3d-interface/js/Hermite.js

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2015-04-14 12:02:35 +02:00
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;
}