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提交 5eaf6ae3 编写于 作者: Z zz85
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Refactoring curve and knot formulas to CurveExtras.js

上级 bbfb8044
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Showing with 320 addition and 326 deletion
examples/js/CurveExtras.js 0 → 100644
浏览文件 @ 5eaf6ae3
/*
* 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);
}
);
\ No newline at end of file
examples/webgl_geometry_extrude_splines.html
浏览文件 @ 5eaf6ae3
......@@ -20,333 +20,14 @@
<script src="../src/extras/core/Curve.js"></script>
<script src="../src/extras/geometries/TubeGeometry.js"></script>
<script src="../src/extras/helpers/CameraHelper.js"></script>
<!-- where curves formulas are defined -->
<script src="js/CurveExtras.js"></script>
<script src="js/Stats.js"></script>
<script>
// 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);
}
);
var container, stats;
var camera, scene, renderer, splineCamera, cameraHelper, cameraPos;
......@@ -405,9 +86,6 @@
var s;
for ( s in splines ) {
dropdown += '<option value="' + s + '"';
// dropdown += (geometryIndex == i) ? ' selected' : '';
dropdown += '>' + s + '</option>';
}
......
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