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https://github.com/Doodle3D/Doodle3D-Slicer.git
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327 lines
5.9 KiB
JavaScript
Executable File
327 lines
5.9 KiB
JavaScript
Executable File
/*
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* A bunch of parametric curves
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* @author zz85
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*
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* Formulas collected from various sources
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* http://mathworld.wolfram.com/HeartCurve.html
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* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page6.html
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* http://en.wikipedia.org/wiki/Viviani%27s_curve
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* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page4.html
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* http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
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* http://prideout.net/blog/?p=44
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*/
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// Lets define some curves
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THREE.Curves = {};
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THREE.Curves.GrannyKnot = THREE.Curve.create( function() {},
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function(t) {
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t = 2 * Math.PI * t;
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var x = -0.22 * Math.cos(t) - 1.28 * Math.sin(t) - 0.44 * Math.cos(3 * t) - 0.78 * Math.sin(3 * t);
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var y = -0.1 * Math.cos(2 * t) - 0.27 * Math.sin(2 * t) + 0.38 * Math.cos(4 * t) + 0.46 * Math.sin(4 * t);
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var z = 0.7 * Math.cos(3 * t) - 0.4 * Math.sin(3 * t);
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return new THREE.Vector3(x, y, z).multiplyScalar(20);
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}
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);
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THREE.Curves.HeartCurve = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 5 : s;
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},
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function(t) {
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t *= 2 * Math.PI;
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var tx = 16 * Math.pow(Math.sin(t), 3);
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var ty = 13 * Math.cos(t) - 5 * Math.cos(2 * t) - 2 * Math.cos(3 * t) - Math.cos(4 * t), tz = 0;
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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// Viviani's Curve
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THREE.Curves.VivianiCurve = THREE.Curve.create(
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function(radius) {
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this.radius = radius;
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},
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function(t) {
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t = t * 4 * Math.PI; // Normalized to 0..1
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var a = this.radius / 2;
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var tx = a * (1 + Math.cos(t)),
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ty = a * Math.sin(t),
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tz = 2 * a * Math.sin(t / 2);
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return new THREE.Vector3(tx, ty, tz);
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}
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);
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THREE.Curves.KnotCurve = THREE.Curve.create(
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function() {
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},
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function(t) {
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t *= 2 * Math.PI;
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var R = 10;
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var s = 50;
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var tx = s * Math.sin(t),
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ty = Math.cos(t) * (R + s * Math.cos(t)),
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tz = Math.sin(t) * (R + s * Math.cos(t));
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return new THREE.Vector3(tx, ty, tz);
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}
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);
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THREE.Curves.HelixCurve = THREE.Curve.create(
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function() {
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},
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function(t) {
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var a = 30; // radius
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var b = 150; //height
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var t2 = 2 * Math.PI * t * b / 30;
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var tx = Math.cos(t2) * a,
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ty = Math.sin(t2) * a,
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tz = b * t;
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return new THREE.Vector3(tx, ty, tz);
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}
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);
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THREE.Curves.TrefoilKnot = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 10 : s;
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},
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function(t) {
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t *= Math.PI * 2;
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var tx = (2 + Math.cos(3 * t)) * Math.cos(2 * t),
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ty = (2 + Math.cos(3 * t)) * Math.sin(2 * t),
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tz = Math.sin(3 * t);
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.TorusKnot = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 10 : s;
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},
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function(t) {
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var p = 3,
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q = 4;
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t *= Math.PI * 2;
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var tx = (2 + Math.cos(q * t)) * Math.cos(p * t),
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ty = (2 + Math.cos(q * t)) * Math.sin(p * t),
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tz = Math.sin(q * t);
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.CinquefoilKnot = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 10 : s;
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},
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function(t) {
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var p = 2,
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q = 5;
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t *= Math.PI * 2;
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var tx = (2 + Math.cos(q * t)) * Math.cos(p * t),
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ty = (2 + Math.cos(q * t)) * Math.sin(p * t),
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tz = Math.sin(q * t);
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.TrefoilPolynomialKnot = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 10 : s;
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},
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function(t) {
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t = t * 4 - 2;
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var tx = Math.pow(t, 3) - 3 * t,
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ty = Math.pow(t, 4) - 4 * t * t,
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tz = 1 / 5 * Math.pow(t, 5) - 2 * t;
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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// var scaleTo = function(x, y) {
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// var r = y - x;
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// return function(t) {
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// t * r + x;
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// };
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// }
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var scaleTo = function(x, y, t) {
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var r = y - x;
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return t * r + x;
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}
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THREE.Curves.FigureEightPolynomialKnot = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 1 : s;
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},
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function(t) {
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t = scaleTo(-4, 4, t);
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var tx = 2 / 5 * t * (t * t - 7) * (t * t - 10),
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ty = Math.pow(t, 4) - 13 * t * t,
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tz = 1 / 10 * t * (t * t - 4) * (t * t - 9) * (t * t - 12);
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return new THREE.Vector3(tx, ty, tz).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.DecoratedTorusKnot4a = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 40 : s;
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},
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function(t) {
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t *= Math.PI * 2;
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var
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x = Math.cos(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t))),
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y = Math.sin(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t))),
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z = 0.35 * Math.sin(5 * t);
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return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.DecoratedTorusKnot4b = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 40 : s;
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},
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function(t) {
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var fi = t * Math.PI * 2;
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var x = Math.cos(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi)),
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y = Math.sin(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi)),
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z = 0.2 * Math.sin(9 * fi);
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return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.DecoratedTorusKnot5a = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 40 : s;
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},
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function(t) {
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var fi = t * Math.PI * 2;
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var x = Math.cos(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi)),
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y = Math.sin(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi)),
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z = 0.2 * Math.sin(20 * fi);
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return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);
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}
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);
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THREE.Curves.DecoratedTorusKnot5c = THREE.Curve.create(
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function(s) {
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this.scale = (s === undefined) ? 40 : s;
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},
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function(t) {
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var fi = t * Math.PI * 2;
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var x = Math.cos(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi))),
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y = Math.sin(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi))),
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z = 0.35 * Math.sin(15 * fi);
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return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);
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}
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); |