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godot/thirdparty/thekla_atlas/nvmath/Fitting.cpp

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Import thekla_atlas As requested by reduz, an import of thekla_atlas into thirdparty/
2017-12-08 14:05:47 +00:00
// This code is in the public domain -- Ignacio Castaño <castano@gmail.com>
#include "Fitting.h"
#include "Vector.inl"
#include "Plane.inl"
#include "nvcore/Array.inl"
#include "nvcore/Utils.h" // max, swap
#include <float.h> // FLT_MAX
//#include <vector>
#include <string.h>
using namespace nv;
// @@ Move to EigenSolver.h
// @@ We should be able to do something cheaper...
static Vector3 estimatePrincipalComponent(const float * __restrict matrix)
{
const Vector3 row0(matrix[0], matrix[1], matrix[2]);
const Vector3 row1(matrix[1], matrix[3], matrix[4]);
const Vector3 row2(matrix[2], matrix[4], matrix[5]);
float r0 = lengthSquared(row0);
float r1 = lengthSquared(row1);
float r2 = lengthSquared(row2);
if (r0 > r1 && r0 > r2) return row0;
if (r1 > r2) return row1;
return row2;
}
static inline Vector3 firstEigenVector_PowerMethod(const float *__restrict matrix)
{
if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
{
return Vector3(0.0f);
}
Vector3 v = estimatePrincipalComponent(matrix);
const int NUM = 8;
for (int i = 0; i < NUM; i++)
{
float x = v.x * matrix[0] + v.y * matrix[1] + v.z * matrix[2];
float y = v.x * matrix[1] + v.y * matrix[3] + v.z * matrix[4];
float z = v.x * matrix[2] + v.y * matrix[4] + v.z * matrix[5];
float norm = max(max(x, y), z);
v = Vector3(x, y, z) / norm;
}
return v;
}
Vector3 nv::Fit::computeCentroid(int n, const Vector3 *__restrict points)
{
Vector3 centroid(0.0f);
for (int i = 0; i < n; i++)
{
centroid += points[i];
}
centroid /= float(n);
return centroid;
}
Vector3 nv::Fit::computeCentroid(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
{
Vector3 centroid(0.0f);
float total = 0.0f;
for (int i = 0; i < n; i++)
{
total += weights[i];
centroid += weights[i]*points[i];
}
centroid /= total;
return centroid;
}
Vector4 nv::Fit::computeCentroid(int n, const Vector4 *__restrict points)
{
Vector4 centroid(0.0f);
for (int i = 0; i < n; i++)
{
centroid += points[i];
}
centroid /= float(n);
return centroid;
}
Vector4 nv::Fit::computeCentroid(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric)
{
Vector4 centroid(0.0f);
float total = 0.0f;
for (int i = 0; i < n; i++)
{
total += weights[i];
centroid += weights[i]*points[i];
}
centroid /= total;
return centroid;
}
Vector3 nv::Fit::computeCovariance(int n, const Vector3 *__restrict points, float *__restrict covariance)
{
// compute the centroid
Vector3 centroid = computeCentroid(n, points);
// compute covariance matrix
for (int i = 0; i < 6; i++)
{
covariance[i] = 0.0f;
}
for (int i = 0; i < n; i++)
{
Vector3 v = points[i] - centroid;
covariance[0] += v.x * v.x;
covariance[1] += v.x * v.y;
covariance[2] += v.x * v.z;
covariance[3] += v.y * v.y;
covariance[4] += v.y * v.z;
covariance[5] += v.z * v.z;
}
return centroid;
}
Vector3 nv::Fit::computeCovariance(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric, float *__restrict covariance)
{
// compute the centroid
Vector3 centroid = computeCentroid(n, points, weights, metric);
// compute covariance matrix
for (int i = 0; i < 6; i++)
{
covariance[i] = 0.0f;
}
for (int i = 0; i < n; i++)
{
Vector3 a = (points[i] - centroid) * metric;
Vector3 b = weights[i]*a;
covariance[0] += a.x * b.x;
covariance[1] += a.x * b.y;
covariance[2] += a.x * b.z;
covariance[3] += a.y * b.y;
covariance[4] += a.y * b.z;
covariance[5] += a.z * b.z;
}
return centroid;
}
Vector4 nv::Fit::computeCovariance(int n, const Vector4 *__restrict points, float *__restrict covariance)
{
// compute the centroid
Vector4 centroid = computeCentroid(n, points);
// compute covariance matrix
for (int i = 0; i < 10; i++)
{
covariance[i] = 0.0f;
}
for (int i = 0; i < n; i++)
{
Vector4 v = points[i] - centroid;
covariance[0] += v.x * v.x;
covariance[1] += v.x * v.y;
covariance[2] += v.x * v.z;
covariance[3] += v.x * v.w;
covariance[4] += v.y * v.y;
covariance[5] += v.y * v.z;
covariance[6] += v.y * v.w;
covariance[7] += v.z * v.z;
covariance[8] += v.z * v.w;
covariance[9] += v.w * v.w;
}
return centroid;
}
Vector4 nv::Fit::computeCovariance(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric, float *__restrict covariance)
{
// compute the centroid
Vector4 centroid = computeCentroid(n, points, weights, metric);
// compute covariance matrix
for (int i = 0; i < 10; i++)
{
covariance[i] = 0.0f;
}
for (int i = 0; i < n; i++)
{
Vector4 a = (points[i] - centroid) * metric;
Vector4 b = weights[i]*a;
covariance[0] += a.x * b.x;
covariance[1] += a.x * b.y;
covariance[2] += a.x * b.z;
covariance[3] += a.x * b.w;
covariance[4] += a.y * b.y;
covariance[5] += a.y * b.z;
covariance[6] += a.y * b.w;
covariance[7] += a.z * b.z;
covariance[8] += a.z * b.w;
covariance[9] += a.w * b.w;
}
return centroid;
}
Vector3 nv::Fit::computePrincipalComponent_PowerMethod(int n, const Vector3 *__restrict points)
{
float matrix[6];
computeCovariance(n, points, matrix);
return firstEigenVector_PowerMethod(matrix);
}
Vector3 nv::Fit::computePrincipalComponent_PowerMethod(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
{
float matrix[6];
computeCovariance(n, points, weights, metric, matrix);
return firstEigenVector_PowerMethod(matrix);
}
static inline Vector3 firstEigenVector_EigenSolver3(const float *__restrict matrix)
{
if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
{
return Vector3(0.0f);
}
float eigenValues[3];
Vector3 eigenVectors[3];
if (!nv::Fit::eigenSolveSymmetric3(matrix, eigenValues, eigenVectors))
{
return Vector3(0.0f);
}
return eigenVectors[0];
}
Vector3 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector3 *__restrict points)
{
float matrix[6];
computeCovariance(n, points, matrix);
return firstEigenVector_EigenSolver3(matrix);
}
Vector3 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric)
{
float matrix[6];
computeCovariance(n, points, weights, metric, matrix);
return firstEigenVector_EigenSolver3(matrix);
}
static inline Vector4 firstEigenVector_EigenSolver4(const float *__restrict matrix)
{
if (matrix[0] == 0 && matrix[4] == 0 && matrix[7] == 0&& matrix[9] == 0)
{
return Vector4(0.0f);
}
float eigenValues[4];
Vector4 eigenVectors[4];
if (!nv::Fit::eigenSolveSymmetric4(matrix, eigenValues, eigenVectors))
{
return Vector4(0.0f);
}
return eigenVectors[0];
}
Vector4 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector4 *__restrict points)
{
float matrix[10];
computeCovariance(n, points, matrix);
return firstEigenVector_EigenSolver4(matrix);
}
Vector4 nv::Fit::computePrincipalComponent_EigenSolver(int n, const Vector4 *__restrict points, const float *__restrict weights, Vector4::Arg metric)
{
float matrix[10];
computeCovariance(n, points, weights, metric, matrix);
return firstEigenVector_EigenSolver4(matrix);
}
void ArvoSVD(int rows, int cols, float * Q, float * diag, float * R);
Vector3 nv::Fit::computePrincipalComponent_SVD(int n, const Vector3 *__restrict points)
{
// Store the points in an n x n matrix
Array<float> Q; Q.resize(n*n, 0.0f);
for (int i = 0; i < n; ++i)
{
Q[i*n+0] = points[i].x;
Q[i*n+1] = points[i].y;
Q[i*n+2] = points[i].z;
}
// Alloc space for the SVD outputs
Array<float> diag; diag.resize(n, 0.0f);
Array<float> R; R.resize(n*n, 0.0f);
ArvoSVD(n, n, &Q[0], &diag[0], &R[0]);
// Get the principal component
return Vector3(R[0], R[1], R[2]);
}
Vector4 nv::Fit::computePrincipalComponent_SVD(int n, const Vector4 *__restrict points)
{
// Store the points in an n x n matrix
Array<float> Q; Q.resize(n*n, 0.0f);
for (int i = 0; i < n; ++i)
{
Q[i*n+0] = points[i].x;
Q[i*n+1] = points[i].y;
Q[i*n+2] = points[i].z;
Q[i*n+3] = points[i].w;
}
// Alloc space for the SVD outputs
Array<float> diag; diag.resize(n, 0.0f);
Array<float> R; R.resize(n*n, 0.0f);
ArvoSVD(n, n, &Q[0], &diag[0], &R[0]);
// Get the principal component
return Vector4(R[0], R[1], R[2], R[3]);
}
Plane nv::Fit::bestPlane(int n, const Vector3 *__restrict points)
{
// compute the centroid and covariance
float matrix[6];
Vector3 centroid = computeCovariance(n, points, matrix);
if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
{
// If no plane defined, then return a horizontal plane.
return Plane(Vector3(0, 0, 1), centroid);
}
float eigenValues[3];
Vector3 eigenVectors[3];
if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
// If no plane defined, then return a horizontal plane.
return Plane(Vector3(0, 0, 1), centroid);
}
return Plane(eigenVectors[2], centroid);
}
bool nv::Fit::isPlanar(int n, const Vector3 * points, float epsilon/*=NV_EPSILON*/)
{
// compute the centroid and covariance
float matrix[6];
computeCovariance(n, points, matrix);
float eigenValues[3];
Vector3 eigenVectors[3];
if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors)) {
return false;
}
return eigenValues[2] < epsilon;
}
// Tridiagonal solver from Charles Bloom.
// Householder transforms followed by QL decomposition.
// Seems to be based on the code from Numerical Recipes in C.
static void EigenSolver3_Tridiagonal(float mat[3][3], float * diag, float * subd);
static bool EigenSolver3_QLAlgorithm(float mat[3][3], float * diag, float * subd);
bool nv::Fit::eigenSolveSymmetric3(const float matrix[6], float eigenValues[3], Vector3 eigenVectors[3])
{
nvDebugCheck(matrix != NULL && eigenValues != NULL && eigenVectors != NULL);
float subd[3];
float diag[3];
float work[3][3];
work[0][0] = matrix[0];
work[0][1] = work[1][0] = matrix[1];
work[0][2] = work[2][0] = matrix[2];
work[1][1] = matrix[3];
work[1][2] = work[2][1] = matrix[4];
work[2][2] = matrix[5];
EigenSolver3_Tridiagonal(work, diag, subd);
if (!EigenSolver3_QLAlgorithm(work, diag, subd))
{
for (int i = 0; i < 3; i++) {
eigenValues[i] = 0;
eigenVectors[i] = Vector3(0);
}
return false;
}
for (int i = 0; i < 3; i++) {
eigenValues[i] = (float)diag[i];
}
// eigenvectors are the columns; make them the rows :
for (int i=0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
eigenVectors[j].component[i] = (float) work[i][j];
}
}
// shuffle to sort by singular value :
if (eigenValues[2] > eigenValues[0] && eigenValues[2] > eigenValues[1])
{
swap(eigenValues[0], eigenValues[2]);
swap(eigenVectors[0], eigenVectors[2]);
}
if (eigenValues[1] > eigenValues[0])
{
swap(eigenValues[0], eigenValues[1]);
swap(eigenVectors[0], eigenVectors[1]);
}
if (eigenValues[2] > eigenValues[1])
{
swap(eigenValues[1], eigenValues[2]);
swap(eigenVectors[1], eigenVectors[2]);
}
nvDebugCheck(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2]);
nvDebugCheck(eigenValues[1] >= eigenValues[2]);
return true;
}
static void EigenSolver3_Tridiagonal(float mat[3][3], float * diag, float * subd)
{
// Householder reduction T = Q^t M Q
// Input:
// mat, symmetric 3x3 matrix M
// Output:
// mat, orthogonal matrix Q
// diag, diagonal entries of T
// subd, subdiagonal entries of T (T is symmetric)
const float epsilon = 1e-08f;
float a = mat[0][0];
float b = mat[0][1];
float c = mat[0][2];
float d = mat[1][1];
float e = mat[1][2];
float f = mat[2][2];
diag[0] = a;
subd[2] = 0.f;
if (fabsf(c) >= epsilon)
{
const float ell = sqrtf(b*b+c*c);
b /= ell;
c /= ell;
const float q = 2*b*e+c*(f-d);
diag[1] = d+c*q;
diag[2] = f-c*q;
subd[0] = ell;
subd[1] = e-b*q;
mat[0][0] = 1; mat[0][1] = 0; mat[0][2] = 0;
mat[1][0] = 0; mat[1][1] = b; mat[1][2] = c;
mat[2][0] = 0; mat[2][1] = c; mat[2][2] = -b;
}
else
{
diag[1] = d;
diag[2] = f;
subd[0] = b;
subd[1] = e;
mat[0][0] = 1; mat[0][1] = 0; mat[0][2] = 0;
mat[1][0] = 0; mat[1][1] = 1; mat[1][2] = 0;
mat[2][0] = 0; mat[2][1] = 0; mat[2][2] = 1;
}
}
static bool EigenSolver3_QLAlgorithm(float mat[3][3], float * diag, float * subd)
{
// QL iteration with implicit shifting to reduce matrix from tridiagonal
// to diagonal
const int maxiter = 32;
for (int ell = 0; ell < 3; ell++)
{
int iter;
for (iter = 0; iter < maxiter; iter++)
{
int m;
for (m = ell; m <= 1; m++)
{
float dd = fabsf(diag[m]) + fabsf(diag[m+1]);
if ( fabsf(subd[m]) + dd == dd )
break;
}
if ( m == ell )
break;
float g = (diag[ell+1]-diag[ell])/(2*subd[ell]);
float r = sqrtf(g*g+1);
if ( g < 0 )
g = diag[m]-diag[ell]+subd[ell]/(g-r);
else
g = diag[m]-diag[ell]+subd[ell]/(g+r);
float s = 1, c = 1, p = 0;
for (int i = m-1; i >= ell; i--)
{
float f = s*subd[i], b = c*subd[i];
if ( fabsf(f) >= fabsf(g) )
{
c = g/f;
r = sqrtf(c*c+1);
subd[i+1] = f*r;
c *= (s = 1/r);
}
else
{
s = f/g;
r = sqrtf(s*s+1);
subd[i+1] = g*r;
s *= (c = 1/r);
}
g = diag[i+1]-p;
r = (diag[i]-g)*s+2*b*c;
p = s*r;
diag[i+1] = g+p;
g = c*r-b;
for (int k = 0; k < 3; k++)
{
f = mat[k][i+1];
mat[k][i+1] = s*mat[k][i]+c*f;
mat[k][i] = c*mat[k][i]-s*f;
}
}
diag[ell] -= p;
subd[ell] = g;
subd[m] = 0;
}
if ( iter == maxiter )
// should not get here under normal circumstances
return false;
}
return true;
}
// Tridiagonal solver for 4x4 symmetric matrices.
static void EigenSolver4_Tridiagonal(float mat[4][4], float * diag, float * subd);
static bool EigenSolver4_QLAlgorithm(float mat[4][4], float * diag, float * subd);
bool nv::Fit::eigenSolveSymmetric4(const float matrix[10], float eigenValues[4], Vector4 eigenVectors[4])
{
nvDebugCheck(matrix != NULL && eigenValues != NULL && eigenVectors != NULL);
float subd[4];
float diag[4];
float work[4][4];
work[0][0] = matrix[0];
work[0][1] = work[1][0] = matrix[1];
work[0][2] = work[2][0] = matrix[2];
work[0][3] = work[3][0] = matrix[3];
work[1][1] = matrix[4];
work[1][2] = work[2][1] = matrix[5];
work[1][3] = work[3][1] = matrix[6];
work[2][2] = matrix[7];
work[2][3] = work[3][2] = matrix[8];
work[3][3] = matrix[9];
EigenSolver4_Tridiagonal(work, diag, subd);
if (!EigenSolver4_QLAlgorithm(work, diag, subd))
{
for (int i = 0; i < 4; i++) {
eigenValues[i] = 0;
eigenVectors[i] = Vector4(0);
}
return false;
}
for (int i = 0; i < 4; i++) {
eigenValues[i] = (float)diag[i];
}
// eigenvectors are the columns; make them the rows
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
eigenVectors[j].component[i] = (float) work[i][j];
}
}
// sort by singular value
for (int i = 0; i < 3; ++i)
{
for (int j = i+1; j < 4; ++j)
{
if (eigenValues[j] > eigenValues[i])
{
swap(eigenValues[i], eigenValues[j]);
swap(eigenVectors[i], eigenVectors[j]);
}
}
}
nvDebugCheck(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2] && eigenValues[0] >= eigenValues[3]);
nvDebugCheck(eigenValues[1] >= eigenValues[2] && eigenValues[1] >= eigenValues[3]);
nvDebugCheck(eigenValues[2] >= eigenValues[2]);
return true;
}
#include "nvmath/Matrix.inl"
inline float signNonzero(float x)
{
return (x >= 0.0f) ? 1.0f : -1.0f;
}
static void EigenSolver4_Tridiagonal(float mat[4][4], float * diag, float * subd)
{
// Householder reduction T = Q^t M Q
// Input:
// mat, symmetric 3x3 matrix M
// Output:
// mat, orthogonal matrix Q
// diag, diagonal entries of T
// subd, subdiagonal entries of T (T is symmetric)
static const int n = 4;
// Set epsilon relative to size of elements in matrix
static const float relEpsilon = 1e-6f;
float maxElement = FLT_MAX;
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
maxElement = max(maxElement, fabsf(mat[i][j]));
float epsilon = relEpsilon * maxElement;
// Iterative algorithm, works for any size of matrix but might be slower than
// a closed-form solution for symmetric 4x4 matrices. Based on this article:
// http://en.wikipedia.org/wiki/Householder_transformation#Tridiagonalization
Matrix A, Q(identity);
memcpy(&A, mat, sizeof(float)*n*n);
// We proceed from left to right, making the off-tridiagonal entries zero in
// one column of the matrix at a time.
for (int k = 0; k < n - 2; ++k)
{
float sum = 0.0f;
for (int j = k+1; j < n; ++j)
sum += A(j,k)*A(j,k);
float alpha = -signNonzero(A(k+1,k)) * sqrtf(sum);
float r = sqrtf(0.5f * (alpha*alpha - A(k+1,k)*alpha));
// If r is zero, skip this column - already in tridiagonal form
if (fabsf(r) < epsilon)
continue;
float v[n] = {};
v[k+1] = 0.5f * (A(k+1,k) - alpha) / r;
for (int j = k+2; j < n; ++j)
v[j] = 0.5f * A(j,k) / r;
Matrix P(identity);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
P(i,j) -= 2.0f * v[i] * v[j];
A = mul(mul(P, A), P);
Q = mul(Q, P);
}
nvDebugCheck(fabsf(A(2,0)) < epsilon);
nvDebugCheck(fabsf(A(0,2)) < epsilon);
nvDebugCheck(fabsf(A(3,0)) < epsilon);
nvDebugCheck(fabsf(A(0,3)) < epsilon);
nvDebugCheck(fabsf(A(3,1)) < epsilon);
nvDebugCheck(fabsf(A(1,3)) < epsilon);
for (int i = 0; i < n; ++i)
diag[i] = A(i,i);
for (int i = 0; i < n - 1; ++i)
subd[i] = A(i+1,i);
subd[n-1] = 0.0f;
memcpy(mat, &Q, sizeof(float)*n*n);
}
static bool EigenSolver4_QLAlgorithm(float mat[4][4], float * diag, float * subd)
{
// QL iteration with implicit shifting to reduce matrix from tridiagonal
// to diagonal
const int maxiter = 32;
for (int ell = 0; ell < 4; ell++)
{
int iter;
for (iter = 0; iter < maxiter; iter++)
{
int m;
for (m = ell; m < 3; m++)
{
float dd = fabsf(diag[m]) + fabsf(diag[m+1]);
if ( fabsf(subd[m]) + dd == dd )
break;
}
if ( m == ell )
break;
float g = (diag[ell+1]-diag[ell])/(2*subd[ell]);
float r = sqrtf(g*g+1);
if ( g < 0 )
g = diag[m]-diag[ell]+subd[ell]/(g-r);
else
g = diag[m]-diag[ell]+subd[ell]/(g+r);
float s = 1, c = 1, p = 0;
for (int i = m-1; i >= ell; i--)
{
float f = s*subd[i], b = c*subd[i];
if ( fabsf(f) >= fabsf(g) )
{
c = g/f;
r = sqrtf(c*c+1);
subd[i+1] = f*r;
c *= (s = 1/r);
}
else
{
s = f/g;
r = sqrtf(s*s+1);
subd[i+1] = g*r;
s *= (c = 1/r);
}
g = diag[i+1]-p;
r = (diag[i]-g)*s+2*b*c;
p = s*r;
diag[i+1] = g+p;
g = c*r-b;
for (int k = 0; k < 4; k++)
{
f = mat[k][i+1];
mat[k][i+1] = s*mat[k][i]+c*f;
mat[k][i] = c*mat[k][i]-s*f;
}
}
diag[ell] -= p;
subd[ell] = g;
subd[m] = 0;
}
if ( iter == maxiter )
// should not get here under normal circumstances
return false;
}
return true;
}
int nv::Fit::compute4Means(int n, const Vector3 *__restrict points, const float *__restrict weights, Vector3::Arg metric, Vector3 *__restrict cluster)
{
// Compute principal component.
float matrix[6];
Vector3 centroid = computeCovariance(n, points, weights, metric, matrix);
Vector3 principal = firstEigenVector_PowerMethod(matrix);
// Pick initial solution.
int mini, maxi;
mini = maxi = 0;
float mindps, maxdps;
mindps = maxdps = dot(points[0] - centroid, principal);
for (int i = 1; i < n; ++i)
{
float dps = dot(points[i] - centroid, principal);
if (dps < mindps) {
mindps = dps;
mini = i;
}
else {
maxdps = dps;
maxi = i;
}
}
cluster[0] = centroid + mindps * principal;
cluster[1] = centroid + maxdps * principal;
cluster[2] = (2.0f * cluster[0] + cluster[1]) / 3.0f;
cluster[3] = (2.0f * cluster[1] + cluster[0]) / 3.0f;
// Now we have to iteratively refine the clusters.
while (true)
{
Vector3 newCluster[4] = { Vector3(0.0f), Vector3(0.0f), Vector3(0.0f), Vector3(0.0f) };
float total[4] = {0, 0, 0, 0};
for (int i = 0; i < n; ++i)
{
// Find nearest cluster.
int nearest = 0;
float mindist = FLT_MAX;
for (int j = 0; j < 4; j++)
{
float dist = lengthSquared((cluster[j] - points[i]) * metric);
if (dist < mindist)
{
mindist = dist;
nearest = j;
}
}
newCluster[nearest] += weights[i] * points[i];
total[nearest] += weights[i];
}
for (int j = 0; j < 4; j++)
{
if (total[j] != 0)
newCluster[j] /= total[j];
}
if (equal(cluster[0], newCluster[0]) && equal(cluster[1], newCluster[1]) &&
equal(cluster[2], newCluster[2]) && equal(cluster[3], newCluster[3]))
{
return (total[0] != 0) + (total[1] != 0) + (total[2] != 0) + (total[3] != 0);
}
cluster[0] = newCluster[0];
cluster[1] = newCluster[1];
cluster[2] = newCluster[2];
cluster[3] = newCluster[3];
// Sort clusters by weight.
for (int i = 0; i < 4; i++)
{
for (int j = i; j > 0 && total[j] > total[j - 1]; j--)
{
swap( total[j], total[j - 1] );
swap( cluster[j], cluster[j - 1] );
}
}
}
}
// Adaptation of James Arvo's SVD code, as found in ZOH.
inline float Sqr(float x) { return x*x; }
inline float svd_pythag( float a, float b )
{
float at = fabsf(a);
float bt = fabsf(b);
if( at > bt )
return at * sqrtf( 1.0f + Sqr( bt / at ) );
else if( bt > 0.0f )
return bt * sqrtf( 1.0f + Sqr( at / bt ) );
else return 0.0f;
}
inline float SameSign( float a, float b )
{
float t;
if( b >= 0.0f ) t = fabsf( a );
else t = -fabsf( a );
return t;
}
void ArvoSVD(int rows, int cols, float * Q, float * diag, float * R)
{
static const int MaxIterations = 30;
int i, j, k, l, p, q, iter;
float c, f, h, s, x, y, z;
float norm = 0.0f;
float g = 0.0f;
float scale = 0.0f;
Array<float> temp; temp.resize(cols, 0.0f);
for( i = 0; i < cols; i++ )
{
temp[i] = scale * g;
scale = 0.0f;
g = 0.0f;
s = 0.0f;
l = i + 1;
if( i < rows )
{
for( k = i; k < rows; k++ ) scale += fabsf( Q[k*cols+i] );
if( scale != 0.0f )
{
for( k = i; k < rows; k++ )
{
Q[k*cols+i] /= scale;
s += Sqr( Q[k*cols+i] );
}
f = Q[i*cols+i];
g = -SameSign( sqrtf(s), f );
h = f * g - s;
Q[i*cols+i] = f - g;
if( i != cols - 1 )
{
for( j = l; j < cols; j++ )
{
s = 0.0f;
for( k = i; k < rows; k++ ) s += Q[k*cols+i] * Q[k*cols+j];
f = s / h;
for( k = i; k < rows; k++ ) Q[k*cols+j] += f * Q[k*cols+i];
}
}
for( k = i; k < rows; k++ ) Q[k*cols+i] *= scale;
}
}
diag[i] = scale * g;
g = 0.0f;
s = 0.0f;
scale = 0.0f;
if( i < rows && i != cols - 1 )
{
for( k = l; k < cols; k++ ) scale += fabsf( Q[i*cols+k] );
if( scale != 0.0f )
{
for( k = l; k < cols; k++ )
{
Q[i*cols+k] /= scale;
s += Sqr( Q[i*cols+k] );
}
f = Q[i*cols+l];
g = -SameSign( sqrtf(s), f );
h = f * g - s;
Q[i*cols+l] = f - g;
for( k = l; k < cols; k++ ) temp[k] = Q[i*cols+k] / h;
if( i != rows - 1 )
{
for( j = l; j < rows; j++ )
{
s = 0.0f;
for( k = l; k < cols; k++ ) s += Q[j*cols+k] * Q[i*cols+k];
for( k = l; k < cols; k++ ) Q[j*cols+k] += s * temp[k];
}
}
for( k = l; k < cols; k++ ) Q[i*cols+k] *= scale;
}
}
norm = max( norm, fabsf( diag[i] ) + fabsf( temp[i] ) );
}
for( i = cols - 1; i >= 0; i-- )
{
if( i < cols - 1 )
{
if( g != 0.0f )
{
for( j = l; j < cols; j++ ) R[i*cols+j] = ( Q[i*cols+j] / Q[i*cols+l] ) / g;
for( j = l; j < cols; j++ )
{
s = 0.0f;
for( k = l; k < cols; k++ ) s += Q[i*cols+k] * R[j*cols+k];
for( k = l; k < cols; k++ ) R[j*cols+k] += s * R[i*cols+k];
}
}
for( j = l; j < cols; j++ )
{
R[i*cols+j] = 0.0f;
R[j*cols+i] = 0.0f;
}
}
R[i*cols+i] = 1.0f;
g = temp[i];
l = i;
}
for( i = cols - 1; i >= 0; i-- )
{
l = i + 1;
g = diag[i];
if( i < cols - 1 ) for( j = l; j < cols; j++ ) Q[i*cols+j] = 0.0f;
if( g != 0.0f )
{
g = 1.0f / g;
if( i != cols - 1 )
{
for( j = l; j < cols; j++ )
{
s = 0.0f;
for( k = l; k < rows; k++ ) s += Q[k*cols+i] * Q[k*cols+j];
f = ( s / Q[i*cols+i] ) * g;
for( k = i; k < rows; k++ ) Q[k*cols+j] += f * Q[k*cols+i];
}
}
for( j = i; j < rows; j++ ) Q[j*cols+i] *= g;
}
else
{
for( j = i; j < rows; j++ ) Q[j*cols+i] = 0.0f;
}
Q[i*cols+i] += 1.0f;
}
for( k = cols - 1; k >= 0; k-- )
{
for( iter = 1; iter <= MaxIterations; iter++ )
{
int jump = 0;
for( l = k; l >= 0; l-- )
{
q = l - 1;
if( fabsf( temp[l] ) + norm == norm ) { jump = 1; break; }
if( fabsf( diag[q] ) + norm == norm ) { jump = 0; break; }
}
if( !jump )
{
c = 0.0f;
s = 1.0f;
for( i = l; i <= k; i++ )
{
f = s * temp[i];
temp[i] *= c;
if( fabsf( f ) + norm == norm ) break;
g = diag[i];
h = svd_pythag( f, g );
diag[i] = h;
h = 1.0f / h;
c = g * h;
s = -f * h;
for( j = 0; j < rows; j++ )
{
y = Q[j*cols+q];
z = Q[j*cols+i];
Q[j*cols+q] = y * c + z * s;
Q[j*cols+i] = z * c - y * s;
}
}
}
z = diag[k];
if( l == k )
{
if( z < 0.0f )
{
diag[k] = -z;
for( j = 0; j < cols; j++ ) R[k*cols+j] *= -1.0f;
}
break;
}
if( iter >= MaxIterations ) return;
x = diag[l];
q = k - 1;
y = diag[q];
g = temp[q];
h = temp[k];
f = ( ( y - z ) * ( y + z ) + ( g - h ) * ( g + h ) ) / ( 2.0f * h * y );
g = svd_pythag( f, 1.0f );
f = ( ( x - z ) * ( x + z ) + h * ( ( y / ( f + SameSign( g, f ) ) ) - h ) ) / x;
c = 1.0f;
s = 1.0f;
for( j = l; j <= q; j++ )
{
i = j + 1;
g = temp[i];
y = diag[i];
h = s * g;
g = c * g;
z = svd_pythag( f, h );
temp[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( p = 0; p < cols; p++ )
{
x = R[j*cols+p];
z = R[i*cols+p];
R[j*cols+p] = x * c + z * s;
R[i*cols+p] = z * c - x * s;
}
z = svd_pythag( f, h );
diag[j] = z;
if( z != 0.0f )
{
z = 1.0f / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
for( p = 0; p < rows; p++ )
{
y = Q[p*cols+j];
z = Q[p*cols+i];
Q[p*cols+j] = y * c + z * s;
Q[p*cols+i] = z * c - y * s;
}
}
temp[l] = 0.0f;
temp[k] = f;
diag[k] = x;
}
}
// Sort the singular values into descending order.
for( i = 0; i < cols - 1; i++ )
{
float biggest = diag[i]; // Biggest singular value so far.
int bindex = i; // The row/col it occurred in.
for( j = i + 1; j < cols; j++ )
{
if( diag[j] > biggest )
{
biggest = diag[j];
bindex = j;
}
}
if( bindex != i ) // Need to swap rows and columns.
{
// Swap columns in Q.
for (int j = 0; j < rows; ++j)
swap(Q[j*cols+i], Q[j*cols+bindex]);
// Swap rows in R.
for (int j = 0; j < rows; ++j)
swap(R[i*cols+j], R[bindex*cols+j]);
// Swap elements in diag.
swap(diag[i], diag[bindex]);
}
}
}