void Quadrangle::shrink(const float &l)
{
Vector2D tab[4];
for(int i=0; i<4; i++){
Vector2D orth1 = Orthogonal(-((*this)[(i+1)%4]-(*this)[i])).normalise();
Vector2D orth2 = Orthogonal( ((*this)[(i-1)%4]-(*this)[i])).normalise();
std::cout << (*this)[i] << " :: " << (*this)[(i+1)%4] << std::endl;
std::cout << (*this)[(i+1)%4]-(*this)[i] << std::endl;
std::cout << "orth1 : " << orth1 << std::endl;
std::cout << (*this)[i] << " :: " << (*this)[(i-1)%4] << std::endl;
std::cout << ((*this)[(i-1)%4]-(*this)[i]) << std::endl;
std::cout << "orth2 : " << orth2 << std::endl;
std::cout << "tab["<<i<<"] : " << tab[i] << std::endl;
Vector2D v = (orth1 + orth2)/2;
std::cout << "v.Norm() : " << v.getNorm() << std::endl;
std::cout << std::endl;
tab[i] = (*this)[i]+Normalized(v)*(l/(v.getNorm()));
}
for(int i=0; i<4; i++){
std::cout << "tab["<<i<<"] : " << tab[i] << std::endl;
(*this)[i] = tab[i];
}
}
void Camera::SetPolar(Pointf3 dz, Pointf3 dx, double d, double a, double b, double r)
{
Pointf3 dy = dz % dx;
Pointf3 az = RotateX(Pointf3(0, 0, -1), -b);
az = d * RotateY(az, a);
Pointf3 loc = az * Matrixf3(dx, dy, dz, target);
Pointf3 dir = Unit(target - loc);
Pointf3 su = Orthogonal(dy, dir);
if(Length(su) <= 1e-10)
su = Orthogonal(FarthestAxis(dir), dir);
su = Unit(su);
Location(loc).Upwards(Rotate(su, dir, r));
}
void calcBezier::calculeOrthogonal(Geometry::Point3D &p0, Geometry::Point3D &p1, Geometry::Point3D &p2, Geometry::Point3D &p3, Geometry::Point3D &p00, Geometry::Point3D &p11, Geometry::Point3D &p22, Geometry::Point3D &p33, double largeur)
{
Geometry::Vector A(p1.getX()-p0.getX(), p1.getY()-p0.getY(), p1.getZ() - p0.getZ());
Geometry::Vector B(p3.getX()-p2.getX(), p3.getY()-p2.getY(), p3.getZ() - p2.getZ());
Geometry::Vector AO = Orthogonal(A);
AO = Normalized(AO);
AO = AO * largeur;
Geometry::Vector BO = Orthogonal(B);
BO = Normalized(BO);
BO = BO * largeur;
p00.setX(p0.getX()+AO[0]);
p00.setY(p0.getY()+AO[1]);
p00.setZ(p0.getZ()+AO[2]);
if (p00.getZ() !=0 )
{
AO = Orthogonal(AO);
AO = Normalized(AO);
AO = AO * largeur;
p00.setX(p0.getX()+AO[0]);
p00.setY(p0.getY()+AO[1]);
p00.setZ(p0.getZ()+AO[2]);
}
p11.setX(p1.getX()+AO[0]);
p11.setY(p1.getY()+AO[1]);
p11.setZ(p1.getZ()+AO[2]);
p22.setX(p2.getX()+BO[0]);
p22.setY(p2.getY()+BO[1]);
p22.setZ(p2.getZ()+BO[2]);
p33.setX(p3.getX()+BO[0]);
p33.setY(p3.getY()+BO[1]);
p33.setZ(p3.getZ()+BO[2]);
}
void Polygone::shrinkPoly(int nb, float l)
{
if(l == 0)
return;
Vector2D tab[nb];
for(int i = 0; i < nb; i++)
{
Vector2D v1 = Orthogonal(get(i)-get(i+1)).normalised();
Vector2D v2 = Orthogonal(get(i-1)-get(i)).normalised();
Vector2D v = (v1+v2)/2; //quand on augmente de 1 sur v1 ou v2, on augment de v.norm() sur le v.
tab[i] = get(i)+Normalized(v)*(l/v.getNorm());
}
for(int i = 0; i < nb; i++)
set(i, tab[i]);
}
void calcBezier::calculeOrthogonalSimple(Geometry::Point3D &p0, Geometry::Point3D &p1, Geometry::Point3D &p00, double largeur)
{
Geometry::Vector A(p1.getX()-p0.getX(), p1.getY()-p0.getY(), p1.getZ() - p0.getZ());
Geometry::Vector AO = Orthogonal(A);
AO = Normalized(AO);
AO = AO * largeur;
p00.setX(p0.getX()+AO[0]);
p00.setY(p0.getY()+AO[1]);
p00.setZ(p0.getZ()+AO[2]);
}
void Camera::Update()
{
direction = Unit(target - location);
distance_delta = -(location ^ direction);
viewing_distance = double(min(width_mm, height_mm) / (2e3 * tan(viewing_angle / 2.0)));
Pointf3 up = Orthogonal(upwards, direction);
if(Squared(up) <= 1e-10)
up = Orthogonal(FarthestAxis(direction), direction);
straight_up = Unit(up);
straight_right = direction % straight_up;
camera_matrix = Matrixf3(straight_right, straight_up, direction, location);
invcam_matrix = Matrixf3Inverse(camera_matrix);
double dw = viewing_distance * view_px * 2e3 / width_mm;
double dh = viewing_distance * view_py * 2e3 / height_mm;
double z_times = far_distance - near_distance;
z_delta = -near_distance / z_times;
transform_matrix = invcam_matrix * Matrixf3(
Pointf3(dw / z_times, 0, 0),
Pointf3(0, dh / z_times, 0),
Pointf3(shift_x, shift_y, 1) / z_times);
}
Pointf3 Orthonormal(Pointf3 v, Pointf3 against)
{
return Unit(Orthogonal(v, against));
}
void Triangles::IntersectConsMetric(const double * s,const Int4 nbsol,const int * typsols,
const Real8 hmin1,const Real8 hmax1,const Real8 coef,
const Real8 anisomax ,const Real8 CutOff,const int NbJacobi,
const int DoNormalisation,const int choice)
{ // the array of solution s is store
// sol0,sol1,...,soln on vertex 0
// sol0,sol1,...,soln on vertex 1
// etc.
const int dim = 2;
int sizeoftype[] = { 1, dim ,dim * (dim+1) / 2, dim * dim } ;
// computation of the nb of field
Int4 ntmp = 0;
if (typsols)
{
for (Int4 i=0;i<nbsol;i++)
ntmp += sizeoftype[typsols[i]];
}
else
ntmp = nbsol;
// n is the total number of fields
const Int4 n = ntmp;
Int4 i,k,iA,iB,iC,iv;
R2 O(0,0);
int RelativeMetric = CutOff>1e-30;
Real8 hmin = Max(hmin1,MinimalHmin());
Real8 hmax = Min(hmax1,MaximalHmax());
Real8 coef2 = 1/(coef*coef);
if(verbosity>1)
{
cout << " -- Construction of Metric: Nb of sol. " << n << " nbt = "
<< nbt << " nbv= " << nbv
<< " coef = " << coef << endl
<< " hmin = " << hmin << " hmax=" << hmax
<< " anisomax = " << anisomax << " Nb Jacobi " << NbJacobi ;
if (RelativeMetric)
cout << " RelativeErr with CutOff= " << CutOff << endl;
else
cout << " Absolute Err" <<endl;
}
double *ss=(double*)s, *ssiii = ss;
double sA,sB,sC;
Real8 *detT = new Real8[nbt];
Real8 *Mmass= new Real8[nbv];
Real8 *Mmassxx= new Real8[nbv];
Real8 *dxdx= new Real8[nbv];
Real8 *dxdy= new Real8[nbv];
Real8 *dydy= new Real8[nbv];
Real8 *workT= new Real8[nbt];
Real8 *workV= new Real8[nbv];
int *OnBoundary = new int[nbv];
for (iv=0;iv<nbv;iv++)
{
Mmass[iv]=0;
OnBoundary[iv]=0;
Mmassxx[iv]=0;
}
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
const Triangle &t=triangles[i];
// coor of 3 vertices
R2 A=t[0];
R2 B=t[1];
R2 C=t[2];
// number of the 3 vertices
iA = Number(t[0]);
iB = Number(t[1]);
iC = Number(t[2]);
Real8 dett = ::Area2(A,B,C);
detT[i]=dett;
dett /= 6;
// construction of on boundary
int nbb =0;
for(int j=0;j<3;j++)
{
Triangle *ta=t.Adj(j);
if ( ! ta || !ta->link) // no adj triangle => edge on boundary
OnBoundary[Number(t[VerticesOfTriangularEdge[j][0]])]=1,
OnBoundary[Number(t[VerticesOfTriangularEdge[j][1]])]=1,
nbb++;
}
workT[i] = nbb;
Mmass[iA] += dett;
Mmass[iB] += dett;
Mmass[iC] += dett;
if((nbb==0)|| !choice)
{
Mmassxx[iA] += dett;
Mmassxx[iB] += dett;
Mmassxx[iC] += dett;
}
}
else
workT[i]=-1;
for (Int4 kcount=0;kcount<n;kcount++,ss++)
{ //for all solution
Real8 smin=ss[0],smax=ss[0];
Real8 h1=1.e30,h2=1e-30,rx=0;
Real8 coef = 1./(anisomax*anisomax);
Real8 hn1=1.e30,hn2=1e-30,rnx =1.e-30;
for ( iv=0,k=0; iv<nbv; iv++,k+=n )
{
dxdx[iv]=dxdy[iv]=dydy[iv]=0;
smin=Min(smin,ss[k]);
smax=Max(smax,ss[k]);
}
Real8 sdelta = smax-smin;
Real8 absmax=Max(Abs(smin),Abs(smax));
Real8 cnorm = DoNormalisation ? coef2/sdelta : coef2;
if(verbosity>2)
cout << " Solution " << kcount << " Min = " << smin << " Max = "
<< smax << " Delta =" << sdelta << " cnorm = " << cnorm << endl;
if ( sdelta < 1.0e-10*Max(absmax,1e-20) )
{
if (verbosity>2)
cout << " Solution " << kcount << " is constant. We skip. "
<< " Min = " << smin << " Max = " << smax << endl;
continue;
}
for (i=0;i<nbt;i++)
if(triangles[i].link)
{// for real all triangles
// coor of 3 vertices
R2 A=triangles[i][0];
R2 B=triangles[i][1];
R2 C=triangles[i][2];
// warning the normal is internal and the
// size is the length of the edge
R2 nAB = Orthogonal(B-A);
R2 nBC = Orthogonal(C-B);
R2 nCA = Orthogonal(A-C);
// remark : nAB + nBC + nCA == 0
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
// for the test of boundary edge
// the 3 adj triangles
Triangle *tBC = triangles[i].TriangleAdj(OppositeEdge[0]);
Triangle *tCA = triangles[i].TriangleAdj(OppositeEdge[1]);
Triangle *tAB = triangles[i].TriangleAdj(OppositeEdge[2]);
// value of the P1 fonction on 3 vertices
sA = ss[iA*n];
sB = ss[iB*n];
sC = ss[iC*n];
R2 Grads = (nAB * sC + nBC * sA + nCA * sB ) /detT[i] ;
if(choice)
{
int nbb = 0;
Real8 dd = detT[i];
Real8 lla,llb,llc,llf;
Real8 taa[3][3],bb[3];
// construction of the trans of lin system
for (int j=0;j<3;j++)
{
int ie = OppositeEdge[j];
TriangleAdjacent ta = triangles[i].Adj(ie);
Triangle *tt = ta;
if (tt && tt->link)
{
Vertex &v = *ta.OppositeVertex();
R2 V = v;
Int4 iV = Number(v);
Real8 lA = ::Area2(V,B,C)/dd;
Real8 lB = ::Area2(A,V,C)/dd;
Real8 lC = ::Area2(A,B,V)/dd;
taa[0][j] = lB*lC;
taa[1][j] = lC*lA;
taa[2][j] = lA*lB;
Real8 xx = V.x-V.y;
Real8 yy = V.x + V.y;
//cout << " iv " << ss[iV*n] << " == " << (8*xx*xx+yy*yy)
// << " l = " << lA << " " << lB << " " << lC
// << " = " << lA+lB+lC << " " << V << " == " << A*lA+B*lB+C*lC << endl;
lla = lA,llb=lB,llc=lC,llf=ss[iV*n] ;
bb[j] = ss[iV*n] - ( sA*lA + sB*lB + sC*lC ) ;
}
else
{
nbb++;
taa[0][j]=0;
taa[1][j]=0;
taa[2][j]=0;
taa[j][j]=1;
bb[j]=0;
}
}
// resolution of 3x3 lineaire system transpose
Real8 det33 = det3x3(taa[0],taa[1],taa[2]);
Real8 cBC = det3x3(bb,taa[1],taa[2]);
Real8 cCA = det3x3(taa[0],bb,taa[2]);
Real8 cAB = det3x3(taa[0],taa[1],bb);
assert(det33);
// det33=1;
// verif
// cout << " " << (taa[0][0]*cBC + taa[1][0]*cCA + taa[2][0] * cAB)/det33 << " == " << bb[0] ;
// cout << " " << (taa[0][1]*cBC + taa[1][1]*cCA + taa[2][1] * cAB)/det33 << " == " << bb[1];
// cout << " " << (taa[0][2]*cBC + taa[1][2]*cCA + taa[2][2] * cAB)/det33 << " == " << bb[2]
// << " -- " ;
//cout << lla*sA + llb*sB+llc*sC+ (lla*llb* cAB + llb*llc* cBC + llc*lla*cCA)/det33
// << " == " << llf << endl;
// computation of the gradient in the element
// H( li*lj) = grad li grad lj + grad lj grad lj
// grad li = njk / detT ; with i j k ={A,B,C)
Real8 Hxx = cAB * ( nBC.x*nCA.x) + cBC * ( nCA.x*nAB.x) + cCA * (nAB.x*nBC.x);
Real8 Hyy = cAB * ( nBC.y*nCA.y) + cBC * ( nCA.y*nAB.y) + cCA * (nAB.y*nBC.y);
Real8 Hxy = cAB * ( nBC.y*nCA.x) + cBC * ( nCA.y*nAB.x) + cCA * (nAB.y*nBC.x)
+ cAB * ( nBC.x*nCA.y) + cBC * ( nCA.x*nAB.y) + cCA * (nAB.x*nBC.y);
Real8 coef = 1.0/(3*dd*det33);
Real8 coef2 = 2*coef;
// cout << " H = " << Hxx << " " << Hyy << " " << Hxy/2 << " coef2 = " << coef2 << endl;
Hxx *= coef2;
Hyy *= coef2;
Hxy *= coef2;
//cout << i << " H = " << 3*Hxx/dd << " " << 3*Hyy/dd << " " << 3*Hxy/(dd*2) << " nbb = " << nbb << endl;
if(nbb==0)
{
dxdx[iA] += Hxx;
dydy[iA] += Hyy;
dxdy[iA] += Hxy;
dxdx[iB] += Hxx;
dydy[iB] += Hyy;
dxdy[iB] += Hxy;
dxdx[iC] += Hxx;
dydy[iC] += Hyy;
dxdy[iC] += Hxy;
}
}
else
{
// if edge on boundary no contribution => normal = 0
if ( ! tBC || ! tBC->link ) nBC = O;
if ( ! tCA || ! tCA->link ) nCA = O;
if ( ! tAB || ! tAB->link ) nAB = O;
// remark we forgot a 1/2 because
// \int_{edge} w_i = 1/2 if i is in edge
// 0 if not
// if we don't take the boundary
// dxdx[iA] += ( nCA.x + nAB.x ) *Grads.x;
dxdx[iA] += ( nCA.x + nAB.x ) *Grads.x;
dxdx[iB] += ( nAB.x + nBC.x ) *Grads.x;
dxdx[iC] += ( nBC.x + nCA.x ) *Grads.x;
// warning optimization (1) the divide by 2 is done on the metrix construction
dxdy[iA] += (( nCA.y + nAB.y ) *Grads.x + ( nCA.x + nAB.x ) *Grads.y) ;
dxdy[iB] += (( nAB.y + nBC.y ) *Grads.x + ( nAB.x + nBC.x ) *Grads.y) ;
dxdy[iC] += (( nBC.y + nCA.y ) *Grads.x + ( nBC.x + nCA.x ) *Grads.y) ;
dydy[iA] += ( nCA.y + nAB.y ) *Grads.y;
dydy[iB] += ( nAB.y + nBC.y ) *Grads.y;
dydy[iC] += ( nBC.y + nCA.y ) *Grads.y;
}
} // for real all triangles
Int4 kk=0;
for ( iv=0,k=0 ; iv<nbv; iv++,k+=n )
if(Mmassxx[iv]>0)
{
dxdx[iv] /= 2*Mmassxx[iv];
// warning optimization (1) on term dxdy[iv]*ci/2
dxdy[iv] /= 4*Mmassxx[iv];
dydy[iv] /= 2*Mmassxx[iv];
// Compute the matrix with abs(eigen value)
Metric M(dxdx[iv], dxdy[iv], dydy[iv]);
MatVVP2x2 Vp(M);
//cout <<iv << " M = " << M << " aniso= " << Vp.Aniso() ;
Vp.Abs();
M = Vp;
dxdx[iv] = M.a11;
dxdy[iv] = M.a21;
dydy[iv] = M.a22;
// cout << " (abs) iv M = " << M << " aniso= " << Vp.Aniso() <<endl;
}
else kk++;
// correction of second derivate
// by a laplacien
Real8 *d2[3] = { dxdx, dxdy, dydy};
Real8 *dd;
for (int xy = 0;xy<3;xy++)
{
dd = d2[xy];
// do leat 2 iteration for boundary problem
for (int ijacobi=0;ijacobi<Max(NbJacobi,2);ijacobi++)
{
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
Real8 cc=3;
if(ijacobi==0)
cc = Max((Real8) ((Mmassxx[iA]>0)+(Mmassxx[iB]>0)+(Mmassxx[iC]>0)),1.);
workT[i] = (dd[iA]+dd[iB]+dd[iC])/cc;
}
for (iv=0;iv<nbv;iv++)
workV[iv]=0;
for (i=0;i<nbt;i++)
if(triangles[i].link) // the real triangles
{
// number of the 3 vertices
iA = Number(triangles[i][0]);
iB = Number(triangles[i][1]);
iC = Number(triangles[i][2]);
Real8 cc = workT[i]*detT[i];
workV[iA] += cc;
workV[iB] += cc;
workV[iC] += cc;
}
for (iv=0;iv<nbv;iv++)
if( ijacobi<NbJacobi || OnBoundary[iv])
dd[iv] = workV[iv]/(Mmass[iv]*6);
}
}
// constuction of the metrix from the Hessian dxdx. dxdy,dydy
Real8 rCutOff=CutOff*absmax;// relative cut off
for ( iv=0,k=0 ; iv<nbv; iv++,k+=n )
{ // for all vertices
//{
//Metric M(dxdx[iv], dxdy[iv], dydy[iv]);
// MatVVP2x2 Vp(M);
//cout << " iv M="<< M << " Vp = " << Vp << " aniso " << Vp.Aniso() << endl;
//}
MetricIso Miso;
Real8 ci = RelativeMetric ? coef2/(Max(Abs(ss[k]),rCutOff)) : cnorm ;
Metric Miv(dxdx[iv]*ci, dxdy[iv]*ci, dydy[iv]*ci);
MatVVP2x2 Vp(Miv);
Vp.Abs();
h1=Min(h1,Vp.lmin());
h2=Max(h2,Vp.lmax());
Vp.Maxh(hmin);
Vp.Minh(hmax);
rx = Max(rx,Vp.Aniso2());
Vp.BoundAniso2(coef);
hn1=Min(hn1,Vp.lmin());
hn2=Max(hn2,Vp.lmax());
rnx = Max(rnx,Vp.Aniso2());
Metric MVp(Vp);
vertices[iv].m.IntersectWith(MVp);
}// for all vertices
if (verbosity>2)
{
cout << " Solution " << kcount << endl;
cout << " before bounding : Hmin = " << sqrt(1/h2) << " Hmax = "
<< sqrt(1/h1) << " factor of anisotropy max = " << sqrt(rx) << endl;
cout << " after bounding : Hmin = " << sqrt(1/hn2) << " Hmax = "
<< sqrt(1/hn1) << " factor of anisotropy max = " << sqrt(rnx) << endl;
}
}// end for all solution
delete [] detT;
delete [] Mmass;
delete [] dxdx;
delete [] dxdy;
delete [] dydy;
delete [] workT;
delete [] workV;
delete [] Mmassxx;
delete [] OnBoundary;
}
