From 79fc9ce029be3e91d3249a654f84c7a1ce1ff9ee Mon Sep 17 00:00:00 2001
From: Samo Penic <samo.penic@gmail.com>
Date: Thu, 07 Jun 2012 19:46:44 +0000
Subject: [PATCH] spherical harmonics coefficients co fixed and working. Zero based indexing was solved in such a manner, that we allocated more memory that is required by coefficients.
---
src/sh.c | 233 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 files changed, 233 insertions(+), 0 deletions(-)
diff --git a/src/sh.c b/src/sh.c
index f0b19fa..12a6ce4 100644
--- a/src/sh.c
+++ b/src/sh.c
@@ -3,6 +3,71 @@
#include "general.h"
#include "sh.h"
+
+
+ts_spharm *sph_init(ts_vertex_list *vlist, ts_uint l){
+ ts_uint j,i;
+ ts_spharm *sph=(ts_spharm *)malloc(sizeof(ts_spharm));
+
+
+ /* lets initialize Ylm for each vertex. */
+ sph->Ylmi=(ts_double ***)calloc(l,sizeof(ts_double **));
+ for(i=0;i<l;i++){
+ sph->Ylmi[i]=(ts_double **)calloc(2*i+1,sizeof(ts_double *));
+ for(j=0;j<(2*i+1);j++){
+ sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double));
+ }
+ }
+
+ /* lets initialize ulm */
+ sph->ulm=(ts_double **)calloc(l,sizeof(ts_double *));
+ for(j=0;j<l;j++){
+ sph->ulm[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
+ }
+
+
+ /* lets initialize co */
+//NOTE: C is has zero based indexing. Code is imported from fortran and to comply with original indexes we actually generate one index more. Also second dimension is 2*j+2 instead of 2*j+2. elements starting with 0 are useles and should be ignored!
+ sph->co=(ts_double **)calloc(l+1,sizeof(ts_double *));
+ for(j=0;j<=l;j++){
+ sph->co[j]=(ts_double *)calloc(2*j+2,sizeof(ts_double));
+ }
+
+ sph->l=l;
+
+ /* Calculate coefficients that will remain constant during all the simulation */
+ precomputeShCoeff(sph);
+
+ return sph;
+}
+
+
+ts_bool sph_free(ts_spharm *sph){
+ int i,j;
+ for(i=0;i<sph->l;i++){
+ if(sph->ulm[i]!=NULL) free(sph->ulm[i]);
+ if(sph->co[i]!=NULL) free(sph->co[i]);
+ }
+ if(sph->co[sph->l]!=NULL) free(sph->co[sph->l]);
+ if(sph->co != NULL) free(sph->co);
+ if(sph->ulm !=NULL) free(sph->ulm);
+
+ if(sph->Ylmi!=NULL) {
+ for(i=0;i<sph->l;i++){
+ if(sph->Ylmi[i]!=NULL){
+ for(j=0;j<i*2+1;j++){
+ if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]);
+ }
+ free(sph->Ylmi[i]);
+ }
+ }
+ free(sph->Ylmi);
+ }
+
+ free(sph);
+ return TS_SUCCESS;
+}
+
/* Gives you legendre polynomials. Taken from NR, p. 254 */
ts_double plgndr(ts_int l, ts_int m, ts_float x){
ts_double fact, pll, pmm, pmmp1, somx2;
@@ -55,6 +120,27 @@
}
+
+ts_bool precomputeShCoeff(ts_spharm *sph){
+ ts_int i,j,al,am;
+ ts_double **co=sph->co;
+ for(i=1;i<=sph->l;i++){
+ al=i;
+ sph->co[i][i+1]=sqrt((2.0*al+1.0)/2.0/M_PI);
+ for(j=1;j<=i-1;j++){
+ am=j;
+ sph->co[i][i+1+j]=co[i][i+j]*sqrt(1.0/(al-am+1.0)/(al+am));
+ sph->co[i][i+1-j]=co[i][i+1+j];
+ }
+ co[i][2*i+1]=co[i][2*i]*sqrt(1.0/(2.0*al));
+ co[i][1]=co[i][2*i+1];
+ co[i][i+1]=sqrt((2.0*al+1.0)/4.0/M_PI);
+ }
+ return TS_SUCCESS;
+
+}
+
+
/*Computes Y(l,m,theta,fi) (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */
ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){
ts_double fac1, fac2, K;
@@ -88,3 +174,150 @@
return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta));
}
+
+
+/* Function transforms coordinates from cartesian to spherical coordinates
+ * (r,phi, theta). */
+ts_bool *cart2sph(ts_coord *coord, ts_double x, ts_double y, ts_double z){
+ coord->coord_type=TS_COORD_SPHERICAL;
+#ifdef TS_DOUBLE_DOUBLE
+ coord->e1=sqrt(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atan(sqrt(x*x+y*y)/z);
+ coord->e2=atan2(y,x);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ coord->e1=sqrtf(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atanf(sqrtf(x*x+y*y)/z);
+ coord->e2=atan2f(y,x);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ coord->e1=sqrtl(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atanl(sqrtl(x*x+y*y)/z);
+ coord->e2=atan2l(y,x);
+#endif
+
+ return TS_SUCCESS;
+}
+
+/* Function returns radius of the sphere with the same volume as vesicle (r0) */
+ts_double getR0(ts_vesicle *vesicle){
+ ts_double r0;
+ #ifdef TS_DOUBLE_DOUBLE
+ r0=pow(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ r0=powf(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ r0=powl(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+ return r0;
+}
+
+
+ts_bool preparationSh(ts_vesicle *vesicle, ts_double r0){
+//TODO: before calling or during the call calculate area of each triangle! Can
+//be also done after vertexmove and bondflip //
+ ts_uint i,j;
+ ts_vertex **vtx=vesicle->vlist->vtx;
+ ts_vertex *cvtx;
+ ts_triangle *ctri;
+ ts_double centroid[3];
+ ts_double r;
+ for (i=0; i<vesicle->vlist->n; i++){
+ cvtx=vtx[i];
+ //cvtx->projArea=4.0*M_PI/1447.0*(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z)/r0/r0;
+ cvtx->projArea=0.0;
+
+ /* go over all triangles that have a common vertex i */
+ for(j=0; j<cvtx->tristar_no; j++){
+ ctri=cvtx->tristar[j];
+ centroid[0]=(ctri->vertex[0]->x + ctri->vertex[1]->x + ctri->vertex[2]->x)/3.0;
+ centroid[1]=(ctri->vertex[0]->y + ctri->vertex[1]->y + ctri->vertex[2]->y)/3.0;
+ centroid[2]=(ctri->vertex[0]->z + ctri->vertex[1]->z + ctri->vertex[2]->z)/3.0;
+ /* calculating projArea+= area(triangle)*cos(theta) */
+#ifdef TS_DOUBLE_DOUBLE
+ cvtx->projArea = cvtx->projArea + ctri->area*(-centroid[0]*ctri->xnorm - centroid[1]*ctri->ynorm - centroid[2]*ctri->znorm)/ sqrt(centroid[0]*centroid[0]+centroid[1]*centroid[1]+centroid[2]*centroid[2]);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ cvtx->projArea = cvtx->projArea + ctri->area*(-centroid[0]*ctri->xnorm - centroid[1]*ctri->ynorm - centroid[2]*ctri->znorm)/ sqrtf(centroid[0]*centroid[0]+centroid[1]*centroid[1]+centroid[2]*centroid[2]);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ cvtx->projArea = cvtx->projArea + ctri->area*(-centroid[0]*ctri->xnorm - centroid[1]*ctri->ynorm - centroid[2]*ctri->znorm)/ sqrtl(centroid[0]*centroid[0]+centroid[1]*centroid[1]+centroid[2]*centroid[2]);
+#endif
+ }
+
+ cvtx->projArea=cvtx->projArea/3.0;
+ //we dont store spherical coordinates of vertex, so we have to calculate
+ //r(i) at this point.
+#ifdef TS_DOUBLE_DOUBLE
+ r=sqrt(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ r=sqrtf(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ r=sqrtl(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+ cvtx->relR=(r-r0)/r0;
+ cvtx->solAngle=cvtx->projArea/cvtx->relR * cvtx->projArea/cvtx->relR;
+ }
+ return TS_SUCCESS;
+}
+
+
+
+ts_bool calculateYlmi(ts_vesicle *vesicle){
+ ts_uint i,j,k;
+ ts_spharm *sph=vesicle->sphHarmonics;
+ ts_coord *coord=(ts_coord *)malloc(sizeof(ts_coord));
+ ts_double fi, theta;
+ ts_vertex *cvtx;
+ for(k=0;k<vesicle->vlist->n;k++){
+ cvtx=vesicle->vlist->vtx[k];
+ sph->Ylmi[0][0][k]=sqrt(1.0/4.0/M_PI);
+ cart2sph(coord,cvtx->x, cvtx->y, cvtx->z);
+ fi=coord->e2;
+ theta=coord->e3;
+ for(i=0; i<sph->l; i++){
+ for(j=0;j<i;j++){
+ sph->Ylmi[i][j][k]=sph->co[i][j]*cos((j-i-1)*fi)*pow(-1,j-i-1)*plgndr(i,abs(j-i-1),cos(theta));
+ }
+ sph->Ylmi[i][j+1][k]=sph->co[i][j+1]*plgndr(i,0,cos(theta));
+ for(j=sph->l;j<2*i;j++){
+ sph->Ylmi[i][j][k]=sph->co[i][j]*sin((j-i-1)*fi)*plgndr(i,j-i-1,cos(theta));
+ }
+ }
+
+ }
+ free(coord);
+ return TS_SUCCESS;
+}
+
+
+
+ts_bool calculateUlm(ts_vesicle *vesicle){
+ ts_uint i,j,k;
+ ts_vertex *cvtx;
+ for(i=0;i<vesicle->sphHarmonics->l;i++){
+ for(j=0;j<2*i;j++) vesicle->sphHarmonics->ulm[i][j]=0.0;
+ }
+
+//TODO: call calculateYlmi !!!
+
+
+ for(k=0;k<vesicle->vlist->n; k++){
+ cvtx=vesicle->vlist->vtx[k];
+ for(i=0;i<vesicle->sphHarmonics->l;i++){
+ for(j=0;j<2*i;j++){
+ vesicle->sphHarmonics->ulm[i][j]+= cvtx->solAngle*cvtx->relR*vesicle->sphHarmonics->Ylmi[i][j][k];
+ }
+
+ }
+ }
+
+ return TS_SUCCESS;
+}
--
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