Skip to content

T
three.js

Ablesons / three.js
与 Fork 源项目一致

从无法访问的项目Fork

通知 2
Star 0
Fork 0
T
three.js

体验新版 GitCode，发现更多精彩内容 >>

提交 ca803d97 编写于 作者: R renej-github 提交者： Mr.doob
浏览文件
操作

moved NURBS utility function to NURBSUtils and code clean-up

上级 e154333d
隐藏空白更改
内联 并排
Showing with 405 addition and 410 deletion
examples/canvas_geometry_nurbs.html
浏览文件 @ ca803d97
......@@ -28,6 +28,7 @@
<script src="../build/three.min.js"></script>
<script src="js/libs/stats.min.js"></script>
<script src="../src/extras/core/NURBSUtils.js"></script>
<script src="../src/extras/core/NURBSCurve.js"></script>
<script>
......
examples/webgl_geometry_nurbs.html
浏览文件 @ ca803d97
<!DOCTYPE html>
<html lang="en">
<!-- based on webgl_geometry_shapes.html -->
<!-- based on webgl_geometry_shapes.html and webgl_geometries2.html -->
<head>
<title>three.js webgl - geometry - NURBS</title>
<meta charset="utf-8">
......@@ -24,9 +24,10 @@
<body>
<canvas id="debug" style="position:absolute; left:100px"></canvas>
<div id="info"><a href="http://threejs.org" target="_blank">three.js</a> - NURBS curve example</div>
<div id="info"><a href="http://threejs.org" target="_blank">three.js</a> - NURBS curve and surface example</div>
<script src="../build/three.min.js"></script>
<script src="../src/extras/core/NURBSUtils.js"></script>
<script src="../src/extras/core/NURBSCurve.js"></script>
<script src="../src/extras/core/NURBSSurface.js"></script>
......@@ -124,7 +125,7 @@
parent.add( nurbsLine );
parent.add( nurbsControlPointsLine );
// NURBS Surface
// NURBS surface
var nsControlPoints = [
[
......@@ -135,8 +136,8 @@
],
[
new THREE.Vector4 ( 0, -200, 0, 1 ),
new THREE.Vector4 ( 0, -100, -100, 1 ),
new THREE.Vector4 ( 0, 100, 150, 1 ),
new THREE.Vector4 ( 0, -100, -100, 5 ),
new THREE.Vector4 ( 0, 100, 150, 5 ),
new THREE.Vector4 ( 0, 200, 0, 1 )
],
[
......@@ -165,7 +166,7 @@
return nurbsSurface.getPoint(u, v);
};
var geo = new THREE.ParametricGeometry( getSurfacePoint, 50, 50 );
var geo = new THREE.ParametricGeometry( getSurfacePoint, 20, 20 );
var object = THREE.SceneUtils.createMultiMaterialObject( geo, materials );
object.position.set( 0, 100, 0 );
object.scale.multiplyScalar( 1 );
......
src/extras/core/NURBSCurve.js
浏览文件 @ ca803d97
......@@ -34,7 +34,7 @@ THREE.NURBSCurve.prototype.getPoint = function ( t ) {
var u = this.knots[0] + t * (this.knots[this.knots.length - 1] - this.knots[0]); // linear mapping t->u
// following results in (wx, wy, wz, w) homogeneous point
var hpoint = THREE.NURBSCurve.Utils.calcBSplinePoint(this.degree, this.knots, this.controlPoints, u);
var hpoint = THREE.NURBSUtils.calcBSplinePoint(this.degree, this.knots, this.controlPoints, u);
if (hpoint.w != 1.0) { // project to 3D space: (wx, wy, wz, w) -> (x, y, z, 1)
hpoint.divideScalar(hpoint.w);
......@@ -47,354 +47,10 @@ THREE.NURBSCurve.prototype.getPoint = function ( t ) {
THREE.NURBSCurve.prototype.getTangent = function ( t ) {
var u = this.knots[0] + t * (this.knots[this.knots.length - 1] - this.knots[0]);
var ders = THREE.NURBSCurve.Utils.calcNURBSDerivatives(this.degree, this.knots, this.controlPoints, u, 1);
var ders = THREE.NURBSUtils.calcNURBSDerivatives(this.degree, this.knots, this.controlPoints, u, 1);
var tangent = ders[1].clone();
tangent.normalize();
return tangent;
};
/**************************************************************
* Utils
**************************************************************/
THREE.NURBSCurve.Utils = {
/*
Finds knot vector span.
p : degree
u : parametric value
U : knot vector
returns the span
*/
findSpan: function( p, u, U ) {
var n = U.length - p - 1;
if (u >= U[n]) {
return n - 1;
}
if (u <= U[p]) {
return p;
}
var low = p;
var high = n;
var mid = Math.floor((low + high) / 2);
while (u < U[mid] || u >= U[mid + 1]) {
if (u < U[mid]) {
high = mid;
} else {
low = mid;
}
mid = Math.floor((low + high) / 2);
}
return mid;
},
/*
Calculate basis functions. See The NURBS Book, page 70, algorithm A2.2
span : span in which u lies
u : parametric point
p : degree
U : knot vector
returns array[p+1] with basis functions values.
*/
calcBasisFunctions: function( span, u, p, U ) {
var N = [];
var left = [];
var right = [];
N[0] = 1.0;
for (var j = 1; j <= p; ++j) {
left[j] = u - U[span + 1 - j];
right[j] = U[span + j] - u;
var saved = 0.0;
for (var r = 0; r < j; ++r) {
var rv = right[r + 1];
var lv = left[j - r];
var temp = N[r] / (rv + lv);
N[r] = saved + rv * temp;
saved = lv * temp;
}
N[j] = saved;
}
return N;
},
/*
Calculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.
p : degree of B-Spline
U : knot vector
P : control points (x, y, z, w)
u : parametric point
returns point for given u
*/
calcBSplinePoint: function( p, U, P, u ) {
var span = this.findSpan(p, u, U);
var N = this.calcBasisFunctions(span, u, p, U);
var C = new THREE.Vector4(0, 0, 0, 0);
for (var j = 0; j <= p; ++j) {
var point = P[span - p + j];
var Nj = N[j];
var wNj = point.w * Nj;
C.x += point.x * wNj;
C.y += point.y * wNj;
C.z += point.z * wNj;
C.w += point.w * Nj;
}
return C;
},
/*
Calculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.
span : span in which u lies
u : parametric point
p : degree
n : number of derivatives to calculate
U : knot vector
returns array[n+1][p+1] with basis functions derivatives
*/
calcBasisFunctionDerivatives: function( span, u, p, n, U ) {
var zeroArr = [];
for (var i = 0; i <= p; ++i)
zeroArr[i] = 0.0;
var ders = [];
for (var i = 0; i <= n; ++i)
ders[i] = zeroArr.slice(0);
var ndu = [];
for (var i = 0; i <= p; ++i)
ndu[i] = zeroArr.slice(0);
ndu[0][0] = 1.0;
var left = zeroArr.slice(0);
var right = zeroArr.slice(0);
for (var j = 1; j <= p; ++j) {
left[j] = u - U[span + 1 - j];
right[j] = U[span + j] - u;
var saved = 0.0;
for (var r = 0; r < j; ++r) {
var rv = right[r + 1];
var lv = left[j - r];
ndu[j][r] = rv + lv;
var temp = ndu[r][j - 1] / ndu[j][r];
ndu[r][j] = saved + rv * temp;
saved = lv * temp;
}
ndu[j][j] = saved;
}
for (var j = 0; j <= p; ++j) {
ders[0][j] = ndu[j][p];
}
for (var r = 0; r <= p; ++r) {
var s1 = 0;
var s2 = 1;
var a = [];
for (var i = 0; i <= p; ++i) {
a[i] = zeroArr.slice(0);
}
a[0][0] = 1.0;
for (var k = 1; k <= n; ++k) {
var d = 0.0;
var rk = r - k;
var pk = p - k;
if (r >= k) {
a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
d = a[s2][0] * ndu[rk][pk];
}
var j1 = (rk >= -1) ? 1 : -rk;
var j2 = (r - 1 <= pk) ? k - 1 : p - r;
for (var j = j1; j <= j2; ++j) {
a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][rk + j];
d += a[s2][j] * ndu[rk + j][pk];
}
if (r <= pk) {
a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];
d += a[s2][k] * ndu[r][pk];
}
ders[k][r] = d;
var j = s1;
s1 = s2;
s2 = j;
}
}
var r = p;
for (var k = 1; k <= n; ++k) {
for (var j = 0; j <= p; ++j) {
ders[k][j] *= r;
}
r *= p - k;
}
return ders;
},
/*
Calculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.
p : degree
U : knot vector
P : control points
u : Parametric points
nd : number of derivatives
returns array[d+1] with derivatives
*/
calcBSplineDerivatives: function( p, U, P, u, nd ) {
var du = nd < p ? nd : p;
var CK = [];
var span = this.findSpan(p, u, U);
var nders = this.calcBasisFunctionDerivatives(span, u, p, du, U);
var Pw = [];
for (var i = 0; i < P.length; ++i) {
var point = P[i].clone();
var w = point.w;
point.x *= w;
point.y *= w;
point.z *= w;
Pw[i] = point;
}
for (var k = 0; k <= du; ++k) {
var point = Pw[span - p].clone().multiplyScalar(nders[k][0]);
for (var j = 1; j <= p; ++j) {
point.add(Pw[span - p + j].clone().multiplyScalar(nders[k][j]));
}
CK[k] = point;
}
for (var k = du + 1; k <= nd + 1; ++k) {
CK[k] = new THREE.Vector4(0, 0, 0);
}
return CK;
},
/*
Calculate "K over I"
returns k!/(i!(k-i)!)
*/
calcKoverI: function( k, i ) {
var nom = 1;
for (var j = 2; j <= k; ++j) {
nom *= j;
}
var denom = 1;
for (var j = 2; j <= i; ++j) {
denom *= j;
}
for (var j = 2; j <= k - i; ++j) {
denom *= j;
}
return nom / denom;
},
/*
Calculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.
Pders : result of function calcBSplineDerivatives
returns array with derivatives for rational curve.
*/
calcRationalCurveDerivatives: function ( Pders ) {
var nd = Pders.length;
var Aders = [];
var wders = [];
for (var i = 0; i < nd; ++i) {
var point = Pders[i];
Aders[i] = new THREE.Vector3(point.x, point.y, point.z);
wders[i] = point.w;
}
var CK = [];
for (var k = 0; k < nd; ++k) {
var v = Aders[k].clone();
for (var i = 1; i <= k; ++i) {
v.sub(CK[k - i].clone().multiplyScalar(this.calcKoverI(k,i) * wders[i]));
}
CK[k] = v.divideScalar(wders[0]);
}
return CK;
},
/*
Calculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.
p : degree
U : knot vector
P : control points in homogeneous space
u : parametric points
nd : number of derivatives
returns array with derivatives.
*/
calcNURBSDerivatives: function( p, U, P, u, nd ) {
var Pders = this.calcBSplineDerivatives(p, U, P, u, nd);
return this.calcRationalCurveDerivatives(Pders);
}
};
src/extras/core/NURBSSurface.js
浏览文件 @ ca803d97
......@@ -2,8 +2,6 @@
* @author renej
* NURBS surface object
*
* Derives from Curve, overriding getPoint and getTangent.
*
* Implementation is based on (x, y [, z=0 [, w=1]]) control points with w=weight.
*
**/
......@@ -24,14 +22,10 @@ THREE.NURBSSurface = function ( degree1, degree2, knots1, knots2 /* arrays of re
var len1 = knots1.length - degree1 - 1;
var len2 = knots2.length - degree2 - 1;
//console.log("controlPoints: " + controlPoints);
//console.log("controlPoints[0][0].x: " + controlPoints[0][0].x);
// ensure Vector4 for control points
for (var i = 0; i < len1; ++i) {
this.controlPoints[i] = []
for (var j = 0; j < len2; ++j) {
//console.log("i=" + i + " j=" + j);
var point = controlPoints[i][j];
this.controlPoints[i][j] = new THREE.Vector4(point.x, point.y, point.z, point.w);
}
......@@ -45,62 +39,11 @@ THREE.NURBSSurface.prototype = {
getPoint: function ( t1, t2 ) {
//console.log("this.knots1=" + this.knots1);
//console.log("this.knots2=" + this.knots2);
//console.log("this.controlPoints=" + this.controlPoints);
var u = this.knots1[0] + t1 * (this.knots1[this.knots1.length - 1] - this.knots1[0]); // linear mapping t1->u
var v = this.knots2[0] + t2 * (this.knots2[this.knots2.length - 1] - this.knots2[0]); // linear mapping t2->u
var point = THREE.NURBSSurface.Utils.calcSurfacePoint(this.degree1, this.degree2, this.knots1, this.knots2, this.controlPoints, u, v);
//console.log("u=" + u + " v=" + v + " point=" + point.x + ", " + point.y + ", " + point.z);
return point;
return THREE.NURBSUtils.calcSurfacePoint(this.degree1, this.degree2, this.knots1, this.knots2, this.controlPoints, u, v);
}
};
/**************************************************************
* Utils
**************************************************************/
THREE.NURBSSurface.Utils = {
/*
Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
p1, p2 : degrees of B-Spline surface
U1, U2 : knot vectors
P : control points (x, y, z, w)
u, v : parametric values
returns point for given (u, v)
*/
calcSurfacePoint: function( p, q, U, V, P, u, v ) {
var uspan = THREE.NURBSCurve.Utils.findSpan(p, u, U);
var vspan = THREE.NURBSCurve.Utils.findSpan(q, v, V);
var Nu = THREE.NURBSCurve.Utils.calcBasisFunctions(uspan, u, p, U);
var Nv = THREE.NURBSCurve.Utils.calcBasisFunctions(vspan, v, q, V);
var temp = [];
for (var l = 0; l <= q; ++l) {
temp[l] = new THREE.Vector4(0, 0, 0, 0);
for (var k = 0; k <= p; ++k) {
var point = P[uspan - p + k][vspan - q + l].clone();
var w = point.w;
point.x *= w;
point.y *= w;
point.z *= w;
temp[l].add(point.multiplyScalar(Nu[k]));
}
}
var Sw = new THREE.Vector4(0, 0, 0, 0);
for (var l = 0; l <= q; ++l) {
Sw.add(temp[l].multiplyScalar(Nv[l]));
}
Sw.divideScalar(Sw.w);
return new THREE.Vector3(Sw.x, Sw.y, Sw.z);
}
};
src/extras/core/NURBSUtils.js 0 → 100644
浏览文件 @ ca803d97
/**
* @author renej
* NURBS utils
*
* See NURBSCurve and NURBSSurface.
*
**/
/**************************************************************
* NURBS Utils
**************************************************************/
THREE.NURBSUtils = {
/*
Finds knot vector span.
p : degree
u : parametric value
U : knot vector
returns the span
*/
findSpan: function( p, u, U ) {
var n = U.length - p - 1;
if (u >= U[n]) {
return n - 1;
}
if (u <= U[p]) {
return p;
}
var low = p;
var high = n;
var mid = Math.floor((low + high) / 2);
while (u < U[mid] || u >= U[mid + 1]) {
if (u < U[mid]) {
high = mid;
} else {
low = mid;
}
mid = Math.floor((low + high) / 2);
}
return mid;
},
/*
Calculate basis functions. See The NURBS Book, page 70, algorithm A2.2
span : span in which u lies
u : parametric point
p : degree
U : knot vector
returns array[p+1] with basis functions values.
*/
calcBasisFunctions: function( span, u, p, U ) {
var N = [];
var left = [];
var right = [];
N[0] = 1.0;
for (var j = 1; j <= p; ++j) {
left[j] = u - U[span + 1 - j];
right[j] = U[span + j] - u;
var saved = 0.0;
for (var r = 0; r < j; ++r) {
var rv = right[r + 1];
var lv = left[j - r];
var temp = N[r] / (rv + lv);
N[r] = saved + rv * temp;
saved = lv * temp;
}
N[j] = saved;
}
return N;
},
/*
Calculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.
p : degree of B-Spline
U : knot vector
P : control points (x, y, z, w)
u : parametric point
returns point for given u
*/
calcBSplinePoint: function( p, U, P, u ) {
var span = this.findSpan(p, u, U);
var N = this.calcBasisFunctions(span, u, p, U);
var C = new THREE.Vector4(0, 0, 0, 0);
for (var j = 0; j <= p; ++j) {
var point = P[span - p + j];
var Nj = N[j];
var wNj = point.w * Nj;
C.x += point.x * wNj;
C.y += point.y * wNj;
C.z += point.z * wNj;
C.w += point.w * Nj;
}
return C;
},
/*
Calculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.
span : span in which u lies
u : parametric point
p : degree
n : number of derivatives to calculate
U : knot vector
returns array[n+1][p+1] with basis functions derivatives
*/
calcBasisFunctionDerivatives: function( span, u, p, n, U ) {
var zeroArr = [];
for (var i = 0; i <= p; ++i)
zeroArr[i] = 0.0;
var ders = [];
for (var i = 0; i <= n; ++i)
ders[i] = zeroArr.slice(0);
var ndu = [];
for (var i = 0; i <= p; ++i)
ndu[i] = zeroArr.slice(0);
ndu[0][0] = 1.0;
var left = zeroArr.slice(0);
var right = zeroArr.slice(0);
for (var j = 1; j <= p; ++j) {
left[j] = u - U[span + 1 - j];
right[j] = U[span + j] - u;
var saved = 0.0;
for (var r = 0; r < j; ++r) {
var rv = right[r + 1];
var lv = left[j - r];
ndu[j][r] = rv + lv;
var temp = ndu[r][j - 1] / ndu[j][r];
ndu[r][j] = saved + rv * temp;
saved = lv * temp;
}
ndu[j][j] = saved;
}
for (var j = 0; j <= p; ++j) {
ders[0][j] = ndu[j][p];
}
for (var r = 0; r <= p; ++r) {
var s1 = 0;
var s2 = 1;
var a = [];
for (var i = 0; i <= p; ++i) {
a[i] = zeroArr.slice(0);
}
a[0][0] = 1.0;
for (var k = 1; k <= n; ++k) {
var d = 0.0;
var rk = r - k;
var pk = p - k;
if (r >= k) {
a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
d = a[s2][0] * ndu[rk][pk];
}
var j1 = (rk >= -1) ? 1 : -rk;
var j2 = (r - 1 <= pk) ? k - 1 : p - r;
for (var j = j1; j <= j2; ++j) {
a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][rk + j];
d += a[s2][j] * ndu[rk + j][pk];
}
if (r <= pk) {
a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];
d += a[s2][k] * ndu[r][pk];
}
ders[k][r] = d;
var j = s1;
s1 = s2;
s2 = j;
}
}
var r = p;
for (var k = 1; k <= n; ++k) {
for (var j = 0; j <= p; ++j) {
ders[k][j] *= r;
}
r *= p - k;
}
return ders;
},
/*
Calculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.
p : degree
U : knot vector
P : control points
u : Parametric points
nd : number of derivatives
returns array[d+1] with derivatives
*/
calcBSplineDerivatives: function( p, U, P, u, nd ) {
var du = nd < p ? nd : p;
var CK = [];
var span = this.findSpan(p, u, U);
var nders = this.calcBasisFunctionDerivatives(span, u, p, du, U);
var Pw = [];
for (var i = 0; i < P.length; ++i) {
var point = P[i].clone();
var w = point.w;
point.x *= w;
point.y *= w;
point.z *= w;
Pw[i] = point;
}
for (var k = 0; k <= du; ++k) {
var point = Pw[span - p].clone().multiplyScalar(nders[k][0]);
for (var j = 1; j <= p; ++j) {
point.add(Pw[span - p + j].clone().multiplyScalar(nders[k][j]));
}
CK[k] = point;
}
for (var k = du + 1; k <= nd + 1; ++k) {
CK[k] = new THREE.Vector4(0, 0, 0);
}
return CK;
},
/*
Calculate "K over I"
returns k!/(i!(k-i)!)
*/
calcKoverI: function( k, i ) {
var nom = 1;
for (var j = 2; j <= k; ++j) {
nom *= j;
}
var denom = 1;
for (var j = 2; j <= i; ++j) {
denom *= j;
}
for (var j = 2; j <= k - i; ++j) {
denom *= j;
}
return nom / denom;
},
/*
Calculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.
Pders : result of function calcBSplineDerivatives
returns array with derivatives for rational curve.
*/
calcRationalCurveDerivatives: function ( Pders ) {
var nd = Pders.length;
var Aders = [];
var wders = [];
for (var i = 0; i < nd; ++i) {
var point = Pders[i];
Aders[i] = new THREE.Vector3(point.x, point.y, point.z);
wders[i] = point.w;
}
var CK = [];
for (var k = 0; k < nd; ++k) {
var v = Aders[k].clone();
for (var i = 1; i <= k; ++i) {
v.sub(CK[k - i].clone().multiplyScalar(this.calcKoverI(k,i) * wders[i]));
}
CK[k] = v.divideScalar(wders[0]);
}
return CK;
},
/*
Calculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.
p : degree
U : knot vector
P : control points in homogeneous space
u : parametric points
nd : number of derivatives
returns array with derivatives.
*/
calcNURBSDerivatives: function( p, U, P, u, nd ) {
var Pders = this.calcBSplineDerivatives(p, U, P, u, nd);
return this.calcRationalCurveDerivatives(Pders);
},
/*
Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
p1, p2 : degrees of B-Spline surface
U1, U2 : knot vectors
P : control points (x, y, z, w)
u, v : parametric values
returns point for given (u, v)
*/
calcSurfacePoint: function( p, q, U, V, P, u, v ) {
var uspan = this.findSpan(p, u, U);
var vspan = this.findSpan(q, v, V);
var Nu = this.calcBasisFunctions(uspan, u, p, U);
var Nv = this.calcBasisFunctions(vspan, v, q, V);
var temp = [];
for (var l = 0; l <= q; ++l) {
temp[l] = new THREE.Vector4(0, 0, 0, 0);
for (var k = 0; k <= p; ++k) {
var point = P[uspan - p + k][vspan - q + l].clone();
var w = point.w;
point.x *= w;
point.y *= w;
point.z *= w;
temp[l].add(point.multiplyScalar(Nu[k]));
}
}
var Sw = new THREE.Vector4(0, 0, 0, 0);
for (var l = 0; l <= q; ++l) {
Sw.add(temp[l].multiplyScalar(Nv[l]));
}
Sw.divideScalar(Sw.w);
return new THREE.Vector3(Sw.x, Sw.y, Sw.z);
}
};
Markdown is supported
0% 或 .
You are about to add 0 people to the discussion. Proceed with caution.
先完成此消息的编辑！
想要评论请 注册 或