void get_reflected_ray(t_ray* ray, t_object* obj, t_ray* new_ray)
{
new_ray->distance = 20000;
mult_vector(&ray->dest, &new_ray->origin, ray->distance);
add_vector(&new_ray->origin, &ray->origin, &new_ray->origin);
get_normal(obj, &new_ray->origin, &new_ray->dest);
mult_vector(&new_ray->dest, &new_ray->dest,
dot_vector(&ray->dest, &new_ray->dest));
mult_vector(&new_ray->dest, &new_ray->dest, 2);
sub_vector(&ray->dest, &new_ray->dest, &new_ray->dest);
}
void get_refracted_ray(t_ray* ray, t_object* obj, t_ray* new_ray)
{
t_vector tmp;
t_vector normal;
double d[3];
t_ray* rays[2];
rays[0] = ray;
rays[1] = new_ray;
init_refraction(rays, &normal, obj, &tmp);
d[0] = dot_vector(&tmp, &normal);
d[1] = ray->refract / new_ray->refract;
d[2] = asin(d[1] * sin(acos(d[0])));
mult_vector(&normal, &new_ray->dest, cos(d[2]) + d[1] * d[0]);
mult_vector(&ray->dest, &tmp, d[1]);
sub_vector(&tmp, &new_ray->dest, &new_ray->dest);
normalize(&new_ray->dest);
}
int hit_plan(t_ray *r, t_plan *p, float *t)
{
float dist;
float denom;
denom = mult_vector(p->dir, r->dir);
if (denom > 0)
{
t_coord p0l0 = minus_vector(p->center, r->start);
dist = mult_vector(p0l0, p->dir) / denom;
if (dist > 0.00001 && *t > dist)
{
*t = dist;
return (1);
}
}
return (0);
}
void init_refraction(t_ray** rays, t_vector* normal,
t_object* obj, t_vector* tmp)
{
(*rays[1]).distance = 20000;
mult_vector(&(*rays[0]).dest, &(*rays[1]).origin, (*rays[0]).distance);
add_vector(&(*rays[1]).origin, &(*rays[0]).origin, &(*rays[1]).origin);
get_normal(obj, &(*rays[1]).origin, normal, rays[0]);
sub_vector(NULL, &(*rays[0]).dest, tmp);
if ((*rays[0]).in_obj == 0)
{
if (obj->obj_type != E_PLANE)
(*rays[1]).in_obj = 1;
else
(*rays[1]).in_obj = 0;
(*rays[1]).refract = obj->material.refract;
}
else
{
sub_vector(NULL, normal, normal);
(*rays[1]).in_obj = 0;
(*rays[1]).refract = 1.0;
}
}
void Calculate_HF_deriv(int *tlist,double *vlist,int nfac,int nvert,double *angles,double *Eo,double *E0o,double *up,double TIME,double dist,double Gamma,double A,double Hdist,int N,double WL,double *freqx,double *freqy,int nfreq,double *offset,double *Fr,double *Fi,double *dFdxr,double *dFdxi,double *dFdyr,double *dFdyi,double *dFdzr,double *dFdzi,double *dFdAr,double *dFdAi,double *dFdoffr,double *dFdoffi)
{
double complex *F=calloc(nfreq,sizeof(double complex));
double complex *F0,*FTda,*FTdb,*FTdc,*FTdd,*FTdh,*FTdg,*FTdx,*FTdy,*FTdz,*FTdA;
FTdx=calloc(nfreq*nvert,sizeof(double complex));
FTdy=calloc(nfreq*nvert,sizeof(double complex));
FTdz=calloc(nfreq*nvert,sizeof(double complex));
FTdA=calloc(nfreq*3,sizeof(double complex));
F0=calloc(nfreq,sizeof(double complex));
FTda=malloc(nfreq*sizeof(double complex));
FTdb=malloc(nfreq*sizeof(double complex));
FTdc=malloc(nfreq*sizeof(double complex));
FTdd=malloc(nfreq*sizeof(double complex));
FTdh=malloc(nfreq*sizeof(double complex));
FTdg=malloc(nfreq*sizeof(double complex));
double M[3][3],dMb[3][3],dMo[3][3],dMl[3][3],Mt[3][3],dMbT[3][3],dMoT[3][3],dMlT[3][3]; //Rotation matrices and their derivatives and transposes
double R[3][3],Rdb[3][3],Rdl[3][3],Rdo[3][3],RT[3][3]; //Projection matrix, and derivatives of combined projection+rotation matrix
double dEdb[3],dEdl[3],dEdo[3],dE0db[3],dE0dl[3],dE0do[3];
double dndx1[3],dndx2[3],dndx3[3],dndy1[3],dndy2[3],dndy3[3],dndz1[3],dndz2[3],dndz3[3]; //Derivatives of the facet normal vector
double dBdx1,dBdy1,dBdz1,dBdx2,dBdy2,dBdz2,dBdx3,dBdy3,dBdz3,dBdb,dBdl,dBdo; //Derivatives of facet brightness
double *dTBdx,*dTBdy,*dTBdz; //Derivatives of total brightness, allocating memory
double *Flux,*Fldx,*Fldy,*Fldz,*FldA;
Flux=calloc(nfac,sizeof(double));
Fldx=calloc(nfac*nvert,sizeof(double));
Fldy=calloc(nfac*nvert,sizeof(double));
Fldz=calloc(nfac*nvert,sizeof(double));
FldA=calloc(nfac*3,sizeof(double));
double dTBdA[3]={0};
dTBdx=calloc(nvert,sizeof(double));
dTBdy=calloc(nvert,sizeof(double));
dTBdz=calloc(nvert,sizeof(double));
double dmudx1,dmudy1,dmudz1,dmudx2,dmudy2,dmudz2,dmudx3,dmudy3,dmudz3;
double dmu0dx1,dmu0dy1,dmu0dz1,dmu0dx2,dmu0dy2,dmu0dz2,dmu0dx3,dmu0dy3,dmu0dz3;
double dmudl,dmudb,dmudo,dmu0dl,dmu0db,dmu0do; //Derivatives of mu and mu0
double dAdx[3],dAdy[3],dAdz[3]; //Facet area derivatives
double dadx,dady,dadz,dbdx,dbdy,dbdz; //Derivatives of projected vertices
double E[3],E0[3]; //Earth and Sun direction, rotated
double side1[3],side2[3];
double n[3];
double v1db[3],v2db[3],v3db[3],v1dl[3],v2dl[3],v3dl[3],v1do[3],v2do[3],v3do[3]; //Derivatives of 2d vertices wrt angles
double vr1[3],vr2[3],vr3[3];
double v1[3],v2[3],v3[3];
double complex scale;
double dp;
double B,TB=0.0;
double norm;
double mut,mu0t;
int t1,t2,t3;
int j1,j2,j3;
double mu,mu0,area;
double *normal;
int *visible;
int tb1,tb2,tb3; //Indices to the vertices of possible blocker facet
int blocked=0;
//Distance km->arcsec
dp=1/(dist*149597871.0)*180.0/PI*3600.0;
visible=calloc(nfac,sizeof(int));
//Calculate_Frame_Matrix_Derivatives(Eo,angles,TIME,rfreq,R,Rdb,Rdl,Rdo);
Calculate_Frame_Matrix(Eo,up,R);
//Calculate frame change matrix
//FacetsOverHorizon(tlist,vlist,nfac,nvert,normal,centroid,NumofBlocks,IndexofBlocks);
rotate(angles[0],angles[1],angles[2],0.0,TIME,M,dMb,dMl,dMo);
//Construct asteroid->Camera frame matrix, which is
//asteroid->world frame->camera frame
transpose(M,Mt); //Transpose, since we rotate the model, not view directions
transpose(dMb,dMbT);
transpose(dMl,dMlT);
transpose(dMo,dMoT);
mult_mat(R,Mt,RT);
mult_vector(M,Eo,E);
mult_vector(M,E0o,E0);
mult_mat(R,dMbT,Rdb);
mult_mat(R,dMlT,Rdl);
mult_mat(R,dMoT,Rdo);
//Derivatives of E,E0 wrt beta,lambda,omega
mult_vector(dMb,Eo,dEdb);
mult_vector(dMl,Eo,dEdl);
mult_vector(dMo,Eo,dEdo);
mult_vector(dMb,E0o,dE0db);
mult_vector(dMl,E0o,dE0dl);
mult_vector(dMo,E0o,dE0do);
dadx=RT[0][0];
dady=RT[0][1];
dadz=RT[0][2];
dbdx=RT[1][0];
dbdy=RT[1][1];
dbdz=RT[1][2];
/*For each facet,
* 1)Check if facet is visible
* 2) Calculate echo
* 3) Convert triangle to range-Doppler frame
* 4) Calculate FT
*/
//Find actual blockers
FindActualBlockers(tlist,vlist,nfac,nvert,E,E,1,visible);
//visible is nfac vector, visible[j]=1 if facet (j+1)th facet is visible
//NOTE INDEXING
Calculate_Radiance(tlist,vlist,nfac,nvert,angles,Eo,E0o,TIME,Gamma, A,Hdist,WL,N,Flux,Fldx,Fldy,Fldz,FldA,1);
//for(int j=0;j<nfac;j++)
for(int j=0;j<nfac;j++)
{
if(visible[j]==0)
continue;
//Calculate normal from facet vertices
//Vertex indices of the current facet
//Note that C indices from 0, matlab from 1
j1=tlist[j*3]-1;
j2=tlist[j*3+1]-1;
j3=tlist[j*3+2]-1;
//Current vertices
for(int i=0;i<3;i++)
{
v1[i]=*(vlist+j1*3+i)*dp; //convert km->arcsec
v2[i]=*(vlist+j2*3+i)*dp;
v3[i]=*(vlist+j3*3+i)*dp;
}
//Calculate Normal derivatives (in the original frame)
Calculate_Area_and_Normal_Derivative(v1,v2,v3,n,dndx1,dndx2,dndx3,dndy1,dndy2,dndy3,dndz1,dndz2,dndz3,&area,dAdx,dAdy,dAdz);
//Calculate normals and centroids
mu=DOT(E,n);
//Convert to camera frame
mult_vector(RT,v1,vr1);
mult_vector(RT,v2,vr2);
mult_vector(RT,v3,vr3);
//Now we should convert to frequency domain, ie calculate the contribution of each facet
// Calc_FTC(freqx,freqy,nfreq,vr1[0],vr1[1],vr2[0],vr2[1],vr3[0],vr3[1],F0);
Calc_FTC_deriv(freqx,freqy,nfreq,vr1[0],vr1[1],vr2[0],vr2[1],vr3[0],vr3[1],F0,FTda,FTdb,FTdc,FTdd,FTdg,FTdh);
//Derivatives wrt angles
mult_vector(Rdb,v1,v1db);
mult_vector(Rdb,v2,v2db);
mult_vector(Rdb,v3,v3db);
mult_vector(Rdl,v1,v1dl);
mult_vector(Rdl,v2,v2dl);
mult_vector(Rdl,v3,v3dl);
mult_vector(Rdo,v1,v1do);
mult_vector(Rdo,v2,v2do);
mult_vector(Rdo,v3,v3do);
//Derivatives of mu,mu0
dmudx1=DOT(E,dndx1);
dmudx2=DOT(E,dndx2);
dmudx3=DOT(E,dndx3);
dmudy1=DOT(E,dndy1);
dmudy2=DOT(E,dndy2);
dmudy3=DOT(E,dndy3);
dmudz1=DOT(E,dndz1);
dmudz2=DOT(E,dndz2);
dmudz3=DOT(E,dndz3);
dmudb=DOT(dEdb,n);
dmudl=DOT(dEdl,n);
dmudo=DOT(dEdo,n);
B=Flux[j];
//Derivatives of B
dBdx1=Fldx[j*nvert+j1]/dp;
dBdx2=Fldx[j*nvert+j2]/dp;
dBdx3=Fldx[j*nvert+j3]/dp;
dBdy1=Fldy[j*nvert+j1]/dp;
dBdy2=Fldy[j*nvert+j2]/dp;
dBdy3=Fldy[j*nvert+j3]/dp;
dBdz1=Fldz[j*nvert+j1]/dp;
dBdz2=Fldz[j*nvert+j2]/dp;
dBdz3=Fldz[j*nvert+j3]/dp;
dBdb=FldA[3*j];
dBdl=FldA[3*j+1];
dBdo=FldA[3*j+2];
//Derivative of total brightness
dTBdx[j1]+=dBdx1*area*mu+B*dAdx[0]*mu+B*area*dmudx1;
dTBdx[j2]+=dBdx2*area*mu+B*dAdx[1]*mu+B*area*dmudx2;
dTBdx[j3]+=dBdx3*area*mu+B*dAdx[2]*mu+B*area*dmudx3;
dTBdy[j1]+=dBdy1*area*mu+B*dAdy[0]*mu+B*area*dmudy1;
dTBdy[j2]+=dBdy2*area*mu+B*dAdy[1]*mu+B*area*dmudy2;
dTBdy[j3]+=dBdy3*area*mu+B*dAdy[2]*mu+B*area*dmudy3;
dTBdz[j1]+=dBdz1*area*mu+B*dAdz[0]*mu+B*area*dmudz1;
dTBdz[j2]+=dBdz2*area*mu+B*dAdz[1]*mu+B*area*dmudz2;
dTBdz[j3]+=dBdz3*area*mu+B*dAdz[2]*mu+B*area*dmudz3;
dTBdA[0]+=dBdb*area*mu+B*area*dmudb;
dTBdA[1]+=dBdl*area*mu+B*area*dmudl;
dTBdA[2]+=dBdo*area*mu+B*area*dmudo;
for(int jf=0;jf<nfreq;jf++)
{
F[jf]+=B*F0[jf];
FTdx[jf*nvert+j1]+=dBdx1*F0[jf]+B*(FTda[jf]*dadx+FTdb[jf]*dbdx);
FTdx[jf*nvert+j2]+=dBdx2*F0[jf]+B*(FTdc[jf]*dadx+FTdd[jf]*dbdx);
FTdx[jf*nvert+j3]+=dBdx3*F0[jf]+B*(FTdg[jf]*dadx+FTdh[jf]*dbdx);
FTdy[jf*nvert+j1]+=dBdy1*F0[jf]+B*(FTda[jf]*dady+FTdb[jf]*dbdy);
FTdy[jf*nvert+j2]+=dBdy2*F0[jf]+B*(FTdc[jf]*dady+FTdd[jf]*dbdy);
FTdy[jf*nvert+j3]+=dBdy3*F0[jf]+B*(FTdg[jf]*dady+FTdh[jf]*dbdy);
FTdz[jf*nvert+j1]+=dBdz1*F0[jf]+B*(FTda[jf]*dadz+FTdb[jf]*dbdz);
FTdz[jf*nvert+j2]+=dBdz2*F0[jf]+B*(FTdc[jf]*dadz+FTdd[jf]*dbdz);
FTdz[jf*nvert+j3]+=dBdz3*F0[jf]+B*(FTdg[jf]*dadz+FTdh[jf]*dbdz);
//angle derivatives
FTdA[jf*3+0]+=dBdb*F0[jf]+B*(FTda[jf]*v1db[0]+FTdb[jf]*v1db[1]+FTdc[jf]*v2db[0]+FTdd[jf]*v2db[1]+FTdg[jf]*v3db[0]+FTdh[jf]*v3db[1]);
FTdA[jf*3+1]+=dBdl*F0[jf]+B*(FTda[jf]*v1dl[0]+FTdb[jf]*v1dl[1]+FTdc[jf]*v2dl[0]+FTdd[jf]*v2dl[1]+FTdg[jf]*v3dl[0]+FTdh[jf]*v3dl[1]);
FTdA[jf*3+2]+=dBdo*F0[jf]+B*(FTda[jf]*v1do[0]+FTdb[jf]*v1do[1]+FTdc[jf]*v2do[0]+FTdd[jf]*v2do[1]+FTdg[jf]*v3do[0]+FTdh[jf]*v3do[1]);
}
TB=TB+B*area*mu;
}
//Normalize with total brightness
double complex temp;
for(int j=0;j<nfreq;j++)
{
scale=cexp(2.0*PI*I*(offset[0]*freqx[j]+offset[1]*freqy[j]));
for(int k=0;k<nvert;k++)
{
temp=dp*scale*(FTdx[j*nvert+k]*TB-F[j]*dTBdx[k])/pow(TB,2);
dFdxr[j*nvert+k]=creal(temp);
dFdxi[j*nvert+k]=cimag(temp);
temp=dp*scale*(FTdy[j*nvert+k]*TB-F[j]*dTBdy[k])/pow(TB,2);
dFdyr[j*nvert+k]=creal(temp);
dFdyi[j*nvert+k]=cimag(temp);
temp=dp*scale*(FTdz[j*nvert+k]*TB-F[j]*dTBdz[k])/pow(TB,2);
dFdzr[j*nvert+k]=creal(temp);
dFdzi[j*nvert+k]=cimag(temp);
}
temp=scale*(FTdA[j*3+0]*TB-F[j]*dTBdA[0])/pow(TB,2);
dFdAr[j*3+0]=creal(temp);
dFdAi[j*3+0]=cimag(temp);
temp=scale*(FTdA[j*3+1]*TB-F[j]*dTBdA[1])/pow(TB,2);
dFdAr[j*3+1]=creal(temp);
dFdAi[j*3+1]=cimag(temp);
temp=scale*(FTdA[j*3+2]*TB-F[j]*dTBdA[2])/pow(TB,2);
dFdAr[j*3+2]=creal(temp);
dFdAi[j*3+2]=cimag(temp);
temp=cexp(2.0*PI*I*(offset[0]*freqx[j]+offset[1]*freqy[j]))*F[j]/TB;
Fr[j]=creal(temp);
Fi[j]=cimag(temp);
temp=2.0*PI*I*freqx[j]*F[j];
dFdoffr[j*2+0]=creal(temp);
dFdoffi[j*2+0]=cimag(temp);
temp=2.0*PI*I*freqy[j]*F[j];
dFdoffr[j*2+1]=creal(temp);
dFdoffi[j*2+1]=cimag(temp);
}
free(FTdx);
free(FTdy);
free(FTdz);
free(FTdA);
free(dTBdx);
free(dTBdy);
free(dTBdz);
free(FTda);
free(FTdb);
free(FTdc);
free(FTdd);
free(FTdg);
free(FTdh);
free(F0);
free(visible);
free(Flux);
free(Fldx);
free(Fldy);
free(Fldz);
free(FldA);
free(F);
}
void Calculate_HF(int *tlist,double *vlist,int nfac,int nvert,double *angles,double *Eo,double *E0o,double *up,double TIME,double dist,double Gamma,double A,double Hdist,int N,double WL,double *freqx,double *freqy,int nfreq,double *offset,double *Fr,double *Fi)
{
double complex *F=calloc(nfreq,sizeof(double complex));
double complex *F0;
F0=(double complex*)calloc(nfreq,sizeof(double complex));
double *Flux,*Fldx,*Fldy,*Fldz,*FldA;
Flux=(double*)calloc(nfac,sizeof(double));
double M[3][3],dMb[3][3],dMo[3][3],dMl[3][3],Mt[3][3];
double R[3][3],Rdb[3][3],Rdl[3][3],Rdo[3][3],RT[3][3];
double E[3],E0[3];
double normalr[3],side1[3],side2[3];
double dechdx[3],dechdy[3],dechdz[3],dechdA[3];
double n[3],*nb,*cent;
double *vb1,*vb2,*vb3;
double vr1[3],vr2[3],vr3[3];
double *v1,*v2,*v3;
double scale;
double complex tscale,FTC;
double dp;
double B,TB=0;
double norm;
int t1,t2,t3,blocker,sign;
int j1,j2,j3;
double mu,mu0,area,mub,ech,rexp;
double *normal,*centroid;
int *visible;
int tb1,tb2,tb3; //Indices to the vertices of possible blocker facet
int blocked=0;
//Distance km->arcsec
dp=1/(dist*149597871.0)*180.0/PI*3600.0;
visible=calloc(nfac,sizeof(int));
//Allocate for memory
// normal=(double*)malloc(3*nfac*sizeof(double));
// centroid=(double*)mxCalloc(3*nfac,sizeof(double));
// IndexofBlocks=(int*)mxCalloc(nfac,sizeof(int));
// NumofBlocks=(int*)mxCalloc(nfac,sizeof(int));
//Calculate frame change matrix
Calculate_Frame_Matrix(Eo,up,R);
//FacetsOverHorizon(tlist,vlist,nfac,nvert,normal,centroid,NumofBlocks,IndexofBlocks);
rotate(angles[0],angles[1],angles[2],0.0,TIME,M,dMb,dMl,dMo);
//Construct asteroid->Camera frame matrix, which is
//asteroid->world frame->camera frame
transpose(M,Mt); //Transpose, since we rotate the model, not view directions
mult_mat(R,Mt,RT);
mult_vector(M,Eo,E);
mult_vector(M,E0o,E0);
/*For each facet,
* 1)Check if facet is visible
* 2) Calculate echo
* 3) Convert triangle to range-Doppler frame
* 4) Calculate FT
*/
//Find actual blockers
FindActualBlockers(tlist,vlist,nfac,nvert,E,E,1,visible);
Calculate_Radiance(tlist,vlist,nfac,nvert,angles,Eo,E0o,TIME,Gamma, A,Hdist,WL,N,Flux,Fldx,Fldy,Fldz,FldA,0);
//for(int i=27;i<nfac;i++)
// mexPrintf("fl%d: %.10e\n",i+1, Flux[i]);
//visible is nfac vector, visible[j]=1 if facet (j+1)th facet is visible
//NOTE INDEXING
//mexPrintf("%f %f %f\n",vlist[0],vlist[1],vlist[2]);
for(int j=0;j<nfac;j++)
{
if(visible[j]==0)
continue;
//Calculate normal from facet vertices
//Vertex indices of the current facet
//Note that C indices from 0, matlab from 1
j1=tlist[j*3]-1;
j2=tlist[j*3+1]-1;
j3=tlist[j*3+2]-1;
//Current vertices
v1=vlist+j1*3;
v2=vlist+j2*3;
v3=vlist+j3*3;
//Calculate normals and centroids
for(int i=0;i<3;i++)
{
side1[i]=dp*(v2[i]-v1[i]); //Convert km->arcsec
side2[i]=dp*(v3[i]-v1[i]);
}
cross(side1,side2,n);
norm=NORM(n);
n[0]=n[0]/norm;
n[1]=n[1]/norm;
n[2]=n[2]/norm;
mu=DOT(E,n);
mu0=DOT(E0,n);
//Convert to camera frame
mult_vector(RT,v1,vr1);
mult_vector(RT,v2,vr2);
mult_vector(RT,v3,vr3);
for(int i=0;i<3;i++)
{
vr1[i]=dp*vr1[i];
vr2[i]=dp*vr2[i];
vr3[i]=dp*vr3[i];
}
//Now we should convert to frequency domain, ie calculate the contribution of each facet
Calc_FTC(freqx,freqy,nfreq,vr1[0],vr1[1],vr2[0],vr2[1],vr3[0],vr3[1],F0);
// printf("Fdd: %f %f\n",creal(FTdd[0]),cimag(FTdd[0]));
//Note that we sum to F at each round, does not work, we need to multiply with the echo
//Derivatives wrt angles
area=0.5*norm;
//if(j==0)
//{
// mexPrintf("area: %f mu: %f F0: %f\n",area,mu,F0[0]);
//}
//mexPrintf("area: %f normal: %f %f %f mu: %f mu0: %f\n",area,n[0],n[1],n[2],mu,mu0);
B=Flux[j];
for(int jf=0;jf<nfreq;jf++)
{
//This should be taken outside of the loop
// mexPrintf("scale:%f offset: %f %f\n",scale,creal(cexp(2*PI*I*(offset[0]*freqx[jf]+offset[1]*freqy[jf]))),cimag(cexp(2*PI*I*(offset[0]*freqx[jf]+offset[1]*freqy[jf]))));
//FTC=tscale*F0[jf];
F[jf]+=B*F0[jf];
}
TB=TB+B*area*mu;
// printf("Flux: %f area: %f mu: %f\n",B,area,mu);
}
//printf("Total brightness: %f\n",TB);
//Normalize with total brightness
double complex temp;
for(int j=0;j<nfreq;j++)
{
temp=cexp(2.0*PI*I*(offset[0]*freqx[j]+offset[1]*freqy[j]))*F[j]/TB;
Fr[j]=creal(temp);
Fi[j]=cimag(temp);
}
free(visible);
free(Flux);
free(F0);
free(F);
}