Rectangle(const Vec p0_, const Vec &a_, const Vec &b_, const Color &emission_, const Color &color_) :
a(a_), b(b_), p0(p0_), emission(emission_), color(color_) {
normal = Cross(a, b);
normal = Normalize(normal);
a_len = a.Length();
b_len = b.Length();
}
void LineSeg<D> :: Project (const Point<D> point, Point<D> & point_on_curve, double & t) const
{
Vec<D> v = p2-p1;
double l = v.Length();
v *= 1./l;
t = (point-p1)*v;
if(t<0) t = 0;
if(t>l) t = l;
point_on_curve = p1+t*v;
t *= 1./l;
}
void GeneralizedCylinder :: CalcHesse (const Point<3> & point, Mat<3> & hesse) const
{
Point<2> p2d, projp;
double t, dist, val;
Point<2> curvp;
Vec<2> curvpp;
Mat<2> h2d;
Mat<3,2> vmat;
int i, j, k, l;
p2d = Point<2> (planee1 * (point - planep), planee2 * (point - planep));
t = crosssection.ProjectParam (p2d);
curvp = crosssection.CurvCircle (t);
curvpp = p2d-curvp;
dist = curvpp.Length();
curvpp /= dist;
h2d(0, 0) = (1 - curvpp(0) * curvpp(0) ) / dist;
h2d(0, 1) = h2d(1, 0) = (- curvpp(0) * curvpp(1) ) / dist;
h2d(1, 1) = (1 - curvpp(1) * curvpp(1) ) / dist;
vmat(0,0) = planee1(0);
vmat(1,0) = planee1(1);
vmat(2,0) = planee1(2);
vmat(0,1) = planee2(0);
vmat(1,1) = planee2(1);
vmat(2,1) = planee2(2);
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
{
val = 0;
for (k = 0; k < 2; k++)
for (l = 0; l < 2; l++)
val += vmat(i,k) * h2d(k,l) * vmat(j,l);
hesse(i,j) = val;
}
}
inline Vec Normalize(const Vec &v) { return v / v.Length(); }
void OCCSurface :: DefineTangentialPlane (const Point<3> & ap1,
const PointGeomInfo & geominfo1,
const Point<3> & ap2,
const PointGeomInfo & geominfo2)
{
if (projecttype == PLANESPACE)
{
p1 = ap1; p2 = ap2;
//cout << "p1 = " << p1 << endl;
//cout << "p2 = " << p2 << endl;
GetNormalVector (p1, geominfo1, ez);
ex = p2 - p1;
ex -= (ex * ez) * ez;
ex.Normalize();
ey = Cross (ez, ex);
GetNormalVector (p2, geominfo2, n2);
nmid = 0.5*(n2+ez);
ez = nmid;
ez.Normalize();
ex = (p2 - p1).Normalize();
ez -= (ez * ex) * ex;
ez.Normalize();
ey = Cross (ez, ex);
nmid = ez;
//cout << "ex " << ex << " ey " << ey << " ez " << ez << endl;
}
else
{
if ( (geominfo1.u < umin) ||
(geominfo1.u > umax) ||
(geominfo2.u < umin) ||
(geominfo2.u > umax) ||
(geominfo1.v < vmin) ||
(geominfo1.v > vmax) ||
(geominfo2.v < vmin) ||
(geominfo2.v > vmax) ) throw UVBoundsException();
p1 = ap1; p2 = ap2;
psp1 = Point<2>(geominfo1.u, geominfo1.v);
psp2 = Point<2>(geominfo2.u, geominfo2.v);
Vec<3> n;
GetNormalVector (p1, geominfo1, n);
gp_Pnt pnt;
gp_Vec du, dv;
occface->D1 (geominfo1.u, geominfo1.v, pnt, du, dv);
DenseMatrix D1(3,2), D1T(2,3), DDTinv(2,2);
D1(0,0) = du.X(); D1(1,0) = du.Y(); D1(2,0) = du.Z();
D1(0,1) = dv.X(); D1(1,1) = dv.Y(); D1(2,1) = dv.Z();
/*
(*testout) << "DefineTangentialPlane" << endl
<< "---------------------" << endl;
(*testout) << "D1 = " << endl << D1 << endl;
*/
Transpose (D1, D1T);
DenseMatrix D1TD1(3,3);
D1TD1 = D1T*D1;
if (D1TD1.Det() == 0) throw SingularMatrixException();
CalcInverse (D1TD1, DDTinv);
DenseMatrix Y(3,2);
Vec<3> y1 = (ap2-ap1).Normalize();
Vec<3> y2 = Cross(n, y1).Normalize();
for (int i = 0; i < 3; i++)
{
Y(i,0) = y1(i);
Y(i,1) = y2(i);
}
DenseMatrix A(2,2);
A = DDTinv * D1T * Y;
DenseMatrix Ainv(2,2);
if (A.Det() == 0) throw SingularMatrixException();
CalcInverse (A, Ainv);
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++)
{
Amat(i,j) = A(i,j);
Amatinv(i,j) = Ainv(i,j);
}
Vec<2> temp = Amatinv * (psp2-psp1);
double r = temp.Length();
// double alpha = -acos (temp(0)/r);
double alpha = -atan2 (temp(1),temp(0));
DenseMatrix R(2,2);
R(0,0) = cos (alpha);
R(1,0) = -sin (alpha);
R(0,1) = sin (alpha);
R(1,1) = cos (alpha);
A = A*R;
if (A.Det() == 0) throw SingularMatrixException();
CalcInverse (A, Ainv);
for (int i = 0; i < 2; i++)
for (int j = 0; j < 2; j++)
{
Amat(i,j) = A(i,j);
Amatinv(i,j) = Ainv(i,j);
}
temp = Amatinv * (psp2-psp1);
};
}
INSOLID_TYPE Polyhedra :: VecInSolid2 (const Point<3> & p,
const Vec<3> & v1,
const Vec<3> & v2,
double eps) const
{
//(*testout) << "VecInSolid2 eps " << eps << endl;
INSOLID_TYPE res = VecInSolid(p,v1,eps);
//(*testout) << "VecInSolid = " <<res <<endl;
if(res != DOES_INTERSECT)
return res;
int point_on_n_faces = 0;
Vec<3> v1n = v1;
v1n.Normalize();
Vec<3> v2n = v2 - (v2 * v1n) * v1n;
v2n.Normalize();
double cosv2, cosv2max = -1;
for (int i = 0; i < faces.Size(); i++)
{
const Point<3> & p1 = points[faces[i].pnums[0]];
Vec<3> v0 = p - p1;
if (fabs (faces[i].nn * v0) > eps) continue; // n->nn
if (fabs (v1n * faces[i].nn) > eps_base1) continue; // n->nn
double lam1 = (faces[i].w1 * v0);
double lam2 = (faces[i].w2 * v0);
if (lam1 >= -eps_base1 && lam2 >= -eps_base1 && lam1+lam2 <= 1+eps_base1)
{
// v1 is in face
Point<3> fc = Center (points[faces[i].pnums[0]],
points[faces[i].pnums[1]],
points[faces[i].pnums[2]]);
Vec<3> vpfc = fc - p;
cosv2 = (v2n * vpfc) / vpfc.Length();
if (cosv2 > cosv2max)
{
cosv2max = cosv2;
point_on_n_faces++;
double scal2 = v2n * faces[i].nn; // n->nn
res = DOES_INTERSECT;
if (scal2 > eps_base1) res = IS_OUTSIDE;
if (scal2 < -eps_base1) res = IS_INSIDE;
}
}
}
if (point_on_n_faces >= 1)
return res;
(*testout) << "primitive::vecinsolid2 makes nonsense for polyhedra" << endl;
cerr << "primitive::vecinsolid2 makes nonsense for polyhedra" << endl;
return Primitive :: VecInSolid2 (p, v1, v2, eps);
}
void CircleCurve2d :: Project (Point<2> & p) const
{
Vec<2> v = p - center;
v *= rad/v.Length();
p = center + v;
}