
                entered_letter += entered_available_letters.length
            }
        }
        leftTimer++
        leftTimer%=15
    } else {
        leftTimer = 0
    }
    if(rightPressed){
        if(rightTimer==0){
            entered_letter++
            if (entered_letter >= entered_available_letters.length)
            {
                entered_letter -= entered_available_letters.length
            }
        }
        rightTimer++
        rightTimer%=15
    } else {
        rightTimer = 0
    }
    if(firePressed){
        if (entered_letter == entered_available_letters.indexOf("!"))
        {
            // END
            scores = load_scores()
            var i = 0
            while (i < scores.length && scores[i][0] >= score){i++}
            new_scores = []
            for (var j = 0; j < i; j++)
            {
                new_scores[new_scores.length] = scores[j]
            }
            new_scores[new_scores.length] = [score, entered_name]
            for (var j = i; j < scores.length && new_scores.length < nscores; j++)
            {
                new_scores[new_scores.length] = scores[j]
            }
            save_scores(new_scores)
            firePressed = false
            gameoveron()
            return;
        } else if (entered_letter == entered_available_letters.indexOf("$")) {
            entered_name = entered_name.substr(0, entered_name.length - 1)
        } else {
            if (entered_name.length >= 3){
            }
            entered_name += entered_available_letters[entered_letter]
            if (entered_name.length == 3){
                entered_letter = entered_available_letters.indexOf("!")
            }
        }
        firePressed = false
    }
    show_enter_name()
}

function gameoveron(){
    clearInterval(interval)
    var canvas = document.getElementById("mathsteroids");
    var ctx = canvas.getContext("2d");
    ctx.fillStyle = "#000000";
    if(game_config("high-scores")){
        ctx.fillRect(40,40,WIDTH-80,WIDTH-40);
    } else {
        ctx.fillRect((WIDTH-430)/2,(HEIGHT-50)/2+60,430,40);
    }

    ctx.strokeStyle = "#FFFFFF"
    ctx.lineWidth = 2;
    ctx.beginPath()
    if(game_config("high-scores")){
        add_scaled_text(ctx, "high scores", (WIDTH-200)/2, 80, 0.6)

        scores = load_scores()
        for (var i = 0; i < scores.length; i++)
        {
          add_scaled_text(ctx, scores[i][1], WIDTH/2 - 70, 140 + 40*i, 0.6)
          add_scaled_text(ctx, scores[i][0]+"", WIDTH/2 + 10, 140 + 40*i, 0.6)
        }
        add_scaled_text(ctx, "press button to continue", (WIDTH-430)/2+10, HEIGHT-40, 0.6)
    } else {
        add_scaled_text(ctx, "press button to continue", (WIDTH-430)/2+10, (HEIGHT-50)/2+90, 0.6)
    }
    ctx.stroke();

    interval = setInterval(overtick,1000/60);
}
function overtick(){
    if(upPressed || firePressed || leftPressed || rightPressed || quitPressed){
        show_menu()
    }
}

function move_fire(){
    var new_fires = Array()
    for(var i=0;i<fires.length;i++){
        fires[i]["age"]++
        if(fires[i]["age"]<40){
            new_pos = move_on_surface(fires[i]["hangle"],fires[i]["vangle"],fires[i]["rotation"],fires[i]["speed"],1)
            fires[i]["hangle"] = new_pos["hangle"]
            fires[i]["vangle"] = new_pos["vangle"]
            fires[i]["rotation"] = new_pos["rotation"]
            new_fires[new_fires.length] = fires[i]
        }
    }
    fires = new_fires
    if(firePressed){
        if(fired==0){
            if(game_config("sound") && !mute){ sound_fire.cloneNode().play() }
            var leng = 0
            var speed = 0
            if(options["surface"].substring(0,4) == "flat" || options["surface"]=="pool"){
                leng = 10
                speed = 5
            } else if(options["surface"] == "sphere"){
                leng = 0.1
                speed = 0.05
            } else if(options["surface"] == "torus"){
                leng = 0.1
                speed = 0.05
            } else if(options["surface"].substr(0,10) == "hyperbolic"){
                leng = 0.05
                speed = 0.03
            }
            new_pos = move_on_surface(spaceship["hangle"],spaceship["vangle"],spaceship["rotation"],leng,1)
            new_pos["speed"] = speed + spaceship["speed"]*(Math.cos(spaceship["rotation"]-spaceship["direction"]))
            new_pos["rotation"] = new_pos["rotation"]
            new_pos["age"] = 0
            fires[fires.length] = new_pos
        }
        fired++
        fired%=15
    }
    if(!firePressed){
        fired=0
    }
}

function move_explodes(){
    var new_explode = Array()
    for(var i=0;i<explode.length;i++){
        explode[i]["age"]++
        if(explode[i]["age"]<20){
            new_explode[new_explode.length] = explode[i]
        }
    }
    explode = new_explode
}

function increase_speed(){
    var speed_add = 0
    var speed_max = 0
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        speed_add = 0.2
        speed_max = 5
    } else if(options["surface"]=="sphere"){
        speed_add = 0.002
        speed_max = 0.05
    } else if(options["surface"]=="torus"){
        speed_add = 0.002
        speed_max = 0.05
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        speed_add = 0.0012
        speed_max = 0.03
    }

    var new_speed_x = spaceship["speed"]*Math.cos(spaceship["direction"]) + speed_add*Math.cos(spaceship["rotation"])
    var new_speed_y = spaceship["speed"]*Math.sin(spaceship["direction"]) + speed_add*Math.sin(spaceship["rotation"])
    var new_speed = Math.sqrt(new_speed_x*new_speed_x+new_speed_y*new_speed_y)
    spaceship["speed"] = Math.min(speed_max,new_speed)
    spaceship["direction"] = Math.atan2(new_speed_y,new_speed_x)
}

function decrease_speed(){
    var slow = 0
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        slow = 0.01
    } else if(options["surface"]=="sphere"){
        slow = 0.0001
    } else if(options["surface"]=="torus"){
        slow = 0.0001
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        slow = 0.00005
    }

    spaceship["speed"] = Math.max(0,spaceship["speed"]-slow)
}

function rotate_left(){
    if(options["surface"].substr(0, 10)=="hyperbolic") {
        spaceship["rotation"] = hyper_compute_bk_angle(
            spaceship["hangle"], spaceship["vangle"],
            hyper_compute_angle_with_diameter(spaceship["hangle"], spaceship["vangle"], spaceship["rotation"])-0.07)
    } else {
        spaceship["rotation"] -= 0.07
    }
}

function rotate_right(){
    if(options["surface"].substr(0, 10)=="hyperbolic") {
        spaceship["rotation"] = hyper_compute_bk_angle(
            spaceship["hangle"], spaceship["vangle"],
            hyper_compute_angle_with_diameter(spaceship["hangle"], spaceship["vangle"], spaceship["rotation"])+ 0.07)
    } else {
        spaceship["rotation"] += 0.07
    }
}

function draw_lives(ctx){
    if(game_config("game-mode") == "lives"){
        for(var i=0;i<lives;i++){
            ctx.moveTo(WIDTH-i*25-30,20)
            ctx.lineTo(WIDTH-i*25-20,40)
            ctx.lineTo(WIDTH-i*25-30,35)
            ctx.lineTo(WIDTH-i*25-40,40)
            ctx.lineTo(WIDTH-i*25-30,20)
        }
    } else if(game_config("game-mode") == "time"){
        var timeleftdisp = Math.ceil(timeleft / 1000)
        add_scaled_text(ctx,""+timeleftdisp,WIDTH-50,38,0.6)
    }
}

function draw_mute(ctx){
    if(game_config("sound")){
        if(mute) {
            ctx.moveTo(15,HEIGHT-20)
            ctx.lineTo(15,HEIGHT-20)
            ctx.lineTo(15,HEIGHT-30)
            ctx.lineTo(20,HEIGHT-30)
            ctx.lineTo(20,HEIGHT-25)
            ctx.moveTo(23+7/5,HEIGHT-20+5/5)
            ctx.lineTo(30,HEIGHT-15)
            ctx.lineTo(30,HEIGHT-25)
            ctx.moveTo(30,HEIGHT-35)
            ctx.lineTo(23,HEIGHT-30)
            ctx.lineTo(23,HEIGHT-28)

            ctx.moveTo(15,HEIGHT-15)
            ctx.lineTo(35,HEIGHT-35)
        } else {
            ctx.moveTo(20,HEIGHT-20)
            ctx.lineTo(15,HEIGHT-20)
            ctx.lineTo(15,HEIGHT-30)
            ctx.lineTo(20,HEIGHT-30)
            ctx.lineTo(20,HEIGHT-20)
            ctx.moveTo(23,HEIGHT-20)
            ctx.lineTo(30,HEIGHT-15)
            ctx.lineTo(30,HEIGHT-35)
            ctx.lineTo(23,HEIGHT-30)
            ctx.lineTo(23,HEIGHT-20)
        }
    }
}

function draw_shape(){
    if(options["surface"]=="flatmobius" || options["surface"]=="flatcylinder"){
        for(var i=0;i<10;i++){
            add_line_to_draw(Array(i*WIDTH/10,MOBIUSY,(i+1)*WIDTH/10,MOBIUSY))
            add_line_to_draw(Array(i*WIDTH/10,HEIGHT-MOBIUSY,(i+1)*WIDTH/10,HEIGHT-MOBIUSY))
        }
    } else if(options["projection"]=="loop"){
        N = 100
        var angle = 0
        var r = 0
        var prex=0
        var prey=0
        for(var i=0;i<=N;i++){
            var x = WIDTH/2+LOOPSIZE[0]*Math.cos(angle)
            var y = HEIGHT/2+LOOPSIZE[1]*Math.sin(angle)
            if(i>0){
                add_line_to_draw(Array(prex,prey,x,y))
            }
            prex = x
            prey = y
            angle += Math.PI*2/N
        }
        add_line_to_draw(Array(WIDTH/2+LOOPFOCUS-3,HEIGHT/2-3,WIDTH/2+LOOPFOCUS+3,HEIGHT/2+3))
        add_line_to_draw(Array(WIDTH/2+LOOPFOCUS-3,HEIGHT/2+3,WIDTH/2+LOOPFOCUS+3,HEIGHT/2-3))
        add_line_to_draw(Array(WIDTH/2-LOOPFOCUS-3,HEIGHT/2-3,WIDTH/2-LOOPFOCUS+3,HEIGHT/2+3))
        add_line_to_draw(Array(WIDTH/2-LOOPFOCUS-3,HEIGHT/2+3,WIDTH/2-LOOPFOCUS+3,HEIGHT/2-3))
    } else if(options["surface"]=="sphere"){
        if(options["projection"]=="isometric"){
            for(var circle=0;circle<2;circle++){
                var vangle = 0
                var hangle = 0
                var N = 100
                if(circle==1){hangle=3*Math.PI/4}
                var prev = vangle
                var preh = hangle
                for(var i=0;i<N;i++){
                    if(circle==0){hangle += Math.PI*2/N}
                    else{vangle += Math.PI*2/N}
                    add_line_to_draw(Array(preh,prev,hangle,vangle))
                    prev = vangle
                    preh = hangle
                }
            }
        } else if(options["projection"]=="stereographic"){
            var hangle = 0
            var N = 100
            var preh = 0
            for(var i=0;i<N;i++){
                hangle += Math.PI*2/N
                add_line_to_draw(Array(preh,0.01,hangle,0.01))
                add_line_to_draw(Array(preh,-0.01,hangle,-0.01))
                preh = hangle
            }
        } else if(options["projection"]=="azim"){
            var hangle = 0
            var N = 100
            var preh = 0
            for(var i=0;i<N;i++){
                hangle += Math.PI*2/N
                add_line_to_draw(Array(preh,-Math.PI/2,hangle,-Math.PI/2))
                preh = hangle
            }
        } else if(options["projection"]=="van der Grinten"){
            var vangle = -Math.PI/2
            var N = 200
            var prev = vangle
            for(var i=1;i<=N;i++){
                vangle = -Math.PI/2 * Math.cos(i/N * Math.PI)
                add_line_to_draw(Array(0, prev,0,vangle))
                prev = vangle
            }
            prev = -Math.PI/2
            for(var i=1;i<=N;i++){
                vangle = -Math.PI/2 * Math.cos(i/N * Math.PI)
                add_line_to_draw(Array(2*Math.PI, prev,2*Math.PI,vangle))
                prev = vangle
            }
        } else if(options["projection"]=="Craig"){
            var leng = 0.02
            add_line_to_draw(Array(Math.PI+leng,Craig_zeroang+leng,Math.PI-leng,Craig_zeroang-leng))
            add_line_to_draw(Array(Math.PI+leng,Craig_zeroang-leng,Math.PI-leng,Craig_zeroang+leng))

            var hangle = 0
            var N = 100
            var preh = 0
            var prev = 0
            for(var i=0;i<=N;i++){
                vangle = Math.atan(-Math.cos(hangle-Math.PI)/Math.tan(Craig_zeroang))-0.01
                if(i>0){
                    add_line_to_draw(Array(preh,Math.PI/2,hangle,Math.PI/2))
                    add_line_to_draw(Array(preh,-Math.PI/2,hangle,-Math.PI/2))
                    add_line_to_draw(Array(preh,prev,hangle,vangle))
                }
                preh = hangle
                prev = vangle
                hangle += Math.PI*2/N
            }
        } else if(options["projection"]=="Robinson"){
            var N = 100

            var vangle = -Math.PI / 2
            var prev = 0
            for(var i=0;i<=N;i++){
                if(i>0){
                    add_line_to_draw(Array(0,prev,0,vangle))
                    add_line_to_draw(Array(2*Math.PI,prev,2*Math.PI,vangle))
                }
                prev = vangle
                vangle += Math.PI/N
            }
            var hangle = 0
            var preh = 0
            for(var i=0;i<=N;i++){
                if(i>0){
                    add_line_to_draw(Array(preh,Math.PI/2,hangle,Math.PI/2))
                    add_line_to_draw(Array(preh,-Math.PI/2,hangle,-Math.PI/2))
                }
                preh = hangle
                hangle += 2 * Math.PI/N
            }
        } else if(options["projection"]=="sinusoidal" || options["projection"] == "Mollweide"){
            var N = 100

            var vangle = -Math.PI / 2
            var prev = 0
            for(var i=0;i<=N;i++){
                if(i>0){
                    add_line_to_draw(Array(0,prev,0,vangle))
                    add_line_to_draw(Array(2*Math.PI,prev,2*Math.PI,vangle))
                }
                prev = vangle
                vangle += Math.PI/N
            }
        } else if(options["projection"]=="Goode"){
            var N = 100
            var eps = 0.0001

            var vangle = -Math.PI / 2
            var prev = 0
            for(var i=0;i<=N;i++){
                if(i>0){
                    add_line_to_draw(Array(0,prev,0,vangle))
                    add_line_to_draw(Array(2*Math.PI,prev,2*Math.PI,vangle))
                }
                prev = vangle
                vangle += Math.PI/N
            }
            vangle = 0
            prev = 0
            for(var i=0;i<=N;i++){
                if(i>0){
                    add_line_to_draw(Array(7*Math.PI/9-eps,-prev,7*Math.PI/9-eps,-vangle))
                    add_line_to_draw(Array(7*Math.PI/9+eps,-prev,7*Math.PI/9+eps,-vangle))
                    add_line_to_draw(Array(4*Math.PI/9-eps,prev,4*Math.PI/9-eps,vangle))
                    add_line_to_draw(Array(4*Math.PI/9+eps,prev,4*Math.PI/9+eps,vangle))
                    add_line_to_draw(Array(8*Math.PI/9-eps,prev,8*Math.PI/9-eps,vangle))
                    add_line_to_draw(Array(8*Math.PI/9+eps,prev,8*Math.PI/9+eps,vangle))
                    add_line_to_draw(Array(14*Math.PI/9-eps,prev,14*Math.PI/9-eps,vangle))
                    add_line_to_draw(Array(14*Math.PI/9+eps,prev,14*Math.PI/9+eps,vangle))
                }
                prev = vangle
                vangle += Math.PI * 0.5/N
            }
        } else if(options["projection"]=="cube"){
            var eps = 0.0001
            // -1, -1+/-eps, -1+eps  to  -1, -1+/-eps, 1-eps
            add_line_to_draw(Array(Math.atan2(-1-eps, -1),Math.atan2(-1+eps, Math.sqrt(2)),Math.atan2(-1-eps, -1),Math.atan2(1-eps, Math.sqrt(2))))
            add_line_to_draw(Array(Math.atan2(-1+eps, -1),Math.atan2(-1+eps, Math.sqrt(2)),Math.atan2(-1+eps, -1),Math.atan2(1-eps, Math.sqrt(2))))
            // -1, -1+eps, -1+/-eps  to  -1, 1-eps, -1+/-eps
            add_line_to_draw(Array(Math.atan2(-1+eps, -1),Math.atan2(-1-eps, Math.sqrt(1+(eps-1)*(eps-1))),Math.atan2(1-eps, -1),Math.atan2(-1-eps, Math.sqrt(1+(1-eps)*(1-eps)))))
            add_line_to_draw(Array(Math.atan2(-1+eps, -1),Math.atan2(-1+eps, Math.sqrt(1+(eps-1)*(eps-1))),Math.atan2(1-eps, -1),Math.atan2(-1+eps, Math.sqrt(1+(1-eps)*(1-eps)))))
            // -1, -1+eps, 1+/-eps  to  -1, 1-eps, 1+/-eps
            add_line_to_draw(Array(Math.atan2(-1+eps, -1),Math.atan2(1-eps, Math.sqrt(1+(eps-1)*(eps-1))),Math.atan2(1-eps, -1),Math.atan2(1-eps, Math.sqrt(1+(1-eps)*(1-eps)))))
            add_line_to_draw(Array(Math.atan2(-1+eps, -1),Math.atan2(1+eps, Math.sqrt(1+(eps-1)*(eps-1))),Math.atan2(1-eps, -1),Math.atan2(1+eps, Math.sqrt(1+(1-eps)*(1-eps)))))
            // -1+eps, -1, -1+/-eps  to  1-eps, -1, -1+/-eps
            add_line_to_draw(Array(Math.atan2(-1, -1+eps),Math.atan2(-1-eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(-1,1-eps),Math.atan2(-1-eps, Math.sqrt((1-eps)*(1-eps)+1))))
            add_line_to_draw(Array(Math.atan2(-1, -1+eps),Math.atan2(-1+eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(-1,1-eps),Math.atan2(-1+eps, Math.sqrt((1-eps)*(1-eps)+1))))
            // -1+eps, -1, 1+/-eps  to  1-eps, -1, 1+/-eps
            add_line_to_draw(Array(Math.atan2(-1, -1+eps),Math.atan2(1-eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(-1,1-eps),Math.atan2(1-eps, Math.sqrt((1-eps)*(1-eps)+1))))
            add_line_to_draw(Array(Math.atan2(-1, -1+eps),Math.atan2(1+eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(-1,1-eps),Math.atan2(1+eps, Math.sqrt((1-eps)*(1-eps)+1))))
            // 1-eps, 1, 1+/-eps  to  -1+eps, 1, 1+/-eps
            add_line_to_draw(Array(Math.atan2(1, 1-eps),Math.atan2(1+eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(1,eps-1),Math.atan2(1+eps, Math.sqrt((1-eps)*(1-eps)+1))))
            add_line_to_draw(Array(Math.atan2(1, 1-eps),Math.atan2(1-eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(1,eps-1),Math.atan2(1-eps, Math.sqrt((1-eps)*(1-eps)+1))))
            // 1-eps, 1, -1+/-eps  to  -1+eps, 1, -1+/-eps
            add_line_to_draw(Array(Math.atan2(1, 1-eps),Math.atan2(-1+eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(1,eps-1),Math.atan2(-1+eps, Math.sqrt((1-eps)*(1-eps)+1))))
            add_line_to_draw(Array(Math.atan2(1, 1-eps),Math.atan2(-1-eps, Math.sqrt((eps-1)*(eps-1)+1)),Math.atan2(1,eps-1),Math.atan2(-1-eps, Math.sqrt((1-eps)*(1-eps)+1))))
        } else if(options["projection"]=="tetrahedron"){
            var eps = 0.0001
            var top = [0, 0, -1]
            var pts = [[-Math.sqrt(8)/3, 0, 1/3], [Math.sqrt(2)/3, -Math.sqrt(2/3), 1/3], [Math.sqrt(2)/3, Math.sqrt(2/3), 1/3]]
            for (var i = 0; i < pts.length; i++){
                for (var j = 0; j < pts.length; j++){
                    if (i != j){
                        var x0 = top[0] + eps * (pts[i][0] + pts[j][0] - 2 * top[0]) / 2
                        var y0 = top[1] + eps * (pts[i][1] + pts[j][1] - 2 * top[1]) / 2
                        var z0 = top[2] + eps * (pts[i][2] + pts[j][2] - 2 * top[2]) / 2
                        var x1 = pts[i][0] + eps * (top[0] + pts[j][0] - 2 * pts[i][0]) / 2
                        var y1 = pts[i][1] + eps * (top[1] + pts[j][1] - 2 * pts[i][1]) / 2
                        var z1 = pts[i][2] + eps * (top[2] + pts[j][2] - 2 * pts[i][2]) / 2
                        add_line_to_draw(Array(Math.atan2(y0, x0),Math.atan2(z0, Math.sqrt(x0*x0+(y0)*(y0))),Math.atan2(y1, x1),Math.atan2(z1, Math.sqrt(x1*x1+(y1)*(y1)))))
                    }
                }
            }
        } else if(options["projection"]=="octahedron"){
            var eps = 0.0001
            var lines = [
                [[0,0,1], [0,1,0]],
                [[0,0,1], [0,-1,0]],
                [[0,0,-1], [1,0,0]],
                [[0,0,-1], [-1,0,0]],
                [[0,-1,0], [-1,0,0]],
            ]
            for(var i=0;i<lines.length;i++){
                var dir = [0,0,0]
                if(lines[i][0][0] == lines[i][1][0]){
                    dir[0] = 1
                } else if(lines[i][0][1] == lines[i][1][1]){
                    dir[1] = 1
                } else {
                    dir[2] = 1
                }
                for (var s=-1;s<=1;s+=2){
                    var x0 = lines[i][0][0] + eps * (lines[i][1][0] + s*dir[0] - 2 * lines[i][0][0]) / 2
                    var y0 = lines[i][0][1] + eps * (lines[i][1][1] + s*dir[1] - 2 * lines[i][0][1]) / 2
                    var z0 = lines[i][0][2] + eps * (lines[i][1][2] + s*dir[2] - 2 * lines[i][0][2]) / 2
                    var x1 = lines[i][1][0] + eps * (lines[i][0][0] + s*dir[0] - 2 * lines[i][1][0]) / 2
                    var y1 = lines[i][1][1] + eps * (lines[i][0][1] + s*dir[1] - 2 * lines[i][1][1]) / 2
                    var z1 = lines[i][1][2] + eps * (lines[i][0][2] + s*dir[2] - 2 * lines[i][1][2]) / 2
                    add_line_to_draw(Array(Math.atan2(y0, x0),Math.atan2(z0, Math.sqrt(x0*x0+(y0)*(y0))),Math.atan2(y1, x1),Math.atan2(z1, Math.sqrt(x1*x1+(y1)*(y1)))))
                }
            }
        } else if(options["projection"]=="dodecahedron"){
            var eps = 0.0001
            var lines = [[[0.9341723589627158, 0.35682208977308993, 0.0], [0.9341723589627158, -0.35682208977308993, 0.0], [0.35682208977308993, 0.0, -0.9341723589627158]], [[0.9341723589627158, -0.35682208977308993, 0.0], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258]], [[0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.35682208977308993, 0.0, -0.9341723589627158], [0.9341723589627158, 0.35682208977308993, 0.0]], [[0.35682208977308993, 0.0, -0.9341723589627158], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.9341723589627158, -0.35682208977308993, 0.0]], [[0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.35682208977308993, 0.0, -0.9341723589627158], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258]], [[0.35682208977308993, 0.0, -0.9341723589627158], [-0.35682208977308993, 0.0, -0.9341723589627158], [0.0, 0.9341723589627158, -0.35682208977308993]], [[-0.35682208977308993, 0.0, -0.9341723589627158], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258]], [[-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.0, 0.9341723589627158, -0.35682208977308993], [0.35682208977308993, 0.0, -0.9341723589627158]], [[0.9341723589627158, 0.35682208977308993, 0.0], [0.9341723589627158, -0.35682208977308993, 0.0], [0.35682208977308993, 0.0, 0.9341723589627158]], [[0.9341723589627158, -0.35682208977308993, 0.0], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.5773502691896258, 0.5773502691896258, 0.5773502691896258]], [[0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.35682208977308993, 0.0, 0.9341723589627158], [0.9341723589627158, 0.35682208977308993, 0.0]], [[0.35682208977308993, 0.0, 0.9341723589627158], [0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.9341723589627158, -0.35682208977308993, 0.0]], [[0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.35682208977308993, 0.0, 0.9341723589627158], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258]], [[0.35682208977308993, 0.0, 0.9341723589627158], [-0.35682208977308993, 0.0, 0.9341723589627158], [0.0, 0.9341723589627158, 0.35682208977308993]], [[-0.35682208977308993, 0.0, 0.9341723589627158], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.5773502691896258, 0.5773502691896258, 0.5773502691896258]], [[-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.0, 0.9341723589627158, 0.35682208977308993], [0.35682208977308993, 0.0, 0.9341723589627158]], [[0.0, 0.9341723589627158, 0.35682208977308993], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258]], [[-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.9341723589627158, 0.35682208977308993, 0.0], [0.0, 0.9341723589627158, -0.35682208977308993]], [[-0.9341723589627158, 0.35682208977308993, 0.0], [-0.9341723589627158, -0.35682208977308993, 0.0], [-0.35682208977308993, 0.0, -0.9341723589627158]], [[0.0, 0.9341723589627158, -0.35682208977308993], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258]], [[-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [-0.35682208977308993, 0.0, -0.9341723589627158], [-0.9341723589627158, -0.35682208977308993, 0.0]], [[-0.35682208977308993, 0.0, -0.9341723589627158], [-0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [-0.9341723589627158, 0.35682208977308993, 0.0]], [[-0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [-0.35682208977308993, 0.0, -0.9341723589627158], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258]], [[-0.35682208977308993, 0.0, -0.9341723589627158], [0.35682208977308993, 0.0, -0.9341723589627158], [0.0, -0.9341723589627158, -0.35682208977308993]], [[0.35682208977308993, 0.0, -0.9341723589627158], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, -0.5773502691896258, -0.5773502691896258]], [[0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.0, -0.9341723589627158, -0.35682208977308993], [-0.35682208977308993, 0.0, -0.9341723589627158]], [[0.0, -0.9341723589627158, -0.35682208977308993], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258]], [[0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.9341723589627158, -0.35682208977308993, 0.0], [0.0, -0.9341723589627158, 0.35682208977308993]], [[0.9341723589627158, -0.35682208977308993, 0.0], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.0, -0.9341723589627158, -0.35682208977308993]], [[0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.0, -0.9341723589627158, 0.35682208977308993], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258]], [[0.0, -0.9341723589627158, 0.35682208977308993], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [-0.35682208977308993, 0.0, 0.9341723589627158]], [[0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.35682208977308993, 0.0, 0.9341723589627158], [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258]], [[0.35682208977308993, 0.0, 0.9341723589627158], [-0.35682208977308993, 0.0, 0.9341723589627158], [0.0, -0.9341723589627158, 0.35682208977308993]], [[-0.35682208977308993, 0.0, 0.9341723589627158], [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258]], [[-0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [-0.35682208977308993, 0.0, 0.9341723589627158], [-0.9341723589627158, 0.35682208977308993, 0.0]], [[-0.35682208977308993, 0.0, 0.9341723589627158], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.9341723589627158, -0.35682208977308993, 0.0]], [[-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.9341723589627158, 0.35682208977308993, 0.0], [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258]], [[-0.9341723589627158, 0.35682208977308993, 0.0], [-0.9341723589627158, -0.35682208977308993, 0.0], [-0.35682208977308993, 0.0, 0.9341723589627158]]]
            for(var i=0;i<lines.length;i++){
                var x0 = lines[i][0][0] + eps * (lines[i][1][0] + lines[i][2][0] - 2 * lines[i][0][0]) / 2
                var y0 = lines[i][0][1] + eps * (lines[i][1][1] + lines[i][2][1] - 2 * lines[i][0][1]) / 2
                var z0 = lines[i][0][2] + eps * (lines[i][1][2] + lines[i][2][2] - 2 * lines[i][0][2]) / 2
                var x1 = lines[i][1][0] + eps * (lines[i][0][0] + lines[i][2][0] - 2 * lines[i][1][0]) / 2
                var y1 = lines[i][1][1] + eps * (lines[i][0][1] + lines[i][2][1] - 2 * lines[i][1][1]) / 2
                var z1 = lines[i][1][2] + eps * (lines[i][0][2] + lines[i][2][2] - 2 * lines[i][1][2]) / 2
                add_line_to_draw(Array(Math.atan2(y0, x0),Math.atan2(z0, Math.sqrt(x0*x0+(y0)*(y0))),Math.atan2(y1, x1),Math.atan2(z1, Math.sqrt(x1*x1+(y1)*(y1)))))
            }
        } else if(options["projection"]=="icosahedron"){
            var eps = 0.0001
            var lines = [[[-0.85065080835204, 0.0, -0.5257311121191336], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, 0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, 0.85065080835204, 0.0], [-0.85065080835204, 0.0, -0.5257311121191336]], [[-0.5257311121191336, 0.85065080835204, 0.0], [-0.85065080835204, 0.0, 0.5257311121191336], [0.0, 0.5257311121191336, 0.85065080835204]], [[-0.85065080835204, 0.0, 0.5257311121191336], [0.0, 0.5257311121191336, 0.85065080835204], [-0.5257311121191336, 0.85065080835204, 0.0]], [[0.0, 0.5257311121191336, 0.85065080835204], [-0.85065080835204, 0.0, 0.5257311121191336], [0.0, -0.5257311121191336, 0.85065080835204]], [[-0.85065080835204, 0.0, 0.5257311121191336], [0.0, -0.5257311121191336, 0.85065080835204], [0.0, 0.5257311121191336, 0.85065080835204]], [[0.0, -0.5257311121191336, 0.85065080835204], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0], [0.0, -0.5257311121191336, 0.85065080835204]], [[-0.5257311121191336, -0.85065080835204, 0.0], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.85065080835204, 0.0, -0.5257311121191336]], [[-0.85065080835204, 0.0, 0.5257311121191336], [-0.85065080835204, 0.0, -0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, -0.85065080835204], [-0.5257311121191336, -0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, -0.85065080835204], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.0, -0.5257311121191336, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204], [0.0, -0.5257311121191336, -0.85065080835204]], [[0.0, 0.5257311121191336, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, 0.85065080835204, 0.0]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, 0.85065080835204, 0.0], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.5257311121191336, 0.85065080835204, 0.0], [0.85065080835204, 0.0, -0.5257311121191336], [0.85065080835204, 0.0, 0.5257311121191336]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.85065080835204, 0.0, 0.5257311121191336], [0.5257311121191336, 0.85065080835204, 0.0]], [[0.85065080835204, 0.0, 0.5257311121191336], [0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, -0.85065080835204, 0.0]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, -0.85065080835204, 0.0], [0.85065080835204, 0.0, 0.5257311121191336]], [[0.5257311121191336, -0.85065080835204, 0.0], [0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, -0.85065080835204]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, -0.85065080835204], [0.5257311121191336, -0.85065080835204, 0.0]]]
            for(var i=0;i<lines.length;i++){
                var x0 = lines[i][0][0] + eps * (lines[i][1][0] + lines[i][2][0] - 2 * lines[i][0][0]) / 2
                var y0 = lines[i][0][1] + eps * (lines[i][1][1] + lines[i][2][1] - 2 * lines[i][0][1]) / 2
                var z0 = lines[i][0][2] + eps * (lines[i][1][2] + lines[i][2][2] - 2 * lines[i][0][2]) / 2
                var x1 = lines[i][1][0] + eps * (lines[i][0][0] + lines[i][2][0] - 2 * lines[i][1][0]) / 2
                var y1 = lines[i][1][1] + eps * (lines[i][0][1] + lines[i][2][1] - 2 * lines[i][1][1]) / 2
                var z1 = lines[i][1][2] + eps * (lines[i][0][2] + lines[i][2][2] - 2 * lines[i][1][2]) / 2
                add_line_to_draw(Array(Math.atan2(y0, x0),Math.atan2(z0, Math.sqrt(x0*x0+(y0)*(y0))),Math.atan2(y1, x1),Math.atan2(z1, Math.sqrt(x1*x1+(y1)*(y1)))))
            }
        } else if(options["projection"]=="dymaxion"){
            var eps = 0.0001
            var lines = [[[-0.85065080835204, 0.0, -0.5257311121191336], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, 0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, 0.5257311121191336], [0.0, -0.5257311121191336, 0.85065080835204], [0.0, 0.5257311121191336, 0.85065080835204]], [[0.0, -0.5257311121191336, 0.85065080835204], [0.0, 0.5257311121191336, 0.85065080835204], [-0.85065080835204, 0.0, 0.5257311121191336]], [[0.0, 0.5257311121191336, 0.85065080835204], [0.0, -0.5257311121191336, 0.85065080835204], [0.85065080835204, 0.0, 0.5257311121191336]], [[0.0, -0.5257311121191336, 0.85065080835204], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, 0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0], [0.0, -0.5257311121191336, 0.85065080835204]], [[-0.5257311121191336, -0.85065080835204, 0.0], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.85065080835204, 0.0, -0.5257311121191336]], [[-0.85065080835204, 0.0, 0.5257311121191336], [-0.85065080835204, 0.0, -0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.0, -0.85065080835204], [0.0, -0.5257311121191336, -0.85065080835204]], [[0.0, 0.0, -0.85065080835204], [0.0, -0.5257311121191336, -0.85065080835204], [-0.85065080835204, 0.0, -0.5257311121191336]], [[0.0, -0.5257311121191336, -0.85065080835204], [0.5257311121191336, -0.85065080835204, 0.0], [-0.5257311121191336, -0.85065080835204, 0.0]], [[0.5257311121191336, -0.85065080835204, 0.0], [0.0, -0.5257311121191336, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336]], [[0.0, -0.5257311121191336, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, -0.85065080835204, 0.0]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.85065080835204, 0.0, 0.5257311121191336], [0.5257311121191336, -0.85065080835204, 0.0]], [[0.85065080835204, 0.0, 0.5257311121191336], [0.85065080835204, 0.0, -0.5257311121191336], [0.5257311121191336, 0.85065080835204, 0.0]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.4587939734903912, 0.4587939734903912, -0.4587939734903912], [0.5257311121191336, 0.85065080835204, 0.0]], [[0.4587939734903912, 0.4587939734903912, -0.4587939734903912], [0.5257311121191336, 0.85065080835204, 0.0], [0.85065080835204, 0.0, -0.5257311121191336]], [[0.5257311121191336, 0.85065080835204, 0.0], [0.4587939734903912, 0.4587939734903912, -0.4587939734903912], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.4587939734903912, 0.4587939734903912, -0.4587939734903912], [0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, -0.85065080835204], [0.0, 0.5257311121191336, -0.85065080835204]], [[0.0, -0.5257311121191336, -0.85065080835204], [0.0, 0.0, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336]], [[0.0, 0.0, -0.85065080835204], [-0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204]], [[-0.85065080835204, 0.0, -0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204], [0.0, 0.0, -0.85065080835204]], [[0.0, 0.5257311121191336, -0.85065080835204], [-0.85065080835204, 0.0, -0.5257311121191336], [-0.5257311121191336, 0.85065080835204, 0.0]], [[-0.85065080835204, 0.0, -0.5257311121191336], [-0.5257311121191336, 0.85065080835204, 0.0], [0.0, 0.5257311121191336, -0.85065080835204]], [[-0.5257311121191336, 0.85065080835204, 0.0], [-0.85065080835204, 0.0, -0.5257311121191336], [-0.85065080835204, 0.0, 0.5257311121191336]]]
            for(var i=0;i<lines.length;i++){
                var x0 = lines[i][0][0] + eps * (lines[i][1][0] + lines[i][2][0] - 2 * lines[i][0][0]) / 2
                var y0 = lines[i][0][1] + eps * (lines[i][1][1] + lines[i][2][1] - 2 * lines[i][0][1]) / 2
                var z0 = lines[i][0][2] + eps * (lines[i][1][2] + lines[i][2][2] - 2 * lines[i][0][2]) / 2
                var x1 = lines[i][1][0] + eps * (lines[i][0][0] + lines[i][2][0] - 2 * lines[i][1][0]) / 2
                var y1 = lines[i][1][1] + eps * (lines[i][0][1] + lines[i][2][1] - 2 * lines[i][1][1]) / 2
                var z1 = lines[i][1][2] + eps * (lines[i][0][2] + lines[i][2][2] - 2 * lines[i][1][2]) / 2
                add_line_to_draw(Array(Math.atan2(y0, x0),Math.atan2(z0, Math.sqrt(x0*x0+(y0)*(y0))),Math.atan2(y1, x1),Math.atan2(z1, Math.sqrt(x1*x1+(y1)*(y1)))))
            }
        }
    } else if(options["surface"]=="torus"){
        if(options["projection"]=="top_v"){
            var hangle = 0
            var N = 100
            var preh = 0
            for(var i=0;i<N;i++){
                hangle += Math.PI*2/N
                add_line_to_draw(Array(preh,0,hangle,0))
                add_line_to_draw(Array(preh,Math.PI,hangle,Math.PI))
                preh = hangle
            }
        }
    } else if(options["surface"]=="hyperbolic"){
        if(options["projection"] == "hyperboloid"){
            var N = 100
            var prev = 0
            var preh = 0
            var a = Math.PI / 2 + 0.15
            var p1 = hyper_add(0, 0, Math.PI/4 + a, HYPER_RADIUS)
            var p2 = hyper_add(0, 0, Math.PI/4 - a, HYPER_RADIUS)

            for(var i=0;i<=N;i++){
                p = [p1[0] + (p2[0]-p1[0])*i/N,p1[1] + (p2[1]-p1[1])*i/N]
                if (i > 0) {
                    add_line_to_draw(Array(preh,prev,p[0], p[1]))
                }
                prev = p[1]
                preh = p[0]
            }

            var angle = -Math.PI / 4
            for(var i=0;i<=N;i++){
                angle += 2*Math.PI/N
                p = hyper_add(0, 0, angle, HYPER_RADIUS)
                if (i > 0) {
                    add_line_to_draw(Array(preh,prev,p[0], p[1]))
                }
                prev = p[1]
                preh = p[0]
            }
        } else {
            var N = 100
            if(options["projection"] == "Poincare HP" || options["projection"] == "band"){N=600}
            var angle = 0
            var prev = 0
            var preh = 0
            for(var i=0;i<=N;i++){
                angle += Math.PI*2/N
                var p = hyper_add(0, 0, angle, HYPER_RADIUS)
                if (i > 0) {
                    add_line_to_draw(Array(preh,prev,p[0], p[1]))
                }
                prev = p[1]
                preh = p[0]
            }
        }
    } else if(options["surface"]=="hyperbolicunbounded"){
        if(options["projection"] == "Poincare" || options["projection"] == "Beltrami-Klein"){
            var N = 100
            var angle = 0
            var prev = 0
            var preh = 0
            for(var i=0;i<=N;i++){
                angle += Math.PI*2/N
                p = [Math.cos(angle), Math.sin(angle)]
                if (i > 0) {
                    add_line_to_draw(Array(preh,prev,p[0], p[1]))
                }
                prev = p[1]
                preh = p[0]
            }
        }
    }
}

function draw_ship(){
    if(lives>0){
        draw_sprite(ship_sprite(15))
    }
}

function draw_asteroids(){
    for(var i=0;i<asteroids.length;i++){
        draw_sprite(asteroid_sprite(asteroids[i]))
    }
    if(options["surface"] == "flatunbounded"){
        for(var i=0;i<asteroids.length;i++){
            if(asteroids[i]["hangle"] < -5 || asteroids[i]["hangle"] > WIDTH + 5 || asteroids[i]["vangle"] < -5 || asteroids[i]["vangle"] > HEIGHT + 5){
                var ang = Math.atan2(asteroids[i]["vangle"] - spaceship["vangle"], asteroids[i]["hangle"] - spaceship["hangle"])
                var x = 0
                var y = 0
                if (ang > -Math.PI / 2 && ang < Math.PI / 2){
                    x = WIDTH
                } else {
                    x = 0
                }
                // Math.tan(ang) = (y - spaceship["vangle"]) / (x - spaceship["hangle"])
                y = spaceship["vangle"] + (x - spaceship["hangle"]) * Math.tan(ang)
                if (y > HEIGHT || y < 0) {
                    if (y > HEIGHT) {
                        y = HEIGHT
                    } else {
                        y = 0
                    }
                    // Math.tan(ang) = (HEIGHT - spaceship["vangle"]) / (x - spaceship["hangle"])
                    x = spaceship["hangle"] + (y - spaceship["vangle"]) / Math.tan(ang)
                }
                var d = Math.sqrt(Math.pow(x - asteroids[i]["hangle"], 2) + Math.pow(y - asteroids[i]["vangle"], 2))
                var alen = 10 + 40/(1+d/50)

                add_line_to_draw(Array(x-(alen + 3)*Math.cos(ang), y-(alen + 3)*Math.sin(ang), x - 3*Math.cos(ang), y - 3*Math.sin(ang)))
                add_line_to_draw(Array(x-(3 + alen/2)*Math.cos(ang)+alen/3*Math.cos(ang+Math.PI/2), y-(3+alen/2)*Math.sin(ang)+alen/3*Math.sin(ang+Math.PI/2), x - 3*Math.cos(ang), y - 3*Math.sin(ang)))
                add_line_to_draw(Array(x-(3 + alen/2)*Math.cos(ang)+alen/3*Math.cos(ang-Math.PI/2), y-(3+alen/2)*Math.sin(ang)+alen/3*Math.sin(ang-Math.PI/2), x - 3*Math.cos(ang), y - 3*Math.sin(ang)))

            }
        }
    } else if(options["surface"] == "hyperbolicunbounded"){
        if(options["projection"] == "Poincare" || options["projection"] == "Beltrami-Klein"){
            var max_d = 4
            var a0 = 0.1
            var a1 = 2
            if(options["projection"] == "Beltrami-Klein"){
                max_d = 2
                a1 = 1.2
            }
            for(var i=0;i<asteroids.length;i++){
                if(hyper_compute_distance(0, 0, asteroids[i]["hangle"], asteroids[i]["vangle"]) > max_d){
                    var ang = Math.atan2(asteroids[i]["vangle"], asteroids[i]["hangle"])
                    var d = hyper_compute_distance(0, 0, asteroids[i]["hangle"], asteroids[i]["vangle"])
                    var alen = a0 + a1/(1+d/5)
                    var arrow_st = hyper_add(0,0, ang, max_d)
                    var arrow_end = hyper_add(0,0, ang, max_d-alen)
                    var p0 = [0,0]
                    var p1 = [0,0]
                    if(options["projection"] == "Poincare") {
                        p0 = hyper_add(arrow_st[0],arrow_st[1], hyper_compute_bk_angle(arrow_st[0],arrow_st[1], 5*Math.PI/6), alen/2)
                        p1 = hyper_add(arrow_st[0],arrow_st[1], hyper_compute_bk_angle(arrow_st[0],arrow_st[1], -5*Math.PI/6), alen/2)
                    } else if(options["projection"] == "Beltrami-Klein"){
                        p0 = hyper_add(arrow_st[0],arrow_st[1], ang + 5*Math.PI/6, alen/2)
                        p1 = hyper_add(arrow_st[0],arrow_st[1], ang - 5*Math.PI/6, alen/2)
                    }

                    add_line_to_draw(Array(arrow_st[0], arrow_st[1], arrow_end[0], arrow_end[1]))
                    add_line_to_draw(Array(arrow_st[0], arrow_st[1], p0[0], p0[1]))
                    add_line_to_draw(Array(arrow_st[0], arrow_st[1], p1[0], p1[1]))
                }
            }
        }
    }
}

function draw_fire(){
    for(var i=0;i<fires.length;i++){
        draw_sprite(fire_sprite(fires[i]))
    }
}

function draw_explodes(){
    for(var i=0;i<explode.length;i++){
        draw_sprite(explode_sprite(explode[i]))
    }
}

function draw_sprite(points_list){
    points_list.push(points_list[0])
    var preh = 0
    var prev = 0
    for(var j=0;j<points_list.length;j++){
        points = points_list[j]
        for(var i=0;i<points.length;i++){
            var hangle = points[i][0]
            var vangle = points[i][1]
            if(i>0){
                add_line_to_draw(Array(preh,prev,hangle,vangle))
            }
            preh = hangle
            prev = vangle
        }
    }
}

function move_ship(){
    spaceship = move_sprite(spaceship)
    if(options["surface"] == "flatunbounded"){
        var pad = 150
        if(spaceship["hangle"] < pad) {
            move = pad - spaceship["hangle"]
            spaceship["hangle"] += move
            for(var i=0;i<asteroids.length;i++){
                asteroids[i]["hangle"] += move
            }
            for(var i=0;i<fires.length;i++){
                fires[i]["hangle"] += move
            }
        }
        if(spaceship["hangle"] > WIDTH - pad) {
            move = WIDTH - pad - spaceship["hangle"]
            spaceship["hangle"] += move
            for(var i=0;i<asteroids.length;i++){
                asteroids[i]["hangle"] += move
            }
            for(var i=0;i<fires.length;i++){
                fires[i]["hangle"] += move
            }
        }
        if(spaceship["vangle"] < pad) {
            move = pad - spaceship["vangle"]
            spaceship["vangle"] += move
            for(var i=0;i<asteroids.length;i++){
                asteroids[i]["vangle"] += move
            }
            for(var i=0;i<fires.length;i++){
                fires[i]["vangle"] += move
            }
        }
        if(spaceship["vangle"] > HEIGHT - pad) {
            move = HEIGHT - pad - spaceship["vangle"]
            spaceship["vangle"] += move
            for(var i=0;i<asteroids.length;i++){
                asteroids[i]["vangle"] += move
            }
            for(var i=0;i<fires.length;i++){
                fires[i]["vangle"] += move
            }
        }
    } else if(options["surface"] == "hyperbolicunbounded"){
        if(options["projection"] == "Poincare" || options["projection"] == "Beltrami-Klein"){
            var pad = 2
            if(options["projection"] == "Beltrami-Klein"){
                pad = 0.6
            }
            if(hyper_compute_distance(0, 0, spaceship["hangle"], spaceship["vangle"]) > pad){
                var ang = Math.atan2(spaceship["vangle"], spaceship["hangle"])
                var new_spaceship = hyper_add(0, 0, ang, pad)

                for(var i=0;i<asteroids.length;i++){
                    var a = hyper_compute_angle_with_diameter(spaceship["hangle"], spaceship["vangle"], Math.atan2(asteroids[i]["vangle"] - spaceship["vangle"], asteroids[i]["hangle"] - spaceship["hangle"]))
                    var d = hyper_compute_distance(asteroids[i]["hangle"], asteroids[i]["vangle"], spaceship["hangle"], spaceship["vangle"])
                    var p = hyper_add(new_spaceship[0], new_spaceship[1], hyper_compute_bk_angle(new_spaceship[0], new_spaceship[1], a), d)
                    asteroids[i]["hangle"] = p[0]
                    asteroids[i]["vangle"] = p[1]
                }
                for(var i=0;i<fires.length;i++){
                    var a = hyper_compute_angle_with_diameter(spaceship["hangle"], spaceship["vangle"], Math.atan2(fires[i]["vangle"] - spaceship["vangle"], fires[i]["hangle"] - spaceship["hangle"]))
                    var d = hyper_compute_distance(fires[i]["hangle"], fires[i]["vangle"], spaceship["hangle"], spaceship["vangle"])
                    var p = hyper_add(new_spaceship[0], new_spaceship[1], hyper_compute_bk_angle(new_spaceship[0], new_spaceship[1], a), d)
                    fires[i]["hangle"] = p[0]
                    fires[i]["vangle"] = p[1]
                }

                spaceship["hangle"] = new_spaceship[0]
                spaceship["vangle"] = new_spaceship[1]
            }
        }
    }
}

function move_sprite(sprite){
    var a = 0
    if(options["surface"].substr(0,10)=="hyperbolic"){
        a = hyper_compute_angle_with_diameter(sprite["hangle"], sprite["vangle"], sprite["direction"]) - hyper_compute_angle_with_diameter(sprite["hangle"], sprite["vangle"], sprite["rot"])
    }
    var new_pos = move_on_surface(sprite["hangle"],sprite["vangle"],sprite["direction"],sprite["speed"],1)
    var rot = sprite["rotation"]
    sprite["rotation"] *= new_pos["flip"]
    sprite["rotation"] -= sprite["direction"]
    sprite["direction"] = new_pos["rotation"]
    sprite["rotation"] += new_pos["flip"]*sprite["direction"]
    sprite["hangle"] = new_pos["hangle"]
    sprite["vangle"] = new_pos["vangle"]
    if(options["surface"]=="pool" || options["surface"]=="flatcylinder" || options["surface"]=="hyperbolic"){sprite["rotation"]=rot}
    if(options["surface"]=="flatmobius" && new_pos["flip"]==1){sprite["rotation"]=rot}
    if(options["surface"]=="flatcylinder"){sprite["rotation"]=rot}
    if(options["surface"].substr(0,10)=="hyperbolic"){
        sprite["rot"] = hyper_compute_bk_angle(sprite["hangle"], sprite["vangle"], hyper_compute_angle_with_diameter(sprite["hangle"], sprite["vangle"], sprite["direction"]) - a)
    }
    return sprite
}

function get_a_s(a){
    var mult = 1
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        mult = 100
    }
    if (options["surface"].substr(0,10) == "hyperbolic"){
        mult = 0.5
    }
    var out = {}
    if(a["size"]==4){
        out["radius"] = 0.1*mult
        out["sides"] = 6
    }
    if(a["size"]==3){
         out["radius"] = 0.085*mult
         out["sides"] = 5
    }
    if(a["size"]==2){
         out["radius"] = 0.07*mult
         out["sides"] = 4
    }
    if(a["size"]==1){
         out["radius"] = 0.06*mult
         out["sides"] = 3
    }
    return out
}

function close_to_asteroid(){
    for(var i=0;i<asteroids.length;i++){
        var a = asteroids[i]
        if(too_close(a,spaceship)){
            return true
        }
    }
    return false
}

function in_contact(points, a){
    if(options["surface"]=="torus"){
        var r = TRADIUS[1]
        var R = TRADIUS[0] + TRADIUS[1] * Math.cos(a["vangle"])
        for(var j=0;j<points.length;j++){
            if(Math.abs(a["hangle"]-points[j][0])<1.5*a["radius"]/R && Math.abs(a["vangle"]-points[j][1])<1.5*a["radius"]/r){
                return true;
            }
        }
        return false;
    }
    if(options["surface"].substr(0,10)=="hyperbolic"){
        for(var j=0;j<points.length;j++){
            if(hyper_compute_distance(a["hangle"], a["vangle"], points[j][0], points[j][1]) < 0.9*a["radius"]){
                return true;
            }
        }
        return false;
    }
    for(var j=0;j<points.length;j++){
        if(Math.abs(a["hangle"]-points[j][0])<0.9*a["radius"] && Math.abs(a["vangle"]-points[j][1])<0.9*a["radius"]){
            return true;
        }
    }
    return false;
}

function move_asteroids(){
    if(asteroids.length==0){
        asterN++
        score += 1000
        if(game_config("sound") && !mute){ sound_level_up.cloneNode().play() }
        asteroids = make_new_asteroids(asterN)
    }
    var new_asteroids = Array()
    for(var i=0;i<asteroids.length;i++){
        var a = asteroids[i]
        move_sprite(a)

        var fireRemove = Array()

        var points = ship_sprite(1)[0]
        if(in_contact(ship_sprite(1)[0], a)){
            if(game_config("sound") && !mute){ sound_bang_large.cloneNode().play() }
            explode[explode.length] = {"hangle":spaceship["hangle"],"vangle":spaceship["vangle"],"age":0,"rotation":Math.random()*Math.PI,"speed":3}
            spaceship["rotation"] = Math.random()*2*Math.PI
            spaceship["direction"] = spaceship["rotation"]
            spaceship["speed"] = 0
            var counter = 0
            while(close_to_asteroid() && counter<50){
                counter ++
                if(options["surface"].substring(0,4)=="flat"){
                    spaceship["hangle"] = Math.random()*WIDTH
                    spaceship["vangle"] = Math.random()*HEIGHT
                } else if(options["surface"]=="sphere"){
                    spaceship["hangle"] = Math.random()*2*Math.PI
                    spaceship["vangle"] = Math.random()*Math.PI-Math.PI/2
                } else if(options["surface"]=="torus"){
                    spaceship["hangle"] = Math.random()*2*Math.PI
                    spaceship["vangle"] = Math.random()*Math.PI-Math.PI/2
                } else if(options["surface"].substr(0,10)=="hyperbolic"){
                    var ang = Math.random() * 2 * Math.PI
                    var dist = Math.random() * HYPER_RADIUS
                    var pt = hyper_add(0, 0, Math.random() * 2 * Math.PI, Math.random() * HYPER_RADIUS)
                    spaceship["hangle"] = pt[0]
                    spaceship["vangle"] = pt[1]
                }
                if(options["projection"] == "loop"){
                    var angle = Math.random()*Math.PI*2
                    var rad = Math.random()
                    spaceship["hangle"] = WIDTH/2+rad*LOOPSIZE[0]*Math.cos(angle)
                    spaceship["vangle"] = HEIGHT/2+rad*LOOPSIZE[1]*Math.sin(angle)
                }
            }
            if(game_config("game-mode") == "lives") {
                lives--
            }
            if(game_config("game-mode") == "time") {
                score -= 300
            }
        }

        for(var j=0;j<fires.length;j++){
            if(in_contact([[fires[j]["hangle"],fires[j]["vangle"]]], a)){
                if(game_config("sound") && !mute){
                    if(a["sides"] == 3){
                        sound_bang_small.cloneNode().play()
                    } else {
                        sound_bang_medium.cloneNode().play()
                    }
                }
                fireRemove[fireRemove.length]=j
                explode[explode.length] = {"hangle":a["hangle"],"vangle":a["vangle"],"age":0,"rotation":Math.random()*Math.PI,"speed":1}
            }
        }
        if(fireRemove.length==0){
            new_asteroids[new_asteroids.length] = a
        } else {
            if(a["size"]==4){score+=10}
            if(a["size"]==3){score+=15}
            if(a["size"]==2){score+=20}
            if(a["size"]==1){score+=30}
            var new_fires = Array()
            for(var j=0;j<fires.length;j++){
                if(!(j in fireRemove)){
                    new_fires[new_fires.length] = fires[j]
                }
            }
            fires = new_fires
            if(a["size"]>1){
                if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
                    var speed_start = 0.5
                } else if(options["surface"]=="sphere"){
                    var speed_start = 0.005
                } else if(options["surface"]=="torus"){
                    var speed_start = 0.005
                } else if(options["surface"].substr(0,10)=="hyperbolic"){
                    var speed_start = 0.003
                }

                var new_a = {"hangle":a["hangle"],"vangle":a["vangle"],
                             "rotation":a["rotation"]-Math.PI/4+Math.random()*Math.PI/2,"speed":speed_start+Math.random()*1.1*a["speed"],
                             "direction":a["direction"]-Math.PI/4+Math.random()*Math.PI/2,
                             "size":a["size"]-1,"radius":0.01,"sides":2}
                var as = get_a_s(new_a)
                new_a["radius"] = as["radius"]
                new_a["sides"] = as["sides"]
                new_asteroids[new_asteroids.length] = new_a

                var new_b = {"hangle":a["hangle"],"vangle":a["vangle"],
                             "rotation":a["rotation"]+Math.PI/4+Math.random()*Math.PI/2,"speed":speed_start+Math.random()*1.1*a["speed"],
                             "direction":a["direction"]+Math.PI/4+Math.random()*Math.PI/2,
                             "size":a["size"]-1,"radius":0.01,"sides":2}
                var as = get_a_s(new_b)
                new_b["radius"] = as["radius"]
                new_b["sides"] = as["sides"]
                new_asteroids[new_asteroids.length] = new_b
            }
        }
    }
    asteroids = new_asteroids
}

// sprites
function ship_sprite(N){
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        var size1 = 10
        var size2 = 15
        var leng = size1
        var leng2 = Math.sqrt(size1*size1+size2*size2+Math.sqrt(2)*size1*size2)
        var angle = Math.asin(size2/(Math.sqrt(2)*leng2))
        var bngle = Math.asin(size1/(Math.sqrt(2)*leng2))
        var cngle = Math.PI/4
    } else if(options["surface"]=="sphere"){
        var size1 = 0.05
        var size2 = 0.15
        var leng = Math.acos(Math.cos(size1)*Math.cos(size1))
        var leng2 = Math.acos(Math.cos(size1)*Math.cos(size2))
        var angle = Math.atan2(Math.sin(0.15),Math.sin(0.05)*Math.cos(0.15))-Math.atan2(1,Math.cos(0.05))
        var bngle = Math.atan2(Math.sin(0.05),Math.sin(0.15)*Math.cos(0.05))
        var cngle = Math.atan2(1,Math.cos(0.05))
    } else if(options["surface"]=="torus"){
        return torus_ship_sprite(N)
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        return hyper_ship_sprite(N)
    }
    var out = Array()
    var p = {"hangle":spaceship["hangle"],"vangle":spaceship["vangle"],"rotation":spaceship["rotation"],"flip":1}
    out[out.length] = Array(p["hangle"],p["vangle"])

    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*(Math.PI-cngle),0,p["flip"])
    for(var i=1;i<=N;i++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],leng/N,p["flip"])
        out[out.length] = Array(p["hangle"],p["vangle"])
    }
    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*(Math.PI+angle),0,p["flip"])
    for(var i=1;i<=N;i++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],leng2/N,p["flip"])
        out[out.length] = Array(p["hangle"],p["vangle"])
    }


    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*(Math.PI+2*bngle),0,p["flip"])
    for(var i=1;i<=N;i++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],leng2/N,p["flip"])
        out[out.length] = Array(p["hangle"],p["vangle"])
    }

    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*(Math.PI+angle),0,p["flip"])
    for(var i=1;i<=N;i++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],leng/N,p["flip"])
        out[out.length] = Array(p["hangle"],p["vangle"])
    }
    return Array(out)
}

function torus_ship_sprite(N){
    ship2d = Array(Array(0,0))
    var size1 = 0.1
    var size2 = 0.15
    var leng = size1
    var leng2 = Math.sqrt(size1*size1 + size2*size2 + Math.sqrt(2)*size1*size2)
    var angle = Math.asin(size2/(Math.sqrt(2)*leng2))
    var cngle = Math.PI/4

    var px = 0
    var py = 0
    for(var i=1;i<=N;i++){
        px -= leng/N * Math.sin(cngle)
        py -= leng/N * Math.cos(cngle)
        ship2d[ship2d.length] = Array(px,py)
    }
    for(var i=1;i<=N;i++){
        px += leng2/N * Math.sin(cngle + angle)
        py += leng2/N * Math.cos(cngle + angle)
        ship2d[ship2d.length] = Array(px,py)
    }
    for(var i=1;i<=N;i++){
        px -= leng2/N * Math.sin(cngle + angle)
        py += leng2/N * Math.cos(cngle + angle)
        ship2d[ship2d.length] = Array(px,py)
    }
    for(var i=1;i<=N;i++){
        px += leng/N * Math.cos(cngle)
        py -= leng/N * Math.sin(cngle)
        ship2d[ship2d.length] = Array(px,py)
    }
    return Array(sprite_to_torus(ship2d, spaceship["hangle"], spaceship["vangle"], spaceship["rotation"]))
}

function hyper_sprite(endpoints, N){
    var points = Array(endpoints[0])
    var x = endpoints[0][0]
    var y = endpoints[0][1]
    for(var i=0;i<endpoints.length-1;i++){
        var start = endpoints[i]
        var end = endpoints[i+1]
        for (var j=1;j<=N;j++){
            x += (end[0] - start[0]) / N
            y += (end[1] - start[1]) / N
            points[points.length] = Array(x, y)
        }
    }
    return points
}

function hyper_ship_sprite(N){
    var endpoints = Array()
    var size1 = 0.05
    var size2 = 0.06
    var h = spaceship["hangle"]
    var v = spaceship["vangle"]
    var r = spaceship["rotation"]

    endpoints[endpoints.length] = hyper_add(h, v, r, size2)
    endpoints[endpoints.length] = hyper_add(h, v, r + Math.PI*3/4, size1)
    endpoints[endpoints.length] = Array(h, v)
    endpoints[endpoints.length] = hyper_add(h, v, r - Math.PI*3/4, size1)
    endpoints[endpoints.length] = hyper_add(h, v, r, size2)
    return Array(hyper_sprite(endpoints, N));
}

function sprite_to_torus(sprite2d, hangle, vangle, rot){
    var x = (TRADIUS[0] + TRADIUS[1]*Math.cos(vangle)) * Math.cos(hangle)
    var y = (TRADIUS[0] + TRADIUS[1]*Math.cos(vangle)) * Math.sin(hangle)
    var z = TRADIUS[1]*Math.sin(vangle)

    var dx = -Math.sin(hangle)*Math.cos(rot) - Math.cos(hangle)*Math.sin(vangle)*Math.sin(rot)
    var dy = Math.cos(hangle)*Math.cos(rot) - Math.sin(hangle)*Math.sin(vangle)*Math.sin(rot)
    var dz = Math.cos(vangle)*Math.sin(rot)

    var tx = Math.sin(hangle)*Math.sin(rot) - Math.cos(hangle)*Math.sin(vangle)*Math.cos(rot)
    var ty = -Math.cos(hangle)*Math.sin(rot) - Math.sin(hangle)*Math.sin(vangle)*Math.cos(rot)
    var tz = Math.cos(vangle)*Math.cos(rot)

    sprite_torus = Array()
    for(var i=0;i<sprite2d.length;i++){
        var px = sprite2d[i][0]
        var py = sprite2d[i][1]
        var x3 = x+dx*px+tx*py
        var y3 = y+dy*px+ty*py
        var z3 = z+dz*px+tz*py

        var hangle = Math.atan2(y3,x3)
        var vangle = Math.atan2(z3,Math.sqrt(x3*x3 + y3*y3)-TRADIUS[0])
        if(vangle > 2*Math.PI){
            vangle -= 2*Math.PI
        }
        if(vangle < 0){
            vangle += Math.PI*2
        }
        while(hangle < 0){
            hangle += 2*Math.PI
        }
        while(hangle > 2*Math.PI){
            hangle -= 2*Math.PI
        }
        sprite_torus[sprite_torus.length] = Array(hangle, vangle)
    }
    return sprite_torus
}

function fire_sprite(f){
    var out = Array()
    var leng = 0.1
    if(options["surface"].substring(0,4)=="flat" || options["surface"]=="pool"){
        leng = 10
    }
    var p = {"hangle":f["hangle"],"vangle":f["vangle"],"rotation":f["rotation"]}
    out[out.length] = Array(p["hangle"],p["vangle"])

    var N = 10
    for(var j=0;j<N;j++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],leng/N,1)
        out[out.length] = Array(p["hangle"],p["vangle"])
    }
    return Array(out)
}

function explode_sprite(f){
    var out = Array()
    var angles = Array(1,3,5)
    var mult = 1
    if(options["surface"].substring(0,4) == "flat" || options["surface"]=="pool"){
        mult = 100
    }

    if(f["speed"]>1){
        for(var i=0;i<angles.length;i++){
            var part = Array()
            var p = {"hangle":f["hangle"],"vangle":f["vangle"],"rotation":angles[i]+f["rotation"]}
            p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],f["speed"]*0.01*f["age"]*mult,1)
            part[part.length] = Array(p["hangle"],p["vangle"])
            var N = 10
            for(var j=0;j<N;j++){
                p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],0.1*mult/N,1)
                part[part.length] = Array(p["hangle"],p["vangle"])
            }
            out[out.length] = part
        }
    }
    for(var i=0;i<angles.length;i++){
        var part = Array()
        var p = {"hangle":f["hangle"],"vangle":f["vangle"],"rotation":angles[i]+3*f["rotation"]}
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],f["speed"]*0.005*mult*(f["age"]*(200-f["age"]))/60,1)
        part[part.length] = Array(p["hangle"],p["vangle"])

        var N = 10
        for(var j=0;j<N;j++){
            p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],0.05*mult/N,1)
            part[part.length] = Array(p["hangle"],p["vangle"])
        }
        out[out.length] = part
    }
    return out
}

function asteroid_sprite(a){
    var out = Array()
    var r = a["radius"]
    var sides = a["sides"]
    if(options["surface"].substring(0,4) == "flat" || options["surface"]=="pool"){
        var side_l = r*Math.sqrt(2-2*Math.cos(2*Math.PI/sides))
        var angle = (sides-2)*Math.PI/(2*sides)
    } else if(options["surface"] == "sphere"){
        var side_l = Math.acos(Math.cos(r)*Math.cos(r)+Math.sin(r)*Math.sin(r)*Math.cos(2*Math.PI/sides))
        var angle = Math.acos(Math.cos(r)*(1-Math.cos(side_l)) / (Math.sin(r)*Math.sin(side_l)))
    } else if(options["surface"] == "torus"){
        return torus_asteroid_sprite(a)
    } else if(options["surface"].substr(0,10) == "hyperbolic"){
        return hyper_asteroid_sprite(a)
    }
    var p = {"hangle":a["hangle"],"vangle":a["vangle"],"rotation":a["rotation"],"flip":1}
    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],r,p["flip"])
    p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*angle,0,p["flip"])

    out[out.length] = Array(p["hangle"],p["vangle"])

    for(var i=0;i<sides;i++){
        p = add_to_surface(p["hangle"],p["vangle"],p["rotation"]+p["flip"]*(Math.PI-2*angle),0,p["flip"])

        var N = 10
        for(var j=0;j<N;j++){
            p = add_to_surface(p["hangle"],p["vangle"],p["rotation"],side_l/N,p["flip"])
            out[out.length] = Array(p["hangle"],p["vangle"])
        }
    }
    return Array(out)
}

function torus_asteroid_sprite(a){
    var out = Array()
    var r = a["radius"]
    var sides = a["sides"]
    var side_l = r*Math.sqrt(2-2*Math.cos(2*Math.PI/sides))
    var angle = 2*Math.PI/(sides)

    var asteroid2d = Array()
    var x=r
    var y=0
    asteroid2d[asteroid2d.length] = Array(x,y)

    for(var i=0;i<sides;i++){
        var N = 10
        for(var j=0;j<N;j++){
            x += side_l/N * Math.cos(i*angle)
            y -= side_l/N * Math.sin(i*angle)
            asteroid2d[asteroid2d.length] = Array(x,y)
        }
    }

    return Array(sprite_to_torus(asteroid2d, a["hangle"], a["vangle"], a["rotation"]))
}

function hyper_asteroid_sprite(a){
    var out = Array()
    var r = a["radius"]
    var sides = a["sides"]
    var angle = 2*Math.PI/sides

    var endpoints = Array()

    for(var i=0;i<=sides;i++){
        endpoints[endpoints.length]=hyper_add(a["hangle"], a["vangle"], i * angle, r)
    }

    return Array(hyper_sprite(endpoints, 10));
}


// surface code
function add_line_to_draw(thing){
    if(options["surface"]=="torus" && options["projection"]=="top_v"){
        var vangle = (thing[1]+thing[3])/2
        var z = TRADIUS[1]*Math.sin(vangle)
        if(z<0){
            back_points[back_points.length] = thing
            return
        }
    }
    if(options["surface"]=="sphere" && options["projection"]=="isometric"){
        var hangle = (thing[0]+thing[2])/2
        var vangle = (thing[1]+thing[3])/2
        var x = Math.cos(vangle) * Math.cos(hangle)
        var y = Math.cos(vangle) * Math.sin(hangle)
        if(x+y<-0.1){
            back_points[back_points.length] = thing
            return
        }
    }
    if(options["surface"]=="sphere" && options["projection"]=="Craig"){
        var hangle = (thing[0]+thing[2])/2
        var vangle = (thing[1]+thing[3])/2
        if(vangle > Math.atan(-Math.cos(hangle-Math.PI)/Math.tan(Craig_zeroang))){
            back_points[back_points.length] = thing
            return
        }
    }
    if(options["surface"].substr(0,10)=="hyperbolic" && options["projection"]=="hyperboloid"){
        var hangle = (thing[0]+thing[2])/2
        var vangle = (thing[1]+thing[3])/2
        if (hangle + vangle < -0.3) {
            back_points[back_points.length] = thing
            return
        }
    }
    front_points[front_points.length] = thing
}

function draw_line(ctx,preh,prev,hangle,vangle){
    if(options["surface"].substring(0,4)=="flat"){
        if(options["surface"]=="flattorus"){
            if(options["projection"]=="flat"){
                flat_torus_draw_line(ctx,preh,prev,hangle,vangle)
            }
        } else if(options["surface"]=="flatKlein"){
            if(options["projection"]=="flat"){
                flat_Klein_draw_line(ctx,preh,prev,hangle,vangle)
            }
        } else if(options["surface"]=="flatreal-pp"){
            if(options["projection"]=="flat"){
                flat_real_pp_draw_line(ctx,preh,prev,hangle,vangle)
            }
        } else if(options["surface"]=="flatmobius"){
            if(options["projection"]=="flat"){
                flat_mobius_draw_line(ctx,preh,prev,hangle,vangle)
            }
        } else if(options["surface"]=="flatcylinder"){
            if(options["projection"]=="flat"){
                flat_cylinder_draw_line(ctx,preh,prev,hangle,vangle)
            }
        } else if(options["surface"]=="flatunbounded"){
            if(options["projection"]=="unbounded"){
                flat_unbounded_draw_line(ctx,preh,prev,hangle,vangle)
            }
        }
    } else if(options["surface"]=="sphere"){
        if(options["projection"]=="Mercator"){
            Mercator_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="plate caree"){
            plate_caree_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="van der Grinten"){
            van_der_Grinten_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Robinson"){
            Robinson_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="sinusoidal"){
            sinusoidal_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Mollweide"){
            Mollweide_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Goode"){
            Goode_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="cube"){
            cube_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="tetrahedron"){
            tetrahedron_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="octahedron"){
            octahedron_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="dodecahedron"){
            dodecahedron_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="icosahedron"){
            icosahedron_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="dymaxion"){
            dymaxion_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Gall"){
            Gall_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="azim"){
            azim_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Craig"){
            Craig_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="isometric"){
            isometric_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="stereographic"){
            stereographic_draw_line(ctx,preh,prev,hangle,vangle)
        }
    } else if(options["surface"]=="torus"){
        if(options["projection"]=="top_v"){
            torus_top_v_draw_line(ctx,preh,prev,hangle,vangle)
        }
        if(options["projection"]=="projected"){
            torus_projected_draw_line(ctx,preh,prev,hangle,vangle)
        }
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        if(options["projection"]=="Beltrami-Klein"){
            hyper_bk_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Poincare"){
            hyper_poincare_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="Poincare HP"){
            hyper_poincare_hp_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="hyperboloid"){
            hyper_hyperboloid_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="gans"){
            hyper_gans_draw_line(ctx,preh,prev,hangle,vangle)
        } else if(options["projection"]=="band"){
            hyper_band_draw_line(ctx,preh,prev,hangle,vangle)
        }
    } else if(options["surface"]=="pool"){
        if(options["projection"]=="loop"){
            loop_draw_line(ctx,preh,prev,hangle,vangle)
        }
    }
}

function draw_xy(ctx,prex,prey,x,y){
    if( ( ( x>0 && x<WIDTH ) || ( prex>0 && prex<WIDTH) ) && ( ( y>0 && y<HEIGHT ) || ( prey>0 && prey<HEIGHT ) ) ){
        ctx.moveTo(prex,prey)
        ctx.lineTo(x,y)
    }
}

function add_to_surface(hangle,vangle,rot,badd,flip){
    return _add_to_surface_internal(hangle,vangle,rot,badd,flip,false)
}

function move_on_surface(hangle,vangle,rot,badd,flip){
    return _add_to_surface_internal(hangle,vangle,rot,badd,flip,true)
}

function _add_to_surface_internal(hangle, vangle, rot, badd, flip, moving){
    if(options["surface"]=="flatmobius"){
        hangle += badd*Math.cos(rot)
        vangle += badd*Math.sin(rot)
        if(hangle>WIDTH){
            hangle-=WIDTH
            vangle = HEIGHT - vangle
            rot *= -1
            flip *= -1
        }
        if(hangle<0){
            hangle+=WIDTH
            vangle = HEIGHT - vangle
            flip *= -1
            rot *= -1
        }
        if(moving){
            if(vangle < MOBIUSY){
                vangle = MOBIUSY + (MOBIUSY-vangle)
                rot = 2*Math.PI - rot
            }
            if(vangle > HEIGHT-MOBIUSY){
                vangle = HEIGHT-MOBIUSY + (HEIGHT-MOBIUSY-vangle)
                rot = 2*Math.PI - rot
            }
        }
        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}
    }
    if(options["surface"]=="flatcylinder"){
        hangle += badd*Math.cos(rot)
        vangle += badd*Math.sin(rot)
        if(hangle>WIDTH){
            hangle-=WIDTH
        }
        if(hangle<0){
            hangle+=WIDTH
        }
        if(moving){
            if(vangle < MOBIUSY){
                vangle = MOBIUSY + (MOBIUSY-vangle)
                rot = 2*Math.PI - rot
            }
            if(vangle > HEIGHT-MOBIUSY){
                vangle = HEIGHT-MOBIUSY + (HEIGHT-MOBIUSY-vangle)
                rot = 2*Math.PI - rot
            }
        }
        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}
    }
    if(options["surface"]=="pool"){
        hangle += badd*Math.cos(rot)
        vangle += badd*Math.sin(rot)
        if(moving){
            var sin = (vangle - HEIGHT/2) / LOOPSIZE[1]
            var cos = (hangle - WIDTH/2) / LOOPSIZE[0]
            if(Math.pow(sin,2)+Math.pow(cos,2) > 1){
                var Aa = Math.pow(LOOPSIZE[1],2) + Math.pow(LOOPSIZE[0]*Math.tan(rot),2)
                var Bb = Math.pow(LOOPSIZE[0],2) * (2*(vangle-HEIGHT/2)*Math.tan(rot) - 2*(hangle-WIDTH/2)*Math.pow(Math.tan(rot),2))
                var Cc = Math.pow(LOOPSIZE[0],2) * (Math.pow((hangle-WIDTH/2)*Math.tan(rot),2)-2*(hangle-WIDTH/2)*(vangle-HEIGHT/2)*Math.tan(rot)+Math.pow(vangle-HEIGHT/2,2)-Math.pow(LOOPSIZE[1],2))
                var x1 = WIDTH/2+(-Bb + Math.sqrt(Bb*Bb-4*Aa*Cc))/(2*Aa)
                var x2 = WIDTH/2+(-Bb - Math.sqrt(Bb*Bb-4*Aa*Cc))/(2*Aa)
                if(Math.abs(x1-hangle)<Math.abs(x2-hangle)){
                    var Xx = x1
                } else {
                    var Xx = x2
                }
                var Yy = (Xx-hangle)*Math.tan(rot) + vangle

                var dydx = Math.atan2((Xx-WIDTH/2)*LOOPSIZE[1]*LOOPSIZE[1], (Yy-HEIGHT/2)*LOOPSIZE[0]*LOOPSIZE[0])
                rot = 2*Math.PI - 2*dydx - rot
                dist = Math.sqrt(Math.pow(hangle-Xx,2)+Math.pow(vangle-Yy,2))
                hangle = Xx + dist*Math.cos(rot)
                vangle = Yy + dist*Math.sin(rot)
            }
        }
        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}
    }
    if(options["surface"].substring(0,4)=="flat"){
        hangle += badd*Math.cos(rot)
        vangle += badd*Math.sin(rot)
        if(options["surface"]=="flattorus"){
            if(hangle>WIDTH){hangle-=WIDTH}
            if(hangle<0){hangle+=WIDTH}
            if(vangle>HEIGHT){vangle-=HEIGHT}
            if(vangle<0){vangle+=HEIGHT}
        } else if(options["surface"]=="flatKlein"){
            if(hangle>WIDTH){
                hangle-=WIDTH
                vangle = HEIGHT - vangle
                rot *= -1
                flip *= -1
            }
            if(hangle<0){
                hangle+=WIDTH
                vangle = HEIGHT - vangle
                flip *= -1
                rot *= -1
            }
            if(vangle>HEIGHT){vangle-=HEIGHT}
            if(vangle<0){vangle+=HEIGHT}
        } else if(options["surface"]=="flatreal-pp"){
            if(hangle>WIDTH){
                hangle-=WIDTH
                vangle = HEIGHT - vangle
                rot *= -1
                flip *= -1
            }
            if(hangle<0){
                hangle+=WIDTH
                vangle = HEIGHT - vangle
                flip *= -1
                rot *= -1
            }
            if(vangle>HEIGHT){
                vangle-=HEIGHT
                hangle = WIDTH - hangle
                rot = Math.PI - rot
                flip *= -1
            }
            if(vangle<0){
                vangle+=HEIGHT
                hangle = WIDTH - hangle
                rot = Math.PI - rot
                flip *= -1
            }
        }

        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}

    } else if(options["surface"]=="sphere"){
        var alpha = Math.acos(Math.cos(rot)*Math.cos(vangle))
        var a = hangle - Math.atan2(Math.cos(rot) * Math.sin(vangle),Math.sin(rot))
        var b = Math.atan2(Math.sin(vangle), Math.sin(rot)*Math.cos(vangle))

        b += badd/RADIUS

        hangle = a + Math.atan2(Math.cos(alpha)*Math.sin(b),Math.cos(b))
        vangle = Math.asin(Math.sin(b) * Math.sin(alpha))
        rot = Math.atan2(Math.cos(b)*Math.sin(alpha),Math.cos(alpha))

        if(vangle > Math.PI/2){
            hangle += Math.PI
            vangle = Math.PI-vangle
        }
        if(vangle < -Math.PI/2){
            hangle += Math.PI
            vangle = -Math.PI-vangle
        }
        while(hangle < 0){
            hangle += 2*Math.PI
        }
        while(hangle > 2*Math.PI){
            hangle -= 2*Math.PI
        }
        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}
    } else if(options["surface"]=="torus"){

        var steps = 1 + Math.floor(badd * 1000)
        var stepsize = badd / steps
        for(var i=0;i<steps;i++){
            var x = (TRADIUS[0] + TRADIUS[1]*Math.cos(vangle)) * Math.cos(hangle)
            var y = (TRADIUS[0] + TRADIUS[1]*Math.cos(vangle)) * Math.sin(hangle)
            var z = TRADIUS[1]*Math.sin(vangle)

            var dx = -Math.sin(hangle)*Math.cos(rot) - Math.cos(hangle)*Math.sin(vangle)*Math.sin(rot)
            var dy = Math.cos(hangle)*Math.cos(rot) - Math.sin(hangle)*Math.sin(vangle)*Math.sin(rot)
            var dz = Math.cos(vangle)*Math.sin(rot)

            x += stepsize * dx
            y += stepsize * dy
            z += stepsize * dz

            hangle = Math.atan2(y,x)
            vangle = Math.atan2(z,Math.sqrt(x*x + y*y)-TRADIUS[0])

            v1 = -Math.sin(hangle)*dx + Math.cos(hangle)*dy
            v2 = -Math.cos(hangle)*Math.sin(vangle)*dx - Math.sin(hangle)*Math.sin(vangle)*dy + Math.cos(vangle)*dz
            rot = Math.atan2(v2, v1)

            if(vangle > 2*Math.PI){
                vangle -= 2*Math.PI
            }
            if(vangle < 0){
                vangle += Math.PI*2
            }
            while(hangle < 0){
                hangle += 2*Math.PI
            }
            while(hangle > 2*Math.PI){
                hangle -= 2*Math.PI
            }
            while(rot < 0){
                rot += 2*Math.PI
            }
            while(rot >= 2*Math.PI){
                rot -= 2*Math.PI
            }
        }

        return {"hangle":hangle,"vangle":vangle,"rotation":rot,"flip":flip}
    } else if(options["surface"].substr(0,10)=="hyperbolic"){
        var pt = hyper_add(hangle, vangle, rot, badd)
        if(moving && options["surface"] != "hyperbolicunbounded"){
            if(hyper_compute_distance(0, 0, pt[0], pt[1]) >= HYPER_RADIUS){
                var pts = Array(Array(hangle, vangle), pt)
                for (var i = 0; i < 20; i++){
                    var half = Array((pts[0][0] + pts[1][0]) / 2, (pts[0][1] + pts[1][1]) / 2)
                    if(hyper_compute_distance(0,0,half[0], half[1]) > HYPER_RADIUS) {
                        pts = Array(pts[0], half)
                    } else {
                        pts = Array(half, pts[1])
                    }
                }
                var pt_on_circle = pts[0]
                var ang = Math.atan2(pt_on_circle[1], pt_on_circle[0])
                rot = Math.PI - rot + 2 * ang
                pt = hyper_add(pt_on_circle[0], pt_on_circle[1], rot, badd - hyper_compute_distance(hangle, vangle, pt_on_circle[0], pt_on_circle[1]))
            }
        }
        return {"hangle":pt[0],"vangle":pt[1],"rotation":rot,"flip":flip}
    }
}

// isometric
function isometric_xy(hangle,vangle){
    var x = RADIUS * Math.cos(vangle) * Math.cos(hangle)
    var y = RADIUS * Math.cos(vangle) * Math.sin(hangle)
    var z = RADIUS * Math.sin(vangle)
    var x2 = (x-y) * Math.sin(30)
    var y2 = z + (x+y) * Math.cos(30)
    var out = {}
    out["x"] = WIDTH/2 + x2/(2.2*RADIUS) * Math.min(HEIGHT, WIDTH)
    out["y"] = HEIGHT/2 + y2/(2.2*RADIUS) * Math.min(HEIGHT, WIDTH)
    return out
}

function isometric_draw_line(ctx,preh,prev,h,v){
    var xy = isometric_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = isometric_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    draw_xy(ctx,prex,prey,x,y)
}

// stereographic
function stereographic_xy(hangle,vangle){
    var x = Math.cos(vangle) * Math.cos(hangle)
    var y = Math.cos(vangle) * Math.sin(hangle)
    var z = Math.sin(vangle)
    var out = {}
    var R = WIDTH/5
    if(z>0){
        out["x"] = WIDTH/4+R*x/(1+z)
        out["y"] = HEIGHT/2+R*y/(1+z)
    } else {
        out["x"] = 3*WIDTH/4-R*x/(1-z)
        out["y"] = HEIGHT/2+R*y/(1-z)
    }
    return out
}

function stereographic_draw_line(ctx,preh,prev,h,v){
    var xy = stereographic_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = stereographic_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]

    if(Math.max(x,prex)>WIDTH/2 && Math.min(x,prex)<WIDTH/2){
        hmid = preh+Math.tan(preh-h)*Math.sin(prev)/Math.sin(prev-v)
        var mid1 = stereographic_xy(hmid,0.01)
        var mid2 = stereographic_xy(hmid,-0.01)
        ctx.moveTo(mid1["x"],mid1["y"])
        if(x<prex){
            draw_xy(ctx,mid1["x"],mid1["y"],x,y)
        } else {
            draw_xy(ctx,mid1["x"],mid1["y"],prex,prey)
        }
        if(x>prex){
            draw_xy(ctx,mid2["x"],mid2["y"],x,y)
        } else {
            draw_xy(ctx,mid2["x"],mid2["y"],prex,prey)
        }
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Craig
function Craig_xy(hangle,vangle){
    hangle -= Math.PI
    var x = WIDTH/2 + hangle * WIDTH/(2*Math.PI)
    if(Math.abs(hangle)<0.01){
        var k = 1
    } else {
        var k = hangle/Math.sin(hangle)
    }
    var y = HEIGHT/2 + WIDTH/(2*Math.PI)*k*(Math.sin(vangle)*Math.cos(hangle) - Math.tan(Craig_zeroang)*Math.cos(vangle))
    return {"x":x,"y":y}
}

function Craig_draw_line(ctx,preh,prev,h,v){
    if(Math.abs(prev) < Math.PI/2-0.02 || Math.abs(h-preh)<0.1){
        var xy = Craig_xy(preh,prev)
        var prex = xy["x"]
        var prey = xy["y"]
        xy = Craig_xy(h,v)
        var x = xy["x"]
        var y = xy["y"]
        if(Math.abs(y-prey) < HEIGHT/2 && Math.abs(x-prex) < WIDTH/2){
            draw_xy(ctx,prex,prey,x,y)
        }
    }
}

// azim
function azim_xy(hangle,vangle){
    var p = HEIGHT/7 * (Math.PI/2 - vangle)
    y = HEIGHT/2 -p*Math.cos(hangle)
    x = WIDTH/2 + p*Math.sin(hangle)
    return {"x":x,"y":y}
}

function azim_draw_line(ctx,preh,prev,h,v){
    var xy = azim_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = azim_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(x-prex) + Math.abs(y-prey) < 50){
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Mercator
function Mercator_xy(hangle,vangle){
    var x = WIDTH * hangle/(2*Math.PI)
    var y = 0
    var maxa = 87.05 * Math.PI/180
    if(-maxa <= vangle <= maxa){
        y = HEIGHT/2 + HEIGHT/2 * Math.log(Math.tan(Math.PI/4+vangle/2))/Math.log(Math.tan(Math.PI/4+maxa/2))
    } else if(vangle > maxa){
        y = -5
    } else {
        y = HEIGHT+5
    }
    return {"x":x,"y":y}
}

function Mercator_draw_line(ctx,preh,prev,h,v){
    var xy = Mercator_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = Mercator_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// plate caree
function plate_caree_xy(hangle,vangle){
    var x = WIDTH * hangle/(2*Math.PI)
    var y = HEIGHT * (vangle + Math.PI/2) / (Math.PI)
    return {"x":x,"y":y}
}

function plate_caree_draw_line(ctx,preh,prev,h,v){
    var xy = plate_caree_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = plate_caree_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// van der Grinten
function van_der_Grinten_xy(hangle,vangle){
    var x = 0
    var y = 0

    if (vangle == 0) {
        x = hangle - Math.PI
        y = 0
    } else if (hangle == Math.PI || Math.abs(vangle) > Math.PI/2-0.0001) {
        x = 0
        y = Math.PI * Math.tan(Math.asin(Math.min(1, Math.abs(2*vangle / Math.PI)))/2)
    } else {
        var sinO = Math.abs(2*vangle / Math.PI)
        var cosO = Math.sqrt(1 - sinO * sinO)
        var a = Math.abs(Math.PI / (hangle - Math.PI) - (hangle - Math.PI) / Math.PI) / 2
        var g = cosO / (sinO + cosO - 1)
        var p = g * (2 / sinO - 1)
        var q = a * a + g

        x = Math.PI * (a * (g - p*p) + Math.sqrt(a*a*Math.pow(g - p*p, 2)-(p*p+a*a)*(g*g-p*p))) / (p*p + a*a)
        y = Math.PI * (p * q - a * Math.sqrt((a*a+1)*(p*p+a*a) - q*q)) / (p*p + a*a)
    }
    if (hangle < Math.PI) { x *= -1 }
    if (vangle < 0) { y *= -1 }

    return {"x":WIDTH/2 + HEIGHT/7 * x,"y":HEIGHT/2 + HEIGHT/7 * y}
}

function van_der_Grinten_draw_line(ctx,preh,prev,h,v){
    var xy = van_der_Grinten_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = van_der_Grinten_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if (Math.min(h, preh) > Math.PI/4 || Math.max(h, preh) < 7*Math.PI/4) {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Robinson
function Robinson_compute(vangle){
    var Robinson_interpolation = {
       0: [1.0000, 0.0000],
       5: [0.9986, 0.0620],
      10: [0.9954, 0.1240],
      15: [0.9900, 0.1860],
      20: [0.9822, 0.2480],
      25: [0.9730, 0.3100],
      30: [0.9600, 0.3720],
      35: [0.9427, 0.4340],
      40: [0.9216, 0.4958],
      45: [0.8962, 0.5571],
      50: [0.8679, 0.6176],
      55: [0.8350, 0.6769],
      60: [0.7986, 0.7346],
      65: [0.7597, 0.7903],
      70: [0.7186, 0.8435],
      75: [0.6732, 0.8936],
      80: [0.6213, 0.9394],
      85: [0.5722, 0.9761],
      90: [0.5322, 1.0000]
    }
    var post = 5
    var vangle_deg = Math.abs(vangle * 180 / Math.PI)
    while (vangle_deg > post){
        post += 5
    }
    if (post > 90){ post = 90 }
    var pre_v = Robinson_interpolation[post - 5]
    var post_v = Robinson_interpolation[post]
    var X = pre_v[0] + (post_v[0] - pre_v[0]) * (vangle_deg - post + 5) / 5
    var Y = pre_v[1] + (post_v[1] - pre_v[1]) * (vangle_deg - post + 5) / 5
    return [X, Y]
}

function Robinson_xy(hangle,vangle){
    var XY = Robinson_compute(vangle)
    var R = 140
    var x = WIDTH/2 + 0.8487 * R * XY[0] * (hangle - Math.PI)
    var y = HEIGHT/2
    if (vangle < 0){
        y -= 1.3523 * R * XY[1]
    } else {
        y += 1.3523 * R * XY[1]
    }
    return {"x":x,"y":y}
}

function Robinson_draw_line(ctx,preh,prev,h,v){
    var xy = Robinson_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = Robinson_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(h-preh) < Math.PI / 5){
        draw_xy(ctx,prex,prey,x,y)
    }
}

// sinusoidal
function sinusoidal_xy(hangle,vangle){
    var R = 120
    var x = WIDTH/2 + R * (hangle - Math.PI) * Math.cos(vangle)
    var y = HEIGHT/2 + R * vangle
    return {"x":x,"y":y}
}

function sinusoidal_draw_line(ctx,preh,prev,h,v){
    var xy = sinusoidal_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = sinusoidal_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(h-preh) < Math.PI / 5){
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Mollweide
function compute_theta(vangle){
    var theta = vangle
    if (theta > -Math.PI/2 + 0.02 && theta < Math.PI/2 - 0.02){
        for (var i = 0; i < 10; i++){
            theta = theta - (2 * theta + Math.sin(2 * theta) - Math.PI * Math.sin(vangle)) / (2 + 2 * Math.cos(2 * theta))
        }
    }
    return theta
}

function Mollweide_xy(hangle,vangle){
    var R = 120
    var theta = compute_theta(vangle)
    var x = WIDTH/2 + R * 2 * Math.sqrt(2) / Math.PI * (hangle - Math.PI) * Math.cos(theta)
    var y = HEIGHT/2 + R * Math.sqrt(2) * Math.sin(theta)
    return {"x":x,"y":y}
}

function Mollweide_draw_line(ctx,preh,prev,h,v){
    var xy = Mollweide_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = Mollweide_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(h-preh) < Math.PI / 5){
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Goode
function Goode_xy(hangle,vangle){
    var R = 120
    var start = 0
    var mid = Math.PI
    if (vangle < 0){
        if (hangle < 7*Math.PI/9){
            mid = 4*Math.PI/9
        } else {
            start = 7*Math.PI/9
            mid = 21*Math.PI/18
        }
    } else {
        if (hangle < 4*Math.PI/9){
            mid = Math.PI/9
        } else if (hangle < 8*Math.PI/9){
            start = 4*Math.PI/9
            mid = 6*Math.PI/9
        } else if (hangle < 14*Math.PI/9){
            start = 8*Math.PI/9
            mid = 10*Math.PI/9
        } else {
            start = 14*Math.PI/9
            mid = 16*Math.PI/9
        }
    }

    var A = 40.7 * Math.PI/180

    var x = 0
    var y = 0
    if (vangle < -A || vangle > A){
        if (vangle < -A){
            A = -A
        }
        var theta = compute_theta(vangle)
        var theta_A = compute_theta(A)
        x = WIDTH/2
        y = HEIGHT/2

        x += R * (mid - Math.PI) + R * (start - mid) * Math.cos(A)
        y += R * A
        x -= R * 2 * Math.sqrt(2) / Math.PI * (start - mid) * Math.cos(theta_A)
        y -= R * Math.sqrt(2) * Math.sin(theta_A)

        x += R * 2 * Math.sqrt(2) / Math.PI * (hangle - mid) * Math.cos(theta)
        y += R * Math.sqrt(2) * Math.sin(theta)

    } else {
        var R = 120
        x = WIDTH/2 + R * (mid - Math.PI) + R * (hangle - mid) * Math.cos(vangle)
        y = HEIGHT/2 + R * vangle
    }
    return {"x":x,"y":y}
}

function Goode_draw_line(ctx,preh,prev,h,v){
    var xy = Goode_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = Goode_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if (v < 0){
        if(h > 7*Math.PI/9 && preh < 7*Math.PI/9){ return }
        if(preh > 7*Math.PI/9 && h < 7*Math.PI/9){ return }
    } else {
        if(h > 4*Math.PI/9 && preh < 4*Math.PI/9){ return }
        if(preh > 4*Math.PI/9 && h < 4*Math.PI/9){ return }
        if(h > 8*Math.PI/9 && preh < 8*Math.PI/9){ return }
        if(preh > 8*Math.PI/9 && h < 8*Math.PI/9){ return }
        if(h > 14*Math.PI/9 && preh < 14*Math.PI/9){ return }
        if(preh > 14*Math.PI/9 && h < 14*Math.PI/9){ return }
    }

    if(Math.abs(h-preh) < Math.PI / 5){
        draw_xy(ctx,prex,prey,x,y)
    }
}

// nets
function net_xy(hangle, vangle, centres, map_centres, axes, size){
    var x = Math.cos(hangle) * Math.cos(vangle)
    var y = Math.sin(hangle) * Math.cos(vangle)
    var z = Math.sin(vangle)

    var abs = []
    var m = -2
    for (var i = 0; i < centres.length; i++){
        abs.push(centres[i][0]*x + centres[i][1] * y + centres[i][2] * z)
        m = Math.max(m, abs[i])
    }
    index = -1
    for (var i = 0; i < centres.length; i++){
        if(abs[i] == m){
            index = i
            break
        }
    }

    if(options["projection"]=="dymaxion"){
        if (index == 9 && x * axes[index][0][0] + y * axes[index][0][1] + z * axes[index][0][2] > 0){
            index = 20
        }
        if (index == 11 && x * axes[index][0][0] + y * axes[index][0][1] + z * axes[index][0][2] > 0 && x * axes[21][0][0] + y * axes[21][0][1] + z * axes[21][0][2] > 0){
            index = 21
        }
    }

    var scale = x * centres[index][0] + y * centres[index][1] + z * centres[index][2]
    x /= scale
    y /= scale
    z /= scale
    return {
        "x": WIDTH/2 + size * (map_centres[index][0] + x * axes[index][0][0] + y * axes[index][0][1] + z * axes[index][0][2]),
        "y": HEIGHT/2 + size * (map_centres[index][1] + x * axes[index][1][0] + y * axes[index][1][1] + z * axes[index][1][2]),
        "part": index
    }
}

function are_eq(a, b, c, d){
    return (a == c && b == d) || (a == d && b == c)
}

// cube
function cube_xy(hangle,vangle){
    return net_xy(hangle, vangle,
        [[0, 0, 1], [1, 0, 0], [0, 0, -1], [-1, 0, 0], [0, 1, 0], [0, -1, 0]],
        [[-1, 2], [-1, 0], [-1, -2], [3, 0], [1, 0], [-3, 0]],
        [[[0, 1, 0], [-1, 0, 0]], [[0, 1, 0], [0, 0, 1]], [[0, 1, 0], [1, 0, 0]], [[0, -1, 0], [0, 0, 1]], [[-1, 0, 0], [0, 0, 1]], [[1, 0, 0], [0, 0, 1]]],
        HEIGHT / 7)
}

function cube_draw_line(ctx,preh,prev,h,v){
    var prexy = cube_xy(preh,prev)
    var xy = cube_xy(h,v)
    var p = prexy["part"]
    var q = xy["part"]

    if(p == q || are_eq(p, q, 0, 1) || are_eq(p, q, 1, 2) || are_eq(p, q, 3, 4) || are_eq(p, q, 1, 5) || are_eq(p, q, 1, 4)){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// tetrahedron
function tetrahedron_xy(hangle,vangle){
    var h = Math.tan(Math.acos(-1/3)/2) * Math.sqrt(3)
    var v = Math.tan(Math.acos(-1/3)/2)
    return net_xy(hangle, vangle,
        [[0, 0, 1], [Math.sqrt(8)/3, 0, -1/3], [-Math.sqrt(2)/3, Math.sqrt(2/3), -1/3], [-Math.sqrt(2)/3, -Math.sqrt(2/3), -1/3]],
        [[0,2*v-1.5], [0,-1.5], [h, 3*v-1.5], [-h,3*v-1.5]],
        [[[0, 1, 0], [-1, 0, 0]], [[0, 1, 0], [1/3, 0, Math.sqrt(8)/3]], [[Math.sqrt(3)/3, 0, -Math.sqrt(6)/3],[-2/3, -Math.sqrt(3)/3, -Math.sqrt(2)/3]], [[-Math.sqrt(3)/3, 0, Math.sqrt(6)/3],[-2/3, Math.sqrt(3)/3, -Math.sqrt(2)/3]]],
        HEIGHT / 10)
}

function tetrahedron_draw_line(ctx,preh,prev,h,v){
    var prexy = tetrahedron_xy(preh,prev)
    var xy = tetrahedron_xy(h,v)
    if(prexy["part"] == xy["part"] || prexy["part"] == 0 || xy["part"] == 0 || 0 == 0){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// octahedron
function octahedron_xy(hangle,vangle){
    var rt2 = Math.sqrt(2)
    var irt2 = 1/rt2
    var rt6 = Math.sqrt(6)
    return net_xy(hangle, vangle,
        [[1/3,1/3,1/3],[1/3,1/3,-1/3],[1/3,-1/3,1/3],[1/3,-1/3,-1/3],[-1/3,1/3,1/3],[-1/3,1/3,-1/3],[-1/3,-1/3,1/3],[-1/3,-1/3,-1/3]],
        [[0,1],[0,1-rt6],[-1.5*rt2,1+rt6/2],[-3*rt2,1],[3*rt2,1-rt6],[1.5*rt2,1-rt6*1.5],[4.5*rt2,1-rt6*1.5],[-4.5*rt2,1+rt6*0.5]],
        [[[-irt2, irt2, 0], [-1/rt6, -1/rt6, 2/rt6]],[[-irt2, irt2, 0], [1/rt6, 1/rt6, 2/rt6]],[[0, irt2, irt2],[-2/rt6, -1/rt6, 1/rt6]],[[irt2, 0, irt2],[-1/rt6, -2/rt6, 1/rt6]],[[0, -irt2, irt2],[2/rt6, 1/rt6, 1/rt6]],[[-irt2, 0, irt2],[1/rt6, 2/rt6, 1/rt6]],[[irt2, -irt2, 0],[1/rt6, 1/rt6, 2/rt6]],[[irt2, -irt2, 0],[-1/rt6, -1/rt6, 2/rt6]]],

        HEIGHT / 10)
}

function octahedron_draw_line(ctx,preh,prev,h,v){
    var prexy = octahedron_xy(preh,prev)
    var xy = octahedron_xy(h,v)
    var p = prexy["part"]
    var q = xy["part"]
    if(p == q || are_eq(p, q, 0, 1) || are_eq(p, q, 0, 3) || are_eq(p, q, 3, 4) || are_eq(p, q, 1, 5) || are_eq(p, q, 5, 6) || are_eq(p, q, 4, 7) || are_eq(p, q, 6, 8)){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// dodecahedron
function dodecahedron_xy(hangle,vangle){
    return net_xy(hangle, vangle,
        [[0.0, 0.5257311121191336, 0.85065080835204], [0.5257311121191336, 0.85065080835204, 0.0], [0.85065080835204, 0.0, 0.5257311121191336], [0.0, 0.5257311121191336, -0.85065080835204], [0.85065080835204, 0.0, -0.5257311121191336], [0.0, -0.5257311121191336, 0.85065080835204], [0.5257311121191336, -0.85065080835204, 0.0], [0.0, -0.5257311121191336, -0.85065080835204], [-0.5257311121191336, 0.85065080835204, 0.0], [-0.85065080835204, 0.0, 0.5257311121191336], [-0.85065080835204, 0.0, -0.5257311121191336], [-0.5257311121191336, -0.85065080835204, 0.0]],
        [[-1.2909944487358058, 0.7946544722917662], [-1.2909944487358058, -0.18759247408507995], [-2.225166807698521, 0.11593852501826318], [-0.7136441795461798, -0.9822469463768463], [-1.8683447179254318, -0.9822469463768463], [2.088872897341968, 0.9105929973100294], [2.4456949871150577, -0.18759247408507995], [1.5115226281523417, -0.8663084213585831], [-0.35682208977308993, 0.11593852501826318], [0.934172358962716, 0.9105929973100294], [0.577350269189626, -0.18759247408507995], [1.5115226281523417, 0.11593852501826318]],
        [[[-0.6428889727400947, 0.39732723614588306, -0.2455617365942116], [-0.4670861794813579, -0.5468740243419741, 0.33798673460777734]], [[-0.6428889727400947, 0.39732723614588306, -0.2455617365942116], [-0.20888728973419682, 0.1290994448735806, 0.7557613140761708]], [[0.0, 0.7946544722917662, 0.0], [-0.41777457946839347, -0.0, 0.6759734692155547]], [[-0.7946544722917662, 0.0, 0.0], [-0.0, 0.6759734692155547, 0.41777457946839347]], [[-0.2455617365942116, 0.6428889727400947, -0.39732723614588306], [0.33798673460777734, 0.4670861794813579, 0.5468740243419741]], [[0.7946544722917662, 0.0, 0.0], [-0.0, 0.6759734692155547, 0.41777457946839347]], [[0.6428889727400946, 0.3973272361458832, 0.2455617365942116], [-0.2088872897341968, -0.1290994448735807, 0.7557613140761708]], [[0.6428889727400947, -0.39732723614588306, 0.2455617365942116], [-0.4670861794813579, -0.5468740243419741, 0.33798673460777734]], [[-0.6428889727400947, -0.39732723614588306, -0.2455617365942116], [-0.20888728973419682, -0.1290994448735806, 0.7557613140761708]], [[0.24556173659421152, -0.6428889727400947, 0.3973272361458831], [0.33798673460777734, 0.4670861794813579, 0.5468740243419741]], [[0.0, -0.7946544722917662, 0.0], [-0.41777457946839347, -0.0, 0.6759734692155547]], [[0.6428889727400947, -0.3973272361458831, 0.24556173659421152], [-0.2088872897341967, 0.1290994448735806, 0.7557613140761709]]],
        HEIGHT / 3.5)
}

function dodecahedron_draw_line(ctx,preh,prev,h,v){
    var prexy = dodecahedron_xy(preh,prev)
    var xy = dodecahedron_xy(h,v)
    var p = prexy["part"]
    var q = xy["part"]
    if(p == q || are_eq(p, q, 1, 0) || are_eq(p, q, 1, 2) || are_eq(p, q, 1, 4) || are_eq(p, q, 1, 3) || are_eq(p, q, 1, 8) || are_eq(p, q, 8, 10) || are_eq(p, q, 11, 10) || are_eq(p, q, 11, 9) || are_eq(p, q, 11, 5) || are_eq(p, q, 11, 6) || are_eq(p, q, 11, 7)){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// icosahedron
function icosahedron_xy(hangle,vangle){
    return net_xy(hangle, vangle,
        [[0.35682208977308993, 0.0, 0.9341723589627157], [-0.35682208977308993, 0.0, 0.9341723589627157], [0.0, 0.9341723589627157, 0.35682208977308993], [0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.0, -0.9341723589627157, 0.35682208977308993], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.35682208977308993, 0.0, -0.9341723589627157], [-0.35682208977308993, 0.0, -0.9341723589627157], [0.0, 0.9341723589627157, -0.35682208977308993], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.0, -0.9341723589627157, -0.35682208977308993], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.9341723589627157, 0.35682208977308993, 0.0], [-0.9341723589627157, 0.35682208977308993, 0.0], [0.9341723589627157, -0.35682208977308993, 0.0], [-0.9341723589627157, -0.35682208977308993, 0.0]],
        [[0.2628655560595668, 0], [0.2628655560595668, -0.6070619982066863], [-0.7885966681787004, 0], [-0.2628655560595668, 0.30353099910334314], [-0.7885966681787004, -0.6070619982066863], [1.314327780297834, 0], [0.7885966681787004, 0.30353099910334314], [1.314327780297834, -0.6070619982066863], [-2.365790004536101, 0.9105929973100294], [-2.365790004536101, 0.30353099910334314], [-1.3143277802978341, 0.30353099910334314], [-1.3143277802978341, 0.9105929973100294], [-1.8400588924169676, 0], [1.8400588924169676, 0.30353099910334314], [1.8400588924169676, 0.9105929973100294], [2.3657900045361013, 0], [-0.2628655560595668, 0.9105929973100294], [-1.8400588924169676, -0.6070619982066863], [0.7885966681787004, 0.9105929973100294], [2.3657900045361013, -0.6070619982066863]],
        [[[0.0, -0.7946544722917661, 0.0], [0.7423442429410712, -0.0, -0.28355026945067996]], [[0.0, -0.7946544722917661, 0.0], [0.7423442429410712, -0.0, 0.28355026945067996]], [[0.39732723614588306, -0.24556173659421157, 0.6428889727400946], [0.6881909602355868, 0.14177513472533998, -0.3711721214705356]], [[0.24556173659421157, -0.6428889727400946, 0.39732723614588306], [0.6005691082157313, -0.08762185201985556, -0.5129472561958758]], [[0.39732723614588306, -0.24556173659421157, 0.6428889727400946], [0.5129472561958758, 0.6005691082157313, -0.08762185201985556]], [[-0.39732723614588306, -0.24556173659421157, -0.6428889727400946], [0.6881909602355868, -0.14177513472533998, -0.3711721214705356]], [[-0.24556173659421157, -0.6428889727400946, -0.39732723614588306], [0.6005691082157313, 0.08762185201985556, -0.5129472561958758]], [[-0.39732723614588306, -0.24556173659421157, -0.6428889727400946], [0.5129472561958758, -0.6005691082157313, -0.08762185201985556]], [[0.0, 0.7946544722917661, 0.0], [0.7423442429410712, -0.0, 0.28355026945067996]], [[0.0, 0.7946544722917661, 0.0], [0.7423442429410712, -0.0, -0.28355026945067996]], [[0.39732723614588306, 0.24556173659421157, 0.6428889727400946], [0.6881909602355868, -0.14177513472533998, -0.3711721214705356]], [[0.39732723614588306, 0.24556173659421157, 0.6428889727400946], [0.5129472561958758, -0.6005691082157313, -0.08762185201985556]], [[0.24556173659421157, 0.6428889727400946, 0.39732723614588306], [0.6005691082157313, 0.08762185201985556, -0.5129472561958758]], [[-0.39732723614588306, 0.24556173659421157, -0.6428889727400946], [0.6881909602355868, 0.14177513472533998, -0.3711721214705356]], [[-0.39732723614588306, 0.24556173659421157, -0.6428889727400946], [0.5129472561958758, 0.6005691082157313, -0.08762185201985556]], [[-0.24556173659421157, 0.6428889727400946, -0.39732723614588306], [0.6005691082157313, -0.08762185201985556, -0.5129472561958758]], [[0.24556173659421157, -0.6428889727400946, 0.39732723614588306], [0.14177513472533998, -0.3711721214705356, -0.6881909602355868]], [[0.24556173659421157, 0.6428889727400946, 0.39732723614588306], [0.14177513472533998, 0.3711721214705356, -0.6881909602355868]], [[-0.24556173659421157, -0.6428889727400946, -0.39732723614588306], [0.14177513472533998, 0.3711721214705356, -0.6881909602355868]], [[-0.24556173659421157, 0.6428889727400946, -0.39732723614588306], [0.14177513472533998, -0.3711721214705356, -0.6881909602355868]]],
        HEIGHT / 3.5)
}

function icosahedron_draw_line(ctx,preh,prev,h,v){
    var prexy = icosahedron_xy(preh,prev)
    var xy = icosahedron_xy(h,v)
    var p = prexy["part"]
    var q = xy["part"]
    if(p == q || are_eq(p, q, 8, 9) || are_eq(p, q, 9, 12) || are_eq(p, q, 12, 17) || are_eq(p, q, 12, 10) || are_eq(p, q, 11, 10) || are_eq(p, q, 10, 2) || are_eq(p, q, 2, 4) || are_eq(p, q, 2, 3) || are_eq(p, q, 16, 3) || are_eq(p, q, 3, 0) || are_eq(p, q, 0, 1) || are_eq(p, q, 0, 6) || are_eq(p, q, 18, 6) || are_eq(p, q, 6, 5) || are_eq(p, q, 5, 7) || are_eq(p, q, 5, 13) || are_eq(p, q, 14, 13) || are_eq(p, q, 13, 15) || are_eq(p, q, 15, 19)){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// dymaxion
function dymaxion_xy(hangle,vangle){
    return net_xy(hangle, vangle,
[[0.35682208977308993, 0.0, 0.9341723589627157], [-0.35682208977308993, 0.0, 0.9341723589627157], [0.0, 0.9341723589627157, 0.35682208977308993], [0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, 0.5773502691896258], [0.0, -0.9341723589627157, 0.35682208977308993], [0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [-0.5773502691896258, -0.5773502691896258, 0.5773502691896258], [0.35682208977308993, 0.0, -0.9341723589627157], [-0.35682208977308993, 0.0, -0.9341723589627157], [0.0, 0.9341723589627157, -0.35682208977308993], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, 0.5773502691896258, -0.5773502691896258], [0.0, -0.9341723589627157, -0.35682208977308993], [0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [-0.5773502691896258, -0.5773502691896258, -0.5773502691896258], [0.9341723589627157, 0.35682208977308993, 0.0], [-0.9341723589627157, 0.35682208977308993, 0.0], [0.9341723589627157, -0.35682208977308993, 0.0], [-0.9341723589627157, -0.35682208977308993, 0.0], [-0.35682208977308993, 0.0, -0.9341723589627157], [0.5773502691896258, 0.5773502691896258, -0.5773502691896258]],

[[0.2628655560595668, 0], [-0.2628655560595668, -0.9105929973100294], [-0.7885966681787004, 0], [-0.2628655560595668, 0.30353099910334314], [-0.7885966681787004, -0.6070619982066863], [1.314327780297834, 0], [0.7885966681787004, 0.30353099910334314], [1.314327780297834, -0.6070619982066863], [-1.8400588924169676, 1.2141239964133725], [2.891521116655235, 0.30353099910334314], [-1.3143277802978341, 0.30353099910334314], [-1.3143277802978341, 0.9105929973100294], [-1.8400588924169676, 0], [1.8400588924169676, 0.30353099910334314], [1.314327780297834, 1.2141239964133725], [2.3657900045361013, 0], [-0.2628655560595668, 0.9105929973100294], [-1.3143277802978341, -0.9105929973100294], [0.7885966681787004, 0.9105929973100294], [2.3657900045361013, -0.6070619982066863], [-2.365790004536101, 0.9105929973100294], [-0.7885966681787004, 1.2141239964133725]],

[[[0.0, -0.7946544722917661, 0.0], [0.7423442429410712, -0.0, -0.28355026945067996]], [[0.6428889727400946, -0.39732723614588306, 0.24556173659421157], [0.3711721214705356, 0.6881909602355868, 0.14177513472533998]], [[0.39732723614588306, -0.24556173659421157, 0.6428889727400946], [0.6881909602355868, 0.14177513472533998, -0.3711721214705356]], [[0.24556173659421157, -0.6428889727400946, 0.39732723614588306], [0.6005691082157313, -0.08762185201985556, -0.5129472561958758]], [[0.39732723614588306, -0.24556173659421157, 0.6428889727400946], [0.5129472561958758, 0.6005691082157313, -0.08762185201985556]], [[-0.39732723614588306, -0.24556173659421157, -0.6428889727400946], [0.6881909602355868, -0.14177513472533998, -0.3711721214705356]], [[-0.24556173659421157, -0.6428889727400946, -0.39732723614588306], [0.6005691082157313, 0.08762185201985556, -0.5129472561958758]], [[-0.39732723614588306, -0.24556173659421157, -0.6428889727400946], [0.5129472561958758, -0.6005691082157313, -0.08762185201985556]], [[0.6428889727400946, 0.39732723614588306, 0.24556173659421157], [0.3711721214705356, -0.6881909602355868, 0.14177513472533998]], [[0.0, 0.7946544722917661, 0.0], [0.7423442429410712, -0.0, -0.28355026945067996]], [[0.39732723614588306, 0.24556173659421157, 0.6428889727400946], [0.6881909602355868, -0.14177513472533998, -0.3711721214705356]], [[0.39732723614588306, 0.24556173659421157, 0.6428889727400946], [0.5129472561958758, -0.6005691082157313, -0.08762185201985556]], [[0.24556173659421157, 0.6428889727400946, 0.39732723614588306], [0.6005691082157313, 0.08762185201985556, -0.5129472561958758]], [[-0.39732723614588306, 0.24556173659421157, -0.6428889727400946], [0.6881909602355868, 0.14177513472533998, -0.3711721214705356]], [[-0.6428889727400946, -0.39732723614588306, -0.24556173659421157], [-0.08762185201985556, 0.5129472561958758, -0.6005691082157313]], [[-0.24556173659421157, 0.6428889727400946, -0.39732723614588306], [0.6005691082157313, -0.08762185201985556, -0.5129472561958758]], [[0.24556173659421157, -0.6428889727400946, 0.39732723614588306], [0.14177513472533998, -0.3711721214705356, -0.6881909602355868]], [[0.0, 0.0, 0.7946544722917661], [0.28355026945067996, 0.7423442429410712, -0.0]], [[-0.24556173659421157, -0.6428889727400946, -0.39732723614588306], [0.14177513472533998, 0.3711721214705356, -0.6881909602355868]], [[-0.24556173659421157, 0.6428889727400946, -0.39732723614588306], [0.14177513472533998, -0.3711721214705356, -0.6881909602355868]], [[0.6428889727400946, 0.39732723614588306, -0.24556173659421157], [0.3711721214705356, -0.6881909602355868, -0.14177513472533998]], [[0.6428889727400946, -0.39732723614588306, 0.24556173659421152], [-0.0876218520198556, -0.5129472561958756, -0.6005691082157311]]],
        HEIGHT / 3.5)
}

function dymaxion_draw_line(ctx,preh,prev,h,v){
    var prexy = dymaxion_xy(preh,prev)
    var xy = dymaxion_xy(h,v)
    var p = prexy["part"]
    var q = xy["part"]
    if(p == q || are_eq(p, q, 8, 20) || are_eq(p, q, 8, 11) || are_eq(p, q, 11, 10) || are_eq(p, q, 10, 12) || are_eq(p, q, 10, 2) || are_eq(p, q, 2, 4) || are_eq(p, q, 4, 1) || are_eq(p, q, 4, 17) || are_eq(p, q, 2, 3) || are_eq(p, q, 21, 16) || are_eq(p, q, 16, 3) || are_eq(p, q, 3, 0) || are_eq(p, q, 0, 6) || are_eq(p, q, 6, 18) || are_eq(p, q, 18, 14) || are_eq(p, q, 6, 5) || are_eq(p, q, 5, 7) || are_eq(p, q, 5, 13) || are_eq(p, q, 13, 15) || are_eq(p, q, 15, 19) || are_eq(p, q, 15, 9)){
        draw_xy(ctx,prexy["x"],prexy["y"],xy["x"],xy["y"])
    }
}

// Gall
function Gall_xy(hangle,vangle){
    var x = WIDTH * hangle/(2*Math.PI)
    var y = HEIGHT/2+HEIGHT/2*Math.sin(vangle)
    return {"x":x,"y":y}
}

function Gall_draw_line(ctx,preh,prev,h,v){
    var xy = Gall_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = Gall_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// flat_torus
function flat_torus_draw_line(ctx,prex,prey,x,y){
    if(Math.abs(x-prex)>WIDTH/2 && Math.abs(y-prey)>HEIGHT/2){
        // currently hide these lines
    } else if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else if(Math.abs(y-prey)>HEIGHT/2){
        if(y < prey){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        xmid = yb*(xb-xa)/(ya-yb-HEIGHT) + xb
        draw_xy(ctx,xa,ya,xmid,HEIGHT)
        draw_xy(ctx,xmid,0,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// flat_Klein
function flat_Klein_draw_line(ctx,prex,prey,x,y){
    if(Math.abs(x-prex)>WIDTH/2 && Math.abs(y-prey)>HEIGHT/2){
        // currently hide these lines
    } else if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-HEIGHT+ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,HEIGHT-ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else if(Math.abs(y-prey)>HEIGHT/2){
        if(y < prey){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        xmid = yb*(xb-xa)/(ya-yb-HEIGHT) + xb
        draw_xy(ctx,xa,ya,xmid,HEIGHT)
        draw_xy(ctx,xmid,0,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// flat_real_pp
function flat_real_pp_draw_line(ctx,prex,prey,x,y){
    if(Math.abs(x-prex)>WIDTH/2 && Math.abs(y-prey)>HEIGHT/2){
        // currently hide these lines
    } else if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-HEIGHT+ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,HEIGHT-ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else if(Math.abs(y-prey)>HEIGHT/2){
        if(y < prey){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        xmid = yb*(xb-WIDTH+xa)/(ya-yb-HEIGHT) + xb
        draw_xy(ctx,xa,ya,WIDTH-xmid,HEIGHT)
        draw_xy(ctx,xmid,0,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// Torus top_v
function torus_top_v_xy(hangle,vangle){
    var x = Math.cos(hangle)*(TRADIUS[0]+TRADIUS[1]*Math.cos(vangle))
    var y = Math.sin(hangle)*(TRADIUS[0]+TRADIUS[1]*Math.cos(vangle))
    var z = TRADIUS[1]*Math.sin(vangle)
    //var x2 = (x-y) * Math.sin(30)
    //var y2 = z + (x+y) * Math.cos(30)
    var x2 = x
    var y2 = y
    var out = {}
    out["x"] = WIDTH/2 + x2/(3.2*RADIUS) * Math.min(HEIGHT, WIDTH)
    out["y"] = HEIGHT/2 + y2/(3.2*RADIUS) * Math.min(HEIGHT, WIDTH)
    return out
}

function torus_top_v_draw_line(ctx,preh,prev,h,v){
    var xy = torus_top_v_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = torus_top_v_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    draw_xy(ctx,prex,prey,x,y)
}


// Torus projected
function torus_projected_xy(hangle,vangle){
    var out = {}
    out["x"] = WIDTH*hangle/(2*Math.PI)
    out["y"] = HEIGHT*vangle/(2*Math.PI)
    return out
}

function torus_projected_draw_line(ctx,preh,prev,h,v){
    var xy = torus_projected_xy(preh,prev)
    var prex = xy["x"]
    var prey = xy["y"]
    xy = torus_projected_xy(h,v)
    var x = xy["x"]
    var y = xy["y"]
    flat_torus_draw_line(ctx,prex,prey,x,y)
}

// loop
function loop_draw_line(ctx,prex,prey,x,y){
    draw_xy(ctx,prex,prey,x,y)
}
// mobius
function flat_mobius_draw_line(ctx,prex,prey,x,y){
    if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-HEIGHT+ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,HEIGHT-ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}


// cylinder
function flat_cylinder_draw_line(ctx,prex,prey,x,y){
    if(Math.abs(x-prex)>WIDTH/2){
        if(x < prex){
            xa = prex
            xb = x
            ya = prey
            yb = y
        } else {
            xa = x
            xb = prex
            ya = y
            yb = prey
        }
        ymid = xb*(yb-ya)/(xa-xb-WIDTH) + yb
        draw_xy(ctx,xa,ya,WIDTH,ymid)
        draw_xy(ctx,0,ymid,xb,yb)
    } else {
        draw_xy(ctx,prex,prey,x,y)
    }
}

// unbounded
function flat_unbounded_draw_line(ctx,prex,prey,x,y){
    draw_xy(ctx,prex,prey,x,y)
}

// hyperbolic surface
function hyper_compute_distance(px, py, qx, qy){
    var bk_angle = Math.atan2(py - qy, px - qx)
    var e = hyper_compute_endpoints(px, py, bk_angle)
    var x0 = e[0]
    var y0 = e[1]
    var x1 = e[2]
    var y1 = e[3]

    d0_to_point1 = Math.sqrt(Math.pow(x0-px, 2) + Math.pow(y0-py, 2))
    d0_to_point2 = Math.sqrt(Math.pow(x0-qx, 2) + Math.pow(y0-qy, 2))
    d1_to_point1 = Math.sqrt(Math.pow(x1-px, 2) + Math.pow(y1-py, 2))
    d1_to_point2 = Math.sqrt(Math.pow(x1-qx, 2) + Math.pow(y1-qy, 2))
    if (d1_to_point2 * d0_to_point1 < 0.00001){
        return 10000000000
    }

    return Math.abs(Math.log(d1_to_point1 * d0_to_point2 / d1_to_point2 / d0_to_point1) / 2)
}

function hyper_compute_angle_with_diameter(px, py, bk_angle){
    while(bk_angle < 0){bk_angle += 2*Math.PI}
    while(bk_angle >= 2*Math.PI){bk_angle -= 2*Math.PI}
    if(px==0 && py==0){
        return bk_angle
    }
    // y * px = x * py
    // y - py = tan(bk_angle) * (x - px)
    //
    // (py)x + (-px)y = 0
    // (tan(bk_angle))x + (-1)y = tan(bk_angle) * px - py
    //
    var cos = Math.abs((py*Math.sin(bk_angle)+px*Math.cos(bk_angle)) / (Math.sqrt((py*py+px*px)*(1-Math.pow(Math.sin(bk_angle)*px-Math.cos(bk_angle)*py, 2)))))
    if(cos > 1){cos = 1}
    var gamma = Math.acos(cos)
    var bk2 = bk_angle - Math.atan2(py, px)
    while(bk2>=Math.PI){bk2-=2*Math.PI}
    while(bk2<-Math.PI){bk2+=2*Math.PI}
    if(bk2 > Math.PI / 2){
        return Math.PI - gamma
    } else if(bk2 > 0){
        return gamma
    } else if(bk2 > -Math.PI/2){
        return -gamma
    } else {
        return gamma - Math.PI
    }
}

function hyper_compute_bk_angle(px, py, angle_with_d){
    if(angle_with_d >= Math.PI){angle_with_d -= 2*Math.PI}
    if(angle_with_d < -Math.PI){angle_with_d += 2*Math.PI}
    if(px==0 && py==0){
        return angle_with_d
    }
    var pang = Math.atan2(py, px)
    var e = [[0, 0], [0, 0]]
    if(angle_with_d > Math.PI/2){
        e = [[pang+Math.PI/2, Math.PI/2], [pang+Math.PI, Math.PI]]
    } else if(angle_with_d > 0){
        e = [[pang, 0], [pang+Math.PI/2, Math.PI/2]]
    } else if(angle_with_d > -Math.PI/2){
        e = [[pang-Math.PI/2, -Math.PI/2], [pang, 0]]
    } else {
        e = [[pang-Math.PI, -Math.PI], [pang-Math.PI/2, -Math.PI/2]]
    }

    for(var i=0;i<10;i++){
        var a = (e[0][0] + e[1][0]) / 2
        var a2 = hyper_compute_angle_with_diameter(px, py, a)
        if(a2 < angle_with_d) {
            e[0] = [a, a2]
        } else {
            e[1] = [a, a2]
        }
    }
    while(e[0][0] < 0){e[0][0] += 2*Math.PI}
    while(e[0][0] >= 2*Math.PI){e[0][0] -= 2*Math.PI}
    return e[0][0]
}

function hyper_compute_endpoints(px, py, bk_angle){
    k = (Math.sqrt(Math.pow(2 * px * Math.cos(bk_angle) + 2 * py * Math.sin(bk_angle), 2) - 4 * (px * px + py * py - 1))-(2 * px * Math.cos(bk_angle) + 2 * py * Math.sin(bk_angle))) / 2
    x1 = px + k * Math.cos(bk_angle)
    y1 = py + k * Math.sin(bk_angle)

    k = (-Math.sqrt(Math.pow(2 * px * Math.cos(bk_angle) + 2 * py * Math.sin(bk_angle), 2) - 4 * (px * px + py * py - 1))-(2 * px * Math.cos(bk_angle) + 2 * py * Math.sin(bk_angle))) / 2
    x0 = px + k * Math.cos(bk_angle)
    y0 = py + k * Math.sin(bk_angle)

    return [x0, y0, x1, y1]
}

function hyper_add(px, py, angle, length){
    var e = hyper_compute_endpoints(px, py, angle)
    var x0 = e[0]
    var y0 = e[1]
    var x1 = e[2]
    var y1 = e[3]

    d = [[[px, py], 0], [[x1, y1], 2*length]]
    for(var i = 0; i < 20; i++){
        var ptx = (d[0][0][0] + d[1][0][0]) / 2
        var pty = (d[0][0][1] + d[1][0][1]) / 2
        var try_l = hyper_compute_distance(px, py, ptx, pty)
        if(d[0][1] <= length && length < try_l){
            d = [d[0], [[ptx, pty], try_l]]
        } else {
            d = [[[ptx, pty], try_l], d[1]]
        }
    }
    return d[0][0]
}

function hyper_bk_draw_line(ctx,prex,prey,x,y){
    var scale = 0.45 * HEIGHT
    draw_xy(ctx,WIDTH/2 + scale * prex, HEIGHT/2 + scale * prey, WIDTH/2 + scale * x, HEIGHT/2 + scale * y)
}

function to_poincare(x, y){
    var ss = x*x + y*y
    var rt = Math.sqrt(1 - ss)
    return [x / (1 + rt), y / (1 + rt)]
}

function hyper_poincare_draw_line(ctx,prex,prey,x,y){
    var scale = 0.6 * HEIGHT
    if(options["surface"] == "hyperbolicunbounded") {
        scale = 0.48*HEIGHT
    }
    var pre = to_poincare(prex, prey)
    var pt = to_poincare(x, y)

    draw_xy(ctx,WIDTH/2 + scale * pre[0], HEIGHT/2 + scale * pre[1], WIDTH/2 + scale * pt[0], HEIGHT/2 + scale * pt[1])
}

function to_poincare_hp(x, y){
    var p = to_poincare(x, y)
    return [2*p[0] / (p[0]*p[0] + (1 + p[1])*(1 + p[1])),(p[0]*p[0] + p[1] * p[1] - 1) / (p[0]*p[0] + (1 + p[1])*(1 + p[1]))]
}

function to_poincare_hp_scaled(x, y){
    var scale = 0.12 * HEIGHT
    var p = to_poincare_hp(x, y)
    return [WIDTH / 2 + scale * p[0], 0.96*HEIGHT + scale * p[1]]
}

function hyper_poincare_hp_draw_line(ctx,prex,prey,x,y){
    var pre = to_poincare_hp_scaled(prex, prey)
    var pt = to_poincare_hp_scaled(x, y)

    draw_xy(ctx,pre[0], pre[1], pt[0], pt[1])
}

function to_hyperboloid(x, y){
    var d = Math.sqrt(1 - x*x - y*y)
    return [x / d, y/d, 1/d]
}

function hyper_hyperboloid_draw_line(ctx,prex,prey,x,y){
    var scale = 0.16 * HEIGHT
    var pre = to_hyperboloid(prex, prey)
    var pt = to_hyperboloid(x, y)
    var x0 = (pre[0]-pre[1]) * Math.sin(30)
    var y0 = pre[2] + (pre[0]+pre[1]) * Math.cos(30)
    var x1 = (pt[0]-pt[1]) * Math.sin(30)
    var y1 = pt[2] + (pt[0]+pt[1]) * Math.cos(30)

    draw_xy(ctx,WIDTH/2 - scale * x0, HEIGHT/8 + scale * y0,
                WIDTH/2 - scale * x1, HEIGHT/8 + scale * y1)
}

function hyper_gans_draw_line(ctx,prex,prey,x,y){
    var scale = 0.13 * HEIGHT
    var pre = to_hyperboloid(prex, prey)
    var pt = to_hyperboloid(x, y)

    draw_xy(ctx,WIDTH/2 + scale * pre[0], HEIGHT/2 + scale * pre[1],
                WIDTH/2 + scale * pt[0], HEIGHT/2 + scale * pt[1])
}

function to_hyperband(x, y){
    var p = to_poincare(x, y)
    var d = ((1-p[0])*(1-p[0])+p[1]*p[1])
    var real = ((1 + p[0])*(1 - p[0]) - p[1]*p[1]) / d
    var imag = 2*p[1] / d
    var r = Math.sqrt(real*real + imag*imag)
    var theta = Math.atan2(imag, real)
    return [Math.log(r), theta]
}

function hyper_band_draw_line(ctx,prex,prey,x,y){
    var scale = 0.36 * HEIGHT
    var pre = to_hyperband(prex, prey)
    var pt = to_hyperband(x, y)

    draw_xy(ctx,WIDTH/2 + scale * pre[0], HEIGHT/2 + scale * pre[1],
                WIDTH/2 + scale * pt[0], HEIGHT/2 + scale * pt[1])
}