implicit.c

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/*
 * $Id: implicit.c 36423 2011-05-02 03:44:02Z campbellbarton $
 *
 * ***** 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 *****
 */

#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 "BLI_threads.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"


#define CLOTH_OPENMP_LIMIT 512

#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;
         void itstart(void)
{
        gettimeofday(&_itstart, &itz);
}
static void itend(void)
{
        gettimeofday(&_itend,&itz);
}
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

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 cross product */
/* STATUS: verified */
DO_INLINE void cross_fvector(float to[3], float vectorA[3], float vectorB[3])
{
        to[0] = vectorA[1] * vectorB[2] - vectorA[2] * vectorB[1];
        to[1] = vectorA[2] * vectorB[0] - vectorA[0] * vectorB[2];
        to[2] = vectorA[0] * vectorB[1] - vectorA[1] * vectorB[0];
}
/* 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);
}


/* 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]);
        }
}
/* create long vector */
DO_INLINE lfVector *create_lfvector(unsigned int verts)
{
        // TODO: check if memory allocation was successfull */
        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++)
        {
                VECCOPY(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 += INPR(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++)
        {
                VECSUB(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]);
}
#endif

/* copy 3x3 matrix */
DO_INLINE void cp_fmatrix(float to[3][3], float from[3][3])
{
        // memcpy(to, from, sizeof (float) * 9);
        VECCOPY(to[0], from[0]);
        VECCOPY(to[1], from[1]);
        VECCOPY(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;
}

/* 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;
                        */
                }
        }

}

/* 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)
{
        to[0] = INPR(matrix[0],from);
        to[1] = INPR(matrix[1],from);
        to[2] = INPR(matrix[2],from);
}
/* 3x3 matrix multiplied by a 3x3 matrix */
/* STATUS: verified */
DO_INLINE void mul_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        mul_fvector_fmatrix(to[0], matrixA[0],matrixB);
        mul_fvector_fmatrix(to[1], matrixA[1],matrixB);
        mul_fvector_fmatrix(to[2], matrixA[2],matrixB);
}
/* 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]);
}
/* 3x3 matrix add-addition with 3x3 matrix */
DO_INLINE void addadd_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        VECADDADD(to[0], matrixA[0], matrixB[0]);
        VECADDADD(to[1], matrixA[1], matrixB[1]);
        VECADDADD(to[2], matrixA[2], matrixB[2]);
}
/* 3x3 matrix sub-addition with 3x3 matrix */
DO_INLINE void addsub_fmatrixS_fmatrixS(float to[3][3], float matrixA[3][3], float aS, float matrixB[3][3], float bS)
{
        VECADDSUBSS(to[0], matrixA[0], aS, matrixB[0], bS);
        VECADDSUBSS(to[1], matrixA[1], aS, matrixB[1], bS);
        VECADDSUBSS(to[2], matrixA[2], aS, matrixB[2], bS);
}
/* A -= B + C (3x3 matrix sub-addition with 3x3 matrix) */
DO_INLINE void subadd_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        VECSUBADD(to[0], matrixA[0], matrixB[0]);
        VECSUBADD(to[1], matrixA[1], matrixB[1]);
        VECSUBADD(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])
{
        VECSUB(to[0], matrixA[0], matrixB[0]);
        VECSUB(to[1], matrixA[1], matrixB[1]);
        VECSUB(to[2], matrixA[2], matrixB[2]);
}
/* A += B - C (3x3 matrix add-subtraction with 3x3 matrix) */
DO_INLINE void addsub_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        VECADDSUB(to[0], matrixA[0], matrixB[0]);
        VECADDSUB(to[1], matrixA[1], matrixB[1]);
        VECADDSUB(to[2], matrixA[2], matrixB[2]);
}
// special functions
/* a vector multiplied and added to/by a 3x3 matrix */
DO_INLINE void muladd_fvector_fmatrix(float to[3], float from[3], 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 and added  to/by a 3x3 matrix  and added to another 3x3 matrix */
DO_INLINE void muladd_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        muladd_fvector_fmatrix(to[0], matrixA[0],matrixB);
        muladd_fvector_fmatrix(to[1], matrixA[1],matrixB);
        muladd_fvector_fmatrix(to[2], matrixA[2],matrixB);
}
/* a vector multiplied and sub'd to/by a 3x3 matrix */
DO_INLINE void mulsub_fvector_fmatrix(float to[3], float from[3], 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 and sub'd  to/by a 3x3 matrix  and added to another 3x3 matrix */
DO_INLINE void mulsub_fmatrix_fmatrix(float to[3][3], float matrixA[3][3], float matrixB[3][3])
{
        mulsub_fvector_fmatrix(to[0], matrixA[0],matrixB);
        mulsub_fvector_fmatrix(to[1], matrixA[1],matrixB);
        mulsub_fvector_fmatrix(to[2], matrixA[2],matrixB);
}
/* 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] += INPR(matrix[0],from);
        to[1] += INPR(matrix[1],from);
        to[2] += INPR(matrix[2],from);  
}
/* 3x3 matrix multiplied+sub'ed by a vector */
DO_INLINE void mulsub_fmatrix_fvector(float to[3], float matrix[3][3], float from[3])
{
        to[0] -= INPR(matrix[0],from);
        to[1] -= INPR(matrix[1],from);
        to[2] -= INPR(matrix[2],from);
}

// 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

/* create big matrix */
DO_INLINE fmatrix3x3 *create_bfmatrix(unsigned int verts, unsigned int springs)
{
        // TODO: check if memory allocation was successfull */
        fmatrix3x3 *temp = (fmatrix3x3 *)MEM_callocN (sizeof (fmatrix3x3) * (verts + springs), "cloth_implicit_alloc_matrix");
        temp[0].vcount = verts;
        temp[0].scount = springs;
        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); 
        }
}

/* multiply big matrix with scalar*/
DO_INLINE void mul_bfmatrix_S(fmatrix3x3 *matrix, float scalar)
{
        unsigned int i = 0;
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                mul_fmatrix_S(matrix[i].m, scalar);
        }
}

/* 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 multiply big matrix with long vector (for diagonal preconditioner) */
/* STATUS: verified */
DO_INLINE void mul_prevfmatrix_lfvector( float (*to)[3], fmatrix3x3 *from, lfVector *fLongVector)
{
        unsigned int i = 0;
        
        for(i = 0; i < from[0].vcount; i++)
        {
                mul_fmatrix_fvector(to[from[i].r], from[i].m, fLongVector[from[i].c]);
        }
}

/* SPARSE SYMMETRIC add big matrix with big matrix: A = B + C*/
DO_INLINE void add_bfmatrix_bfmatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                add_fmatrix_fmatrix(to[i].m, from[i].m, matrix[i].m);   
        }

}
/* SPARSE SYMMETRIC add big matrix with big matrix: A += B + C */
DO_INLINE void addadd_bfmatrix_bfmatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                addadd_fmatrix_fmatrix(to[i].m, from[i].m, matrix[i].m);        
        }

}
/* SPARSE SYMMETRIC subadd big matrix with big matrix: A -= B + C */
DO_INLINE void subadd_bfmatrix_bfmatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                subadd_fmatrix_fmatrix(to[i].m, from[i].m, matrix[i].m);        
        }

}
/*  A = B - C (SPARSE SYMMETRIC sub big matrix with big matrix) */
DO_INLINE void sub_bfmatrix_bfmatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                sub_fmatrix_fmatrix(to[i].m, from[i].m, matrix[i].m);   
        }

}
/* SPARSE SYMMETRIC sub big matrix with big matrix S (special constraint matrix with limited entries) */
DO_INLINE void sub_bfmatrix_Smatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount; i++)
        {
                sub_fmatrix_fmatrix(to[matrix[i].c].m, from[matrix[i].c].m, matrix[i].m);       
        }

}
/* A += B - C (SPARSE SYMMETRIC addsub big matrix with big matrix) */
DO_INLINE void addsub_bfmatrix_bfmatrix( fmatrix3x3 *to, fmatrix3x3 *from,  fmatrix3x3 *matrix)
{
        unsigned int i = 0;

        /* process diagonal elements */
        for(i = 0; i < matrix[0].vcount+matrix[0].scount; i++)
        {
                addsub_fmatrix_fmatrix(to[i].m, from[i].m, matrix[i].m);        
        }

}
/* 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 
{
        lfVector *X, *V, *Xnew, *Vnew, *olddV, *F, *B, *dV, *z;
        fmatrix3x3 *A, *dFdV, *dFdX, *S, *P, *Pinv, *bigI, *M; 
} Implicit_Data;

int implicit_init (Object *UNUSED(ob), ClothModifierData *clmd)
{
        unsigned int i = 0;
        unsigned int pinned = 0;
        Cloth *cloth = NULL;
        ClothVertex *verts = NULL;
        ClothSpring *spring = NULL;
        Implicit_Data *id = NULL;
        LinkNode *search = NULL;
        
        if(G.rt > 0)
                printf("implicit_init\n");

        // init memory guard
        // MEMORY_BASE.first = MEMORY_BASE.last = NULL;

        cloth = (Cloth *)clmd->clothObject;
        verts = cloth->verts;

        // create implicit base
        id = (Implicit_Data *)MEM_callocN (sizeof(Implicit_Data), "implicit vecmat");
        cloth->implicit = id;

        /* process diagonal elements */         
        id->A = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->dFdV = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->dFdX = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->S = create_bfmatrix(cloth->numverts, 0);
        id->Pinv = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->P = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->bigI = create_bfmatrix(cloth->numverts, cloth->numsprings); // TODO 0 springs
        id->M = create_bfmatrix(cloth->numverts, cloth->numsprings);
        id->X = create_lfvector(cloth->numverts);
        id->Xnew = create_lfvector(cloth->numverts);
        id->V = create_lfvector(cloth->numverts);
        id->Vnew = create_lfvector(cloth->numverts);
        id->olddV = create_lfvector(cloth->numverts);
        zero_lfvector(id->olddV, cloth->numverts);
        id->F = create_lfvector(cloth->numverts);
        id->B = create_lfvector(cloth->numverts);
        id->dV = create_lfvector(cloth->numverts);
        id->z = create_lfvector(cloth->numverts);
        
        for(i=0;i<cloth->numverts;i++) 
        {
                id->A[i].r = id->A[i].c = id->dFdV[i].r = id->dFdV[i].c = id->dFdX[i].r = id->dFdX[i].c = id->P[i].c = id->P[i].r = id->Pinv[i].c = id->Pinv[i].r = id->bigI[i].c = id->bigI[i].r = id->M[i].r = id->M[i].c = i;

                if(verts [i].flags & CLOTH_VERT_FLAG_PINNED)
                {
                        id->S[pinned].pinned = 1;
                        id->S[pinned].c = id->S[pinned].r = i;
                        pinned++;
                }
                
                initdiag_fmatrixS(id->M[i].m, verts[i].mass);
        }

        // S is special and needs specific vcount and scount
        id->S[0].vcount = pinned; id->S[0].scount = 0;

        // init springs 
        search = cloth->springs;
        for(i=0;i<cloth->numsprings;i++) 
        {
                spring = search->link;
                
                // dFdV_start[i].r = big_I[i].r = big_zero[i].r = 
                id->A[i+cloth->numverts].r = id->dFdV[i+cloth->numverts].r = id->dFdX[i+cloth->numverts].r = 
                                id->P[i+cloth->numverts].r = id->Pinv[i+cloth->numverts].r = id->bigI[i+cloth->numverts].r = id->M[i+cloth->numverts].r = spring->ij;

                // dFdV_start[i].c = big_I[i].c = big_zero[i].c = 
                id->A[i+cloth->numverts].c = id->dFdV[i+cloth->numverts].c = id->dFdX[i+cloth->numverts].c = 
                                id->P[i+cloth->numverts].c = id->Pinv[i+cloth->numverts].c = id->bigI[i+cloth->numverts].c = id->M[i+cloth->numverts].c = spring->kl;

                spring->matrix_index = i + cloth->numverts;
                
                search = search->next;
        }
        
        initdiag_bfmatrix(id->bigI, I);

        for(i = 0; i < cloth->numverts; i++)
        {               
                VECCOPY(id->X[i], verts[i].x);
        }

        return 1;
}
int     implicit_free (ClothModifierData *clmd)
{
        Implicit_Data *id;
        Cloth *cloth;
        cloth = (Cloth *)clmd->clothObject;

        if(cloth)
        {
                id = cloth->implicit;

                if(id)
                {
                        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->olddV);
                        del_lfvector(id->F);
                        del_lfvector(id->B);
                        del_lfvector(id->dV);
                        del_lfvector(id->z);

                        MEM_freeN(id);
                }
        }

        return 1;
}

DO_INLINE float fb(float length, float L)
{
        float x = length/L;
        return (-11.541f*pow(x,4)+34.193f*pow(x,3)-39.083f*pow(x,2)+23.116f*x-9.713f);
}

DO_INLINE float fbderiv(float length, float L)
{
        float x = length/L;

        return (-46.164f*pow(x,3)+102.579f*pow(x,2)-78.166f*x+23.116f);
}

DO_INLINE float fbstar(float length, float L, float kb, float cb)
{
        float tempfb = kb * fb(length, L);

        float fbstar = cb * (length - L);
        
        if(tempfb < fbstar)
                return fbstar;
        else
                return tempfb;          
}

// function to calculae bending spring force (taken from Choi & Co)
DO_INLINE float fbstar_jacobi(float length, float L, float kb, float cb)
{
        float tempfb = kb * fb(length, L);
        float fbstar = cb * (length - L);

        if(tempfb < fbstar)
        {               
                return cb;
        }
        else
        {
                return kb * fbderiv(length, L); 
        }       
}

DO_INLINE void filter(lfVector *V, fmatrix3x3 *S)
{
        unsigned int i=0;

        for(i=0;i<S[0].vcount;i++)
        {
                mul_fvector_fmatrix(V[S[i].r], V[S[i].r], S[i].m);
        }
}

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;
        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 * sqrt(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;

        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
}

// 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);
                
        }
}
#if 0
/*
// 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

// outer product is NOT cross product!!!
DO_INLINE void dfdx_spring_type1(float to[3][3], float extent[3], float length, float L, float dot, float k)
{
        // dir is unit length direction, rest is spring's restlength, k is spring constant.
        // return  (outerprod(dir,dir)*k + (I - outerprod(dir,dir))*(k - ((k*L)/length)));
        float temp[3][3];
        float temp1 = k*(1.0 - (L/length));     
        
        mul_fvectorT_fvectorS(temp, extent, extent, 1.0 / dot);
        sub_fmatrix_fmatrix(to, I, temp);
        mul_fmatrix_S(to, temp1);
        
        mul_fvectorT_fvectorS(temp, extent, extent, k/ dot);
        add_fmatrix_fmatrix(to, to, temp);
        
        /*
        mul_fvectorT_fvector(temp, dir, dir);
        sub_fmatrix_fmatrix(to, I, temp);
        mul_fmatrix_S(to, k* (1.0f-(L/length)));
        mul_fmatrix_S(temp, k);
        add_fmatrix_fmatrix(to, temp, to);
        */
}

DO_INLINE void dfdx_spring_type2(float to[3][3], float dir[3], float length, float L, float k, float cb)
{
        // return  outerprod(dir,dir)*fbstar_jacobi(length, L, k, cb);
        mul_fvectorT_fvectorS(to, dir, dir, fbstar_jacobi(length, L, k, cb));
}

DO_INLINE void dfdv_damp(float to[3][3], float dir[3], float damping)
{
        // derivative of force wrt velocity.  
        mul_fvectorT_fvectorS(to, dir, dir, damping);
        
}

DO_INLINE void dfdx_spring(float to[3][3],  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;
        mul_fvectorT_fvector(to, dir, dir);
        sub_fmatrix_fmatrix(to, I, to);

        mul_fmatrix_S(to, (L/length)); 
        sub_fmatrix_fmatrix(to, to, I);
        mul_fmatrix_S(to, -k);
}

// unused atm
DO_INLINE void dfdx_damp(float to[3][3],  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 * -(INPR(dir,vel)/MAX2(length,rest)))); 

}

DO_INLINE void cloth_calc_spring_force(ClothModifierData *clmd, ClothSpring *s, lfVector *UNUSED(lF), lfVector *X, lfVector *V, fmatrix3x3 *UNUSED(dFdV), fmatrix3x3 *UNUSED(dFdX), float time)
{
        Cloth *cloth = clmd->clothObject;
        ClothVertex *verts = cloth->verts;
        float extent[3];
        float length = 0, dot = 0;
        float dir[3] = {0,0,0};
        float vel[3];
        float k = 0.0f;
        float L = s->restlen;
        float cb; /* = clmd->sim_parms->structural; */ /*UNUSED*/

        float nullf[3] = {0,0,0};
        float stretch_force[3] = {0,0,0};
        float bending_force[3] = {0,0,0};
        float damping_force[3] = {0,0,0};
        float nulldfdx[3][3]={ {0,0,0}, {0,0,0}, {0,0,0}};
        
        float scaling = 0.0;

        int no_compress = clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_NO_SPRING_COMPRESS;
        
        VECCOPY(s->f, nullf);
        cp_fmatrix(s->dfdx, nulldfdx);
        cp_fmatrix(s->dfdv, nulldfdx);

        // calculate elonglation
        VECSUB(extent, X[s->kl], X[s->ij]);
        VECSUB(vel, V[s->kl], V[s->ij]);
        dot = INPR(extent, extent);
        length = sqrt(dot);
        
        s->flags &= ~CLOTH_SPRING_FLAG_NEEDED;
        
        if(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;
        }
        } 
                */
                mul_fvector_S(dir, extent, 1.0f/length);
        }
        else    
        {
                mul_fvector_S(dir, extent, 0.0f);
        }
        
        // calculate force of structural + shear springs
        if((s->type & CLOTH_SPRING_TYPE_STRUCTURAL) || (s->type & CLOTH_SPRING_TYPE_SHEAR))
        {
                if(length > L || no_compress)
                {
                        s->flags |= CLOTH_SPRING_FLAG_NEEDED;
                        
                        k = clmd->sim_parms->structural;
                                
                        scaling = k + s->stiffness * ABS(clmd->sim_parms->max_struct-k);
                        
                        k = scaling / (clmd->sim_parms->avg_spring_len + FLT_EPSILON);
                        
                        // TODO: verify, half verified (couldn't see error)
                        mul_fvector_S(stretch_force, dir, k*(length-L)); 

                        VECADD(s->f, s->f, stretch_force);

                        // Ascher & Boxman, p.21: Damping only during elonglation
                        // something wrong with it...
                        mul_fvector_S(damping_force, dir, clmd->sim_parms->Cdis * INPR(vel,dir));
                        VECADD(s->f, s->f, damping_force);
                        
                        /* VERIFIED */
                        dfdx_spring(s->dfdx, dir, length, L, k);
                        
                        /* VERIFIED */
                        dfdv_damp(s->dfdv, dir, clmd->sim_parms->Cdis);
                        
                }
        }
        else if(s->type & CLOTH_SPRING_TYPE_GOAL)
        {
                float tvect[3];
                
                s->flags |= CLOTH_SPRING_FLAG_NEEDED;
                
                // current_position = xold + t * (newposition - xold)
                VECSUB(tvect, verts[s->ij].xconst, verts[s->ij].xold);
                mul_fvector_S(tvect, tvect, time);
                VECADD(tvect, tvect, verts[s->ij].xold);

                VECSUB(extent, X[s->ij], tvect);
                
                // SEE MSG BELOW (these are UNUSED)
                // dot = INPR(extent, extent);
                // length = sqrt(dot);
                
                k = clmd->sim_parms->goalspring;
                
                scaling = k + s->stiffness * ABS(clmd->sim_parms->max_struct-k);
                        
                k = verts [s->ij].goal * scaling / (clmd->sim_parms->avg_spring_len + FLT_EPSILON);
                
                VECADDS(s->f, s->f, extent, -k);
                
                mul_fvector_S(damping_force, dir, clmd->sim_parms->goalfrict * 0.01 * INPR(vel,dir));
                VECADD(s->f, s->f, damping_force);
                
                // HERE IS THE PROBLEM!!!!
                // dfdx_spring(s->dfdx, dir, length, 0.0, k);
                // dfdv_damp(s->dfdv, dir, MIN2(1.0, (clmd->sim_parms->goalfrict/100.0)));
        }
        else // calculate force of bending springs
        {
                if(length < L)
                {
                        s->flags |= CLOTH_SPRING_FLAG_NEEDED;
                        
                        k = clmd->sim_parms->bending;   
                        
                        scaling = k + s->stiffness * ABS(clmd->sim_parms->max_bend-k);                  
                        cb = k = scaling / (20.0*(clmd->sim_parms->avg_spring_len + FLT_EPSILON));

                        mul_fvector_S(bending_force, dir, fbstar(length, L, k, cb));
                        VECADD(s->f, s->f, bending_force);

                        dfdx_spring_type2(s->dfdx, dir, length,L, k, cb);
                }
        }
}

DO_INLINE void cloth_apply_spring_force(ClothModifierData *UNUSED(clmd), ClothSpring *s, lfVector *lF, lfVector *UNUSED(X), lfVector *UNUSED(V), fmatrix3x3 *dFdV, fmatrix3x3 *dFdX)
{
        if(s->flags & CLOTH_SPRING_FLAG_NEEDED)
        {
                if(!(s->type & CLOTH_SPRING_TYPE_BENDING))
                {
                        sub_fmatrix_fmatrix(dFdV[s->ij].m, dFdV[s->ij].m, s->dfdv);
                        sub_fmatrix_fmatrix(dFdV[s->kl].m, dFdV[s->kl].m, s->dfdv);
                        add_fmatrix_fmatrix(dFdV[s->matrix_index].m, dFdV[s->matrix_index].m, s->dfdv); 
                }

                VECADD(lF[s->ij], lF[s->ij], s->f);
                
                if(!(s->type & CLOTH_SPRING_TYPE_GOAL))
                        VECSUB(lF[s->kl], lF[s->kl], s->f);
                
                sub_fmatrix_fmatrix(dFdX[s->kl].m, dFdX[s->kl].m, s->dfdx);
                sub_fmatrix_fmatrix(dFdX[s->ij].m, dFdX[s->ij].m, s->dfdx);
                add_fmatrix_fmatrix(dFdX[s->matrix_index].m, dFdX[s->matrix_index].m, s->dfdx);
        }       
}


static void CalcFloat( float *v1, float *v2, float *v3, float *n)
{
        float n1[3],n2[3];

        n1[0]= v1[0]-v2[0];
        n2[0]= v2[0]-v3[0];
        n1[1]= v1[1]-v2[1];
        n2[1]= v2[1]-v3[1];
        n1[2]= v1[2]-v2[2];
        n2[2]= v2[2]-v3[2];
        n[0]= n1[1]*n2[2]-n1[2]*n2[1];
        n[1]= n1[2]*n2[0]-n1[0]*n2[2];
        n[2]= n1[0]*n2[1]-n1[1]*n2[0];
}

static void CalcFloat4( float *v1, float *v2, float *v3, float *v4, float *n)
{
        /* real cross! */
        float n1[3],n2[3];

        n1[0]= v1[0]-v3[0];
        n1[1]= v1[1]-v3[1];
        n1[2]= v1[2]-v3[2];

        n2[0]= v2[0]-v4[0];
        n2[1]= v2[1]-v4[1];
        n2[2]= v2[2]-v4[2];

        n[0]= n1[1]*n2[2]-n1[2]*n2[1];
        n[1]= n1[2]*n2[0]-n1[0]*n2[2];
        n[2]= n1[0]*n2[1]-n1[1]*n2[0];
}

static float calculateVertexWindForce(float wind[3], float vertexnormal[3])  
{
        return (INPR(wind, vertexnormal));
}

typedef struct HairGridVert {
        float velocity[3];
        float density;
} HairGridVert;
#define HAIR_GRID_INDEX(vec, min, max, axis) (int)( (vec[axis] - min[axis]) / (max[axis] - min[axis]) * 9.99f );
/* Smoothing of hair velocities:
 * adapted from
                Volumetric Methods for Simulation and Rendering of Hair
                by Lena Petrovic, Mark Henne and John Anderson
 *              Pixar Technical Memo #06-08, Pixar Animation Studios
 */
static void hair_velocity_smoothing(ClothModifierData *clmd, lfVector *lF, lfVector *lX, lfVector *lV, unsigned int numverts)
{
        /* TODO: This is an initial implementation and should be made much better in due time.
         * What should at least be implemented is a grid size parameter and a smoothing kernel
         * for bigger grids.
         */

        /* 10x10x10 grid gives nice initial results */
        HairGridVert grid[10][10][10];
        HairGridVert colg[10][10][10];
        ListBase *colliders = get_collider_cache(clmd->scene, NULL, NULL);
        ColliderCache *col = NULL;
        float gmin[3], gmax[3], density;
        /* 2.0f is an experimental value that seems to give good results */
        float smoothfac = 2.0f * clmd->sim_parms->velocity_smooth;
        float collfac = 2.0f * clmd->sim_parms->collider_friction;
        unsigned int    v = 0;
        unsigned int    i = 0;
        int                             j = 0;
        int                             k = 0;

        INIT_MINMAX(gmin, gmax);

        for(i = 0; i < numverts; i++)
                DO_MINMAX(lX[i], gmin, gmax);

        /* initialize grid */
        for(i = 0; i < 10; i++) {
                for(j = 0; j < 10; j++) {
                        for(k = 0; k < 10; k++) {
                                grid[i][j][k].velocity[0] = 0.0f;
                                grid[i][j][k].velocity[1] = 0.0f;
                                grid[i][j][k].velocity[2] = 0.0f;
                                grid[i][j][k].density = 0.0f;

                                colg[i][j][k].velocity[0] = 0.0f;
                                colg[i][j][k].velocity[1] = 0.0f;
                                colg[i][j][k].velocity[2] = 0.0f;
                                colg[i][j][k].density = 0.0f;
                        }
                }
        }

        /* gather velocities & density */
        if(smoothfac > 0.0f) for(v = 0; v < numverts; v++) {
                i = HAIR_GRID_INDEX(lX[v], gmin, gmax, 0);
                j = HAIR_GRID_INDEX(lX[v], gmin, gmax, 1);
                k = HAIR_GRID_INDEX(lX[v], gmin, gmax, 2);
                if (i < 0 || j < 0 || k < 0 || i > 10 || j >= 10 || k >= 10)
                        continue;

                grid[i][j][k].velocity[0] += lV[v][0];
                grid[i][j][k].velocity[1] += lV[v][1];
                grid[i][j][k].velocity[2] += lV[v][2];
                grid[i][j][k].density += 1.0f;
        }

        /* gather colliders */
        if(colliders && collfac > 0.0f) for(col = colliders->first; col; col = col->next)
        {
                MVert *loc0 = col->collmd->x;
                MVert *loc1 = col->collmd->xnew;
                float vel[3];

                for(v=0; v<col->collmd->numverts; v++, loc0++, loc1++) {
                        i = HAIR_GRID_INDEX(loc1->co, gmin, gmax, 0);

                        if(i>=0 && i<10) {
                                j = HAIR_GRID_INDEX(loc1->co, gmin, gmax, 1);

                                if(j>=0 && j<10) {
                                        k = HAIR_GRID_INDEX(loc1->co, gmin, gmax, 2);

                                        if(k>=0 && k<10) {
                                                VECSUB(vel, loc1->co, loc0->co);

                                                colg[i][j][k].velocity[0] += vel[0];
                                                colg[i][j][k].velocity[1] += vel[1];
                                                colg[i][j][k].velocity[2] += vel[2];
                                                colg[i][j][k].density += 1.0;
                                        }
                                }
                        }
                }
        }
        

        /* divide velocity with density */
        for(i = 0; i < 10; i++) {
                for(j = 0; j < 10; j++) {
                        for(k = 0; k < 10; k++) {
                                density = grid[i][j][k].density;
                                if(density > 0.0f) {
                                        grid[i][j][k].velocity[0] /= density;
                                        grid[i][j][k].velocity[1] /= density;
                                        grid[i][j][k].velocity[2] /= density;
                                }

                                density = colg[i][j][k].density;
                                if(density > 0.0f) {
                                        colg[i][j][k].velocity[0] /= density;
                                        colg[i][j][k].velocity[1] /= density;
                                        colg[i][j][k].velocity[2] /= density;
                                }
                        }
                }
        }

        /* calculate forces */
        for(v = 0; v < numverts; v++) {
                i = HAIR_GRID_INDEX(lX[v], gmin, gmax, 0);
                j = HAIR_GRID_INDEX(lX[v], gmin, gmax, 1);
                k = HAIR_GRID_INDEX(lX[v], gmin, gmax, 2);
                if (i < 0 || j < 0 || k < 0 || i > 10 || j >= 10 || k >= 10)
                        continue;

                lF[v][0] += smoothfac * (grid[i][j][k].velocity[0] - lV[v][0]);
                lF[v][1] += smoothfac * (grid[i][j][k].velocity[1] - lV[v][1]);
                lF[v][2] += smoothfac * (grid[i][j][k].velocity[2] - lV[v][2]);

                if(colg[i][j][k].density > 0.0f) {
                        lF[v][0] += collfac * (colg[i][j][k].velocity[0] - lV[v][0]);
                        lF[v][1] += collfac * (colg[i][j][k].velocity[1] - lV[v][1]);
                        lF[v][2] += collfac * (colg[i][j][k].velocity[2] - lV[v][2]);
                }
        }

        free_collider_cache(&colliders);
}

static void cloth_calc_force(ClothModifierData *clmd, float UNUSED(frame), lfVector *lF, lfVector *lX, lfVector *lV, fmatrix3x3 *dFdV, fmatrix3x3 *dFdX, ListBase *effectors, float time, fmatrix3x3 *M)
{
        /* Collect forces and derivatives:  F,dFdX,dFdV */
        Cloth           *cloth          = clmd->clothObject;
        unsigned int i  = 0;
        float           spring_air      = clmd->sim_parms->Cvi * 0.01f; /* viscosity of air scaled in percent */
        float           gravity[3] = {0.0f, 0.0f, 0.0f};
        float           tm2[3][3]       = {{0}};
        MFace           *mfaces         = cloth->mfaces;
        unsigned int numverts = cloth->numverts;
        LinkNode *search;
        lfVector *winvec;
        EffectedPoint epoint;

        tm2[0][0]= tm2[1][1]= tm2[2][2]= -spring_air;
        
        /* global acceleration (gravitation) */
        if(clmd->scene->physics_settings.flag & PHYS_GLOBAL_GRAVITY) {
                VECCOPY(gravity, clmd->scene->physics_settings.gravity);
                mul_fvector_S(gravity, gravity, 0.001f * clmd->sim_parms->effector_weights->global_gravity); /* scale gravity force */
        }

        /* set dFdX jacobi matrix to zero */
        init_bfmatrix(dFdX, ZERO);
        /* set dFdX jacobi matrix diagonal entries to -spring_air */ 
        initdiag_bfmatrix(dFdV, tm2);

        init_lfvector(lF, gravity, numverts);
        
        if(clmd->sim_parms->velocity_smooth > 0.0f || clmd->sim_parms->collider_friction > 0.0f)
                hair_velocity_smoothing(clmd, lF, lX, lV, numverts);

        /* multiply lF with mass matrix
        // force = mass * acceleration (in this case: gravity)
        */
        for(i = 0; i < numverts; i++)
        {
                float temp[3];
                VECCOPY(temp, lF[i]);
                mul_fmatrix_fvector(lF[i], M[i].m, temp);
        }

        submul_lfvectorS(lF, lV, spring_air, numverts);
        
        /* handle external forces like wind */
        if(effectors)
        {       
                // 0 = force, 1 = normalized force
                winvec = create_lfvector(cloth->numverts);
                
                if(!winvec)
                        printf("winvec: out of memory in implicit.c\n");
                
                // precalculate wind forces
                for(i = 0; i < cloth->numverts; i++)
                {       
                        pd_point_from_loc(clmd->scene, (float*)lX[i], (float*)lV[i], i, &epoint);
                        pdDoEffectors(effectors, NULL, clmd->sim_parms->effector_weights, &epoint, winvec[i], NULL);
                }
                
                for(i = 0; i < cloth->numfaces; i++)
                {
                        float trinormal[3]={0,0,0}; // normalized triangle normal
                        float triunnormal[3]={0,0,0}; // not-normalized-triangle normal
                        float tmp[3]={0,0,0};
                        float factor = (mfaces[i].v4) ? 0.25 : 1.0 / 3.0;
                        factor *= 0.02;
                        
                        // calculate face normal
                        if(mfaces[i].v4)
                                CalcFloat4(lX[mfaces[i].v1],lX[mfaces[i].v2],lX[mfaces[i].v3],lX[mfaces[i].v4],triunnormal);
                        else
                                CalcFloat(lX[mfaces[i].v1],lX[mfaces[i].v2],lX[mfaces[i].v3],triunnormal);

                        normalize_v3_v3(trinormal, triunnormal);
                        
                        // add wind from v1
                        VECCOPY(tmp, trinormal);
                        mul_v3_fl(tmp, calculateVertexWindForce(winvec[mfaces[i].v1], triunnormal));
                        VECADDS(lF[mfaces[i].v1], lF[mfaces[i].v1], tmp, factor);
                        
                        // add wind from v2
                        VECCOPY(tmp, trinormal);
                        mul_v3_fl(tmp, calculateVertexWindForce(winvec[mfaces[i].v2], triunnormal));
                        VECADDS(lF[mfaces[i].v2], lF[mfaces[i].v2], tmp, factor);
                        
                        // add wind from v3
                        VECCOPY(tmp, trinormal);
                        mul_v3_fl(tmp, calculateVertexWindForce(winvec[mfaces[i].v3], triunnormal));
                        VECADDS(lF[mfaces[i].v3], lF[mfaces[i].v3], tmp, factor);
                        
                        // add wind from v4
                        if(mfaces[i].v4)
                        {
                                VECCOPY(tmp, trinormal);
                                mul_v3_fl(tmp, calculateVertexWindForce(winvec[mfaces[i].v4], triunnormal));
                                VECADDS(lF[mfaces[i].v4], lF[mfaces[i].v4], tmp, factor);
                        }
                }

                /* Hair has only edges */
                if(cloth->numfaces == 0) {
                        ClothSpring *spring;
                        float edgevec[3]={0,0,0}; //edge vector
                        float edgeunnormal[3]={0,0,0}; // not-normalized-edge normal
                        float tmp[3]={0,0,0};
                        float factor = 0.01;

                        search = cloth->springs;
                        while(search) {
                                spring = search->link;
                                
                                if(spring->type == CLOTH_SPRING_TYPE_STRUCTURAL) {
                                        VECSUB(edgevec, (float*)lX[spring->ij], (float*)lX[spring->kl]);

                                        project_v3_v3v3(tmp, winvec[spring->ij], edgevec);
                                        VECSUB(edgeunnormal, winvec[spring->ij], tmp);
                                        /* hair doesn't stretch too much so we can use restlen pretty safely */
                                        VECADDS(lF[spring->ij], lF[spring->ij], edgeunnormal, spring->restlen * factor);

                                        project_v3_v3v3(tmp, winvec[spring->kl], edgevec);
                                        VECSUB(edgeunnormal, winvec[spring->kl], tmp);
                                        VECADDS(lF[spring->kl], lF[spring->kl], edgeunnormal, spring->restlen * factor);
                                }

                                search = search->next;
                        }
                }

                del_lfvector(winvec);
        }
                
        // calculate spring forces
        search = cloth->springs;
        while(search)
        {
                // only handle active springs
                // if(((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) && !(springs[i].flags & CSPRING_FLAG_DEACTIVATE))|| !(clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED)){}
                cloth_calc_spring_force(clmd, search->link, lF, lX, lV, dFdV, dFdX, time);

                search = search->next;
        }
        
        // apply spring forces
        search = cloth->springs;
        while(search)
        {
                // only handle active springs
                // if(((clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED) && !(springs[i].flags & CSPRING_FLAG_DEACTIVATE))|| !(clmd->sim_parms->flags & CSIMSETT_FLAG_TEARING_ENABLED))  
                cloth_apply_spring_force(clmd, search->link, lF, lX, lV, dFdV, dFdX);
                search = search->next;
        }
        // printf("\n");
}

static void simulate_implicit_euler(lfVector *Vnew, lfVector *UNUSED(lX), lfVector *lV, lfVector *lF, fmatrix3x3 *dFdV, fmatrix3x3 *dFdX, float dt, fmatrix3x3 *A, lfVector *B, lfVector *dV, fmatrix3x3 *S, lfVector *z, lfVector *olddV, fmatrix3x3 *UNUSED(P), fmatrix3x3 *UNUSED(Pinv), fmatrix3x3 *M, fmatrix3x3 *UNUSED(bigI))
{
        unsigned int numverts = dFdV[0].vcount;

        lfVector *dFdXmV = create_lfvector(numverts);
        zero_lfvector(dV, numverts);
        
        cp_bfmatrix(A, M);
        
        subadd_bfmatrixS_bfmatrixS(A, dFdV, dt, dFdX, (dt*dt));

        mul_bfmatrix_lfvector(dFdXmV, dFdX, lV);

        add_lfvectorS_lfvectorS(B, lF, dt, dFdXmV, (dt*dt), numverts);
        
        itstart();
        
        cg_filtered(dV, A, B, z, S); /* conjugate gradient algorithm to solve Ax=b */
        // cg_filtered_pre(dV, A, B, z, S, P, Pinv, bigI);
        
        itend();
        // printf("cg_filtered calc time: %f\n", (float)itval());
        
        cp_lfvector(olddV, dV, numverts);

        // advance velocities
        add_lfvector_lfvector(Vnew, lV, dV, numverts);
        

        del_lfvector(dFdXmV);
}

/*computes where the cloth would be if it were subject to perfectly stiff edges
  (edge distance constraints) in a lagrangian solver.  then add forces to help
  guide the implicit solver to that state.  this function is called after
  collisions*/
int cloth_calc_helper_forces(Object *UNUSED(ob), ClothModifierData * clmd, float (*initial_cos)[3], float UNUSED(step), float dt)
{
        Cloth *cloth= clmd->clothObject;
        float (*cos)[3] = MEM_callocN(sizeof(float)*3*cloth->numverts, "cos cloth_calc_helper_forces");
        float *masses = MEM_callocN(sizeof(float)*cloth->numverts, "cos cloth_calc_helper_forces");
        LinkNode *node;
        ClothSpring *spring;
        ClothVertex *cv;
        int i, steps;
        
        cv = cloth->verts;
        for (i=0; i<cloth->numverts; i++, cv++) {
                copy_v3_v3(cos[i], cv->tx);
                
                if (cv->goal == 1.0f || len_v3v3(initial_cos[i], cv->tx) != 0.0) {
                        masses[i] = 1e+10;      
                } else {
                        masses[i] = cv->mass;
                }
        }
        
        steps = 55;
        for (i=0; i<steps; i++) {
                for (node=cloth->springs; node; node=node->next) {
                        ClothVertex *cv1, *cv2;
                        int v1, v2;
                        float len, c, l, vec[3];
                        
                        spring = node->link;
                        if (spring->type != CLOTH_SPRING_TYPE_STRUCTURAL && spring->type != CLOTH_SPRING_TYPE_SHEAR) 
                                continue;
                        
                        v1 = spring->ij; v2 = spring->kl;
                        cv1 = cloth->verts + v1;
                        cv2 = cloth->verts + v2;
                        len = len_v3v3(cos[v1], cos[v2]);
                        
                        sub_v3_v3v3(vec, cos[v1], cos[v2]);
                        normalize_v3(vec);
                        
                        c = (len - spring->restlen);
                        if (c == 0.0)
                                continue;
                        
                        l = c / ((1.0/masses[v1]) + (1.0/masses[v2]));
                        
                        mul_v3_fl(vec, -(1.0/masses[v1])*l);
                        add_v3_v3(cos[v1], vec);
        
                        sub_v3_v3v3(vec, cos[v2], cos[v1]);
                        normalize_v3(vec);
                        
                        mul_v3_fl(vec, -(1.0/masses[v2])*l);
                        add_v3_v3(cos[v2], vec);
                }
        }
        
        cv = cloth->verts;
        for (i=0; i<cloth->numverts; i++, cv++) {
                float vec[3];
                
                /*compute forces*/
                sub_v3_v3v3(vec, cos[i], cv->tx);
                mul_v3_fl(vec, cv->mass*dt*20.0);
                add_v3_v3(cv->tv, vec);
                //copy_v3_v3(cv->tx, cos[i]);
        }
        
        MEM_freeN(cos);
        MEM_freeN(masses);
        
        return 1;
}
int implicit_solver (Object *ob, float frame, ClothModifierData *clmd, ListBase *effectors)
{               
        unsigned int i=0;
        float step=0.0f, tf=clmd->sim_parms->timescale;
        Cloth *cloth = clmd->clothObject;
        ClothVertex *verts = cloth->verts, *cv;
        unsigned int numverts = cloth->numverts;
        float dt = clmd->sim_parms->timescale / clmd->sim_parms->stepsPerFrame;
        float spf = (float)clmd->sim_parms->stepsPerFrame / clmd->sim_parms->timescale;
        float (*initial_cos)[3] = MEM_callocN(sizeof(float)*3*cloth->numverts, "initial_cos implicit.c");
        Implicit_Data *id = cloth->implicit;
        int do_extra_solve;

        if(clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_GOAL) /* do goal stuff */
        {
                for(i = 0; i < numverts; i++)
                {                       
                        // update velocities with constrained velocities from pinned verts
                        if(verts [i].flags & CLOTH_VERT_FLAG_PINNED)
                        {                       
                                VECSUB(id->V[i], verts[i].xconst, verts[i].xold);
                                // mul_v3_fl(id->V[i], clmd->sim_parms->stepsPerFrame);
                        }
                }       
        }
        
        while(step < tf)
        {       
                // calculate forces
                cloth_calc_force(clmd, frame, id->F, id->X, id->V, id->dFdV, id->dFdX, effectors, step, id->M);
                
                // calculate new velocity
                simulate_implicit_euler(id->Vnew, id->X, id->V, id->F, id->dFdV, id->dFdX, dt, id->A, id->B, id->dV, id->S, id->z, id->olddV, id->P, id->Pinv, id->M, id->bigI);
                
                // advance positions
                add_lfvector_lfvectorS(id->Xnew, id->X, id->Vnew, dt, numverts);
                
                /* move pinned verts to correct position */
                for(i = 0; i < numverts; i++)
                {       
                        if(clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_GOAL) 
                        {                       
                                if(verts [i].flags & CLOTH_VERT_FLAG_PINNED)
                                {                       
                                        float tvect[3] = {.0,.0,.0};
                                        VECSUB(tvect, verts[i].xconst, verts[i].xold);
                                        mul_fvector_S(tvect, tvect, step+dt);
                                        VECADD(tvect, tvect, verts[i].xold);
                                        VECCOPY(id->Xnew[i], tvect);
                                }       
                        }
                        
                        VECCOPY(verts[i].txold, id->X[i]);
                }

                if(clmd->coll_parms->flags & CLOTH_COLLSETTINGS_FLAG_ENABLED && clmd->clothObject->bvhtree)
                {
                        // collisions 
                        // itstart();
                        
                        // update verts to current positions
                        for(i = 0; i < numverts; i++)
                        {
                                VECCOPY(verts[i].tx, id->Xnew[i]);

                                VECSUB(verts[i].tv, verts[i].tx, verts[i].txold);
                                VECCOPY(verts[i].v, verts[i].tv);
                        }

                        for (i=0, cv=cloth->verts; i<cloth->numverts; i++, cv++) {
                                copy_v3_v3(initial_cos[i], cv->tx);
                        }
                        
                        // call collision function
                        // TODO: check if "step" or "step+dt" is correct - dg
                        do_extra_solve = cloth_bvh_objcollision(ob, clmd, step/clmd->sim_parms->timescale, dt/clmd->sim_parms->timescale);
                                                
                        // copy corrected positions back to simulation
                        for(i = 0; i < numverts; i++)
                        {               
                                // correct velocity again, just to be sure we had to change it due to adaptive collisions
                                VECSUB(verts[i].tv, verts[i].tx, id->X[i]);
                        }

                        //if (do_extra_solve)
                        //      cloth_calc_helper_forces(ob, clmd, initial_cos, step/clmd->sim_parms->timescale, dt/clmd->sim_parms->timescale);
                        
                        for(i = 0; i < numverts; i++)
                        {               

                                if(do_extra_solve)
                                {
                                        
                                        if((clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_GOAL) && (verts [i].flags & CLOTH_VERT_FLAG_PINNED))
                                                continue;

                                        VECCOPY(id->Xnew[i], verts[i].tx);
                                        VECCOPY(id->Vnew[i], verts[i].tv);
                                        mul_v3_fl(id->Vnew[i], spf);
                                }
                        }
                        
                        // X = Xnew;
                        cp_lfvector(id->X, id->Xnew, numverts);

                        // if there were collisions, advance the velocity from v_n+1/2 to v_n+1
                        
                        if(do_extra_solve)
                        {
                                // V = Vnew;
                                cp_lfvector(id->V, id->Vnew, numverts);

                                // calculate 
                                cloth_calc_force(clmd, frame, id->F, id->X, id->V, id->dFdV, id->dFdX, effectors, step+dt, id->M);      
                                
                                simulate_implicit_euler(id->Vnew, id->X, id->V, id->F, id->dFdV, id->dFdX, dt / 2.0f, id->A, id->B, id->dV, id->S, id->z, id->olddV, id->P, id->Pinv, id->M, id->bigI);
                        }
                }
                else
                {
                        // X = Xnew;
                        cp_lfvector(id->X, id->Xnew, numverts);
                }
                
                // itend();
                // printf("collision time: %f\n", (float)itval());
                
                // V = Vnew;
                cp_lfvector(id->V, id->Vnew, numverts);
                
                step += dt;
        }

        for(i = 0; i < numverts; i++)
        {                               
                if((clmd->sim_parms->flags & CLOTH_SIMSETTINGS_FLAG_GOAL) && (verts [i].flags & CLOTH_VERT_FLAG_PINNED))
                {
                        VECCOPY(verts[i].txold, verts[i].xconst); // TODO: test --> should be .x 
                        VECCOPY(verts[i].x, verts[i].xconst);
                        VECCOPY(verts[i].v, id->V[i]);
                }
                else
                {
                        VECCOPY(verts[i].txold, id->X[i]);
                        VECCOPY(verts[i].x, id->X[i]);
                        VECCOPY(verts[i].v, id->V[i]);
                }
        }
        
        MEM_freeN(initial_cos);
        
        return 1;
}

void implicit_set_positions (ClothModifierData *clmd)
{               
        Cloth *cloth = clmd->clothObject;
        ClothVertex *verts = cloth->verts;
        unsigned int numverts = cloth->numverts, i;
        Implicit_Data *id = cloth->implicit;
        
        for(i = 0; i < numverts; i++)
        {                               
                VECCOPY(id->X[i], verts[i].x);
                VECCOPY(id->V[i], verts[i].v);
        }
        if(G.rt > 0)
                printf("implicit_set_positions\n");     
}