Doodle3D-Slicer/three.js-master/examples/js/CurveExtras.js
2015-06-12 15:58:26 +02:00

327 lines
5.9 KiB
JavaScript
Executable File

/*
* A bunch of parametric curves
* @author zz85
*
* Formulas collected from various sources
* http://mathworld.wolfram.com/HeartCurve.html
* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page6.html
* http://en.wikipedia.org/wiki/Viviani%27s_curve
* http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page4.html
* http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
* http://prideout.net/blog/?p=44
*/
// Lets define some curves
THREE.Curves = {};
THREE.Curves.GrannyKnot = THREE.Curve.create( function() {},
function(t) {
t = 2 * Math.PI * t;
var x = -0.22 * Math.cos(t) - 1.28 * Math.sin(t) - 0.44 * Math.cos(3 * t) - 0.78 * Math.sin(3 * t);
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);
var z = 0.7 * Math.cos(3 * t) - 0.4 * Math.sin(3 * t);
return new THREE.Vector3(x, y, z).multiplyScalar(20);
}
);
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);
var 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
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);
}
);
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);
}
);
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 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 = Math.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);
}
);
THREE.Curves.DecoratedTorusKnot4a = THREE.Curve.create(
function(s) {
this.scale = (s === undefined) ? 40 : s;
},
function(t) {
t *= Math.PI * 2;
var
x = Math.cos(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t))),
y = Math.sin(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t))),
z = 0.35 * Math.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 = Math.cos(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi)),
y = Math.sin(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi)),
z = 0.2 * Math.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 = Math.cos(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi)),
y = Math.sin(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi)),
z = 0.2 * Math.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 = Math.cos(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi))),
y = Math.sin(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi))),
z = 0.35 * Math.sin(15 * fi);
return new THREE.Vector3(x, y, z).multiplyScalar(this.scale);
}
);