created

README.md

@@ -0,0 +1,24 @@
+# dmap-front
+
+## Project setup
+```
+npm install
+```
+
+### Compiles and hot-reloads for development
+```
+npm run serve
+```
+
+### Compiles and minifies for production
+```
+npm run build
+```
+
+### Lints and fixes files
+```
+npm run lint
+```
+
+### Customize configuration
+See [Configuration Reference](https://cli.vuejs.org/config/).

babel.config.js

@@ -0,0 +1,5 @@
+module.exports = {
+  presets: [
+    '@vue/cli-plugin-babel/preset'
+  ]
+}

jsconfig.json

@@ -0,0 +1,19 @@
+{
+  "compilerOptions": {
+    "target": "es5",
+    "module": "esnext",
+    "baseUrl": "./",
+    "moduleResolution": "node",
+    "paths": {
+      "@/*": [
+        "src/*"
+      ]
+    },
+    "lib": [
+      "esnext",
+      "dom",
+      "dom.iterable",
+      "scripthost"
+    ]
+  }
+}

package.json

@@ -0,0 +1,54 @@
+{
+  "name": "dmap-front",
+  "version": "0.1.0",
+  "private": true,
+  "scripts": {
+    "serve": "vue-cli-service serve",
+    "build": "vue-cli-service build",
+    "lint": "vue-cli-service lint"
+  },
+  "dependencies": {
+    "axios": "^0.18.1",
+    "core-js": "^3.8.3",
+    "element-ui": "^2.15.14",
+    "less": "^4.2.0",
+    "less-loader": "^11.1.3",
+    "mitt": "^3.0.1",
+    "three": "^0.100.0",
+    "vue": "^2.6.14",
+    "vue-router": "^3.6.5",
+    "vue-socket.io": "^3.0.10",
+    "vuescroll": "^4.18.1",
+    "vuex": "^3.0.1"
+  },
+  "devDependencies": {
+    "@babel/core": "^7.12.16",
+    "@babel/eslint-parser": "^7.12.16",
+    "@iconify/vue": "^4.1.1",
+    "@vue/cli-plugin-babel": "~5.0.0",
+    "@vue/cli-plugin-eslint": "~5.0.0",
+    "@vue/cli-service": "~5.0.0",
+    "eslint": "^7.32.0",
+    "eslint-plugin-vue": "^8.0.3",
+    "vue-template-compiler": "^2.6.14"
+  },
+  "eslintConfig": {
+    "root": true,
+    "env": {
+      "node": true
+    },
+    "extends": [
+      "plugin:vue/essential",
+      "eslint:recommended"
+    ],
+    "parserOptions": {
+      "parser": "@babel/eslint-parser"
+    },
+    "rules": {}
+  },
+  "browserslist": [
+    "> 1%",
+    "last 2 versions",
+    "not dead"
+  ]
+}

public/cert/2022/zh3x.cn.crt

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public/cert/2022/zh3x.cn.csr

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public/cert/2022/zh3x.cn.key

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+-----END CERTIFICATE-----

public/cert/2022/zh3x.cn_ca.crt

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public/cert/zh3x.cn.key

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public/cert/zh3x.cn.pem

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public/cert/zh3x.cn_ca.crt

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public/curves/CurveExtras.js

@@ -0,0 +1,422 @@
+import {
+	Curve,
+	Vector3
+} from 'three';
+
+/**
+ * A bunch of parametric curves
+ *
+ * Formulas collected from various sources
+ * http://mathworld.wolfram.com/HeartCurve.html
+ * http://en.wikipedia.org/wiki/Viviani%27s_curve
+ * http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
+ * https://prideout.net/blog/old/blog/index.html@p=44.html
+ */
+
+// GrannyKnot
+
+class GrannyKnot extends Curve {
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t = 2 * Math.PI * t;
+
+		const x = - 0.22 * Math.cos( t ) - 1.28 * Math.sin( t ) - 0.44 * Math.cos( 3 * t ) - 0.78 * Math.sin( 3 * t );
+		const 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 );
+		const z = 0.7 * Math.cos( 3 * t ) - 0.4 * Math.sin( 3 * t );
+
+		return point.set( x, y, z ).multiplyScalar( 20 );
+
+	}
+
+}
+
+// HeartCurve
+
+class HeartCurve extends Curve {
+
+	constructor( scale = 5 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t *= 2 * Math.PI;
+
+		const x = 16 * Math.pow( Math.sin( t ), 3 );
+		const y = 13 * Math.cos( t ) - 5 * Math.cos( 2 * t ) - 2 * Math.cos( 3 * t ) - Math.cos( 4 * t );
+		const z = 0;
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// Viviani's Curve
+
+class VivianiCurve extends Curve {
+
+	constructor( scale = 70 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t = t * 4 * Math.PI; // normalized to 0..1
+		const a = this.scale / 2;
+
+		const x = a * ( 1 + Math.cos( t ) );
+		const y = a * Math.sin( t );
+		const z = 2 * a * Math.sin( t / 2 );
+
+		return point.set( x, y, z );
+
+	}
+
+}
+
+// KnotCurve
+
+class KnotCurve extends Curve {
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t *= 2 * Math.PI;
+
+		const R = 10;
+		const s = 50;
+
+		const x = s * Math.sin( t );
+		const y = Math.cos( t ) * ( R + s * Math.cos( t ) );
+		const z = Math.sin( t ) * ( R + s * Math.cos( t ) );
+
+		return point.set( x, y, z );
+
+	}
+
+}
+
+
+// HelixCurve
+
+class HelixCurve extends Curve {
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const a = 30; // radius
+		const b = 150; // height
+
+		const t2 = 2 * Math.PI * t * b / 30;
+
+		const x = Math.cos( t2 ) * a;
+		const y = Math.sin( t2 ) * a;
+		const z = b * t;
+
+		return point.set( x, y, z );
+
+	}
+
+}
+
+// TrefoilKnot
+
+class TrefoilKnot extends Curve {
+
+	constructor( scale = 10 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t *= Math.PI * 2;
+
+		const x = ( 2 + Math.cos( 3 * t ) ) * Math.cos( 2 * t );
+		const y = ( 2 + Math.cos( 3 * t ) ) * Math.sin( 2 * t );
+		const z = Math.sin( 3 * t );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// TorusKnot
+
+class TorusKnot extends Curve {
+
+	constructor( scale = 10 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const p = 3;
+		const q = 4;
+
+		t *= Math.PI * 2;
+
+		const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
+		const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
+		const z = Math.sin( q * t );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// CinquefoilKnot
+
+class CinquefoilKnot extends Curve {
+
+	constructor( scale = 10 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const p = 2;
+		const q = 5;
+
+		t *= Math.PI * 2;
+
+		const x = ( 2 + Math.cos( q * t ) ) * Math.cos( p * t );
+		const y = ( 2 + Math.cos( q * t ) ) * Math.sin( p * t );
+		const z = Math.sin( q * t );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+
+// TrefoilPolynomialKnot
+
+class TrefoilPolynomialKnot extends Curve {
+
+	constructor( scale = 10 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t = t * 4 - 2;
+
+		const x = Math.pow( t, 3 ) - 3 * t;
+		const y = Math.pow( t, 4 ) - 4 * t * t;
+		const z = 1 / 5 * Math.pow( t, 5 ) - 2 * t;
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+function scaleTo( x, y, t ) {
+
+	const r = y - x;
+	return t * r + x;
+
+}
+
+// FigureEightPolynomialKnot
+
+class FigureEightPolynomialKnot extends Curve {
+
+	constructor( scale = 1 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t = scaleTo( - 4, 4, t );
+
+		const x = 2 / 5 * t * ( t * t - 7 ) * ( t * t - 10 );
+		const y = Math.pow( t, 4 ) - 13 * t * t;
+		const z = 1 / 10 * t * ( t * t - 4 ) * ( t * t - 9 ) * ( t * t - 12 );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// DecoratedTorusKnot4a
+
+class DecoratedTorusKnot4a extends Curve {
+
+	constructor( scale = 40 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		t *= Math.PI * 2;
+
+		const x = Math.cos( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
+		const y = Math.sin( 2 * t ) * ( 1 + 0.6 * ( Math.cos( 5 * t ) + 0.75 * Math.cos( 10 * t ) ) );
+		const z = 0.35 * Math.sin( 5 * t );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// DecoratedTorusKnot4b
+
+class DecoratedTorusKnot4b extends Curve {
+
+	constructor( scale = 40 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const fi = t * Math.PI * 2;
+
+		const x = Math.cos( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
+		const y = Math.sin( 2 * fi ) * ( 1 + 0.45 * Math.cos( 3 * fi ) + 0.4 * Math.cos( 9 * fi ) );
+		const z = 0.2 * Math.sin( 9 * fi );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+
+// DecoratedTorusKnot5a
+
+class DecoratedTorusKnot5a extends Curve {
+
+	constructor( scale = 40 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const fi = t * Math.PI * 2;
+
+		const x = Math.cos( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
+		const y = Math.sin( 3 * fi ) * ( 1 + 0.3 * Math.cos( 5 * fi ) + 0.5 * Math.cos( 10 * fi ) );
+		const z = 0.2 * Math.sin( 20 * fi );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+// DecoratedTorusKnot5c
+
+class DecoratedTorusKnot5c extends Curve {
+
+	constructor( scale = 40 ) {
+
+		super();
+
+		this.scale = scale;
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const fi = t * Math.PI * 2;
+
+		const x = Math.cos( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
+		const y = Math.sin( 4 * fi ) * ( 1 + 0.5 * ( Math.cos( 5 * fi ) + 0.4 * Math.cos( 20 * fi ) ) );
+		const z = 0.35 * Math.sin( 15 * fi );
+
+		return point.set( x, y, z ).multiplyScalar( this.scale );
+
+	}
+
+}
+
+export {
+	GrannyKnot,
+	HeartCurve,
+	VivianiCurve,
+	KnotCurve,
+	HelixCurve,
+	TrefoilKnot,
+	TorusKnot,
+	CinquefoilKnot,
+	TrefoilPolynomialKnot,
+	FigureEightPolynomialKnot,
+	DecoratedTorusKnot4a,
+	DecoratedTorusKnot4b,
+	DecoratedTorusKnot5a,
+	DecoratedTorusKnot5c
+};

public/curves/NURBSCurve.js

@@ -0,0 +1,80 @@
+import {
+	Curve,
+	Vector3,
+	Vector4
+} from 'three';
+import * as NURBSUtils from '../curves/NURBSUtils.js';
+
+/**
+ * NURBS curve object
+ *
+ * Derives from Curve, overriding getPoint and getTangent.
+ *
+ * Implementation is based on (x, y [, z=0 [, w=1]]) control points with w=weight.
+ *
+ **/
+
+class NURBSCurve extends Curve {
+
+	constructor(
+		degree,
+		knots /* array of reals */,
+		controlPoints /* array of Vector(2|3|4) */,
+		startKnot /* index in knots */,
+		endKnot /* index in knots */
+	) {
+
+		super();
+
+		this.degree = degree;
+		this.knots = knots;
+		this.controlPoints = [];
+		// Used by periodic NURBS to remove hidden spans
+		this.startKnot = startKnot || 0;
+		this.endKnot = endKnot || ( this.knots.length - 1 );
+
+		for ( let i = 0; i < controlPoints.length; ++ i ) {
+
+			// ensure Vector4 for control points
+			const point = controlPoints[ i ];
+			this.controlPoints[ i ] = new Vector4( point.x, point.y, point.z, point.w );
+
+		}
+
+	}
+
+	getPoint( t, optionalTarget = new Vector3() ) {
+
+		const point = optionalTarget;
+
+		const u = this.knots[ this.startKnot ] + t * ( this.knots[ this.endKnot ] - this.knots[ this.startKnot ] ); // linear mapping t->u
+
+		// following results in (wx, wy, wz, w) homogeneous point
+		const hpoint = 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 );
+
+		}
+
+		return point.set( hpoint.x, hpoint.y, hpoint.z );
+
+	}
+
+	getTangent( t, optionalTarget = new Vector3() ) {
+
+		const tangent = optionalTarget;
+
+		const u = this.knots[ 0 ] + t * ( this.knots[ this.knots.length - 1 ] - this.knots[ 0 ] );
+		const ders = NURBSUtils.calcNURBSDerivatives( this.degree, this.knots, this.controlPoints, u, 1 );
+		tangent.copy( ders[ 1 ] ).normalize();
+
+		return tangent;
+
+	}
+
+}
+
+export { NURBSCurve };

public/curves/NURBSSurface.js

@@ -0,0 +1,52 @@
+import {
+	Vector4
+} from 'three';
+import * as NURBSUtils from '../curves/NURBSUtils.js';
+
+/**
+ * NURBS surface object
+ *
+ * Implementation is based on (x, y [, z=0 [, w=1]]) control points with w=weight.
+ **/
+
+class NURBSSurface {
+
+	constructor( degree1, degree2, knots1, knots2 /* arrays of reals */, controlPoints /* array^2 of Vector(2|3|4) */ ) {
+
+		this.degree1 = degree1;
+		this.degree2 = degree2;
+		this.knots1 = knots1;
+		this.knots2 = knots2;
+		this.controlPoints = [];
+
+		const len1 = knots1.length - degree1 - 1;
+		const len2 = knots2.length - degree2 - 1;
+
+		// ensure Vector4 for control points
+		for ( let i = 0; i < len1; ++ i ) {
+
+			this.controlPoints[ i ] = [];
+
+			for ( let j = 0; j < len2; ++ j ) {
+
+				const point = controlPoints[ i ][ j ];
+				this.controlPoints[ i ][ j ] = new Vector4( point.x, point.y, point.z, point.w );
+
+			}
+
+		}
+
+	}
+
+	getPoint( t1, t2, target ) {
+
+		const u = this.knots1[ 0 ] + t1 * ( this.knots1[ this.knots1.length - 1 ] - this.knots1[ 0 ] ); // linear mapping t1->u
+		const v = this.knots2[ 0 ] + t2 * ( this.knots2[ this.knots2.length - 1 ] - this.knots2[ 0 ] ); // linear mapping t2->u
+
+		NURBSUtils.calcSurfacePoint( this.degree1, this.degree2, this.knots1, this.knots2, this.controlPoints, u, v, target );
+
+	}
+
+}
+
+export { NURBSSurface };

public/curves/NURBSUtils.js

@@ -0,0 +1,487 @@
+import {
+	Vector3,
+	Vector4
+} from 'three';
+
+/**
+ * NURBS utils
+ *
+ * See NURBSCurve and NURBSSurface.
+ **/
+
+
+/**************************************************************
+ *	NURBS Utils
+ **************************************************************/
+
+/*
+Finds knot vector span.
+
+p : degree
+u : parametric value
+U : knot vector
+
+returns the span
+*/
+function findSpan( p, u, U ) {
+
+	const n = U.length - p - 1;
+
+	if ( u >= U[ n ] ) {
+
+		return n - 1;
+
+	}
+
+	if ( u <= U[ p ] ) {
+
+		return p;
+
+	}
+
+	let low = p;
+	let high = n;
+	let 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.
+*/
+function calcBasisFunctions( span, u, p, U ) {
+
+	const N = [];
+	const left = [];
+	const right = [];
+	N[ 0 ] = 1.0;
+
+	for ( let j = 1; j <= p; ++ j ) {
+
+		left[ j ] = u - U[ span + 1 - j ];
+		right[ j ] = U[ span + j ] - u;
+
+		let saved = 0.0;
+
+		for ( let r = 0; r < j; ++ r ) {
+
+			const rv = right[ r + 1 ];
+			const lv = left[ j - r ];
+			const 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
+*/
+function calcBSplinePoint( p, U, P, u ) {
+
+	const span = findSpan( p, u, U );
+	const N = calcBasisFunctions( span, u, p, U );
+	const C = new Vector4( 0, 0, 0, 0 );
+
+	for ( let j = 0; j <= p; ++ j ) {
+
+		const point = P[ span - p + j ];
+		const Nj = N[ j ];
+		const 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
+*/
+function calcBasisFunctionDerivatives( span, u, p, n, U ) {
+
+	const zeroArr = [];
+	for ( let i = 0; i <= p; ++ i )
+		zeroArr[ i ] = 0.0;
+
+	const ders = [];
+
+	for ( let i = 0; i <= n; ++ i )
+		ders[ i ] = zeroArr.slice( 0 );
+
+	const ndu = [];
+
+	for ( let i = 0; i <= p; ++ i )
+		ndu[ i ] = zeroArr.slice( 0 );
+
+	ndu[ 0 ][ 0 ] = 1.0;
+
+	const left = zeroArr.slice( 0 );
+	const right = zeroArr.slice( 0 );
+
+	for ( let j = 1; j <= p; ++ j ) {
+
+		left[ j ] = u - U[ span + 1 - j ];
+		right[ j ] = U[ span + j ] - u;
+
+		let saved = 0.0;
+
+		for ( let r = 0; r < j; ++ r ) {
+
+			const rv = right[ r + 1 ];
+			const lv = left[ j - r ];
+			ndu[ j ][ r ] = rv + lv;
+
+			const temp = ndu[ r ][ j - 1 ] / ndu[ j ][ r ];
+			ndu[ r ][ j ] = saved + rv * temp;
+			saved = lv * temp;
+
+		}
+
+		ndu[ j ][ j ] = saved;
+
+	}
+
+	for ( let j = 0; j <= p; ++ j ) {
+
+		ders[ 0 ][ j ] = ndu[ j ][ p ];
+
+	}
+
+	for ( let r = 0; r <= p; ++ r ) {
+
+		let s1 = 0;
+		let s2 = 1;
+
+		const a = [];
+		for ( let i = 0; i <= p; ++ i ) {
+
+			a[ i ] = zeroArr.slice( 0 );
+
+		}
+
+		a[ 0 ][ 0 ] = 1.0;
+
+		for ( let k = 1; k <= n; ++ k ) {
+
+			let d = 0.0;
+			const rk = r - k;
+			const pk = p - k;
+
+			if ( r >= k ) {
+
+				a[ s2 ][ 0 ] = a[ s1 ][ 0 ] / ndu[ pk + 1 ][ rk ];
+				d = a[ s2 ][ 0 ] * ndu[ rk ][ pk ];
+
+			}
+
+			const j1 = ( rk >= - 1 ) ? 1 : - rk;
+			const j2 = ( r - 1 <= pk ) ? k - 1 : p - r;
+
+			for ( let 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;
+
+			const j = s1;
+			s1 = s2;
+			s2 = j;
+
+		}
+
+	}
+
+	let r = p;
+
+	for ( let k = 1; k <= n; ++ k ) {
+
+		for ( let 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
+	*/
+function calcBSplineDerivatives( p, U, P, u, nd ) {
+
+	const du = nd < p ? nd : p;
+	const CK = [];
+	const span = findSpan( p, u, U );
+	const nders = calcBasisFunctionDerivatives( span, u, p, du, U );
+	const Pw = [];
+
+	for ( let i = 0; i < P.length; ++ i ) {
+
+		const point = P[ i ].clone();
+		const w = point.w;
+
+		point.x *= w;
+		point.y *= w;
+		point.z *= w;
+
+		Pw[ i ] = point;
+
+	}
+
+	for ( let k = 0; k <= du; ++ k ) {
+
+		const point = Pw[ span - p ].clone().multiplyScalar( nders[ k ][ 0 ] );
+
+		for ( let j = 1; j <= p; ++ j ) {
+
+			point.add( Pw[ span - p + j ].clone().multiplyScalar( nders[ k ][ j ] ) );
+
+		}
+
+		CK[ k ] = point;
+
+	}
+
+	for ( let k = du + 1; k <= nd + 1; ++ k ) {
+
+		CK[ k ] = new Vector4( 0, 0, 0 );
+
+	}
+
+	return CK;
+
+}
+
+
+/*
+Calculate "K over I"
+
+returns k!/(i!(k-i)!)
+*/
+function calcKoverI( k, i ) {
+
+	let nom = 1;
+
+	for ( let j = 2; j <= k; ++ j ) {
+
+		nom *= j;
+
+	}
+
+	let denom = 1;
+
+	for ( let j = 2; j <= i; ++ j ) {
+
+		denom *= j;
+
+	}
+
+	for ( let 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.
+*/
+function calcRationalCurveDerivatives( Pders ) {
+
+	const nd = Pders.length;
+	const Aders = [];
+	const wders = [];
+
+	for ( let i = 0; i < nd; ++ i ) {
+
+		const point = Pders[ i ];
+		Aders[ i ] = new Vector3( point.x, point.y, point.z );
+		wders[ i ] = point.w;
+
+	}
+
+	const CK = [];
+
+	for ( let k = 0; k < nd; ++ k ) {
+
+		const v = Aders[ k ].clone();
+
+		for ( let i = 1; i <= k; ++ i ) {
+
+			v.sub( CK[ k - i ].clone().multiplyScalar( 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.
+*/
+function calcNURBSDerivatives( p, U, P, u, nd ) {
+
+	const Pders = calcBSplineDerivatives( p, U, P, u, nd );
+	return 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)
+*/
+function calcSurfacePoint( p, q, U, V, P, u, v, target ) {
+
+	const uspan = findSpan( p, u, U );
+	const vspan = findSpan( q, v, V );
+	const Nu = calcBasisFunctions( uspan, u, p, U );
+	const Nv = calcBasisFunctions( vspan, v, q, V );
+	const temp = [];
+
+	for ( let l = 0; l <= q; ++ l ) {
+
+		temp[ l ] = new Vector4( 0, 0, 0, 0 );
+		for ( let k = 0; k <= p; ++ k ) {
+
+			const point = P[ uspan - p + k ][ vspan - q + l ].clone();
+			const w = point.w;
+			point.x *= w;
+			point.y *= w;
+			point.z *= w;
+			temp[ l ].add( point.multiplyScalar( Nu[ k ] ) );
+
+		}
+
+	}
+
+	const Sw = new Vector4( 0, 0, 0, 0 );
+	for ( let l = 0; l <= q; ++ l ) {
+
+		Sw.add( temp[ l ].multiplyScalar( Nv[ l ] ) );
+
+	}
+
+	Sw.divideScalar( Sw.w );
+	target.set( Sw.x, Sw.y, Sw.z );
+
+}
+
+
+
+export {
+	findSpan,
+	calcBasisFunctions,
+	calcBSplinePoint,
+	calcBasisFunctionDerivatives,
+	calcBSplineDerivatives,
+	calcKoverI,
+	calcRationalCurveDerivatives,
+	calcNURBSDerivatives,
+	calcSurfacePoint,
+};

public/images/ball-triangle.svg

@@ -0,0 +1,47 @@
+<!-- By Sam Herbert (@sherb), for everyone. More @ http://goo.gl/7AJzbL -->
+<!-- Todo: add easing -->
+<svg width="57" height="57" viewBox="0 0 57 57" xmlns="http://www.w3.org/2000/svg" stroke="#fff">
+    <g fill="none" fill-rule="evenodd">
+        <g transform="translate(1 1)" stroke-width="2">
+            <circle cx="5" cy="50" r="5">
+                <animate attributeName="cy"
+                     begin="0s" dur="2.2s"
+                     values="50;5;50;50"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+                <animate attributeName="cx"
+                     begin="0s" dur="2.2s"
+                     values="5;27;49;5"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+            </circle>
+            <circle cx="27" cy="5" r="5">
+                <animate attributeName="cy"
+                     begin="0s" dur="2.2s"
+                     from="5" to="5"
+                     values="5;50;50;5"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+                <animate attributeName="cx"
+                     begin="0s" dur="2.2s"
+                     from="27" to="27"
+                     values="27;49;5;27"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+            </circle>
+            <circle cx="49" cy="50" r="5">
+                <animate attributeName="cy"
+                     begin="0s" dur="2.2s"
+                     values="50;50;5;50"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+                <animate attributeName="cx"
+                     from="49" to="49"
+                     begin="0s" dur="2.2s"
+                     values="49;5;27;49"
+                     calcMode="linear"
+                     repeatCount="indefinite" />
+            </circle>
+        </g>
+    </g>
+</svg>