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Added Hermite functions

This commit is contained in:
Thomas FORGIONE 2015-04-14 12:02:35 +02:00
parent e16e971a87
commit 848587f11b
5 changed files with 251 additions and 0 deletions
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7
HermiteTest/index.html Normal file
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<section>
<h2>Hermite test</h2>
<code>
<div id="content"></div>
</code>
#
</section>

28
HermiteTest/index.py Executable file
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#!/usr/bin/python
# -*- coding: utf-8 -*-
import sys
from webtools import Web
def main():
print('Content-type: text/html')
print()
page = Web.Element(Web.ROOT_DIR + 'templates/page.html')
head = Web.Element(Web.ROOT_DIR + 'templates/head.html')
body = Web.Element(Web.ROOT_DIR + 'templates/body.html')
jsIncludes = Web.Element(Web.ROOT_DIR + 'templates/jsIncludes.html')
mainJs = Web.Element()
mainJs.open_string = ' <script src="js/HermiteTest.js"></script>'
content = Web.Element('index.html')
page.add_child(head)
page.add_child(body)
body.add_child(content)
body.add_child(jsIncludes)
jsIncludes.add_child(mainJs)
page.print()
if __name__ == '__main__':
main()

44
HermiteTest/js/HermiteTest.js Normal file
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var container = document.getElementById('content');
function print(text) {
var content = document.createTextNode(text);
var new_line = document.createElement('br');
container.appendChild(content);
container.appendChild(new_line);
}
function toString(variable) {
if (variable instanceof THREE.Vector3) {
return variable.x + ', ' + variable.y + ', ' + variable.z;
} else {
return variable;
}
}
// Test with THREE.Vector3
t = [0,1];
f = [new THREE.Vector3(0,0,0), new THREE.Vector3(1,1,1)];
fp = [new THREE.Vector3(0,1,2), new THREE.Vector3(0,0,0)];
// Test with doubles
// t = [0,1];
// f = [0,1];
// fp = [-1,-1]0;
var hermite = new Hermite.Polynom(t, f, fp);
print('M = [');
for (var t = 0; t < 1; t += 0.01) {
var res = hermite.eval(t);
print(t + ',' + toString(res) + ';');
}
print('];');
print('MP = [');
for (var t = 0; t < 1; t += 0.01) {
var res = hermite.prime(t);
print(t + ',' + toString(res) + ';');
}
print('];');

171
js/Hermite.js Normal file
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var Hermite = {};
Hermite.Polynom = function(t, f, fp) {
this.times = t;
this.evals = f;
this.primes = fp;
this.baseFunctions = new Array();
for (var i in this.times) {
this.baseFunctions.push(new Hermite.BaseFunction(i, this.times));
}
// Let's do something at least a little reusable
this.tools = {};
if (f[0] instanceof THREE.Vector3) {
this.tools.whatType = 'THREE.Vector3';
this.tools.sum = Tools.sum;
this.tools.prod = Tools.mul;
} else {
this.tools.whatType = 'number';
this.tools.sum = function(a, b) { return a + b; };
this.tools.prod = function(a, b) { return a * b; };
}
}
Hermite.Polynom.prototype.eval = function(t) {
var ret;
if (this.tools.whatType === 'THREE.Vector3') {
ret = new THREE.Vector3();
} else {
ret = 0;
}
for (var i in this.times) {
var ti = this.times[i];
var qi_t = this.baseFunctions[i].eval(t);
// var qi_ti = this.baseFunctions[i].eval(ti);
var qip_ti = this.baseFunctions[i].prime(ti);
var f_ti = this.evals[i];
var fp_ti = this.primes[i];
// This is the wikipedia formula
// ret += (qi_t / qi_ti) * ((1 - (t - ti) * (qip_ti / qi_ti)) * f_ti + (t - ti) * fp_ti);
// Let's not forget that qi_ti = 1
// This is the final formula
// ret += (qi_t) * ((1 - (t - ti) * (qip_ti)) * f_ti + (t - ti) * fp_ti);
// This is the implementation working with THREE.Vector3
// In terms of disgusting code, we're quite good there
ret =
this.tools.sum(
ret,
this.tools.prod(
this.tools.sum(
this.tools.prod(f_ti, 1 - (t - ti) * (qip_ti)),
this.tools.prod(fp_ti, t - ti)
),
qi_t
)
);
}
return ret;
}
Hermite.Polynom.prototype.prime = function(t) {
var ret;
if (this.tools.whatType === 'THREE.Vector3') {
ret = new THREE.Vector3();
} else {
ret = 0;
}
for (var i in this.times) {
var ti = this.times[i];
var qi_t = this.baseFunctions[i].eval(t);
// var qi_ti = this.baseFunctions[i].eval(ti);
var qip_t = this.baseFunctions[i].prime(t );
var qip_ti = this.baseFunctions[i].prime(ti);
var f_ti = this.evals[i];
var fp_ti = this.primes[i];
// The return of the disgusting code...
// First part is the same that the eval function, but changing qi_t by qip_t
// (first part of the derivative)
ret =
this.tools.sum(
ret,
this.tools.prod(
this.tools.sum(
this.tools.prod(f_ti, 1 - (t - ti) * (qip_ti)),
this.tools.prod(fp_ti, t - ti)
),
qip_t
)
);
// Here, we just add
// ret += qi_t * (-qip_t * f_ti + fp_ti);
ret =
this.tools.sum(
ret,
this.tools.prod(
this.tools.sum(
this.tools.prod(
f_ti,
-qip_t
),
fp_ti
),
qi_t
)
);
// Now the following code is the same as the precedent affectation
// However it doesn't work, and I can't see the difference between
// this and the previous one... so I keep it here, to find the
// mistate later
// ret =
// this.tools.sum(
// ret,
// this.tools.prod(
// this.tools.sum(
// fp_ti,
// this.tools.prod(
// f_ti,
// -qip_ti
// )
// ),
// qi_t
// )
// );
}
return ret;
}
Hermite.BaseFunction = function(index, times) {
this.index = index;
this.times = times;
}
Hermite.BaseFunction.prototype.eval = function(t) {
var ret = 1;
for (var i in this.times) {
if (i !== this.index) {
ret *= (t - this.times[i]) / (this.times[this.index] - this.times[i]);
}
}
return ret * ret;
}
Hermite.BaseFunction.prototype.prime = function(t) {
var ret = 0;
for (var i in this.times) {
if (i !== this.index) {
ret += 2 / (t - this.times[i]);
}
}
return this.eval(t) * ret;
}

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templates/jsIncludes.html
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<script src="/js/PointerCamera.js"></script> <script src="/js/PointerCamera.js"></script>
<script src="/js/CameraContainer.js"></script> <script src="/js/CameraContainer.js"></script>
<script src="/js/three/stats.min.js"></script> <script src="/js/three/stats.min.js"></script>
<script src="/js/Hermite.js"></script>
# #