three.js/examples/js/CurveExtras.js

/*
 * A bunch of curves
 * @author zz85
 */

// Lets define some curves
THREE.Curves = {};

// Formula from http://mathworld.wolfram.com/HeartCurve.html
THREE.Curves.HeartCurve = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 5 : s;

},

function(t) {

	t *= 2 * Math.PI;

	var tx = 16 * Math.pow(Math.sin(t), 3);
	ty = 13 * Math.cos(t) - 5 * Math.cos(2 * t) - 2 * Math.cos(3 * t) - Math.cos(4 * t), tz = 0;

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);



// Viviani's Curve
// http://en.wikipedia.org/wiki/Viviani%27s_curve
THREE.Curves.VivianiCurve = THREE.Curve.create(

function(radius) {

	this.radius = radius;
},

function(t) {

	t = t * 4 * Math.PI; // Normalized to 0..1
	var a = this.radius / 2;
	var tx = a * (1 + Math.cos(t)),
		ty = a * Math.sin(t),
		tz = 2 * a * Math.sin(t / 2);

	return new THREE.Vector3(tx, ty, tz);

}

);


THREE.Curves.KnotCurve = THREE.Curve.create(

function() {

},

function(t) {

	t *= 2 * Math.PI;

	var R = 10;
	var s = 50;
	var tx = s * Math.sin(t),
		ty = Math.cos(t) * (R + s * Math.cos(t)),
		tz = Math.sin(t) * (R + s * Math.cos(t));

	return new THREE.Vector3(tx, ty, tz);

}

);

THREE.Curves.HelixCurve = THREE.Curve.create(

function() {

},

function(t) {

	var a = 30; // radius
	var b = 150; //height
	var t2 = 2 * Math.PI * t * b / 30;
	var tx = Math.cos(t2) * a,
		ty = Math.sin(t2) * a,
		tz = b * t;

	return new THREE.Vector3(tx, ty, tz);

}

);

// Replacement for TorusKnotGeometry?
THREE.Curves.TrefoilKnot = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 10 : s;

},

function(t) {

	t *= Math.PI * 2;
	var tx = (2 + Math.cos(3 * t)) * Math.cos(2 * t),
		ty = (2 + Math.cos(3 * t)) * Math.sin(2 * t),
		tz = Math.sin(3 * t);

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);

// Formulas from http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page6.html
THREE.Curves.TorusKnot = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 10 : s;

},

function(t) {

	var p = 3,
		q = 4;
	t *= Math.PI * 2;
	var tx = (2 + Math.cos(q * t)) * Math.cos(p * t),
		ty = (2 + Math.cos(q * t)) * Math.sin(p * t),
		tz = Math.sin(q * t);

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);


THREE.Curves.CinquefoilKnot = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 10 : s;

},

function(t) {

	var p = 2,
		q = 5;
	t *= Math.PI * 2;
	var tx = (2 + Math.cos(q * t)) * Math.cos(p * t),
		ty = (2 + Math.cos(q * t)) * Math.sin(p * t),
		tz = Math.sin(q * t);

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);


THREE.Curves.TrefoilPolynomialKnot = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 10 : s;

},

function(t) {

	t = t * 4 - 2;
	var tx = Math.pow(t, 3) - 3 * t,
		ty = Math.pow(t, 4) - 4 * t * t,
		tz = 1 / 5 * Math.pow(t, 5) - 2 * t;

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);

var sin = Math.sin,
	pow = Math.pow,
	cos = Math.cos;
// var scaleTo = function(x, y) {
//   var r = y - x;
//   return function(t) {
//     t * r + x;
//   };
// }
var scaleTo = function(x, y, t) {

		var r = y - x;
		return t * r + x;

	}

THREE.Curves.FigureEightPolynomialKnot = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 1 : s;

},

function(t) {

	t = scaleTo(-4, 4, t);
	var tx = 2 / 5 * t * (t * t - 7) * (t * t - 10),
		ty = pow(t, 4) - 13 * t * t,
		tz = 1 / 10 * t * (t * t - 4) * (t * t - 9) * (t * t - 12);

	return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);

}

);

// When there's time, try more formulas at http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page4.html

//http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
THREE.Curves.DecoratedTorusKnot4a = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 40 : s;

},

function(t) {

	t *= Math.PI * 2;
	var
	x = cos(2 * t) * (1 + 0.6 * (cos(5 * t) + 0.75 * cos(10 * t))),
		y = sin(2 * t) * (1 + 0.6 * (cos(5 * t) + 0.75 * cos(10 * t))),
		z = 0.35 * sin(5 * t);

	return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);

}

);


THREE.Curves.DecoratedTorusKnot4b = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 40 : s;

},

function(t) {
	var fi = t * Math.PI * 2;
	var x = cos(2 * fi) * (1 + 0.45 * cos(3 * fi) + 0.4 * cos(9 * fi)),
		y = sin(2 * fi) * (1 + 0.45 * cos(3 * fi) + 0.4 * cos(9 * fi)),
		z = 0.2 * sin(9 * fi);

	return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);

}

);


THREE.Curves.DecoratedTorusKnot5a = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 40 : s;

},

function(t) {

	var fi = t * Math.PI * 2;
	var x = cos(3 * fi) * (1 + 0.3 * cos(5 * fi) + 0.5 * cos(10 * fi)),
		y = sin(3 * fi) * (1 + 0.3 * cos(5 * fi) + 0.5 * cos(10 * fi)),
		z = 0.2 * sin(20 * fi);

	return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);

}

);

THREE.Curves.DecoratedTorusKnot5c = THREE.Curve.create(

function(s) {

	this.scale = (s === undefined) ? 40 : s;

},

function(t) {

	var fi = t * Math.PI * 2;
	var x = cos(4 * fi) * (1 + 0.5 * (cos(5 * fi) + 0.4 * cos(20 * fi))),
		y = sin(4 * fi) * (1 + 0.5 * (cos(5 * fi) + 0.4 * cos(20 * fi))),
		z = 0.35 * sin(15 * fi);

	return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);

}

);