#include<math.h>
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#include<stdlib.h>
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#include "general.h"
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#include "sh.h"
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ts_spharm *sph_init(ts_vertex_list *vlist, ts_uint l){
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ts_uint j,i;
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ts_spharm *sph=(ts_spharm *)malloc(sizeof(ts_spharm));
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/* lets initialize Ylm for each vertex. */
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sph->Ylmi=(ts_double ***)calloc(l,sizeof(ts_double **));
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for(i=0;i<l;i++){
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sph->Ylmi[i]=(ts_double **)calloc(2*i+1,sizeof(ts_double *));
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for(j=0;j<(2*i+1);j++){
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sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double));
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}
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}
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/* lets initialize ulm */
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sph->ulm=(ts_double **)calloc(l,sizeof(ts_double *));
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for(j=0;j<l;j++){
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sph->ulm[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
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}
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/* lets initialize co */
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//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!
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sph->co=(ts_double **)calloc(l+1,sizeof(ts_double *));
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for(j=0;j<=l;j++){
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sph->co[j]=(ts_double *)calloc(2*j+2,sizeof(ts_double));
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}
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sph->l=l;
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/* Calculate coefficients that will remain constant during all the simulation */
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precomputeShCoeff(sph);
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return sph;
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}
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ts_bool sph_free(ts_spharm *sph){
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int i,j;
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for(i=0;i<sph->l;i++){
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if(sph->ulm[i]!=NULL) free(sph->ulm[i]);
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if(sph->co[i]!=NULL) free(sph->co[i]);
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}
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if(sph->co[sph->l]!=NULL) free(sph->co[sph->l]);
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if(sph->co != NULL) free(sph->co);
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if(sph->ulm !=NULL) free(sph->ulm);
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if(sph->Ylmi!=NULL) {
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for(i=0;i<sph->l;i++){
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if(sph->Ylmi[i]!=NULL){
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for(j=0;j<i*2+1;j++){
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if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]);
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}
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free(sph->Ylmi[i]);
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}
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}
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free(sph->Ylmi);
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}
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free(sph);
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return TS_SUCCESS;
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}
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/* Gives you legendre polynomials. Taken from NR, p. 254 */
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ts_double plgndr(ts_int l, ts_int m, ts_float x){
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ts_double fact, pll, pmm, pmmp1, somx2;
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ts_int i,ll;
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#ifdef TS_DOUBLE_DOUBLE
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if(m<0 || m>l || fabs(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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if(m<0 || m>l || fabsf(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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if(m<0 || m>l || fabsl(x)>1.0)
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fatal("Bad arguments in routine plgndr",1);
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#endif
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pmm=1.0;
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if (m>0) {
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#ifdef TS_DOUBLE_DOUBLE
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somx2=sqrt((1.0-x)*(1.0+x));
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#endif
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#ifdef TS_DOUBLE_FLOAT
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somx2=sqrtf((1.0-x)*(1.0+x));
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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somx2=sqrtl((1.0-x)*(1.0+x));
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#endif
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fact=1.0;
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for (i=1; i<=m;i++){
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pmm *= -fact*somx2;
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fact +=2.0;
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}
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}
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if (l == m) return pmm;
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else {
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pmmp1=x*(2*m+1)*pmm;
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if(l==(m+1)) return(pmmp1);
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else {
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pll=0; /* so it can not be uninitialized */
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for(ll=m+2;ll<=l;ll++){
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pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m);
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pmm=pmmp1;
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pmmp1=pll;
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}
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return(pll);
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}
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}
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}
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ts_bool precomputeShCoeff(ts_spharm *sph){
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ts_int i,j,al,am;
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ts_double **co=sph->co;
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for(i=1;i<=sph->l;i++){
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al=i;
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sph->co[i][i+1]=sqrt((2.0*al+1.0)/2.0/M_PI);
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for(j=1;j<=i-1;j++){
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am=j;
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sph->co[i][i+1+j]=co[i][i+j]*sqrt(1.0/(al-am+1.0)/(al+am));
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sph->co[i][i+1-j]=co[i][i+1+j];
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}
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co[i][2*i+1]=co[i][2*i]*sqrt(1.0/(2.0*al));
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co[i][1]=co[i][2*i+1];
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co[i][i+1]=sqrt((2.0*al+1.0)/4.0/M_PI);
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}
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return TS_SUCCESS;
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}
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/*Computes Y(l,m,theta,fi) (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */
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ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){
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ts_double fac1, fac2, K;
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int i;
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if(l<0 || m>l || m<-l)
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fatal("Error using shY function!",1);
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fac1=1.0;
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for(i=1; i<=l-abs(m);i++){
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fac1 *= i;
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}
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fac2=1.0;
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for(i=1; i<=l+abs(m);i++){
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fac2 *= i;
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}
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if(m==0){
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K=sqrt(1.0/(2.0*M_PI));
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}
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else if (m>0) {
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K=sqrt(1.0/(M_PI))*cos(m*fi);
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}
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else {
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//K=pow(-1.0,abs(m))*sqrt(1.0/(2.0*M_PI))*cos(m*fi);
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if(abs(m)%2==0)
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K=sqrt(1.0/(M_PI))*cos(m*fi);
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else
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K=-sqrt(1.0/(M_PI))*cos(m*fi);
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}
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return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta));
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}
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/* Function transforms coordinates from cartesian to spherical coordinates
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* (r,phi, theta). */
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ts_bool *cart2sph(ts_coord *coord, ts_double x, ts_double y, ts_double z){
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coord->coord_type=TS_COORD_SPHERICAL;
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#ifdef TS_DOUBLE_DOUBLE
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coord->e1=sqrt(x*x+y*y+z*z);
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if(z==0) coord->e3=M_PI/2.0;
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else coord->e3=atan(sqrt(x*x+y*y)/z);
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coord->e2=atan2(y,x);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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coord->e1=sqrtf(x*x+y*y+z*z);
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if(z==0) coord->e3=M_PI/2.0;
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else coord->e3=atanf(sqrtf(x*x+y*y)/z);
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coord->e2=atan2f(y,x);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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coord->e1=sqrtl(x*x+y*y+z*z);
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if(z==0) coord->e3=M_PI/2.0;
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else coord->e3=atanl(sqrtl(x*x+y*y)/z);
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coord->e2=atan2l(y,x);
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#endif
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return TS_SUCCESS;
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}
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/* Function returns radius of the sphere with the same volume as vesicle (r0) */
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ts_double getR0(ts_vesicle *vesicle){
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ts_double r0;
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#ifdef TS_DOUBLE_DOUBLE
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r0=pow(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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r0=powf(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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r0=powl(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
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#endif
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return r0;
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}
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ts_bool preparationSh(ts_vesicle *vesicle, ts_double r0){
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//TODO: before calling or during the call calculate area of each triangle! Can
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//be also done after vertexmove and bondflip //
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ts_uint i,j;
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ts_vertex **vtx=vesicle->vlist->vtx;
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ts_vertex *cvtx;
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ts_triangle *ctri;
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ts_double centroid[3];
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ts_double r;
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for (i=0; i<vesicle->vlist->n; i++){
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cvtx=vtx[i];
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//cvtx->projArea=4.0*M_PI/1447.0*(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z)/r0/r0;
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cvtx->projArea=0.0;
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/* go over all triangles that have a common vertex i */
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for(j=0; j<cvtx->tristar_no; j++){
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ctri=cvtx->tristar[j];
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centroid[0]=(ctri->vertex[0]->x + ctri->vertex[1]->x + ctri->vertex[2]->x)/3.0;
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centroid[1]=(ctri->vertex[0]->y + ctri->vertex[1]->y + ctri->vertex[2]->y)/3.0;
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centroid[2]=(ctri->vertex[0]->z + ctri->vertex[1]->z + ctri->vertex[2]->z)/3.0;
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/* calculating projArea+= area(triangle)*cos(theta) */
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#ifdef TS_DOUBLE_DOUBLE
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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]);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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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]);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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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]);
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#endif
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}
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cvtx->projArea=cvtx->projArea/3.0;
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//we dont store spherical coordinates of vertex, so we have to calculate
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//r(i) at this point.
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#ifdef TS_DOUBLE_DOUBLE
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r=sqrt(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
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#endif
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#ifdef TS_DOUBLE_FLOAT
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r=sqrtf(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
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#endif
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#ifdef TS_DOUBLE_LONGDOUBLE
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r=sqrtl(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
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#endif
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cvtx->relR=(r-r0)/r0;
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cvtx->solAngle=cvtx->projArea/cvtx->relR * cvtx->projArea/cvtx->relR;
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}
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return TS_SUCCESS;
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}
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ts_bool calculateYlmi(ts_vesicle *vesicle){
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ts_uint i,j,k;
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ts_spharm *sph=vesicle->sphHarmonics;
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ts_coord *coord=(ts_coord *)malloc(sizeof(ts_coord));
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ts_double fi, theta;
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ts_vertex *cvtx;
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for(k=0;k<vesicle->vlist->n;k++){
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cvtx=vesicle->vlist->vtx[k];
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sph->Ylmi[0][0][k]=sqrt(1.0/4.0/M_PI);
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cart2sph(coord,cvtx->x, cvtx->y, cvtx->z);
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fi=coord->e2;
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theta=coord->e3;
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for(i=0; i<sph->l; i++){
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for(j=0;j<i;j++){
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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));
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}
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sph->Ylmi[i][j+1][k]=sph->co[i][j+1]*plgndr(i,0,cos(theta));
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for(j=sph->l;j<2*i;j++){
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sph->Ylmi[i][j][k]=sph->co[i][j]*sin((j-i-1)*fi)*plgndr(i,j-i-1,cos(theta));
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}
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}
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}
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free(coord);
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return TS_SUCCESS;
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}
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ts_bool calculateUlm(ts_vesicle *vesicle){
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ts_uint i,j,k;
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ts_vertex *cvtx;
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for(i=0;i<vesicle->sphHarmonics->l;i++){
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for(j=0;j<2*i;j++) vesicle->sphHarmonics->ulm[i][j]=0.0;
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}
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//TODO: call calculateYlmi !!!
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for(k=0;k<vesicle->vlist->n; k++){
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cvtx=vesicle->vlist->vtx[k];
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for(i=0;i<vesicle->sphHarmonics->l;i++){
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for(j=0;j<2*i;j++){
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vesicle->sphHarmonics->ulm[i][j]+= cvtx->solAngle*cvtx->relR*vesicle->sphHarmonics->Ylmi[i][j][k];
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}
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}
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}
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return TS_SUCCESS;
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}
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