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6b655ca62cb5e480ab3da95d8afd98713a835025
blender-archive/source/blender/physics/intern/implicit_blender.c
Campbell Barton 6b655ca62c Cleanup: style
2015-01-21 11:57:11 +11:00

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/*
* ***** BEGIN GPL LICENSE BLOCK *****
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* The Original Code is Copyright (C) Blender Foundation
* All rights reserved.
*
* The Original Code is: all of this file.
*
* Contributor(s): none yet.
*
* ***** END GPL LICENSE BLOCK *****
*/
/** \file blender/physics/intern/implicit_blender.c
* \ingroup bph
*/
#include "implicit.h"
#ifdef IMPLICIT_SOLVER_BLENDER
#include "MEM_guardedalloc.h"
#include "DNA_scene_types.h"
#include "DNA_object_types.h"
#include "DNA_object_force.h"
#include "DNA_meshdata_types.h"
#include "DNA_texture_types.h"
#include "BLI_math.h"
#include "BLI_linklist.h"
#include "BLI_utildefines.h"
#include "BKE_cloth.h"
#include "BKE_collision.h"
#include "BKE_effect.h"
#include "BKE_global.h"
#include "BPH_mass_spring.h"
#ifdef __GNUC__
# pragma GCC diagnostic ignored "-Wtype-limits"
#endif
#ifdef _OPENMP
# define CLOTH_OPENMP_LIMIT 512
#endif
#if 0 /* debug timing */
#ifdef _WIN32
#include <windows.h>
static LARGE_INTEGER _itstart, _itend;
static LARGE_INTEGER ifreq;
static void itstart(void)
{
static int first = 1;
if (first) {
QueryPerformanceFrequency(&ifreq);
first = 0;
}
QueryPerformanceCounter(&_itstart);
}
static void itend(void)
{
QueryPerformanceCounter(&_itend);
}
double itval(void)
{
return ((double)_itend.QuadPart -
(double)_itstart.QuadPart)/((double)ifreq.QuadPart);
}
#else
#include <sys/time.h>
// intrinsics need better compile flag checking
// #include <xmmintrin.h>
// #include <pmmintrin.h>
// #include <pthread.h>
static struct timeval _itstart, _itend;
static struct timezone itz;
static void itstart(void)
{
gettimeofday(&_itstart, &itz);
}
static void itend(void)
{
gettimeofday(&_itend, &itz);
}
static double itval(void)
{
double t1, t2;
t1 = (double)_itstart.tv_sec + (double)_itstart.tv_usec/(1000*1000);
t2 = (double)_itend.tv_sec + (double)_itend.tv_usec/(1000*1000);
return t2-t1;
}
#endif
#endif /* debug timing */
static float I[3][3] = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
static float ZERO[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
/*
#define C99
#ifdef C99
#defineDO_INLINE inline
#else
#defineDO_INLINE static
#endif
*/
struct Cloth;
//////////////////////////////////////////
/* fast vector / matrix library, enhancements are welcome :) -dg */
/////////////////////////////////////////
/* DEFINITIONS */
typedef float lfVector[3];
typedef struct fmatrix3x3 {
float m[3][3]; /* 3x3 matrix */
unsigned int c, r; /* column and row number */
/* int pinned; // is this vertex allowed to move? */
float n1, n2, n3; /* three normal vectors for collision constrains */
unsigned int vcount; /* vertex count */
unsigned int scount; /* spring count */
} fmatrix3x3;
///////////////////////////
// float[3] vector
///////////////////////////
/* simple vector code */
/* STATUS: verified */
DO_INLINE void mul_fvector_S(float to[3], float from[3], float scalar)
{
to[0] = from[0] * scalar;
to[1] = from[1] * scalar;
to[2] = from[2] * scalar;
}
/* simple v^T * v product ("outer product") */
/* STATUS: HAS TO BE verified (*should* work) */
DO_INLINE void mul_fvectorT_fvector(float to[3][3], float vectorA[3], float vectorB[3])
{
mul_fvector_S(to[0], vectorB, vectorA[0]);
mul_fvector_S(to[1], vectorB, vectorA[1]);
mul_fvector_S(to[2], vectorB, vectorA[2]);
}
/* simple v^T * v product with scalar ("outer product") */
/* STATUS: HAS TO BE verified (*should* work) */
DO_INLINE void mul_fvectorT_fvectorS(float to[3][3], float vectorA[3], float vectorB[3], float aS)
{
mul_fvectorT_fvector(to, vectorA, vectorB);
mul_fvector_S(to[0], to[0], aS);
mul_fvector_S(to[1], to[1], aS);
mul_fvector_S(to[2], to[2], aS);
}
#if 0
/* printf vector[3] on console: for debug output */
static void print_fvector(float m3[3])
{
printf("%f\n%f\n%f\n\n", m3[0], m3[1], m3[2]);
}
///////////////////////////
// long float vector float (*)[3]
///////////////////////////
/* print long vector on console: for debug output */
DO_INLINE void print_lfvector(float (*fLongVector)[3], unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
print_fvector(fLongVector[i]);
}
}
#endif
/* create long vector */
DO_INLINE lfVector *create_lfvector(unsigned int verts)
{
/* TODO: check if memory allocation was successful */
return (lfVector *)MEM_callocN(verts * sizeof(lfVector), "cloth_implicit_alloc_vector");
// return (lfVector *)cloth_aligned_malloc(&MEMORY_BASE, verts * sizeof(lfVector));
}
/* delete long vector */
DO_INLINE void del_lfvector(float (*fLongVector)[3])
{
if (fLongVector != NULL) {
MEM_freeN(fLongVector);
// cloth_aligned_free(&MEMORY_BASE, fLongVector);
}
}
/* copy long vector */
DO_INLINE void cp_lfvector(float (*to)[3], float (*from)[3], unsigned int verts)
{
memcpy(to, from, verts * sizeof(lfVector));
}
/* init long vector with float[3] */
DO_INLINE void init_lfvector(float (*fLongVector)[3], float vector[3], unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
copy_v3_v3(fLongVector[i], vector);
}
}
/* zero long vector with float[3] */
DO_INLINE void zero_lfvector(float (*to)[3], unsigned int verts)
{
memset(to, 0.0f, verts * sizeof(lfVector));
}
/* multiply long vector with scalar*/
DO_INLINE void mul_lfvectorS(float (*to)[3], float (*fLongVector)[3], float scalar, unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
mul_fvector_S(to[i], fLongVector[i], scalar);
}
}
/* multiply long vector with scalar*/
/* A -= B * float */
DO_INLINE void submul_lfvectorS(float (*to)[3], float (*fLongVector)[3], float scalar, unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
VECSUBMUL(to[i], fLongVector[i], scalar);
}
}
/* dot product for big vector */
DO_INLINE float dot_lfvector(float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts)
{
long i = 0;
float temp = 0.0;
// XXX brecht, disabled this for now (first schedule line was already disabled),
// due to non-commutative nature of floating point ops this makes the sim give
// different results each time you run it!
// schedule(guided, 2)
//#pragma omp parallel for reduction(+: temp) if (verts > CLOTH_OPENMP_LIMIT)
for (i = 0; i < (long)verts; i++) {
temp += dot_v3v3(fLongVectorA[i], fLongVectorB[i]);
}
return temp;
}
/* A = B + C --> for big vector */
DO_INLINE void add_lfvector_lfvector(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
VECADD(to[i], fLongVectorA[i], fLongVectorB[i]);
}
}
/* A = B + C * float --> for big vector */
DO_INLINE void add_lfvector_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], float bS, unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
VECADDS(to[i], fLongVectorA[i], fLongVectorB[i], bS);
}
}
/* A = B * float + C * float --> for big vector */
DO_INLINE void add_lfvectorS_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float aS, float (*fLongVectorB)[3], float bS, unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
VECADDSS(to[i], fLongVectorA[i], aS, fLongVectorB[i], bS);
}
}
/* A = B - C * float --> for big vector */
DO_INLINE void sub_lfvector_lfvectorS(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], float bS, unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
VECSUBS(to[i], fLongVectorA[i], fLongVectorB[i], bS);
}
}
/* A = B - C --> for big vector */
DO_INLINE void sub_lfvector_lfvector(float (*to)[3], float (*fLongVectorA)[3], float (*fLongVectorB)[3], unsigned int verts)
{
unsigned int i = 0;
for (i = 0; i < verts; i++) {
sub_v3_v3v3(to[i], fLongVectorA[i], fLongVectorB[i]);
}
}
///////////////////////////
// 3x3 matrix
///////////////////////////
#if 0
/* printf 3x3 matrix on console: for debug output */
static void print_fmatrix(float m3[3][3])
{
printf("%f\t%f\t%f\n", m3[0][0], m3[0][1], m3[0][2]);
printf("%f\t%f\t%f\n", m3[1][0], m3[1][1], m3[1][2]);
printf("%f\t%f\t%f\n\n", m3[2][0], m3[2][1], m3[2][2]);
}
static void print_sparse_matrix(fmatrix3x3 *m)
{
if (m) {
unsigned int i;
for (i = 0; i < m[0].vcount + m[0].scount; i++) {
printf("%d:\n", i);
print_fmatrix(m[i].m);
}
}
}
#endif
#if 0
static void print_lvector(lfVector *v, int numverts)
{
int i;
for (i = 0; i < numverts; ++i) {
if (i > 0)
printf("\n");
printf("%f,\n", v[i][0]);
printf("%f,\n", v[i][1]);
printf("%f,\n", v[i][2]);
}
}
#endif
#if 0
static void print_bfmatrix(fmatrix3x3 *m)
{
int tot = m[0].vcount + m[0].scount;
int size = m[0].vcount * 3;
float *t = MEM_callocN(sizeof(float) * size*size, "bfmatrix");
int q, i, j;
for (q = 0; q < tot; ++q) {
int k = 3 * m[q].r;
int l = 3 * m[q].c;
for (j = 0; j < 3; ++j) {
for (i = 0; i < 3; ++i) {
// if (t[k + i + (l + j) * size] != 0.0f) {
// printf("warning: overwriting value at %d, %d\n", m[q].r, m[q].c);
// }
if (k == l) {
t[k + i + (k + j) * size] += m[q].m[i][j];
}
else {
t[k + i + (l + j) * size] += m[q].m[i][j];
t[l + j + (k + i) * size] += m[q].m[j][i];
}
}
}
}
for (j = 0; j < size; ++j) {
if (j > 0 && j % 3 == 0)
printf("\n");
for (i = 0; i < size; ++i) {
if (i > 0 && i % 3 == 0)
printf(" ");
implicit_print_matrix_elem(t[i + j * size]);
}
printf("\n");
}
MEM_freeN(t);
}
#endif
/* copy 3x3 matrix */
DO_INLINE void cp_fmatrix(float to[3][3], float from[3][3])
{
// memcpy(to, from, sizeof (float) * 9);
copy_v3_v3(to[0], from[0]);
copy_v3_v3(to[1], from[1]);
copy_v3_v3(to[2], from[2]);
}
/* copy 3x3 matrix */
DO_INLINE void initdiag_fmatrixS(float to[3][3], float aS)
{
cp_fmatrix(to, ZERO);
to[0][0] = aS;
to[1][1] = aS;
to[2][2] = aS;
}
#if 0
/* calculate determinant of 3x3 matrix */
DO_INLINE float det_fmatrix(float m[3][3])
{
return m[0][0]*m[1][1]*m[2][2] + m[1][0]*m[2][1]*m[0][2] + m[0][1]*m[1][2]*m[2][0] -
m[0][0]*m[1][2]*m[2][1] - m[0][1]*m[1][0]*m[2][2] - m[2][0]*m[1][1]*m[0][2];
}
DO_INLINE void inverse_fmatrix(float to[3][3], float from[3][3])
{
unsigned int i, j;
float d;
if ((d=det_fmatrix(from)) == 0) {
printf("can't build inverse");
exit(0);
}
for (i=0;i<3;i++) {
for (j=0;j<3;j++) {
int i1=(i+1)%3;
int i2=(i+2)%3;
int j1=(j+1)%3;
int j2=(j+2)%3;
// reverse indexs i&j to take transpose
to[j][i] = (from[i1][j1]*from[i2][j2]-from[i1][j2]*from[i2][j1])/d;
/*
if (i==j)
to[i][j] = 1.0f / from[i][j];
else
to[i][j] = 0;
*/
}
}
}
#endif
/* 3x3 matrix multiplied by a scalar */
/* STATUS: verified */
DO_INLINE void mul_fmatrix_S(float matrix[3][3], float scalar)
{
mul_fvector_S(matrix[0], matrix[0], scalar);
mul_fvector_S(matrix[1], matrix[1], scalar);
mul_fvector_S(matrix[2], matrix[2], scalar);
}
/* a vector multiplied by a 3x3 matrix */
/* STATUS: verified */
DO_INLINE void mul_fvector_fmatrix(float *to, float *from, float matrix[3][3])
{
to[0] = matrix[0][0]*from[0] + matrix[1][0]*from[1] + matrix[2][0]*from[2];
to[1] = matrix[0][1]*from[0] + matrix[1][1]*from[1] + matrix[2][1]*from[2];
to[2] = matrix[0][2]*from[0] + matrix[1][2]*from[1] + matrix[2][2]*from[2];
}
/* 3x3 matrix multiplied by a vector */
/* STATUS: verified */
DO_INLINE void mul_fmatrix_fvector(float *to, float matrix[3][3], float from[3])
{
to[0] = dot_v3v3(matrix[0], from);
to[1] = dot_v3v3(matrix[1], from);
to[2] = dot_v3v3(matrix[2], from);
}
/* 3x3 matrix addition with 3x3 matrix */
DO_INLINE void add_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
VECADD(to[0], matrixA[0], matrixB[0]);
VECADD(to[1], matrixA[1], matrixB[1]);
VECADD(to[2], matrixA[2], matrixB[2]);
}
/* A -= B*x + C*y (3x3 matrix sub-addition with 3x3 matrix) */
DO_INLINE void subadd_fmatrixS_fmatrixS(float to[3][3], float matrixA[3][3], float aS, float matrixB[3][3], float bS)
{
VECSUBADDSS(to[0], matrixA[0], aS, matrixB[0], bS);
VECSUBADDSS(to[1], matrixA[1], aS, matrixB[1], bS);
VECSUBADDSS(to[2], matrixA[2], aS, matrixB[2], bS);
}
/* A = B - C (3x3 matrix subtraction with 3x3 matrix) */
DO_INLINE void sub_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
sub_v3_v3v3(to[0], matrixA[0], matrixB[0]);
sub_v3_v3v3(to[1], matrixA[1], matrixB[1]);
sub_v3_v3v3(to[2], matrixA[2], matrixB[2]);
}
/////////////////////////////////////////////////////////////////
// special functions
/////////////////////////////////////////////////////////////////
/* 3x3 matrix multiplied+added by a vector */
/* STATUS: verified */
DO_INLINE void muladd_fmatrix_fvector(float to[3], float matrix[3][3], float from[3])
{
to[0] += dot_v3v3(matrix[0], from);
to[1] += dot_v3v3(matrix[1], from);
to[2] += dot_v3v3(matrix[2], from);
}
BLI_INLINE void outerproduct(float r[3][3], const float a[3], const float b[3])
{
mul_v3_v3fl(r[0], a, b[0]);
mul_v3_v3fl(r[1], a, b[1]);
mul_v3_v3fl(r[2], a, b[2]);
}
BLI_INLINE void cross_m3_v3m3(float r[3][3], const float v[3], float m[3][3])
{
cross_v3_v3v3(r[0], v, m[0]);
cross_v3_v3v3(r[1], v, m[1]);
cross_v3_v3v3(r[2], v, m[2]);
}
BLI_INLINE void cross_v3_identity(float r[3][3], const float v[3])
{
r[0][0] = 0.0f; r[1][0] = v[2]; r[2][0] = -v[1];
r[0][1] = -v[2]; r[1][1] = 0.0f; r[2][1] = v[0];
r[0][2] = v[1]; r[1][2] = -v[0]; r[2][2] = 0.0f;
}
BLI_INLINE void madd_m3_m3fl(float r[3][3], float m[3][3], float f)
{
r[0][0] += m[0][0] * f;
r[0][1] += m[0][1] * f;
r[0][2] += m[0][2] * f;
r[1][0] += m[1][0] * f;
r[1][1] += m[1][1] * f;
r[1][2] += m[1][2] * f;
r[2][0] += m[2][0] * f;
r[2][1] += m[2][1] * f;
r[2][2] += m[2][2] * f;
}
BLI_INLINE void madd_m3_m3m3fl(float r[3][3], float a[3][3], float b[3][3], float f)
{
r[0][0] = a[0][0] + b[0][0] * f;
r[0][1] = a[0][1] + b[0][1] * f;
r[0][2] = a[0][2] + b[0][2] * f;
r[1][0] = a[1][0] + b[1][0] * f;
r[1][1] = a[1][1] + b[1][1] * f;
r[1][2] = a[1][2] + b[1][2] * f;
r[2][0] = a[2][0] + b[2][0] * f;
r[2][1] = a[2][1] + b[2][1] * f;
r[2][2] = a[2][2] + b[2][2] * f;
}
/////////////////////////////////////////////////////////////////
///////////////////////////
// SPARSE SYMMETRIC big matrix with 3x3 matrix entries
///////////////////////////
/* printf a big matrix on console: for debug output */
#if 0
static void print_bfmatrix(fmatrix3x3 *m3)
{
unsigned int i = 0;
for (i = 0; i < m3[0].vcount + m3[0].scount; i++)
{
print_fmatrix(m3[i].m);
}
}
#endif
BLI_INLINE void init_fmatrix(fmatrix3x3 *matrix, int r, int c)
{
matrix->r = r;
matrix->c = c;
}
/* create big matrix */
DO_INLINE fmatrix3x3 *create_bfmatrix(unsigned int verts, unsigned int springs)
{
// TODO: check if memory allocation was successful */
fmatrix3x3 *temp = (fmatrix3x3 *)MEM_callocN(sizeof(fmatrix3x3) * (verts + springs), "cloth_implicit_alloc_matrix");
int i;
temp[0].vcount = verts;
temp[0].scount = springs;
/* vertex part of the matrix is diagonal blocks */
for (i = 0; i < verts; ++i) {
init_fmatrix(temp + i, i, i);
}
return temp;
}
/* delete big matrix */
DO_INLINE void del_bfmatrix(fmatrix3x3 *matrix)
{
if (matrix != NULL) {
MEM_freeN(matrix);
}
}
/* copy big matrix */
DO_INLINE void cp_bfmatrix(fmatrix3x3 *to, fmatrix3x3 *from)
{
// TODO bounds checking
memcpy(to, from, sizeof(fmatrix3x3) * (from[0].vcount+from[0].scount));
}
/* init big matrix */
// slow in parallel
DO_INLINE void init_bfmatrix(fmatrix3x3 *matrix, float m3[3][3])
{
unsigned int i;
for (i = 0; i < matrix[0].vcount+matrix[0].scount; i++) {
cp_fmatrix(matrix[i].m, m3);
}
}
/* init the diagonal of big matrix */
// slow in parallel
DO_INLINE void initdiag_bfmatrix(fmatrix3x3 *matrix, float m3[3][3])
{
unsigned int i, j;
float tmatrix[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
for (i = 0; i < matrix[0].vcount; i++) {
cp_fmatrix(matrix[i].m, m3);
}
for (j = matrix[0].vcount; j < matrix[0].vcount+matrix[0].scount; j++) {
cp_fmatrix(matrix[j].m, tmatrix);
}
}
/* SPARSE SYMMETRIC multiply big matrix with long vector*/
/* STATUS: verified */
DO_INLINE void mul_bfmatrix_lfvector( float (*to)[3], fmatrix3x3 *from, lfVector *fLongVector)
{
unsigned int i = 0;
unsigned int vcount = from[0].vcount;
lfVector *temp = create_lfvector(vcount);
zero_lfvector(to, vcount);
#pragma omp parallel sections private(i) if (vcount > CLOTH_OPENMP_LIMIT)
{
#pragma omp section
{
for (i = from[0].vcount; i < from[0].vcount+from[0].scount; i++) {
muladd_fmatrix_fvector(to[from[i].c], from[i].m, fLongVector[from[i].r]);
}
}
#pragma omp section
{
for (i = 0; i < from[0].vcount+from[0].scount; i++) {
muladd_fmatrix_fvector(temp[from[i].r], from[i].m, fLongVector[from[i].c]);
}
}
}
add_lfvector_lfvector(to, to, temp, from[0].vcount);
del_lfvector(temp);
}
/* SPARSE SYMMETRIC sub big matrix with big matrix*/
/* A -= B * float + C * float --> for big matrix */
/* VERIFIED */
DO_INLINE void subadd_bfmatrixS_bfmatrixS( fmatrix3x3 *to, fmatrix3x3 *from, float aS, fmatrix3x3 *matrix, float bS)
{
unsigned int i = 0;
/* process diagonal elements */
for (i = 0; i < matrix[0].vcount+matrix[0].scount; i++) {
subadd_fmatrixS_fmatrixS(to[i].m, from[i].m, aS, matrix[i].m, bS);
}
}
///////////////////////////////////////////////////////////////////
// simulator start
///////////////////////////////////////////////////////////////////
typedef struct Implicit_Data {
/* inputs */
fmatrix3x3 *bigI; /* identity (constant) */
fmatrix3x3 *tfm; /* local coordinate transform */
fmatrix3x3 *M; /* masses */
lfVector *F; /* forces */
fmatrix3x3 *dFdV, *dFdX; /* force jacobians */
int num_blocks; /* number of off-diagonal blocks (springs) */
/* motion state data */
lfVector *X, *Xnew; /* positions */
lfVector *V, *Vnew; /* velocities */
/* internal solver data */
lfVector *B; /* B for A*dV = B */
fmatrix3x3 *A; /* A for A*dV = B */
lfVector *dV; /* velocity change (solution of A*dV = B) */
lfVector *z; /* target velocity in constrained directions */
fmatrix3x3 *S; /* filtering matrix for constraints */
fmatrix3x3 *P, *Pinv; /* pre-conditioning matrix */
} Implicit_Data;
Implicit_Data *BPH_mass_spring_solver_create(int numverts, int numsprings)
{
Implicit_Data *id = (Implicit_Data *)MEM_callocN(sizeof(Implicit_Data), "implicit vecmat");
/* process diagonal elements */
id->tfm = create_bfmatrix(numverts, 0);
id->A = create_bfmatrix(numverts, numsprings);
id->dFdV = create_bfmatrix(numverts, numsprings);
id->dFdX = create_bfmatrix(numverts, numsprings);
id->S = create_bfmatrix(numverts, 0);
id->Pinv = create_bfmatrix(numverts, numsprings);
id->P = create_bfmatrix(numverts, numsprings);
id->bigI = create_bfmatrix(numverts, numsprings); // TODO 0 springs
id->M = create_bfmatrix(numverts, numsprings);
id->X = create_lfvector(numverts);
id->Xnew = create_lfvector(numverts);
id->V = create_lfvector(numverts);
id->Vnew = create_lfvector(numverts);
id->F = create_lfvector(numverts);
id->B = create_lfvector(numverts);
id->dV = create_lfvector(numverts);
id->z = create_lfvector(numverts);
initdiag_bfmatrix(id->bigI, I);
return id;
}
void BPH_mass_spring_solver_free(Implicit_Data *id)
{
del_bfmatrix(id->tfm);
del_bfmatrix(id->A);
del_bfmatrix(id->dFdV);
del_bfmatrix(id->dFdX);
del_bfmatrix(id->S);
del_bfmatrix(id->P);
del_bfmatrix(id->Pinv);
del_bfmatrix(id->bigI);
del_bfmatrix(id->M);
del_lfvector(id->X);
del_lfvector(id->Xnew);
del_lfvector(id->V);
del_lfvector(id->Vnew);
del_lfvector(id->F);
del_lfvector(id->B);
del_lfvector(id->dV);
del_lfvector(id->z);
MEM_freeN(id);
}
/* ==== Transformation from/to root reference frames ==== */
BLI_INLINE void world_to_root_v3(Implicit_Data *data, int index, float r[3], const float v[3])
{
copy_v3_v3(r, v);
mul_transposed_m3_v3(data->tfm[index].m, r);
}
BLI_INLINE void root_to_world_v3(Implicit_Data *data, int index, float r[3], const float v[3])
{
mul_v3_m3v3(r, data->tfm[index].m, v);
}
BLI_INLINE void world_to_root_m3(Implicit_Data *data, int index, float r[3][3], float m[3][3])
{
float trot[3][3];
copy_m3_m3(trot, data->tfm[index].m);
transpose_m3(trot);
mul_m3_m3m3(r, trot, m);
}
BLI_INLINE void root_to_world_m3(Implicit_Data *data, int index, float r[3][3], float m[3][3])
{
mul_m3_m3m3(r, data->tfm[index].m, m);
}
/* ================================ */
DO_INLINE void filter(lfVector *V, fmatrix3x3 *S)
{
unsigned int i=0;
for (i = 0; i < S[0].vcount; i++) {
mul_m3_v3(S[i].m, V[S[i].r]);
}
}
#if 0 /* this version of the CG algorithm does not work very well with partial constraints (where S has non-zero elements) */
static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S)
{
// Solves for unknown X in equation AX=B
unsigned int conjgrad_loopcount=0, conjgrad_looplimit=100;
float conjgrad_epsilon=0.0001f /* , conjgrad_lasterror=0 */ /* UNUSED */;
lfVector *q, *d, *tmp, *r;
float s, starget, a, s_prev;
unsigned int numverts = lA[0].vcount;
q = create_lfvector(numverts);
d = create_lfvector(numverts);
tmp = create_lfvector(numverts);
r = create_lfvector(numverts);
// zero_lfvector(ldV, CLOTHPARTICLES);
filter(ldV, S);
add_lfvector_lfvector(ldV, ldV, z, numverts);
// r = B - Mul(tmp, A, X); // just use B if X known to be zero
cp_lfvector(r, lB, numverts);
mul_bfmatrix_lfvector(tmp, lA, ldV);
sub_lfvector_lfvector(r, r, tmp, numverts);
filter(r, S);
cp_lfvector(d, r, numverts);
s = dot_lfvector(r, r, numverts);
starget = s * sqrtf(conjgrad_epsilon);
while (s>starget && conjgrad_loopcount < conjgrad_looplimit) {
// Mul(q, A, d); // q = A*d;
mul_bfmatrix_lfvector(q, lA, d);
filter(q, S);
a = s/dot_lfvector(d, q, numverts);
// X = X + d*a;
add_lfvector_lfvectorS(ldV, ldV, d, a, numverts);
// r = r - q*a;
sub_lfvector_lfvectorS(r, r, q, a, numverts);
s_prev = s;
s = dot_lfvector(r, r, numverts);
//d = r+d*(s/s_prev);
add_lfvector_lfvectorS(d, r, d, (s/s_prev), numverts);
filter(d, S);
conjgrad_loopcount++;
}
/* conjgrad_lasterror = s; */ /* UNUSED */
del_lfvector(q);
del_lfvector(d);
del_lfvector(tmp);
del_lfvector(r);
// printf("W/O conjgrad_loopcount: %d\n", conjgrad_loopcount);
return conjgrad_loopcount<conjgrad_looplimit; // true means we reached desired accuracy in given time - ie stable
}
#endif
static int cg_filtered(lfVector *ldV, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, ImplicitSolverResult *result)
{
// Solves for unknown X in equation AX=B
unsigned int conjgrad_loopcount=0, conjgrad_looplimit=100;
float conjgrad_epsilon=0.01f;
unsigned int numverts = lA[0].vcount;
lfVector *fB = create_lfvector(numverts);
lfVector *AdV = create_lfvector(numverts);
lfVector *r = create_lfvector(numverts);
lfVector *c = create_lfvector(numverts);
lfVector *q = create_lfvector(numverts);
lfVector *s = create_lfvector(numverts);
float bnorm2, delta_new, delta_old, delta_target, alpha;
cp_lfvector(ldV, z, numverts);
/* d0 = filter(B)^T * P * filter(B) */
cp_lfvector(fB, lB, numverts);
filter(fB, S);
bnorm2 = dot_lfvector(fB, fB, numverts);
delta_target = conjgrad_epsilon*conjgrad_epsilon * bnorm2;
/* r = filter(B - A * dV) */
mul_bfmatrix_lfvector(AdV, lA, ldV);
sub_lfvector_lfvector(r, lB, AdV, numverts);
filter(r, S);
/* c = filter(P^-1 * r) */
cp_lfvector(c, r, numverts);
filter(c, S);
/* delta = r^T * c */
delta_new = dot_lfvector(r, c, numverts);
#ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT
printf("==== A ====\n");
print_bfmatrix(lA);
printf("==== z ====\n");
print_lvector(z, numverts);
printf("==== B ====\n");
print_lvector(lB, numverts);
printf("==== S ====\n");
print_bfmatrix(S);
#endif
while (delta_new > delta_target && conjgrad_loopcount < conjgrad_looplimit) {
mul_bfmatrix_lfvector(q, lA, c);
filter(q, S);
alpha = delta_new / dot_lfvector(c, q, numverts);
add_lfvector_lfvectorS(ldV, ldV, c, alpha, numverts);
add_lfvector_lfvectorS(r, r, q, -alpha, numverts);
/* s = P^-1 * r */
cp_lfvector(s, r, numverts);
delta_old = delta_new;
delta_new = dot_lfvector(r, s, numverts);
add_lfvector_lfvectorS(c, s, c, delta_new / delta_old, numverts);
filter(c, S);
conjgrad_loopcount++;
}
#ifdef IMPLICIT_PRINT_SOLVER_INPUT_OUTPUT
printf("==== dV ====\n");
print_lvector(ldV, numverts);
printf("========\n");
#endif
del_lfvector(fB);
del_lfvector(AdV);
del_lfvector(r);
del_lfvector(c);
del_lfvector(q);
del_lfvector(s);
// printf("W/O conjgrad_loopcount: %d\n", conjgrad_loopcount);
result->status = conjgrad_loopcount < conjgrad_looplimit ? BPH_SOLVER_SUCCESS : BPH_SOLVER_NO_CONVERGENCE;
result->iterations = conjgrad_loopcount;
result->error = bnorm2 > 0.0f ? sqrt(delta_new / bnorm2) : 0.0f;
return conjgrad_loopcount < conjgrad_looplimit; // true means we reached desired accuracy in given time - ie stable
}
#if 0
// block diagonalizer
DO_INLINE void BuildPPinv(fmatrix3x3 *lA, fmatrix3x3 *P, fmatrix3x3 *Pinv)
{
unsigned int i = 0;
// Take only the diagonal blocks of A
// #pragma omp parallel for private(i) if (lA[0].vcount > CLOTH_OPENMP_LIMIT)
for (i = 0; i<lA[0].vcount; i++) {
// block diagonalizer
cp_fmatrix(P[i].m, lA[i].m);
inverse_fmatrix(Pinv[i].m, P[i].m);
}
}
/*
// version 1.3
static int cg_filtered_pre(lfVector *dv, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, fmatrix3x3 *P, fmatrix3x3 *Pinv)
{
unsigned int numverts = lA[0].vcount, iterations = 0, conjgrad_looplimit=100;
float delta0 = 0, deltaNew = 0, deltaOld = 0, alpha = 0;
float conjgrad_epsilon=0.0001; // 0.2 is dt for steps=5
lfVector *r = create_lfvector(numverts);
lfVector *p = create_lfvector(numverts);
lfVector *s = create_lfvector(numverts);
lfVector *h = create_lfvector(numverts);
BuildPPinv(lA, P, Pinv);
filter(dv, S);
add_lfvector_lfvector(dv, dv, z, numverts);
mul_bfmatrix_lfvector(r, lA, dv);
sub_lfvector_lfvector(r, lB, r, numverts);
filter(r, S);
mul_prevfmatrix_lfvector(p, Pinv, r);
filter(p, S);
deltaNew = dot_lfvector(r, p, numverts);
delta0 = deltaNew * sqrt(conjgrad_epsilon);
// itstart();
while ((deltaNew > delta0) && (iterations < conjgrad_looplimit))
{
iterations++;
mul_bfmatrix_lfvector(s, lA, p);
filter(s, S);
alpha = deltaNew / dot_lfvector(p, s, numverts);
add_lfvector_lfvectorS(dv, dv, p, alpha, numverts);
add_lfvector_lfvectorS(r, r, s, -alpha, numverts);
mul_prevfmatrix_lfvector(h, Pinv, r);
filter(h, S);
deltaOld = deltaNew;
deltaNew = dot_lfvector(r, h, numverts);
add_lfvector_lfvectorS(p, h, p, deltaNew / deltaOld, numverts);
filter(p, S);
}
// itend();
// printf("cg_filtered_pre time: %f\n", (float)itval());
del_lfvector(h);
del_lfvector(s);
del_lfvector(p);
del_lfvector(r);
printf("iterations: %d\n", iterations);
return iterations<conjgrad_looplimit;
}
*/
// version 1.4
static int cg_filtered_pre(lfVector *dv, fmatrix3x3 *lA, lfVector *lB, lfVector *z, fmatrix3x3 *S, fmatrix3x3 *P, fmatrix3x3 *Pinv, fmatrix3x3 *bigI)
{
unsigned int numverts = lA[0].vcount, iterations = 0, conjgrad_looplimit=100;
float delta0 = 0, deltaNew = 0, deltaOld = 0, alpha = 0, tol = 0;
lfVector *r = create_lfvector(numverts);
lfVector *p = create_lfvector(numverts);
lfVector *s = create_lfvector(numverts);
lfVector *h = create_lfvector(numverts);
lfVector *bhat = create_lfvector(numverts);
lfVector *btemp = create_lfvector(numverts);
BuildPPinv(lA, P, Pinv);
initdiag_bfmatrix(bigI, I);
sub_bfmatrix_Smatrix(bigI, bigI, S);
// x = Sx_0+(I-S)z
filter(dv, S);
add_lfvector_lfvector(dv, dv, z, numverts);
// b_hat = S(b-A(I-S)z)
mul_bfmatrix_lfvector(r, lA, z);
mul_bfmatrix_lfvector(bhat, bigI, r);
sub_lfvector_lfvector(bhat, lB, bhat, numverts);
// r = S(b-Ax)
mul_bfmatrix_lfvector(r, lA, dv);
sub_lfvector_lfvector(r, lB, r, numverts);
filter(r, S);
// p = SP^-1r
mul_prevfmatrix_lfvector(p, Pinv, r);
filter(p, S);
// delta0 = bhat^TP^-1bhat
mul_prevfmatrix_lfvector(btemp, Pinv, bhat);
delta0 = dot_lfvector(bhat, btemp, numverts);
// deltaNew = r^TP
deltaNew = dot_lfvector(r, p, numverts);
/*
filter(dv, S);
add_lfvector_lfvector(dv, dv, z, numverts);
mul_bfmatrix_lfvector(r, lA, dv);
sub_lfvector_lfvector(r, lB, r, numverts);
filter(r, S);
mul_prevfmatrix_lfvector(p, Pinv, r);
filter(p, S);
deltaNew = dot_lfvector(r, p, numverts);
delta0 = deltaNew * sqrt(conjgrad_epsilon);
*/
// itstart();
tol = (0.01*0.2);
while ((deltaNew > delta0*tol*tol) && (iterations < conjgrad_looplimit))
{
iterations++;
mul_bfmatrix_lfvector(s, lA, p);
filter(s, S);
alpha = deltaNew / dot_lfvector(p, s, numverts);
add_lfvector_lfvectorS(dv, dv, p, alpha, numverts);
add_lfvector_lfvectorS(r, r, s, -alpha, numverts);
mul_prevfmatrix_lfvector(h, Pinv, r);
filter(h, S);
deltaOld = deltaNew;
deltaNew = dot_lfvector(r, h, numverts);
add_lfvector_lfvectorS(p, h, p, deltaNew / deltaOld, numverts);
filter(p, S);
}
// itend();
// printf("cg_filtered_pre time: %f\n", (float)itval());
del_lfvector(btemp);
del_lfvector(bhat);
del_lfvector(h);
del_lfvector(s);
del_lfvector(p);
del_lfvector(r);
// printf("iterations: %d\n", iterations);
return iterations<conjgrad_looplimit;
}
#endif
bool BPH_mass_spring_solve_velocities(Implicit_Data *data, float dt, ImplicitSolverResult *result)
{
unsigned int numverts = data->dFdV[0].vcount;
lfVector *dFdXmV = create_lfvector(numverts);
zero_lfvector(data->dV, numverts);
cp_bfmatrix(data->A, data->M);
subadd_bfmatrixS_bfmatrixS(data->A, data->dFdV, dt, data->dFdX, (dt*dt));
mul_bfmatrix_lfvector(dFdXmV, data->dFdX, data->V);
add_lfvectorS_lfvectorS(data->B, data->F, dt, dFdXmV, (dt*dt), numverts);
// itstart();
cg_filtered(data->dV, data->A, data->B, data->z, data->S, result); /* conjugate gradient algorithm to solve Ax=b */
// cg_filtered_pre(id->dV, id->A, id->B, id->z, id->S, id->P, id->Pinv, id->bigI);
// itend();
// printf("cg_filtered calc time: %f\n", (float)itval());
// advance velocities
add_lfvector_lfvector(data->Vnew, data->V, data->dV, numverts);
del_lfvector(dFdXmV);
return result->status == BPH_SOLVER_SUCCESS;
}
bool BPH_mass_spring_solve_positions(Implicit_Data *data, float dt)
{
int numverts = data->M[0].vcount;
// advance positions
add_lfvector_lfvectorS(data->Xnew, data->X, data->Vnew, dt, numverts);
return true;
}
void BPH_mass_spring_apply_result(Implicit_Data *data)
{
int numverts = data->M[0].vcount;
cp_lfvector(data->X, data->Xnew, numverts);
cp_lfvector(data->V, data->Vnew, numverts);
}
void BPH_mass_spring_set_vertex_mass(Implicit_Data *data, int index, float mass)
{
unit_m3(data->M[index].m);
mul_m3_fl(data->M[index].m, mass);
}
void BPH_mass_spring_set_rest_transform(Implicit_Data *data, int index, float tfm[3][3])
{
#ifdef CLOTH_ROOT_FRAME
copy_m3_m3(data->tfm[index].m, tfm);
#else
unit_m3(data->tfm[index].m);
(void)tfm;
#endif
}
void BPH_mass_spring_set_motion_state(Implicit_Data *data, int index, const float x[3], const float v[3])
{
world_to_root_v3(data, index, data->X[index], x);
world_to_root_v3(data, index, data->V[index], v);
}
void BPH_mass_spring_set_position(Implicit_Data *data, int index, const float x[3])
{
world_to_root_v3(data, index, data->X[index], x);
}
void BPH_mass_spring_set_velocity(Implicit_Data *data, int index, const float v[3])
{
world_to_root_v3(data, index, data->V[index], v);
}
void BPH_mass_spring_get_motion_state(struct Implicit_Data *data, int index, float x[3], float v[3])
{
if (x) root_to_world_v3(data, index, x, data->X[index]);
if (v) root_to_world_v3(data, index, v, data->V[index]);
}
void BPH_mass_spring_get_position(struct Implicit_Data *data, int index, float x[3])
{
root_to_world_v3(data, index, x, data->X[index]);
}
void BPH_mass_spring_get_new_velocity(struct Implicit_Data *data, int index, float v[3])
{
root_to_world_v3(data, index, v, data->Vnew[index]);
}
void BPH_mass_spring_set_new_velocity(struct Implicit_Data *data, int index, const float v[3])
{
world_to_root_v3(data, index, data->Vnew[index], v);
}
/* -------------------------------- */
static int BPH_mass_spring_add_block(Implicit_Data *data, int v1, int v2)
{
int s = data->M[0].vcount + data->num_blocks; /* index from array start */
BLI_assert(s < data->M[0].vcount + data->M[0].scount);
++data->num_blocks;
/* tfm and S don't have spring entries (diagonal blocks only) */
init_fmatrix(data->bigI + s, v1, v2);
init_fmatrix(data->M + s, v1, v2);
init_fmatrix(data->dFdX + s, v1, v2);
init_fmatrix(data->dFdV + s, v1, v2);
init_fmatrix(data->A + s, v1, v2);
init_fmatrix(data->P + s, v1, v2);
init_fmatrix(data->Pinv + s, v1, v2);
return s;
}
void BPH_mass_spring_clear_constraints(Implicit_Data *data)
{
int i, numverts = data->S[0].vcount;
for (i = 0; i < numverts; ++i) {
unit_m3(data->S[i].m);
zero_v3(data->z[i]);
}
}
void BPH_mass_spring_add_constraint_ndof0(Implicit_Data *data, int index, const float dV[3])
{
zero_m3(data->S[index].m);
world_to_root_v3(data, index, data->z[index], dV);
}
void BPH_mass_spring_add_constraint_ndof1(Implicit_Data *data, int index, const float c1[3], const float c2[3], const float dV[3])
{
float m[3][3], p[3], q[3], u[3], cmat[3][3];
world_to_root_v3(data, index, p, c1);
mul_fvectorT_fvector(cmat, p, p);
sub_m3_m3m3(m, I, cmat);
world_to_root_v3(data, index, q, c2);
mul_fvectorT_fvector(cmat, q, q);
sub_m3_m3m3(m, m, cmat);
/* XXX not sure but multiplication should work here */
copy_m3_m3(data->S[index].m, m);
// mul_m3_m3m3(data->S[index].m, data->S[index].m, m);
world_to_root_v3(data, index, u, dV);
add_v3_v3(data->z[index], u);
}
void BPH_mass_spring_add_constraint_ndof2(Implicit_Data *data, int index, const float c1[3], const float dV[3])
{
float m[3][3], p[3], u[3], cmat[3][3];
world_to_root_v3(data, index, p, c1);
mul_fvectorT_fvector(cmat, p, p);
sub_m3_m3m3(m, I, cmat);
copy_m3_m3(data->S[index].m, m);
// mul_m3_m3m3(data->S[index].m, data->S[index].m, m);
world_to_root_v3(data, index, u, dV);
add_v3_v3(data->z[index], u);
}
void BPH_mass_spring_clear_forces(Implicit_Data *data)
{
int numverts = data->M[0].vcount;
zero_lfvector(data->F, numverts);
init_bfmatrix(data->dFdX, ZERO);
init_bfmatrix(data->dFdV, ZERO);
data->num_blocks = 0;
}
void BPH_mass_spring_force_reference_frame(Implicit_Data *data, int index, const float acceleration[3], const float omega[3], const float domega_dt[3], float mass)
{
#ifdef CLOTH_ROOT_FRAME
float acc[3], w[3], dwdt[3];
float f[3], dfdx[3][3], dfdv[3][3];
float euler[3], coriolis[3], centrifugal[3], rotvel[3];
float deuler[3][3], dcoriolis[3][3], dcentrifugal[3][3], drotvel[3][3];
world_to_root_v3(data, index, acc, acceleration);
world_to_root_v3(data, index, w, omega);
world_to_root_v3(data, index, dwdt, domega_dt);
cross_v3_v3v3(euler, dwdt, data->X[index]);
cross_v3_v3v3(coriolis, w, data->V[index]);
mul_v3_fl(coriolis, 2.0f);
cross_v3_v3v3(rotvel, w, data->X[index]);
cross_v3_v3v3(centrifugal, w, rotvel);
sub_v3_v3v3(f, acc, euler);
sub_v3_v3(f, coriolis);
sub_v3_v3(f, centrifugal);
mul_v3_fl(f, mass); /* F = m * a */
cross_v3_identity(deuler, dwdt);
cross_v3_identity(dcoriolis, w);
mul_m3_fl(dcoriolis, 2.0f);
cross_v3_identity(drotvel, w);
cross_m3_v3m3(dcentrifugal, w, drotvel);
add_m3_m3m3(dfdx, deuler, dcentrifugal);
negate_m3(dfdx);
mul_m3_fl(dfdx, mass);
copy_m3_m3(dfdv, dcoriolis);
negate_m3(dfdv);
mul_m3_fl(dfdv, mass);
add_v3_v3(data->F[index], f);
add_m3_m3m3(data->dFdX[index].m, data->dFdX[index].m, dfdx);
add_m3_m3m3(data->dFdV[index].m, data->dFdV[index].m, dfdv);
#else
(void)data;
(void)index;
(void)acceleration;
(void)omega;
(void)domega_dt;
#endif
}
void BPH_mass_spring_force_gravity(Implicit_Data *data, int index, float mass, const float g[3])
{
/* force = mass * acceleration (in this case: gravity) */
float f[3];
world_to_root_v3(data, index, f, g);
mul_v3_fl(f, mass);
add_v3_v3(data->F[index], f);
}
void BPH_mass_spring_force_drag(Implicit_Data *data, float drag)
{
int i, numverts = data->M[0].vcount;
for (i = 0; i < numverts; i++) {
float tmp[3][3];
/* NB: uses root space velocity, no need to transform */
madd_v3_v3fl(data->F[i], data->V[i], -drag);
copy_m3_m3(tmp, I);
mul_m3_fl(tmp, -drag);
add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, tmp);
}
}
void BPH_mass_spring_force_extern(struct Implicit_Data *data, int i, const float f[3], float dfdx[3][3], float dfdv[3][3])
{
float tf[3], tdfdx[3][3], tdfdv[3][3];
world_to_root_v3(data, i, tf, f);
world_to_root_m3(data, i, tdfdx, dfdx);
world_to_root_m3(data, i, tdfdv, dfdv);
add_v3_v3(data->F[i], tf);
add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, tdfdx);
add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, tdfdv);
}
static float calc_nor_area_tri(float nor[3], const float v1[3], const float v2[3], const float v3[3])
{
float n1[3], n2[3];
sub_v3_v3v3(n1, v1, v2);
sub_v3_v3v3(n2, v2, v3);
cross_v3_v3v3(nor, n1, n2);
return normalize_v3(nor);
}
static float calc_nor_area_quad(float nor[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
float n1[3], n2[3];
sub_v3_v3v3(n1, v1, v3);
sub_v3_v3v3(n2, v2, v4);
cross_v3_v3v3(nor, n1, n2);
return normalize_v3(nor);
}
/* XXX does not support force jacobians yet, since the effector system does not provide them either */
void BPH_mass_spring_force_face_wind(Implicit_Data *data, int v1, int v2, int v3, int v4, const float (*winvec)[3])
{
const float effector_scale = 0.02f;
float win[3], nor[3], area;
float factor;
// calculate face normal and area
if (v4) {
area = calc_nor_area_quad(nor, data->X[v1], data->X[v2], data->X[v3], data->X[v4]);
factor = effector_scale * area * 0.25f;
}
else {
area = calc_nor_area_tri(nor, data->X[v1], data->X[v2], data->X[v3]);
factor = effector_scale * area / 3.0f;
}
world_to_root_v3(data, v1, win, winvec[v1]);
madd_v3_v3fl(data->F[v1], nor, factor * dot_v3v3(win, nor));
world_to_root_v3(data, v2, win, winvec[v2]);
madd_v3_v3fl(data->F[v2], nor, factor * dot_v3v3(win, nor));
world_to_root_v3(data, v3, win, winvec[v3]);
madd_v3_v3fl(data->F[v3], nor, factor * dot_v3v3(win, nor));
if (v4) {
world_to_root_v3(data, v4, win, winvec[v4]);
madd_v3_v3fl(data->F[v4], nor, factor * dot_v3v3(win, nor));
}
}
static void edge_wind_vertex(const float dir[3], float length, float radius, const float wind[3], float f[3], float UNUSED(dfdx[3][3]), float UNUSED(dfdv[3][3]))
{
const float density = 0.01f; /* XXX arbitrary value, corresponds to effect of air density */
float cos_alpha, sin_alpha, cross_section;
float windlen = len_v3(wind);
if (windlen == 0.0f) {
zero_v3(f);
return;
}
/* angle of wind direction to edge */
cos_alpha = dot_v3v3(wind, dir) / windlen;
sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha);
cross_section = radius * (M_PI * radius * sin_alpha + length * cos_alpha);
mul_v3_v3fl(f, wind, density * cross_section);
}
void BPH_mass_spring_force_edge_wind(Implicit_Data *data, int v1, int v2, float radius1, float radius2, const float (*winvec)[3])
{
float win[3], dir[3], length;
float f[3], dfdx[3][3], dfdv[3][3];
sub_v3_v3v3(dir, data->X[v1], data->X[v2]);
length = normalize_v3(dir);
world_to_root_v3(data, v1, win, winvec[v1]);
edge_wind_vertex(dir, length, radius1, win, f, dfdx, dfdv);
add_v3_v3(data->F[v1], f);
world_to_root_v3(data, v2, win, winvec[v2]);
edge_wind_vertex(dir, length, radius2, win, f, dfdx, dfdv);
add_v3_v3(data->F[v2], f);
}
void BPH_mass_spring_force_vertex_wind(Implicit_Data *data, int v, float UNUSED(radius), const float (*winvec)[3])
{
const float density = 0.01f; /* XXX arbitrary value, corresponds to effect of air density */
float wind[3];
float f[3];
world_to_root_v3(data, v, wind, winvec[v]);
mul_v3_v3fl(f, wind, density);
add_v3_v3(data->F[v], f);
}
BLI_INLINE void dfdx_spring(float to[3][3], const float dir[3], float length, float L, float k)
{
// dir is unit length direction, rest is spring's restlength, k is spring constant.
//return ( (I-outerprod(dir, dir))*Min(1.0f, rest/length) - I) * -k;
outerproduct(to, dir, dir);
sub_m3_m3m3(to, I, to);
mul_m3_fl(to, (L/length));
sub_m3_m3m3(to, to, I);
mul_m3_fl(to, k);
}
/* unused */
#if 0
BLI_INLINE void dfdx_damp(float to[3][3], const float dir[3], float length, const float vel[3], float rest, float damping)
{
// inner spring damping vel is the relative velocity of the endpoints.
// return (I-outerprod(dir, dir)) * (-damping * -(dot(dir, vel)/Max(length, rest)));
mul_fvectorT_fvector(to, dir, dir);
sub_fmatrix_fmatrix(to, I, to);
mul_fmatrix_S(to, (-damping * -(dot_v3v3(dir, vel)/MAX2(length, rest))));
}
#endif
BLI_INLINE void dfdv_damp(float to[3][3], const float dir[3], float damping)
{
// derivative of force wrt velocity
outerproduct(to, dir, dir);
mul_m3_fl(to, -damping);
}
BLI_INLINE float fb(float length, float L)
{
float x = length / L;
float xx = x * x;
float xxx = xx * x;
float xxxx = xxx * x;
return (-11.541f * xxxx + 34.193f * xxx - 39.083f * xx + 23.116f * x - 9.713f);
}
BLI_INLINE float fbderiv(float length, float L)
{
float x = length/L;
float xx = x * x;
float xxx = xx * x;
return (-46.164f * xxx + 102.579f * xx - 78.166f * x + 23.116f);
}
BLI_INLINE float fbstar(float length, float L, float kb, float cb)
{
float tempfb_fl = kb * fb(length, L);
float fbstar_fl = cb * (length - L);
if (tempfb_fl < fbstar_fl)
return fbstar_fl;
else
return tempfb_fl;
}
// function to calculae bending spring force (taken from Choi & Co)
BLI_INLINE float fbstar_jacobi(float length, float L, float kb, float cb)
{
float tempfb_fl = kb * fb(length, L);
float fbstar_fl = cb * (length - L);
if (tempfb_fl < fbstar_fl) {
return -cb;
}
else {
return -kb * fbderiv(length, L);
}
}
/* calculate elonglation */
BLI_INLINE bool spring_length(Implicit_Data *data, int i, int j, float r_extent[3], float r_dir[3], float *r_length, float r_vel[3])
{
sub_v3_v3v3(r_extent, data->X[j], data->X[i]);
sub_v3_v3v3(r_vel, data->V[j], data->V[i]);
*r_length = len_v3(r_extent);
if (*r_length > ALMOST_ZERO) {
/*
if (length>L) {
if ((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) &&
( ((length-L)*100.0f/L) > clmd->sim_parms->maxspringlen )) {
// cut spring!
s->flags |= CSPRING_FLAG_DEACTIVATE;
return false;
}
}
*/
mul_v3_v3fl(r_dir, r_extent, 1.0f/(*r_length));
}
else {
zero_v3(r_dir);
}
return true;
}
BLI_INLINE void apply_spring(Implicit_Data *data, int i, int j, const float f[3], float dfdx[3][3], float dfdv[3][3])
{
int block_ij = BPH_mass_spring_add_block(data, i, j);
add_v3_v3(data->F[i], f);
sub_v3_v3(data->F[j], f);
add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfdx);
add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfdx);
sub_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfdx);
add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, dfdv);
add_m3_m3m3(data->dFdV[j].m, data->dFdV[j].m, dfdv);
sub_m3_m3m3(data->dFdV[block_ij].m, data->dFdV[block_ij].m, dfdv);
}
bool BPH_mass_spring_force_spring_linear(Implicit_Data *data, int i, int j, float restlen,
float stiffness, float damping, bool no_compress, float clamp_force,
float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
{
float extent[3], length, dir[3], vel[3];
// calculate elonglation
spring_length(data, i, j, extent, dir, &length, vel);
if (length > restlen || no_compress) {
float stretch_force, f[3], dfdx[3][3], dfdv[3][3];
stretch_force = stiffness * (length - restlen);
if (clamp_force > 0.0f && stretch_force > clamp_force) {
stretch_force = clamp_force;
}
mul_v3_v3fl(f, dir, stretch_force);
// Ascher & Boxman, p.21: Damping only during elonglation
// something wrong with it...
madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir));
dfdx_spring(dfdx, dir, length, restlen, stiffness);
dfdv_damp(dfdv, dir, damping);
apply_spring(data, i, j, f, dfdx, dfdv);
if (r_f) copy_v3_v3(r_f, f);
if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
return true;
}
else {
if (r_f) zero_v3(r_f);
if (r_dfdx) zero_m3(r_dfdx);
if (r_dfdv) zero_m3(r_dfdv);
return false;
}
}
/* See "Stable but Responsive Cloth" (Choi, Ko 2005) */
bool BPH_mass_spring_force_spring_bending(Implicit_Data *data, int i, int j, float restlen,
float kb, float cb,
float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
{
float extent[3], length, dir[3], vel[3];
// calculate elonglation
spring_length(data, i, j, extent, dir, &length, vel);
if (length < restlen) {
float f[3], dfdx[3][3], dfdv[3][3];
mul_v3_v3fl(f, dir, fbstar(length, restlen, kb, cb));
outerproduct(dfdx, dir, dir);
mul_m3_fl(dfdx, fbstar_jacobi(length, restlen, kb, cb));
/* XXX damping not supported */
zero_m3(dfdv);
apply_spring(data, i, j, f, dfdx, dfdv);
if (r_f) copy_v3_v3(r_f, f);
if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
return true;
}
else {
if (r_f) zero_v3(r_f);
if (r_dfdx) zero_m3(r_dfdx);
if (r_dfdv) zero_m3(r_dfdv);
return false;
}
}
/* Jacobian of a direction vector.
* Basically the part of the differential orthogonal to the direction,
* inversely proportional to the length of the edge.
*
* dD_ij/dx_i = -dD_ij/dx_j = (D_ij * D_ij^T - I) / len_ij
*/
BLI_INLINE void spring_grad_dir(Implicit_Data *data, int i, int j, float edge[3], float dir[3], float grad_dir[3][3])
{
float length;
sub_v3_v3v3(edge, data->X[j], data->X[i]);
length = normalize_v3_v3(dir, edge);
if (length > ALMOST_ZERO) {
outerproduct(grad_dir, dir, dir);
sub_m3_m3m3(grad_dir, I, grad_dir);
mul_m3_fl(grad_dir, 1.0f / length);
}
else {
zero_m3(grad_dir);
}
}
BLI_INLINE void spring_angbend_forces(Implicit_Data *data, int i, int j, int k,
const float goal[3],
float stiffness, float damping,
int q, const float dx[3], const float dv[3],
float r_f[3])
{
float edge_ij[3], dir_ij[3];
float edge_jk[3], dir_jk[3];
float vel_ij[3], vel_jk[3], vel_ortho[3];
float f_bend[3], f_damp[3];
float fk[3];
float dist[3];
zero_v3(fk);
sub_v3_v3v3(edge_ij, data->X[j], data->X[i]);
if (q == i) sub_v3_v3(edge_ij, dx);
if (q == j) add_v3_v3(edge_ij, dx);
normalize_v3_v3(dir_ij, edge_ij);
sub_v3_v3v3(edge_jk, data->X[k], data->X[j]);
if (q == j) sub_v3_v3(edge_jk, dx);
if (q == k) add_v3_v3(edge_jk, dx);
normalize_v3_v3(dir_jk, edge_jk);
sub_v3_v3v3(vel_ij, data->V[j], data->V[i]);
if (q == i) sub_v3_v3(vel_ij, dv);
if (q == j) add_v3_v3(vel_ij, dv);
sub_v3_v3v3(vel_jk, data->V[k], data->V[j]);
if (q == j) sub_v3_v3(vel_jk, dv);
if (q == k) add_v3_v3(vel_jk, dv);
/* bending force */
sub_v3_v3v3(dist, goal, edge_jk);
mul_v3_v3fl(f_bend, dist, stiffness);
add_v3_v3(fk, f_bend);
/* damping force */
madd_v3_v3v3fl(vel_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk));
mul_v3_v3fl(f_damp, vel_ortho, damping);
sub_v3_v3(fk, f_damp);
copy_v3_v3(r_f, fk);
}
/* Finite Differences method for estimating the jacobian of the force */
BLI_INLINE void spring_angbend_estimate_dfdx(Implicit_Data *data, int i, int j, int k,
const float goal[3],
float stiffness, float damping,
int q, float dfdx[3][3])
{
const float delta = 0.00001f; // TODO find a good heuristic for this
float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3];
float f[3];
int a, b;
zero_m3(dvec_null);
unit_m3(dvec_pos);
mul_m3_fl(dvec_pos, delta * 0.5f);
copy_m3_m3(dvec_neg, dvec_pos);
negate_m3(dvec_neg);
/* XXX TODO offset targets to account for position dependency */
for (a = 0; a < 3; ++a) {
spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
q, dvec_pos[a], dvec_null[a], f);
copy_v3_v3(dfdx[a], f);
spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
q, dvec_neg[a], dvec_null[a], f);
sub_v3_v3(dfdx[a], f);
for (b = 0; b < 3; ++b) {
dfdx[a][b] /= delta;
}
}
}
/* Finite Differences method for estimating the jacobian of the force */
BLI_INLINE void spring_angbend_estimate_dfdv(Implicit_Data *data, int i, int j, int k,
const float goal[3],
float stiffness, float damping,
int q, float dfdv[3][3])
{
const float delta = 0.00001f; // TODO find a good heuristic for this
float dvec_null[3][3], dvec_pos[3][3], dvec_neg[3][3];
float f[3];
int a, b;
zero_m3(dvec_null);
unit_m3(dvec_pos);
mul_m3_fl(dvec_pos, delta * 0.5f);
copy_m3_m3(dvec_neg, dvec_pos);
negate_m3(dvec_neg);
/* XXX TODO offset targets to account for position dependency */
for (a = 0; a < 3; ++a) {
spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
q, dvec_null[a], dvec_pos[a], f);
copy_v3_v3(dfdv[a], f);
spring_angbend_forces(data, i, j, k, goal, stiffness, damping,
q, dvec_null[a], dvec_neg[a], f);
sub_v3_v3(dfdv[a], f);
for (b = 0; b < 3; ++b) {
dfdv[a][b] /= delta;
}
}
}
/* Angular spring that pulls the vertex toward the local target
* See "Artistic Simulation of Curly Hair" (Pixar technical memo #12-03a)
*/
bool BPH_mass_spring_force_spring_bending_angular(Implicit_Data *data, int i, int j, int k,
const float target[3], float stiffness, float damping)
{
float goal[3];
float fj[3], fk[3];
float dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3];
float dfj_dvi[3][3], dfj_dvj[3][3], dfk_dvi[3][3], dfk_dvj[3][3], dfk_dvk[3][3];
const float vecnull[3] = {0.0f, 0.0f, 0.0f};
int block_ij = BPH_mass_spring_add_block(data, i, j);
int block_jk = BPH_mass_spring_add_block(data, j, k);
int block_ik = BPH_mass_spring_add_block(data, i, k);
world_to_root_v3(data, j, goal, target);
spring_angbend_forces(data, i, j, k, goal, stiffness, damping, k, vecnull, vecnull, fk);
negate_v3_v3(fj, fk); /* counterforce */
spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, i, dfk_dxi);
spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, j, dfk_dxj);
spring_angbend_estimate_dfdx(data, i, j, k, goal, stiffness, damping, k, dfk_dxk);
copy_m3_m3(dfj_dxi, dfk_dxi); negate_m3(dfj_dxi);
copy_m3_m3(dfj_dxj, dfk_dxj); negate_m3(dfj_dxj);
spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, i, dfk_dvi);
spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, j, dfk_dvj);
spring_angbend_estimate_dfdv(data, i, j, k, goal, stiffness, damping, k, dfk_dvk);
copy_m3_m3(dfj_dvi, dfk_dvi); negate_m3(dfj_dvi);
copy_m3_m3(dfj_dvj, dfk_dvj); negate_m3(dfj_dvj);
/* add forces and jacobians to the solver data */
add_v3_v3(data->F[j], fj);
add_v3_v3(data->F[k], fk);
add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj);
add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk);
add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi);
add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj);
add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi);
add_m3_m3m3(data->dFdV[j].m, data->dFdV[j].m, dfj_dvj);
add_m3_m3m3(data->dFdV[k].m, data->dFdV[k].m, dfk_dvk);
add_m3_m3m3(data->dFdV[block_ij].m, data->dFdV[block_ij].m, dfj_dvi);
add_m3_m3m3(data->dFdV[block_jk].m, data->dFdV[block_jk].m, dfk_dvj);
add_m3_m3m3(data->dFdV[block_ik].m, data->dFdV[block_ik].m, dfk_dvi);
/* XXX analytical calculation of derivatives below is incorrect.
* This proved to be difficult, but for now just using the finite difference method for
* estimating the jacobians should be sufficient.
*/
#if 0
float edge_ij[3], dir_ij[3], grad_dir_ij[3][3];
float edge_jk[3], dir_jk[3], grad_dir_jk[3][3];
float dist[3], vel_jk[3], vel_jk_ortho[3], projvel[3];
float target[3];
float tmp[3][3];
float fi[3], fj[3], fk[3];
float dfi_dxi[3][3], dfj_dxi[3][3], dfj_dxj[3][3], dfk_dxi[3][3], dfk_dxj[3][3], dfk_dxk[3][3];
float dfdvi[3][3];
// TESTING
damping = 0.0f;
zero_v3(fi);
zero_v3(fj);
zero_v3(fk);
zero_m3(dfi_dxi);
zero_m3(dfj_dxi);
zero_m3(dfk_dxi);
zero_m3(dfk_dxj);
zero_m3(dfk_dxk);
/* jacobian of direction vectors */
spring_grad_dir(data, i, j, edge_ij, dir_ij, grad_dir_ij);
spring_grad_dir(data, j, k, edge_jk, dir_jk, grad_dir_jk);
sub_v3_v3v3(vel_jk, data->V[k], data->V[j]);
/* bending force */
mul_v3_v3fl(target, dir_ij, restlen);
sub_v3_v3v3(dist, target, edge_jk);
mul_v3_v3fl(fk, dist, stiffness);
/* damping force */
madd_v3_v3v3fl(vel_jk_ortho, vel_jk, dir_jk, -dot_v3v3(vel_jk, dir_jk));
madd_v3_v3fl(fk, vel_jk_ortho, damping);
/* XXX this only holds true as long as we assume straight rest shape!
* eventually will become a bit more involved since the opposite segment
* gets its own target, under condition of having equal torque on both sides.
*/
copy_v3_v3(fi, fk);
/* counterforce on the middle point */
sub_v3_v3(fj, fi);
sub_v3_v3(fj, fk);
/* === derivatives === */
madd_m3_m3fl(dfk_dxi, grad_dir_ij, stiffness * restlen);
madd_m3_m3fl(dfk_dxj, grad_dir_ij, -stiffness * restlen);
madd_m3_m3fl(dfk_dxj, I, stiffness);
madd_m3_m3fl(dfk_dxk, I, -stiffness);
copy_m3_m3(dfi_dxi, dfk_dxk);
negate_m3(dfi_dxi);
/* dfj_dfi == dfi_dfj due to symmetry,
* dfi_dfj == dfk_dfj due to fi == fk
* XXX see comment above on future bent rest shapes
*/
copy_m3_m3(dfj_dxi, dfk_dxj);
/* dfj_dxj == -(dfi_dxj + dfk_dxj) due to fj == -(fi + fk) */
sub_m3_m3m3(dfj_dxj, dfj_dxj, dfj_dxi);
sub_m3_m3m3(dfj_dxj, dfj_dxj, dfk_dxj);
/* add forces and jacobians to the solver data */
add_v3_v3(data->F[i], fi);
add_v3_v3(data->F[j], fj);
add_v3_v3(data->F[k], fk);
add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfi_dxi);
add_m3_m3m3(data->dFdX[j].m, data->dFdX[j].m, dfj_dxj);
add_m3_m3m3(data->dFdX[k].m, data->dFdX[k].m, dfk_dxk);
add_m3_m3m3(data->dFdX[block_ij].m, data->dFdX[block_ij].m, dfj_dxi);
add_m3_m3m3(data->dFdX[block_jk].m, data->dFdX[block_jk].m, dfk_dxj);
add_m3_m3m3(data->dFdX[block_ik].m, data->dFdX[block_ik].m, dfk_dxi);
#endif
return true;
}
bool BPH_mass_spring_force_spring_goal(Implicit_Data *data, int i, const float goal_x[3], const float goal_v[3],
float stiffness, float damping,
float r_f[3], float r_dfdx[3][3], float r_dfdv[3][3])
{
float root_goal_x[3], root_goal_v[3], extent[3], length, dir[3], vel[3];
float f[3], dfdx[3][3], dfdv[3][3];
/* goal is in world space */
world_to_root_v3(data, i, root_goal_x, goal_x);
world_to_root_v3(data, i, root_goal_v, goal_v);
sub_v3_v3v3(extent, root_goal_x, data->X[i]);
sub_v3_v3v3(vel, root_goal_v, data->V[i]);
length = normalize_v3_v3(dir, extent);
if (length > ALMOST_ZERO) {
mul_v3_v3fl(f, dir, stiffness * length);
// Ascher & Boxman, p.21: Damping only during elonglation
// something wrong with it...
madd_v3_v3fl(f, dir, damping * dot_v3v3(vel, dir));
dfdx_spring(dfdx, dir, length, 0.0f, stiffness);
dfdv_damp(dfdv, dir, damping);
add_v3_v3(data->F[i], f);
add_m3_m3m3(data->dFdX[i].m, data->dFdX[i].m, dfdx);
add_m3_m3m3(data->dFdV[i].m, data->dFdV[i].m, dfdv);
if (r_f) copy_v3_v3(r_f, f);
if (r_dfdx) copy_m3_m3(r_dfdx, dfdx);
if (r_dfdv) copy_m3_m3(r_dfdv, dfdv);
return true;
}
else {
if (r_f) zero_v3(r_f);
if (r_dfdx) zero_m3(r_dfdx);
if (r_dfdv) zero_m3(r_dfdv);
return false;
}
}
#endif /* IMPLICIT_SOLVER_BLENDER */
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