aperiodic-monotile-reference/script.js

// derived from https://cs.uwaterloo.ca/~csk/spectre/spectre.js


const {PI, cos, sin} = Math;

function radians(degrees) {
    return degrees * PI / 180;
}

let num_pieces = 0;

class Point {
    constructor(x,y) {
        this.x = x;
        this.y = y;
    }

    add( q ) {
        return { x : this.x + q.x, y : this.y + q.y };
    }

    sub( q ) {
        return { x : this.x - q.x, y : this.y - q.y };
    }

    frame( p, q, a, b ) {
        return{ x : this.x + a*p.x + b*q.x, y : this.y + a*p.y + b*q.y };
    }

}

class Matrix {
    constructor(mat) {
        this.mat = mat;
    }

    determinant() {
        const T = this.mat;
        const det = T[0]*T[4] - T[1]*T[3];
    }

    inverse() {
        const T = this.mat;
        const det = this.determinant();
        return new Matrix([
            T[4]/det,
            -T[1]/det,
            (T[1]*T[5]-T[2]*T[4])/det,
            -T[3]/det,
            T[0]/det,
            (T[2]*T[3]-T[0]*T[5])/det
        ]);
    }

    mul( other ) {
        const A = this.mat;
        const B = other.mat;
        return new Matrix([
            A[0]*B[0] + A[1]*B[3], 
            A[0]*B[1] + A[1]*B[4],
            A[0]*B[2] + A[1]*B[5] + A[2],

            A[3]*B[0] + A[4]*B[3], 
            A[3]*B[1] + A[4]*B[4],
            A[3]*B[2] + A[4]*B[5] + A[5]
        ]);
    }

    // Rotation matrix
    static rotation( ang ) {
        const c = cos( ang );
        const s = sin( ang );
        return new Matrix([c, -s, 0, s, c, 0]);
    }

    static scale(x,y) {
        return new Matrix([x,0,0,0,y,0]);
    }

    static translate( tx, ty ) {
        return new Matrix([1, 0, tx, 0, 1, ty]);
    }

    // Translation matrix moving p to q
    static translateTo( p, q ) {
        return Matrix.translate( q.x - p.x, q.y - p.y );
    }

    transform( P ) {
        const M = this.mat;
        return new Point(M[0]*P.x + M[1]*P.y + M[2], M[3]*P.x + M[4]*P.y + M[5]);
    }

}

const ident = new Matrix([1,0,0,0,1,0]);

const spectre = [
    new Point(0, 0),
    new Point(1.0, 0.0),
    new Point(1.5, -0.8660254037844386),
    new Point(2.366025403784439, -0.36602540378443865),
    new Point(2.366025403784439, 0.6339745962155614),
    new Point(3.366025403784439, 0.6339745962155614),
    new Point(3.866025403784439, 1.5),
    new Point(3.0, 2.0),
    new Point(2.133974596215561, 1.5),
    new Point(1.6339745962155614, 2.3660254037844393),
    new Point(0.6339745962155614, 2.3660254037844393),
    new Point(-0.3660254037844386, 2.3660254037844393),
    new Point(-0.866025403784439, 1.5),
    new Point(0.0, 1.0) 
];

const base_quad = [spectre[3], spectre[5], spectre[7], spectre[11]];

function getsvg(event) {
    let t = event.target;
    while(t && t.tagName.toLowerCase()!='svg') {
      t = t.parentElement;
    }
    return t;
}

function getcoords(event) {
    const t = getsvg(event);
    if(!t) {
        return;
    }
    const point = t.createSVGPoint()
    point.x = event.clientX
    point.y = event.clientY
    const position = point.matrixTransform(t.getScreenCTM().inverse())                
    return position;
}

// Match unit interval to line segment p->q
function matchSeg( p, q )
{
	return [q.x-p.x, p.y-q.y, p.x,  q.y-p.y, q.x-p.x, p.y];
};

// Match line segment p1->q1 to line segment p2->q2
function matchTwo( p1, q1, p2, q2 )
{
	return matchSeg( p2, q2 ).mul(matchSeg( p1, q1 ).inverse());
};

function drawPolygon( shape, T, f, s, w )
{
	beginShape();
	for( let p of shape ) {
		const tp = T.transform( p );
		vertex( tp.x, tp.y );
	}
	endShape( CLOSE );
}

class Shape
{
	constructor( pts, quad) {
		this.pts = pts;
		this.quad = quad;

		this.pts = [pts[pts.length-1]];
		for( const p of pts ) {
			const prev = this.pts[this.pts.length-1];
			const v = p.sub(prev);
			const w = new Point( -v.y, v.x );
            this.pts.push( prev.frame(v, w, 0.5, -0.3 ) );
            this.pts.push( prev.frame(v, w, 0.5, 0.3 ) );
			this.pts.push( p );
		}
	}

	streamSVG( S, stream ) {
        const tpts = this.pts.map(p => S.transform( p ));

        const [a,c,e,b,d,f] = S.mat;
        const matS = [a,b,c,d,e,f].map(p=>p.toFixed(3));
        num_pieces += 1;
		stream.push(`<g class="tile">
<use href="#spectre" transform="matrix(${matS.join(',')}) "/>
<text font-size="0.5" dominant-baseline="middle" text-anchor="middle" transform="matrix(${matS.join(',')}) translate(1 1.6)">${num_pieces}</text>
<text font-size="1" dominant-baseline="middle" text-anchor="middle" transform="matrix(${matS.join(',')}) translate(1 1)">↑</text>
</g>`);
	}

    bounds(S) {
        const points = this.pts.map(p => S.transform(p));
        return {
            minx: Math.min(...points.map(p => p.x)),
            miny: Math.min(...points.map(p => p.y)),
            maxx: Math.max(...points.map(p => p.x)),
            maxy: Math.max(...points.map(p => p.y)),
        };
    }

    * flatten(S) {
        const points = this.pts.map(p => S.transform(p));
        const ymax = Math.max(...points.map(p => p.y));
        yield {points, ymax, shape: this};
    }
}

class Meta {
	constructor() {
		this.geoms = [];
		this.quad = [];
	}

	addChild( g, T ) {
		this.geoms.push( { geom : g, xform: T } );
	}

	draw( S )  {
		for( let g of this.geoms ) {
			g.geom.draw( S.mul( g.xform ) );
		}
	}

	streamSVG( S, stream ) {
        const {minx,miny,maxx,maxy} = this.bounds(S);

		for( let g of this.geoms ) {
			g.geom.streamSVG( S.mul(g.xform), stream );
		}

	}

    bounds(S) {
        const sub_bounds = this.geoms.map(g => g.geom.bounds(S.mul(g.xform)));
        return {
            minx: Math.min(...sub_bounds.map(b=>b.minx)),
            miny: Math.min(...sub_bounds.map(b=>b.miny)),
            maxx: Math.max(...sub_bounds.map(b=>b.maxx)),
            maxy: Math.max(...sub_bounds.map(b=>b.maxy)),
        };
    }

    * flatten(S) {
        for(let g of this.geoms) {
            yield* g.geom.flatten(S.mul(g.xform));
        }
    }
}

function tiles(level, label) {
    let quad;
    let out = [];
    let transform;
    if(level == 0) {
        transform = ident;
        quad = base_quad;
        switch(label) {
            case 'Delta':
            case 'Theta':
            case 'Lambda':
            case 'Xi':
            case 'Pi':
            case 'Sigma':
            case 'Phi':
            case 'Psi':
                out.push(ident);
            case 'Gamma':
                const mystic = new Meta();
                out.push(ident);
                out.push(Matrix.translate( spectre[8].x, spectre[8].y ).mul( Matrix.rotation( PI / 6 ) ));
        }
    } else {
        /*
         * Each of the subtiles is identical, but rotated and translated.
         *
         * Produce transformation matrices Ts for each of the subtiles: they're formed by rotating the quad and then matching up a pair of points.
         *
         * The whole thing is then reflected.
         *
         * The layout of subtiles depends on the larger tile.
         *
         */
        const labels = [
            'Delta',
            'Theta',
            'Lambda',
            'Xi', 
		    'Pi',
            'Sigma',
            'Phi',
            'Psi'
        ];

        const sublevels = Object.fromEntries(labels.map(label => tiles(level-1, label)));
        const subquad = sublevels['Delta'].quad;

        const reflection = Matrix.scale(-1,1);


        // How to get from each subtile to the next.
        const t_rules = [
            [60, 3, 1],
            [0, 2, 0],
            [60, 3, 1],
            [60, 3, 1],
            [0, 2, 0],
            [60, 3, 1],
            [-120, 3, 3]
        ];

        
        let Ts = [ident];
        let total_ang = 0;
        let rot = ident;
        let tquad = [...subquad];
        for( const [ang,from,to] of t_rules ) {
            total_ang += ang;
            if( ang != 0 ) {
                rot = Matrix.rotation( radians( total_ang ) );
                tquad = subquad.map(q => rot.transform(q));
            }

            const ttt = Matrix.translateTo( tquad[to], Ts[Ts.length-1].transform( subquad[from] ) );
            Ts.push( ttt.mul( rot ) );
        }

        Ts = Ts.map(t => mul(reflection, t));

        
        // Now build the actual supertiles, labelling appropriately.
        const super_rules = {
            'Gamma' :  ['Pi','Delta','null','Theta','Sigma','Xi','Phi','Gamma'],
            'Delta' :  ['Xi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
            'Theta' :  ['Psi','Delta','Pi','Phi','Sigma','Pi','Phi','Gamma'],
            'Lambda' : ['Psi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
            'Xi' :     ['Psi','Delta','Pi','Phi','Sigma','Psi','Phi','Gamma'],
            'Pi' :     ['Psi','Delta','Xi','Phi','Sigma','Psi','Phi','Gamma'],
            'Sigma' :  ['Xi','Delta','Xi','Phi','Sigma','Pi','Lambda','Gamma'],
            'Phi' :    ['Psi','Delta','Psi','Phi','Sigma','Pi','Phi','Gamma'],
            'Psi' :    ['Psi','Delta','Psi','Phi','Sigma','Psi','Phi','Gamma']
        };
        const super_quad = [
            Ts[6].transform(subquad[2] ),
            Ts[5].transform(subquad[1] ),
            Ts[3].transform(subquad[2] ),
            Ts[0].transform(subquad[1] ) ]; 
    }
    return {quad, tiles: out};
}


function buildSpectreBase()
{
	const ret = {};

	for( lab of ['Delta', 'Theta', 'Lambda', 'Xi', 
				 'Pi', 'Sigma', 'Phi', 'Psi'] ) {
        ret[lab] = new Shape( spectre, base_quad, lab );
	}

	const mystic = new Meta();
    mystic.addChild( new Shape( spectre, base_quad, 'Gamma1' ), ident );
    mystic.addChild( new Shape( spectre, base_quad, 'Gamma2' ),
        Matrix.translate( spectre[8].x, spectre[8].y ).mul( Matrix.rotation( PI / 6 ) ) );
	mystic.quad = base_quad;
	ret['Gamma'] = mystic;

	return ret;
}

function buildHatTurtleBase( hat_dominant )
{
	const r3 = 1.7320508075688772;
	const hr3 = 0.8660254037844386;

	function hexPt( x, y ) {
		return new Point( x + 0.5*y, -hr3*y );
	}

	function hexPt2( x, y ) {
		return new Point( x + hr3*y, -0.5*y );
	}

	const hat = [
		hexPt(-1, 2), hexPt(0, 2), hexPt(0, 3), hexPt(2, 2), hexPt(3, 0),
		hexPt(4, 0), hexPt(5,-1), hexPt(4,-2), hexPt(2,-1), hexPt(2,-2),
		hexPt( 1, -2), hexPt(0,-2), hexPt(-1,-1), hexPt(0, 0) ];

	const turtle = [
		hexPt(0,0), hexPt(2,-1), hexPt(3,0), hexPt(4,-1), hexPt(4,-2),
		hexPt(6,-3), hexPt(7,-5), hexPt(6,-5), hexPt(5,-4), hexPt(4,-5),
		hexPt(2,-4), hexPt(0,-3), hexPt(-1,-1), hexPt(0,-1)
		];

	const hat_keys = [
		hat[3], hat[5], hat[7], hat[11]
	];
	const turtle_keys = [
		turtle[3], turtle[5], turtle[7], turtle[11]
	];

	const ret = {};

	if( hat_dominant ) {
		for( lab of ['Delta', 'Theta', 'Lambda', 'Xi', 
					 'Pi', 'Sigma', 'Phi', 'Psi'] ) {
			ret[lab] = new Shape( hat, hat_keys, lab );
		}

		const mystic = new Meta();
		mystic.addChild( new Shape( hat, hat_keys, 'Gamma1' ), ident );
		mystic.addChild( new Shape( turtle, turtle_keys, 'Gamma2' ),
			Matrix.translate( hat[8].x, hat[8].y ) );
		mystic.quad = hat_keys;
		ret['Gamma'] = mystic;
	} else {
		for( lab of ['Delta', 'Theta', 'Lambda', 'Xi', 
					 'Pi', 'Sigma', 'Phi', 'Psi'] ) {
			ret[lab] = new Shape( turtle, turtle_keys, lab );
		}

		const mystic = new Meta();
		mystic.addChild( new Shape( turtle, turtle_keys, 'Gamma1' ), ident );
		mystic.addChild( new Shape( hat, hat_keys, 'Gamma2' ),
			Matrix.translate( turtle[9].x, turtle[9].y ).mul( Matrix.rotation( PI/3 ) ) );
		mystic.quad = turtle_keys;
		ret['Gamma'] = mystic;
	}

	return ret;
}

function buildHexBase()
{
	const hr3 = 0.8660254037844386;

	const hex = [
		new Point(0, 0),
		new Point(1.0, 0.0),
		new Point(1.5, hr3),
		new Point(1, 2*hr3),
		new Point(0, 2*hr3),
		new Point(-0.5, hr3) 
	];

	const hex_keys = [ hex[1], hex[2], hex[3], hex[5] ];

	const ret = {};

	for( lab of ['Gamma', 'Delta', 'Theta', 'Lambda', 'Xi', 
				 'Pi', 'Sigma', 'Phi', 'Psi'] ) {
		ret[lab] = new Shape( hex, hex_keys, lab );
	}

	return ret;
}

function buildSupertiles( sys )
{
	// First, use any of the nine-unit tiles in sys to obtain
	// a list of transformation matrices for placing tiles within
	// supertiles.

	const quad = sys['Delta'].quad;
	const R = new Matrix([-1,0,0,0,1,0]);
	
	const t_rules = [
		[60, 3, 1], [0, 2, 0], [60, 3, 1], [60, 3, 1],
		[0, 2, 0], [60, 3, 1], [-120, 3, 3] ];  

	const Ts = [ident];
	let total_ang = 0;
	let rot = ident;
	const tquad = [...quad];
	for( const [ang,from,to] of t_rules ) {
		total_ang += ang;
		if( ang != 0 ) {
			rot = Matrix.rotation( radians( total_ang ) );
			for( i = 0; i < 4; ++i ) {
				tquad[i] = rot.transform(quad[i] );
			}
		}

		const ttt = Matrix.translateTo( tquad[to], 
			Ts[Ts.length-1].transform(quad[from] ) );
		Ts.push( ttt.mul( rot ) );
	}

	for( let idx = 0; idx < Ts.length; ++idx ) {
		Ts[idx] = R.mul( Ts[idx] );
	}

	// Now build the actual supertiles, labelling appropriately.
	const super_rules = {
		'Gamma' :  ['Pi','Delta','null','Theta','Sigma','Xi','Phi','Gamma'],
		'Delta' :  ['Xi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
		'Theta' :  ['Psi','Delta','Pi','Phi','Sigma','Pi','Phi','Gamma'],
		'Lambda' : ['Psi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
		'Xi' :     ['Psi','Delta','Pi','Phi','Sigma','Psi','Phi','Gamma'],
		'Pi' :     ['Psi','Delta','Xi','Phi','Sigma','Psi','Phi','Gamma'],
		'Sigma' :  ['Xi','Delta','Xi','Phi','Sigma','Pi','Lambda','Gamma'],
		'Phi' :    ['Psi','Delta','Psi','Phi','Sigma','Pi','Phi','Gamma'],
		'Psi' :    ['Psi','Delta','Psi','Phi','Sigma','Psi','Phi','Gamma'] };
	const super_quad = [
		Ts[6].transform(quad[2] ),
		Ts[5].transform(quad[1] ),
		Ts[3].transform(quad[2] ),
		Ts[0].transform(quad[1] ) ]; 

	const ret = {};

	for( const [lab, subs] of Object.entries( super_rules ) ) {
		const sup = new Meta();
		for( let idx = 0; idx < 8; ++idx ) {
			if( subs[idx] == 'null' ) {
				continue;
			}
            sup.addChild( sys[subs[idx]], Ts[idx] );
		}
		sup.quad = super_quad;

		ret[lab] = sup;
	}

	return ret;
}

/* modified from https://css-tricks.com/converting-color-spaces-in-javascript/
 */
function hexToHSL(H) {
    const [r,g,b] = [0,1,2].map(i=>H.slice(2*i+1,2*i+3)).map(n=>parseInt(n,16)/255);
    let cmin = Math.min(r,g,b),
        cmax = Math.max(r,g,b),
        delta = cmax - cmin,
        h = 0,
        s = 0,
        l = 0;

    if (delta == 0)
        h = 0;
    else if (cmax == r)
        h = ((g - b) / delta) % 6;
    else if (cmax == g)
        h = (b - r) / delta + 2;
    else
        h = (r - g) / delta + 4;

    h = Math.round(h * 60);

    if (h < 0)
        h += 360;

    l = (cmax + cmin) / 2;
    s = delta == 0 ? 0 : delta / (1 - Math.abs(2 * l - 1));
    s = +(s * 100).toFixed(1);
    l = +(l * 100).toFixed(1);

    return {h,s,l};
}

let last_num_iterations;

function get_settings() {
    return Object.fromEntries(
        Array.from(document.querySelectorAll('input,textarea')).map(i => [i.id, i.type=='number' ? i.valueAsNumber : i.value])
    );
}

function rebuild() {
    num_pieces = 0;
    const svg = document.querySelector('svg');
    const settings = get_settings();
    let sys = buildSpectreBase(false);
    
    for(let i=0;i<settings.num_iterations;i++) {
        sys = buildSupertiles( sys );	
    }

    sys = sys['Delta'];
    window.sys = sys;

    const drawing = [];
    const board = svg.querySelector('#board');
    board.innerHTML = '';
    sys.streamSVG(ident, drawing);
    board.innerHTML = drawing.join(' ');

    const viewbox = svg.getBoundingClientRect();
    function visit(g, t) {
        for(let c of g.children) {
            visit(c, t+Math.random()*10-5);
        }
        if(g.tagName=='path') {
            const b = g.getBoundingClientRect();
            const x = (b.x - viewbox.x) / viewbox.width;
            const y = (b.y - viewbox.y) / viewbox.height;
            g.style.color = '#ccc';
        }
    }
    visit(board,50);

    svg.addEventListener('click', e => {
        console.log('click');
        if(!last_click) {
            return;
        }
        let tile = e.target;
        while(tile && !tile.classList.contains('tile')) {
            tile = tile.parentElement;
        }
        if(!tile) {
            return;
        }

        for(let el of svg.querySelectorAll('.highlight')) {
            el.classList.remove('highlight');
        }
        tile.classList.add('highlight');
    });
}

function update_display() {
    const settings = get_settings();
    const svg = document.querySelector('svg');
    //const bounds = sys.bounds(ident);
    svg.setAttribute('viewBox',`${settings.ox - settings.scale/2} ${settings.oy - settings.scale/2} ${settings.scale} ${settings.scale}`);
    const mx = spectre.map(p=>p.x).reduce((a,b)=>a+b)/spectre.length;
    const my = spectre.map(p=>p.y).reduce((a,b)=>a+b)/spectre.length;
    document.getElementById('spectre').setAttribute('transform',`translate(${mx},${my}) translate(${-mx},${-my})`);
    
    if(settings.num_iterations != last_num_iterations) {
        rebuild();
        last_num_iterations = settings.num_iterations;
    }
}

for(let i of document.querySelectorAll('input')) {
    i.addEventListener('input', update_display);
    i.addEventListener('change', update_display)
}

update_display();

let opos;
let dragging;
let pan = {x:0, y:0};
let npan = pan;
let last_click = false;

const svg = document.querySelector('svg');
svg.addEventListener('pointerdown', e => {
    opos = getcoords(e);
    dragging = true;
    console.log('dragstart');
});

svg.addEventListener('pointermove', e => {
    if(!dragging) {
        return;
    }
    const pos = getcoords(e);
    npan = {x: pan.x + pos.x - opos.x, y: pan.y + pos.y - opos.y};
    document.getElementById('board').setAttribute('transform', `translate(${npan.x} ${npan.y})`);
});

svg.addEventListener('pointerup', e => {
    dragging = false;
    const [dx,dy] = [npan.x - pan.x, npan.y - pan.y];
    const d = Math.sqrt(dx*dx + dy*dy);
    console.log(d);
    last_click = d < 0.5;
    pan = npan;
    console.log('dragend');
});