Added Hermite functions
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Thomas FORGIONE
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e16e971a87
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848587f11b
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<section>
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<h2>Hermite test</h2>
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<code>
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<div id="content"></div>
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</code>
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#
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</section>
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#!/usr/bin/python
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# -*- coding: utf-8 -*-
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import sys
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from webtools import Web
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def main():
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print('Content-type: text/html')
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print()
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page = Web.Element(Web.ROOT_DIR + 'templates/page.html')
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head = Web.Element(Web.ROOT_DIR + 'templates/head.html')
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body = Web.Element(Web.ROOT_DIR + 'templates/body.html')
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jsIncludes = Web.Element(Web.ROOT_DIR + 'templates/jsIncludes.html')
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mainJs = Web.Element()
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mainJs.open_string = ' <script src="js/HermiteTest.js"></script>'
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content = Web.Element('index.html')
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page.add_child(head)
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page.add_child(body)
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body.add_child(content)
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body.add_child(jsIncludes)
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jsIncludes.add_child(mainJs)
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page.print()
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if __name__ == '__main__':
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main()
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var container = document.getElementById('content');
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function print(text) {
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var content = document.createTextNode(text);
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var new_line = document.createElement('br');
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container.appendChild(content);
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container.appendChild(new_line);
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}
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function toString(variable) {
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if (variable instanceof THREE.Vector3) {
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return variable.x + ', ' + variable.y + ', ' + variable.z;
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} else {
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return variable;
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}
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}
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// Test with THREE.Vector3
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t = [0,1];
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f = [new THREE.Vector3(0,0,0), new THREE.Vector3(1,1,1)];
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fp = [new THREE.Vector3(0,1,2), new THREE.Vector3(0,0,0)];
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// Test with doubles
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// t = [0,1];
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// f = [0,1];
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// fp = [-1,-1]0;
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var hermite = new Hermite.Polynom(t, f, fp);
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print('M = [');
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for (var t = 0; t < 1; t += 0.01) {
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var res = hermite.eval(t);
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print(t + ',' + toString(res) + ';');
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}
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print('];');
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print('MP = [');
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for (var t = 0; t < 1; t += 0.01) {
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var res = hermite.prime(t);
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print(t + ',' + toString(res) + ';');
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}
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print('];');
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var Hermite = {};
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Hermite.Polynom = function(t, f, fp) {
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this.times = t;
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this.evals = f;
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this.primes = fp;
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this.baseFunctions = new Array();
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for (var i in this.times) {
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this.baseFunctions.push(new Hermite.BaseFunction(i, this.times));
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}
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// Let's do something at least a little reusable
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this.tools = {};
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if (f[0] instanceof THREE.Vector3) {
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this.tools.whatType = 'THREE.Vector3';
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this.tools.sum = Tools.sum;
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this.tools.prod = Tools.mul;
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} else {
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this.tools.whatType = 'number';
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this.tools.sum = function(a, b) { return a + b; };
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this.tools.prod = function(a, b) { return a * b; };
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}
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}
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Hermite.Polynom.prototype.eval = function(t) {
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var ret;
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if (this.tools.whatType === 'THREE.Vector3') {
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ret = new THREE.Vector3();
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} else {
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ret = 0;
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}
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for (var i in this.times) {
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var ti = this.times[i];
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var qi_t = this.baseFunctions[i].eval(t);
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// var qi_ti = this.baseFunctions[i].eval(ti);
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var qip_ti = this.baseFunctions[i].prime(ti);
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var f_ti = this.evals[i];
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var fp_ti = this.primes[i];
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// This is the wikipedia formula
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// ret += (qi_t / qi_ti) * ((1 - (t - ti) * (qip_ti / qi_ti)) * f_ti + (t - ti) * fp_ti);
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// Let's not forget that qi_ti = 1
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// This is the final formula
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// ret += (qi_t) * ((1 - (t - ti) * (qip_ti)) * f_ti + (t - ti) * fp_ti);
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// This is the implementation working with THREE.Vector3
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// In terms of disgusting code, we're quite good there
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ret =
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this.tools.sum(
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ret,
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this.tools.prod(
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this.tools.sum(
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this.tools.prod(f_ti, 1 - (t - ti) * (qip_ti)),
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this.tools.prod(fp_ti, t - ti)
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),
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qi_t
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)
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);
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}
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return ret;
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}
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Hermite.Polynom.prototype.prime = function(t) {
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var ret;
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if (this.tools.whatType === 'THREE.Vector3') {
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ret = new THREE.Vector3();
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} else {
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ret = 0;
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}
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for (var i in this.times) {
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var ti = this.times[i];
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var qi_t = this.baseFunctions[i].eval(t);
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// var qi_ti = this.baseFunctions[i].eval(ti);
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var qip_t = this.baseFunctions[i].prime(t );
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var qip_ti = this.baseFunctions[i].prime(ti);
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var f_ti = this.evals[i];
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var fp_ti = this.primes[i];
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// The return of the disgusting code...
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// First part is the same that the eval function, but changing qi_t by qip_t
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// (first part of the derivative)
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ret =
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this.tools.sum(
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ret,
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this.tools.prod(
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this.tools.sum(
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this.tools.prod(f_ti, 1 - (t - ti) * (qip_ti)),
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this.tools.prod(fp_ti, t - ti)
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),
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qip_t
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)
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);
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// Here, we just add
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// ret += qi_t * (-qip_t * f_ti + fp_ti);
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ret =
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this.tools.sum(
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ret,
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this.tools.prod(
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this.tools.sum(
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this.tools.prod(
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f_ti,
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-qip_t
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),
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fp_ti
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),
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qi_t
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)
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);
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// Now the following code is the same as the precedent affectation
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// However it doesn't work, and I can't see the difference between
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// this and the previous one... so I keep it here, to find the
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// mistate later
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// ret =
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// this.tools.sum(
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// ret,
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// this.tools.prod(
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// this.tools.sum(
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// fp_ti,
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// this.tools.prod(
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// f_ti,
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// -qip_ti
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// )
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// ),
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// qi_t
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// )
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// );
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}
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return ret;
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}
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Hermite.BaseFunction = function(index, times) {
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this.index = index;
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this.times = times;
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}
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Hermite.BaseFunction.prototype.eval = function(t) {
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var ret = 1;
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for (var i in this.times) {
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if (i !== this.index) {
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ret *= (t - this.times[i]) / (this.times[this.index] - this.times[i]);
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}
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}
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return ret * ret;
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}
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Hermite.BaseFunction.prototype.prime = function(t) {
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var ret = 0;
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for (var i in this.times) {
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if (i !== this.index) {
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ret += 2 / (t - this.times[i]);
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}
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}
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return this.eval(t) * ret;
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}
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@ -13,4 +13,5 @@
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<script src="/js/PointerCamera.js"></script>
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<script src="/js/CameraContainer.js"></script>
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<script src="/js/three/stats.min.js"></script>
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<script src="/js/Hermite.js"></script>
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#
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