mirror of
https://github.com/Jozufozu/Flywheel.git
synced 2024-11-10 12:34:11 +01:00
a42c027b6f
- Fix Resources not being closed properly - Change versioning scheme to match Create - Add LICENSE to built jar - Fix mods.toml version sync - Move JOML code to non-src directory - Update Gradle - Organize imports
355 lines
14 KiB
Java
355 lines
14 KiB
Java
/*
|
|
* The MIT License
|
|
*
|
|
* Copyright (c) 2016-2021 JOML
|
|
*
|
|
* Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
* of this software and associated documentation files (the "Software"), to deal
|
|
* in the Software without restriction, including without limitation the rights
|
|
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
* copies of the Software, and to permit persons to whom the Software is
|
|
* furnished to do so, subject to the following conditions:
|
|
*
|
|
* The above copyright notice and this permission notice shall be included in
|
|
* all copies or substantial portions of the Software.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
|
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
|
|
* THE SOFTWARE.
|
|
*/
|
|
package com.jozufozu.flywheel.repack.joml;
|
|
|
|
/**
|
|
* Computes the weighted average of multiple rotations represented as {@link Quaterniond} instances.
|
|
* <p>
|
|
* Instances of this class are <i>not</i> thread-safe.
|
|
*
|
|
* @author Kai Burjack
|
|
*/
|
|
public class QuaterniondInterpolator {
|
|
|
|
/**
|
|
* Performs singular value decomposition on {@link Matrix3d}.
|
|
* <p>
|
|
* This code was adapted from <a href="http://www.public.iastate.edu/~dicook/JSS/paper/code/svd.c">http://www.public.iastate.edu/</a>.
|
|
*
|
|
* @author Kai Burjack
|
|
*/
|
|
private static class SvdDecomposition3d {
|
|
private final double rv1[];
|
|
private final double w[];
|
|
private final double v[];
|
|
|
|
SvdDecomposition3d() {
|
|
this.rv1 = new double[3];
|
|
this.w = new double[3];
|
|
this.v = new double[9];
|
|
}
|
|
|
|
private double SIGN(double a, double b) {
|
|
return (b) >= 0.0 ? Math.abs(a) : -Math.abs(a);
|
|
}
|
|
|
|
void svd(double[] a, int maxIterations, Matrix3d destU, Matrix3d destV) {
|
|
int flag, i, its, j, jj, k, l = 0, nm = 0;
|
|
double c, f, h, s, x, y, z;
|
|
double anorm = 0.0, g = 0.0, scale = 0.0;
|
|
/* Householder reduction to bidiagonal form */
|
|
for (i = 0; i < 3; i++) {
|
|
/* left-hand reduction */
|
|
l = i + 1;
|
|
rv1[i] = scale * g;
|
|
g = s = scale = 0.0;
|
|
for (k = i; k < 3; k++)
|
|
scale += Math.abs(a[k + 3 * i]);
|
|
if (scale != 0.0) {
|
|
for (k = i; k < 3; k++) {
|
|
a[k + 3 * i] = (a[k + 3 * i] / scale);
|
|
s += (a[k + 3 * i] * a[k + 3 * i]);
|
|
}
|
|
f = a[i + 3 * i];
|
|
g = -SIGN(Math.sqrt(s), f);
|
|
h = f * g - s;
|
|
a[i + 3 * i] = f - g;
|
|
if (i != 3 - 1) {
|
|
for (j = l; j < 3; j++) {
|
|
for (s = 0.0, k = i; k < 3; k++)
|
|
s += a[k + 3 * i] * a[k + 3 * j];
|
|
f = s / h;
|
|
for (k = i; k < 3; k++)
|
|
a[k + 3 * j] += f * a[k + 3 * i];
|
|
}
|
|
}
|
|
for (k = i; k < 3; k++)
|
|
a[k + 3 * i] = a[k + 3 * i] * scale;
|
|
}
|
|
w[i] = (scale * g);
|
|
|
|
/* right-hand reduction */
|
|
g = s = scale = 0.0;
|
|
if (i < 3 && i != 3 - 1) {
|
|
for (k = l; k < 3; k++)
|
|
scale += Math.abs(a[i + 3 * k]);
|
|
if (scale != 0.0) {
|
|
for (k = l; k < 3; k++) {
|
|
a[i + 3 * k] = a[i + 3 * k] / scale;
|
|
s += a[i + 3 * k] * a[i + 3 * k];
|
|
}
|
|
f = a[i + 3 * l];
|
|
g = -SIGN(Math.sqrt(s), f);
|
|
h = f * g - s;
|
|
a[i + 3 * l] = f - g;
|
|
for (k = l; k < 3; k++)
|
|
rv1[k] = a[i + 3 * k] / h;
|
|
if (i != 3 - 1) {
|
|
for (j = l; j < 3; j++) {
|
|
for (s = 0.0, k = l; k < 3; k++)
|
|
s += a[j + 3 * k] * a[i + 3 * k];
|
|
for (k = l; k < 3; k++)
|
|
a[j + 3 * k] += s * rv1[k];
|
|
}
|
|
}
|
|
for (k = l; k < 3; k++)
|
|
a[i + 3 * k] = a[i + 3 * k] * scale;
|
|
}
|
|
}
|
|
anorm = Math.max(anorm, (Math.abs(w[i]) + Math.abs(rv1[i])));
|
|
}
|
|
|
|
/* accumulate the right-hand transformation */
|
|
for (i = 3 - 1; i >= 0; i--) {
|
|
if (i < 3 - 1) {
|
|
if (g != 0.0) {
|
|
for (j = l; j < 3; j++)
|
|
v[j + 3 * i] = (a[i + 3 * j] / a[i + 3 * l]) / g;
|
|
/* double division to avoid underflow */
|
|
for (j = l; j < 3; j++) {
|
|
for (s = 0.0, k = l; k < 3; k++)
|
|
s += a[i + 3 * k] * v[k + 3 * j];
|
|
for (k = l; k < 3; k++)
|
|
v[k + 3 * j] += s * v[k + 3 * i];
|
|
}
|
|
}
|
|
for (j = l; j < 3; j++)
|
|
v[i + 3 * j] = v[j + 3 * i] = 0.0;
|
|
}
|
|
v[i + 3 * i] = 1.0;
|
|
g = rv1[i];
|
|
l = i;
|
|
}
|
|
|
|
/* accumulate the left-hand transformation */
|
|
for (i = 3 - 1; i >= 0; i--) {
|
|
l = i + 1;
|
|
g = w[i];
|
|
if (i < 3 - 1)
|
|
for (j = l; j < 3; j++)
|
|
a[i + 3 * j] = 0.0;
|
|
if (g != 0.0) {
|
|
g = 1.0 / g;
|
|
if (i != 3 - 1) {
|
|
for (j = l; j < 3; j++) {
|
|
for (s = 0.0, k = l; k < 3; k++)
|
|
s += a[k + 3 * i] * a[k + 3 * j];
|
|
f = s / a[i + 3 * i] * g;
|
|
for (k = i; k < 3; k++)
|
|
a[k + 3 * j] += f * a[k + 3 * i];
|
|
}
|
|
}
|
|
for (j = i; j < 3; j++)
|
|
a[j + 3 * i] = a[j + 3 * i] * g;
|
|
} else {
|
|
for (j = i; j < 3; j++)
|
|
a[j + 3 * i] = 0.0;
|
|
}
|
|
++a[i + 3 * i];
|
|
}
|
|
|
|
/* diagonalize the bidiagonal form */
|
|
for (k = 3 - 1; k >= 0; k--) { /* loop over singular values */
|
|
for (its = 0; its < maxIterations; its++) { /* loop over allowed iterations */
|
|
flag = 1;
|
|
for (l = k; l >= 0; l--) { /* test for splitting */
|
|
nm = l - 1;
|
|
if (Math.abs(rv1[l]) + anorm == anorm) {
|
|
flag = 0;
|
|
break;
|
|
}
|
|
if (Math.abs(w[nm]) + anorm == anorm)
|
|
break;
|
|
}
|
|
if (flag != 0) {
|
|
c = 0.0;
|
|
s = 1.0;
|
|
for (i = l; i <= k; i++) {
|
|
f = s * rv1[i];
|
|
if (Math.abs(f) + anorm != anorm) {
|
|
g = w[i];
|
|
h = PYTHAG(f, g);
|
|
w[i] = h;
|
|
h = 1.0 / h;
|
|
c = g * h;
|
|
s = (-f * h);
|
|
for (j = 0; j < 3; j++) {
|
|
y = a[j + 3 * nm];
|
|
z = a[j + 3 * i];
|
|
a[j + 3 * nm] = y * c + z * s;
|
|
a[j + 3 * i] = z * c - y * s;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
z = w[k];
|
|
if (l == k) { /* convergence */
|
|
if (z < 0.0) { /* make singular value nonnegative */
|
|
w[k] = -z;
|
|
for (j = 0; j < 3; j++)
|
|
v[j + 3 * k] = (-v[j + 3 * k]);
|
|
}
|
|
break;
|
|
}
|
|
if (its == maxIterations - 1) {
|
|
throw new RuntimeException("No convergence after " + maxIterations + " iterations");
|
|
}
|
|
|
|
/* shift from bottom 2 x 2 minor */
|
|
x = w[l];
|
|
nm = k - 1;
|
|
y = w[nm];
|
|
g = rv1[nm];
|
|
h = rv1[k];
|
|
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
|
|
g = PYTHAG(f, 1.0);
|
|
f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x;
|
|
|
|
/* next QR transformation */
|
|
c = s = 1.0;
|
|
for (j = l; j <= nm; j++) {
|
|
i = j + 1;
|
|
g = rv1[i];
|
|
y = w[i];
|
|
h = s * g;
|
|
g = c * g;
|
|
z = PYTHAG(f, h);
|
|
rv1[j] = z;
|
|
c = f / z;
|
|
s = h / z;
|
|
f = x * c + g * s;
|
|
g = g * c - x * s;
|
|
h = y * s;
|
|
y = y * c;
|
|
for (jj = 0; jj < 3; jj++) {
|
|
x = v[jj + 3 * j];
|
|
z = v[jj + 3 * i];
|
|
v[jj + 3 * j] = x * c + z * s;
|
|
v[jj + 3 * i] = z * c - x * s;
|
|
}
|
|
z = PYTHAG(f, h);
|
|
w[j] = z;
|
|
if (z != 0.0) {
|
|
z = 1.0 / z;
|
|
c = f * z;
|
|
s = h * z;
|
|
}
|
|
f = (c * g) + (s * y);
|
|
x = (c * y) - (s * g);
|
|
for (jj = 0; jj < 3; jj++) {
|
|
y = a[jj + 3 * j];
|
|
z = a[jj + 3 * i];
|
|
a[jj + 3 * j] = y * c + z * s;
|
|
a[jj + 3 * i] = z * c - y * s;
|
|
}
|
|
}
|
|
rv1[l] = 0.0;
|
|
rv1[k] = f;
|
|
w[k] = x;
|
|
}
|
|
}
|
|
destU.set(a);
|
|
destV.set(v);
|
|
}
|
|
|
|
private static double PYTHAG(double a, double b) {
|
|
double at = Math.abs(a), bt = Math.abs(b), ct, result;
|
|
if (at > bt) {
|
|
ct = bt / at;
|
|
result = at * Math.sqrt(1.0 + ct * ct);
|
|
} else if (bt > 0.0) {
|
|
ct = at / bt;
|
|
result = bt * Math.sqrt(1.0 + ct * ct);
|
|
} else
|
|
result = 0.0;
|
|
return (result);
|
|
}
|
|
}
|
|
|
|
private final SvdDecomposition3d svdDecomposition3d = new SvdDecomposition3d();
|
|
private final double[] m = new double[9];
|
|
private final Matrix3d u = new Matrix3d();
|
|
private final Matrix3d v = new Matrix3d();
|
|
|
|
/**
|
|
* Compute the weighted average of all of the quaternions given in <code>qs</code> using the specified interpolation factors <code>weights</code>, and store the result in <code>dest</code>.
|
|
*
|
|
* @param qs
|
|
* the quaternions to interpolate over
|
|
* @param weights
|
|
* the weights of each individual quaternion in <code>qs</code>
|
|
* @param maxSvdIterations
|
|
* the maximum number of iterations in the Singular Value Decomposition step used by this method
|
|
* @param dest
|
|
* will hold the result
|
|
* @return dest
|
|
*/
|
|
public Quaterniond computeWeightedAverage(Quaterniond[] qs, double[] weights, int maxSvdIterations, Quaterniond dest) {
|
|
double m00 = 0.0, m01 = 0.0, m02 = 0.0;
|
|
double m10 = 0.0, m11 = 0.0, m12 = 0.0;
|
|
double m20 = 0.0, m21 = 0.0, m22 = 0.0;
|
|
// Sum the rotation matrices of qs
|
|
for (int i = 0; i < qs.length; i++) {
|
|
Quaterniond q = qs[i];
|
|
double dx = q.x + q.x;
|
|
double dy = q.y + q.y;
|
|
double dz = q.z + q.z;
|
|
double q00 = dx * q.x;
|
|
double q11 = dy * q.y;
|
|
double q22 = dz * q.z;
|
|
double q01 = dx * q.y;
|
|
double q02 = dx * q.z;
|
|
double q03 = dx * q.w;
|
|
double q12 = dy * q.z;
|
|
double q13 = dy * q.w;
|
|
double q23 = dz * q.w;
|
|
m00 += weights[i] * (1.0 - q11 - q22);
|
|
m01 += weights[i] * (q01 + q23);
|
|
m02 += weights[i] * (q02 - q13);
|
|
m10 += weights[i] * (q01 - q23);
|
|
m11 += weights[i] * (1.0 - q22 - q00);
|
|
m12 += weights[i] * (q12 + q03);
|
|
m20 += weights[i] * (q02 + q13);
|
|
m21 += weights[i] * (q12 - q03);
|
|
m22 += weights[i] * (1.0 - q11 - q00);
|
|
}
|
|
m[0] = m00;
|
|
m[1] = m01;
|
|
m[2] = m02;
|
|
m[3] = m10;
|
|
m[4] = m11;
|
|
m[5] = m12;
|
|
m[6] = m20;
|
|
m[7] = m21;
|
|
m[8] = m22;
|
|
// Compute the Singular Value Decomposition of 'm'
|
|
svdDecomposition3d.svd(m, maxSvdIterations, u, v);
|
|
// Compute rotation matrix
|
|
u.mul(v.transpose());
|
|
// Build quaternion from it
|
|
return dest.setFromNormalized(u).normalize();
|
|
}
|
|
|
|
}
|