| commit | author | age | ||
| 88f451 | 1 | #include<math.h> |
| SP | 2 | #include<stdlib.h> |
| 3 | #include "general.h" | |
| 4 | #include "sh.h" | |
| 5 | ||
| 074a17 | 6 | |
| SP | 7 | |
| 8 | ts_spharm *sph_init(ts_vertex_list *vlist, ts_uint l){ | |
| eb8605 | 9 | ts_uint j,i; |
| 074a17 | 10 | ts_spharm *sph=(ts_spharm *)malloc(sizeof(ts_spharm)); |
| SP | 11 | |
| 5bb11d | 12 | |
| eb8605 | 13 | /* lets initialize Ylm for each vertex. */ |
| SP | 14 | sph->Ylmi=(ts_double ***)calloc(l,sizeof(ts_double **)); |
| 5bb11d | 15 | for(i=0;i<l;i++){ |
| SP | 16 | sph->Ylmi[i]=(ts_double **)calloc(2*i+1,sizeof(ts_double *)); |
| 17 | for(j=0;j<(2*i+1);j++){ | |
| eb8605 | 18 | sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double)); |
| 074a17 | 19 | } |
| SP | 20 | } |
| 21 | ||
| 22 | /* lets initialize ulm */ | |
| 23 | sph->ulm=(ts_double **)calloc(l,sizeof(ts_double *)); | |
| 24 | for(j=0;j<l;j++){ | |
| 25 | sph->ulm[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double)); | |
| 26 | } | |
| 27 | ||
| 28 | ||
| 29 | /* lets initialize co */ | |
| 30 | sph->co=(ts_double **)calloc(l,sizeof(ts_double *)); | |
| 31 | for(j=0;j<l;j++){ | |
| 32 | sph->co[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double)); | |
| 33 | } | |
| 34 | ||
| 5bb11d | 35 | sph->l=l; |
| SP | 36 | |
| 37 | /* Calculate coefficients that will remain constant during all the simulation */ | |
| 38 | precomputeShCoeff(sph); | |
| 39 | ||
| 074a17 | 40 | return sph; |
| SP | 41 | } |
| 42 | ||
| 43 | ||
| eb8605 | 44 | ts_bool sph_free(ts_spharm *sph){ |
| SP | 45 | int i,j; |
| 074a17 | 46 | for(i=0;i<sph->l;i++){ |
| SP | 47 | if(sph->ulm[i]!=NULL) free(sph->ulm[i]); |
| 48 | if(sph->co[i]!=NULL) free(sph->co[i]); | |
| 49 | } | |
| 50 | if(sph->co != NULL) free(sph->co); | |
| 51 | if(sph->ulm !=NULL) free(sph->ulm); | |
| 52 | ||
| eb8605 | 53 | if(sph->Ylmi!=NULL) { |
| 074a17 | 54 | for(i=0;i<sph->l;i++){ |
| eb8605 | 55 | if(sph->Ylmi[i]!=NULL){ |
| 5bb11d | 56 | for(j=0;j<i*2+1;j++){ |
| eb8605 | 57 | if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]); |
| SP | 58 | } |
| 59 | free(sph->Ylmi[i]); | |
| 60 | } | |
| 074a17 | 61 | } |
| eb8605 | 62 | free(sph->Ylmi); |
| 074a17 | 63 | } |
| eb8605 | 64 | |
| 074a17 | 65 | free(sph); |
| SP | 66 | return TS_SUCCESS; |
| 67 | } | |
| 68 | ||
| 88f451 | 69 | /* Gives you legendre polynomials. Taken from NR, p. 254 */ |
| SP | 70 | ts_double plgndr(ts_int l, ts_int m, ts_float x){ |
| 71 | ts_double fact, pll, pmm, pmmp1, somx2; | |
| 72 | ts_int i,ll; | |
| 73 | ||
| 74 | #ifdef TS_DOUBLE_DOUBLE | |
| 75 | if(m<0 || m>l || fabs(x)>1.0) | |
| 76 | fatal("Bad arguments in routine plgndr",1); | |
| 77 | #endif | |
| 78 | #ifdef TS_DOUBLE_FLOAT | |
| 79 | if(m<0 || m>l || fabsf(x)>1.0) | |
| 80 | fatal("Bad arguments in routine plgndr",1); | |
| 81 | #endif | |
| 82 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 83 | if(m<0 || m>l || fabsl(x)>1.0) | |
| 84 | fatal("Bad arguments in routine plgndr",1); | |
| 85 | #endif | |
| 86 | pmm=1.0; | |
| 87 | if (m>0) { | |
| 88 | #ifdef TS_DOUBLE_DOUBLE | |
| 89 | somx2=sqrt((1.0-x)*(1.0+x)); | |
| 90 | #endif | |
| 91 | #ifdef TS_DOUBLE_FLOAT | |
| 92 | somx2=sqrtf((1.0-x)*(1.0+x)); | |
| 93 | #endif | |
| 94 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 95 | somx2=sqrtl((1.0-x)*(1.0+x)); | |
| 96 | #endif | |
| 97 | fact=1.0; | |
| 98 | for (i=1; i<=m;i++){ | |
| 99 | pmm *= -fact*somx2; | |
| 100 | fact +=2.0; | |
| 101 | } | |
| 102 | } | |
| 103 | ||
| 104 | if (l == m) return pmm; | |
| 105 | else { | |
| 106 | pmmp1=x*(2*m+1)*pmm; | |
| 107 | if(l==(m+1)) return(pmmp1); | |
| 108 | else { | |
| 109 | pll=0; /* so it can not be uninitialized */ | |
| 110 | for(ll=m+2;ll<=l;ll++){ | |
| 111 | pll=(x*(2*ll-1)*pmmp1-(ll+m-1)*pmm)/(ll-m); | |
| 112 | pmm=pmmp1; | |
| 113 | pmmp1=pll; | |
| 114 | } | |
| 115 | return(pll); | |
| 116 | } | |
| 117 | } | |
| 118 | } | |
| 119 | ||
| 120 | ||
| 523bf1 | 121 | |
| SP | 122 | ts_bool precomputeShCoeff(ts_spharm *sph){ |
| 074a17 | 123 | ts_int i,j,al,am; |
| SP | 124 | ts_double **co=sph->co; |
| 523bf1 | 125 | for(i=0;i<sph->l;i++){ |
| 074a17 | 126 | al=i+1; |
| SP | 127 | sph->co[i][i+1]=sqrt((2.0*al+1.0)/2.0/M_PI); |
| 128 | for(j=0;j<al;j++){ | |
| 129 | am=j+1; | |
| 130 | sph->co[i][i+1+j]=co[i][i+j]*sqrt(1.0/(al-am+1)/(al+am)); | |
| 131 | sph->co[i][i+1-j]=co[i][i+1+j]; | |
| 523bf1 | 132 | } |
| 074a17 | 133 | co[i][2*i]=co[i][2*i]*sqrt(1.0/(2.0*al)); |
| SP | 134 | co[i][0]=co[i][2*i+1]; |
| 135 | co[i][i+1]=sqrt((2.0*al+1.0)/4.0/M_PI); | |
| 523bf1 | 136 | } |
| SP | 137 | return TS_SUCCESS; |
| 138 | ||
| 139 | } | |
| 140 | ||
| 141 | ||
| 88f451 | 142 | /*Computes Y(l,m,theta,fi) (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */ |
| SP | 143 | ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){ |
| 144 | ts_double fac1, fac2, K; | |
| 145 | int i; | |
| 146 | ||
| 147 | if(l<0 || m>l || m<-l) | |
| 148 | fatal("Error using shY function!",1); | |
| 149 | ||
| 150 | fac1=1.0; | |
| af3bad | 151 | for(i=1; i<=l-abs(m);i++){ |
| 88f451 | 152 | fac1 *= i; |
| SP | 153 | } |
| 154 | fac2=1.0; | |
| af3bad | 155 | for(i=1; i<=l+abs(m);i++){ |
| 88f451 | 156 | fac2 *= i; |
| SP | 157 | } |
| 158 | ||
| 159 | if(m==0){ | |
| 160 | K=sqrt(1.0/(2.0*M_PI)); | |
| 161 | } | |
| 162 | else if (m>0) { | |
| 163 | K=sqrt(1.0/(M_PI))*cos(m*fi); | |
| 164 | } | |
| 165 | else { | |
| 166 | //K=pow(-1.0,abs(m))*sqrt(1.0/(2.0*M_PI))*cos(m*fi); | |
| 167 | if(abs(m)%2==0) | |
| af3bad | 168 | K=sqrt(1.0/(M_PI))*cos(m*fi); |
| 88f451 | 169 | else |
| af3bad | 170 | K=-sqrt(1.0/(M_PI))*cos(m*fi); |
| 88f451 | 171 | } |
| SP | 172 | |
| 173 | return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta)); | |
| 174 | } | |
| 523bf1 | 175 | |
| SP | 176 | |
| 177 | /* Function transforms coordinates from cartesian to spherical coordinates | |
| 178 | * (r,phi, theta). */ | |
| 179 | ts_bool *cart2sph(ts_coord *coord, ts_double x, ts_double y, ts_double z){ | |
| 180 | coord->coord_type=TS_COORD_SPHERICAL; | |
| 181 | #ifdef TS_DOUBLE_DOUBLE | |
| 182 | coord->e1=sqrt(x*x+y*y+z*z); | |
| 183 | if(z==0) coord->e3=M_PI/2.0; | |
| 184 | else coord->e3=atan(sqrt(x*x+y*y)/z); | |
| 185 | coord->e2=atan2(y,x); | |
| 186 | #endif | |
| 187 | #ifdef TS_DOUBLE_FLOAT | |
| 188 | coord->e1=sqrtf(x*x+y*y+z*z); | |
| 189 | if(z==0) coord->e3=M_PI/2.0; | |
| 190 | else coord->e3=atanf(sqrtf(x*x+y*y)/z); | |
| 191 | coord->e2=atan2f(y,x); | |
| 192 | #endif | |
| 193 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 194 | coord->e1=sqrtl(x*x+y*y+z*z); | |
| 195 | if(z==0) coord->e3=M_PI/2.0; | |
| 196 | else coord->e3=atanl(sqrtl(x*x+y*y)/z); | |
| 197 | coord->e2=atan2l(y,x); | |
| 198 | #endif | |
| 199 | ||
| 200 | return TS_SUCCESS; | |
| 201 | } | |
| 202 | ||
| 203 | /* Function returns radius of the sphere with the same volume as vesicle (r0) */ | |
| 204 | ts_double getR0(ts_vesicle *vesicle){ | |
| 205 | ts_double r0; | |
| 206 | #ifdef TS_DOUBLE_DOUBLE | |
| 207 | r0=pow(vesicle->volume*3.0/4.0/M_PI,1.0/3.0); | |
| 208 | #endif | |
| 209 | #ifdef TS_DOUBLE_FLOAT | |
| 210 | r0=powf(vesicle->volume*3.0/4.0/M_PI,1.0/3.0); | |
| 211 | #endif | |
| 212 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 213 | r0=powl(vesicle->volume*3.0/4.0/M_PI,1.0/3.0); | |
| 214 | #endif | |
| 215 | return r0; | |
| 216 | } | |
| 217 | ||
| 218 | ||
| 219 | ts_bool preparationSh(ts_vesicle *vesicle, ts_double r0){ | |
| 220 | //TODO: before calling or during the call calculate area of each triangle! Can | |
| 221 | //be also done after vertexmove and bondflip // | |
| 222 | ts_uint i,j; | |
| 223 | ts_vertex **vtx=vesicle->vlist->vtx; | |
| 224 | ts_vertex *cvtx; | |
| 225 | ts_triangle *ctri; | |
| 226 | ts_double centroid[3]; | |
| 227 | ts_double r; | |
| 228 | for (i=0; i<vesicle->vlist->n; i++){ | |
| 229 | cvtx=vtx[i]; | |
| 230 | //cvtx->projArea=4.0*M_PI/1447.0*(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z)/r0/r0; | |
| 231 | cvtx->projArea=0.0; | |
| 232 | ||
| 233 | /* go over all triangles that have a common vertex i */ | |
| 234 | for(j=0; j<cvtx->tristar_no; j++){ | |
| 235 | ctri=cvtx->tristar[j]; | |
| 236 | centroid[0]=(ctri->vertex[0]->x + ctri->vertex[1]->x + ctri->vertex[2]->x)/3.0; | |
| 237 | centroid[1]=(ctri->vertex[0]->y + ctri->vertex[1]->y + ctri->vertex[2]->y)/3.0; | |
| 238 | centroid[2]=(ctri->vertex[0]->z + ctri->vertex[1]->z + ctri->vertex[2]->z)/3.0; | |
| 239 | /* calculating projArea+= area(triangle)*cos(theta) */ | |
| 240 | #ifdef TS_DOUBLE_DOUBLE | |
| 241 | 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]); | |
| 242 | #endif | |
| 243 | #ifdef TS_DOUBLE_FLOAT | |
| 244 | 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]); | |
| 245 | #endif | |
| 246 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 247 | 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]); | |
| 248 | #endif | |
| 249 | } | |
| 250 | ||
| 251 | cvtx->projArea=cvtx->projArea/3.0; | |
| 252 | //we dont store spherical coordinates of vertex, so we have to calculate | |
| 253 | //r(i) at this point. | |
| 254 | #ifdef TS_DOUBLE_DOUBLE | |
| 255 | r=sqrt(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z); | |
| 256 | #endif | |
| 257 | #ifdef TS_DOUBLE_FLOAT | |
| 258 | r=sqrtf(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z); | |
| 259 | #endif | |
| 260 | #ifdef TS_DOUBLE_LONGDOUBLE | |
| 261 | r=sqrtl(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z); | |
| 262 | #endif | |
| 263 | cvtx->relR=(r-r0)/r0; | |
| 264 | cvtx->solAngle=cvtx->projArea/cvtx->relR * cvtx->projArea/cvtx->relR; | |
| 265 | } | |
| 266 | return TS_SUCCESS; | |
| 267 | } | |
| 268 | ||
| 269 | ||
| 270 | ||
| 271 | ts_bool calculateYlmi(ts_vesicle *vesicle){ | |
| 272 | ts_uint i,j,k; | |
| 273 | ts_spharm *sph=vesicle->sphHarmonics; | |
| 274 | ts_coord *coord=(ts_coord *)malloc(sizeof(ts_coord)); | |
| 275 | ts_double fi, theta; | |
| 074a17 | 276 | ts_vertex *cvtx; |
| 523bf1 | 277 | for(k=0;k<vesicle->vlist->n;k++){ |
| 074a17 | 278 | cvtx=vesicle->vlist->vtx[k]; |
| eb8605 | 279 | sph->Ylmi[0][0][k]=sqrt(1.0/4.0/M_PI); |
| 074a17 | 280 | cart2sph(coord,cvtx->x, cvtx->y, cvtx->z); |
| 523bf1 | 281 | fi=coord->e2; |
| SP | 282 | theta=coord->e3; |
| 283 | for(i=0; i<sph->l; i++){ | |
| 284 | for(j=0;j<i;j++){ | |
| eb8605 | 285 | 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)); |
| 523bf1 | 286 | } |
| eb8605 | 287 | sph->Ylmi[i][j+1][k]=sph->co[i][j+1]*plgndr(i,0,cos(theta)); |
| 523bf1 | 288 | for(j=sph->l;j<2*i;j++){ |
| eb8605 | 289 | sph->Ylmi[i][j][k]=sph->co[i][j]*sin((j-i-1)*fi)*plgndr(i,j-i-1,cos(theta)); |
| 523bf1 | 290 | } |
| SP | 291 | } |
| 292 | ||
| 293 | } | |
| 294 | free(coord); | |
| 295 | return TS_SUCCESS; | |
| 296 | } | |
| 297 | ||
| 298 | ||
| 299 | ||
| 300 | ts_bool calculateUlm(ts_vesicle *vesicle){ | |
| 301 | ts_uint i,j,k; | |
| 302 | ts_vertex *cvtx; | |
| 303 | for(i=0;i<vesicle->sphHarmonics->l;i++){ | |
| 304 | for(j=0;j<2*i;j++) vesicle->sphHarmonics->ulm[i][j]=0.0; | |
| 305 | } | |
| 306 | ||
| 307 | //TODO: call calculateYlmi !!! | |
| 308 | ||
| 309 | ||
| 310 | for(k=0;k<vesicle->vlist->n; k++){ | |
| 311 | cvtx=vesicle->vlist->vtx[k]; | |
| 312 | for(i=0;i<vesicle->sphHarmonics->l;i++){ | |
| 313 | for(j=0;j<2*i;j++){ | |
| eb8605 | 314 | vesicle->sphHarmonics->ulm[i][j]+= cvtx->solAngle*cvtx->relR*vesicle->sphHarmonics->Ylmi[i][j][k]; |
| 523bf1 | 315 | } |
| SP | 316 | |
| 317 | } | |
| 318 | } | |
| 319 | ||
| 320 | return TS_SUCCESS; | |
| 321 | } | |
