Metaball Contour Lines

A small and very unoptimized utility turtle that can be used to calculate contour lines. The ContourLines function will return an array of unsorted line-segments.

#contourlines #utility

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// Metaball Contour Lines. Created by Reinder Nijhoff 2020 - @reindernijhoff
// The MIT License
//
// https://turtletoy.net/turtle/104c4775c5
//

const turtle = new Turtle();

const ball = () => [-75+Math.random()*150, -75+Math.random()*150, 50+100*Math.random()];
const metaballs = [ball(), ball(), ball(), ball(), ball(), ball()];
const zFunc = p => metaballs.reduce((a, c) => a+c[2]/(1+Math.sqrt((c[0]-p[0])**2+(c[1]-p[1])**2)), 0);

function walk(i) {
    const lines = ContourLines(i, 10/(1+i), zFunc);
    lines.forEach(line => {
        turtle.jump(line[0]);
        turtle.goto(line[1]);
    });
    return i < 25;
}

////////////////////////////////////////////////////////////////
// Contour Lines utility code. Created by Reinder Nijhoff 2020
// https://turtletoy.net/turtle/104c4775c5
////////////////////////////////////////////////////////////////
function ContourLines(z, step, zFunc) {
    const intersectSegmentZ = (z, v1, v2) => {
    	if (v1[2] == v2[2]) return false;
    	const t = (z - v1[2]) / (v2[2] - v1[2]);
    	if (t < 0 || t > 1) return false;
    	return [v1[0]+(v2[0]-v1[0])*t, v1[1]+(v2[1]-v1[1])*t];
    }
    const intersectTriangleZ = (z, p1, p2, p3) => {
    	const v1 = intersectSegmentZ(z, p1, p2);
    	const v2 = intersectSegmentZ(z, p2, p3);
    	if (v1 && v2) return [v1, v2];
    	const v3 = intersectSegmentZ(z, p3, p1);
        if (v1 && v3) return [v1, v3];
    	if (v2 && v3) return [v2, v3];
		return false;
    }
	const result = [];
	for (let x = -100; x <= 100; x += step) {
    	for (let y = -100; y <= 100; y += step) {
			const corners = [[x, y], [x+step, y], [x+step, y+step], [x, y+step]];
			corners.forEach( c => c[2] = zFunc(c) );
			const c3 = [x+step/2, y+step/2, zFunc([x+step/2, y+step/2])];
			corners.forEach( (c, i) => {
			    const pair = intersectTriangleZ(z, c, corners[(i+1) & 3], c3);
			    if (pair) {
			        result.push(pair);
			    }
			});
		}
	}
	return result;
}