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46aa785828
netgen/libsrc/csg/algprim.cpp
Joachim Schoeberl 46aa785828 fix SetMaxH in python
2014-12-05 15:58:49 +00:00

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#include <mystdlib.h>
#include <linalg.hpp>
#include <csg.hpp>
namespace netgen
{
double
QuadraticSurface :: CalcFunctionValue (const Point<3> & p) const
{
return p(0) * (cxx * p(0) + cxy * p(1) + cxz * p(2) + cx) +
p(1) * (cyy * p(1) + cyz * p(2) + cy) +
p(2) * (czz * p(2) + cz) + c1;
}
void
QuadraticSurface :: CalcGradient (const Point<3> & p, Vec<3> & grad) const
{
grad(0) = 2 * cxx * p(0) + cxy * p(1) + cxz * p(2) + cx;
grad(1) = 2 * cyy * p(1) + cxy * p(0) + cyz * p(2) + cy;
grad(2) = 2 * czz * p(2) + cxz * p(0) + cyz * p(1) + cz;
}
void
QuadraticSurface :: CalcHesse (const Point<3> & /* p */, Mat<3> & hesse) const
{
hesse(0,0) = 2 * cxx;
hesse(1,1) = 2 * cyy;
hesse(2,2) = 2 * czz;
hesse(0,1) = hesse(1,0) = cxy;
hesse(0,2) = hesse(2,0) = cxz;
hesse(1,2) = hesse(2,1) = cyz;
}
void QuadraticSurface :: Read (istream & ist)
{
ist >> cxx >> cyy >> czz >> cxy >> cxz >> cyz >> cx >> cy >> cz >> c1;
}
void QuadraticSurface :: Print (ostream & ost) const
{
ost << cxx << " " << cyy << " " << czz << " "
<< cxy << " " << cxz << " " << cyz << " "
<< cx << " " << cy << " " << cz << " "
<< c1;
}
void QuadraticSurface :: PrintCoeff (ostream & ost) const
{
ost << " cxx = " << cxx
<< " cyy = " << cyy
<< " czz = " << czz
<< " cxy = " << cxy
<< " cxz = " << cxz
<< " cyz = " << cyz
<< " cx = " << cx
<< " cy = " << cy
<< " cz = " << cz
<< " c1 = " << c1 << endl;
}
Point<3> QuadraticSurface :: GetSurfacePoint () const
{
MyError ("GetSurfacePoint called for QuadraticSurface");
return Point<3> (0, 0, 0);
}
Plane :: Plane (const Point<3> & ap, Vec<3> an)
{
eps_base = 1e-8;
p = ap;
n = an;
CalcData();
}
void Plane :: CalcData()
{
n.Normalize();
cxx = cyy = czz = cxy = cxz = cyz = 0;
cx = n(0); cy = n(1); cz = n(2);
c1 = - (cx * p(0) + cy * p(1) + cz * p(2));
}
Primitive * Plane :: Copy () const
{
return new Plane (p, n);
}
void Plane :: Print (ostream & ost) const
{
ost << "plane(" << p << "; " << n << ")";
}
void Plane :: Transform (Transformation<3> & trans)
{
Point<3> hp;
Vec<3> hn;
trans.Transform (p, hp);
trans.Transform (n, hn);
p = hp;
n = hn;
CalcData();
}
void Plane :: GetPrimitiveData (const char *& classname,
Array<double> & coeffs) const
{
classname = "plane";
coeffs.SetSize (6);
coeffs.Elem(1) = p(0);
coeffs.Elem(2) = p(1);
coeffs.Elem(3) = p(2);
coeffs.Elem(4) = n(0);
coeffs.Elem(5) = n(1);
coeffs.Elem(6) = n(2);
}
void Plane :: SetPrimitiveData (Array<double> & coeffs)
{
p(0) = coeffs.Elem(1);
p(1) = coeffs.Elem(2);
p(2) = coeffs.Elem(3);
n(0) = coeffs.Elem(4);
n(1) = coeffs.Elem(5);
n(2) = coeffs.Elem(6);
CalcData();
}
Primitive * Plane :: CreateDefault ()
{
return new Plane (Point<3> (0,0,0), Vec<3> (0,0,1));
}
int Plane :: IsIdentic (const Surface & s2, int & inv, double eps) const
{
const Plane * ps2 = dynamic_cast<const Plane*>(&s2);
if(ps2)
{
Point<3> pp2 = ps2->GetSurfacePoint();
Vec<3> n2 = s2.GetNormalVector(pp2);
if(fabs(n*n2) < 1.-eps_base)
return 0;
if (fabs (s2.CalcFunctionValue(p)) > eps) return 0;
}
else
{
if (fabs (s2.CalcFunctionValue(p)) > eps) return 0;
Vec<3> hv1, hv2;
hv1 = n.GetNormal ();
hv2 = Cross (n, hv1);
Point<3> hp = p + hv1;
if (fabs (s2.CalcFunctionValue(hp)) > eps) return 0;
hp = p + hv2;
if (fabs (s2.CalcFunctionValue(hp)) > eps) return 0;
}
Vec<3> n1, n2;
n1 = GetNormalVector (p);
n2 = s2.GetNormalVector (p);
inv = (n1 * n2 < 0);
return 1;
}
void Plane :: DefineTangentialPlane (const Point<3> & ap1, const Point<3> & ap2)
{
Surface::DefineTangentialPlane (ap1, ap2);
}
void Plane :: ToPlane (const Point<3> & p3d,
Point<2> & pplane,
double h, int & zone) const
{
Vec<3> p1p;
p1p = p3d - p1;
p1p /= h;
pplane(0) = p1p * ex;
pplane(1) = p1p * ey;
zone = 0;
}
void Plane :: FromPlane (const Point<2> & pplane, Point<3> & p3d, double h) const
{
p3d = p1 + (h * pplane(0)) * ex + (h * pplane(1)) * ey;
}
void Plane :: Project (Point<3> & p3d) const
{
double val = Plane::CalcFunctionValue (p3d);
p3d -= val * n;
}
INSOLID_TYPE Plane :: BoxInSolid (const BoxSphere<3> & box) const
{
int i;
double val;
Point<3> pp;
val = Plane::CalcFunctionValue (box.Center());
if (val > box.Diam() / 2) return IS_OUTSIDE;
if (val < -box.Diam() / 2) return IS_INSIDE;
if (val > 0)
{
/*
double modify =
((box.MaxX()-box.MinX()) * fabs (cx) +
(box.MaxY()-box.MinY()) * fabs (cy) +
(box.MaxZ()-box.MinZ()) * fabs (cz)) / 2;
*/
Vec<3> vdiag = box.PMax() - box.PMin();
double modify = (vdiag(0) * fabs (cx) +
vdiag(1) * fabs (cy) +
vdiag(2) * fabs (cz) ) / 2;
if (val - modify < 0)
return DOES_INTERSECT;
return IS_OUTSIDE;
// only outside or intersect possible
for (i = 0; i < 8; i++)
{
pp = box.GetPointNr (i);
val = Plane::CalcFunctionValue (pp);
if (val < 0)
return DOES_INTERSECT;
}
return IS_OUTSIDE;
}
else
{
/*
double modify =
((box.MaxX()-box.MinX()) * fabs (cx) +
(box.MaxY()-box.MinY()) * fabs (cy) +
(box.MaxZ()-box.MinZ()) * fabs (cz)) / 2;
*/
Vec<3> vdiag = box.PMax() - box.PMin();
double modify = (vdiag(0) * fabs (cx) +
vdiag(1) * fabs (cy) +
vdiag(2) * fabs (cz) ) / 2;
if (val + modify > 0)
return DOES_INTERSECT;
return IS_INSIDE;
// only inside or intersect possible
for (i = 0; i < 8; i++)
{
pp = box.GetPointNr (i);
val = Plane::CalcFunctionValue (pp);
if (val > 0)
return DOES_INTERSECT;
}
return IS_INSIDE;
}
/*
for (i = 1; i <= 8; i++)
{
box.GetPointNr (i, p);
val = CalcFunctionValue (p);
if (val > 0) inside = 0;
if (val < 0) outside = 0;
}
if (inside) return IS_INSIDE;
if (outside) return IS_OUTSIDE;
return DOES_INTERSECT;
*/
}
// double Plane :: CalcFunctionValue (const Point<3> & p3d) const
// {
// return cx * p3d(0) + cy * p3d(1) + cz * p3d(2) + c1;
// }
void Plane :: CalcGradient (const Point<3> & /* p */, Vec<3> & grad) const
{
grad(0) = cx;
grad(1) = cy;
grad(2) = cz;
}
void Plane :: CalcHesse (const Point<3> & /* p */, Mat<3> & hesse) const
{
hesse = 0;
}
double Plane :: HesseNorm () const
{
return 0;
}
Point<3> Plane :: GetSurfacePoint () const
{
return p;
}
void Plane :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & boundingbox, double /* facets */) const
{
// find triangle, such that
// boundingbox \cap plane is contained in it
Point<3> c = boundingbox.Center();
double r = boundingbox.Diam();
Project (c);
Vec<3> t1 = n.GetNormal();
Vec<3> t2 = Cross (n, t1);
t1.Normalize();
t2.Normalize();
tas.AddPoint (c + (-0.5 * r) * t2 + (sqrt(0.75) * r) * t1);
tas.AddPoint (c + (-0.5 * r) * t2 + (-sqrt(0.75) * r) * t1);
tas.AddPoint (c + r * t2);
tas.AddTriangle (TATriangle (0, 0, 1, 2));
}
Sphere :: Sphere (const Point<3> & ac, double ar)
{
c = ac;
r = ar;
invr = 1.0/r;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - c(0) / r;
cy = - c(1) / r;
cz = - c(2) / r;
c1 = (c(0) * c(0) + c(1) * c(1) + c(2) * c(2)) / (2 * r) - r / 2;
}
void Sphere :: GetPrimitiveData (const char *& classname, Array<double> & coeffs) const
{
classname = "sphere";
coeffs.SetSize (4);
coeffs.Elem(1) = c(0);
coeffs.Elem(2) = c(1);
coeffs.Elem(3) = c(2);
coeffs.Elem(4) = r;
}
void Sphere :: SetPrimitiveData (Array<double> & coeffs)
{
c(0) = coeffs.Elem(1);
c(1) = coeffs.Elem(2);
c(2) = coeffs.Elem(3);
r = coeffs.Elem(4);
invr = 1.0/r;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - c(0) / r;
cy = - c(1) / r;
cz = - c(2) / r;
c1 = (c(0) * c(0) + c(1) * c(1) + c(2) * c(2)) / (2 * r) - r / 2;
}
Primitive * Sphere :: CreateDefault ()
{
return new Sphere (Point<3> (0,0,0), 1);
}
Primitive * Sphere :: Copy () const
{
return new Sphere (c, r);
}
void Sphere :: Transform (Transformation<3> & trans)
{
Point<3> hp;
trans.Transform (c, hp);
c = hp;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - c(0) / r;
cy = - c(1) / r;
cz = - c(2) / r;
c1 = (c(0) * c(0) + c(1) * c(1) + c(2) * c(2)) / (2 * r) - r / 2;
}
double Sphere :: CalcFunctionValue (const Point<3> & point) const
{
return 0.5* (invr * Abs2 (point-c) - r);
}
int Sphere :: IsIdentic (const Surface & s2, int & inv, double eps) const
{
const Sphere * sp2 = dynamic_cast<const Sphere*> (&s2);
if (!sp2) return 0;
if (Dist (sp2->c, c) > eps) return 0;
if (fabs (sp2->r - r) > eps) return 0;
inv = 0;
return 1;
}
void Sphere :: DefineTangentialPlane (const Point<3> & ap1, const Point<3> & ap2)
{
Surface::DefineTangentialPlane (ap1, ap2);
ez = p1 - c;
ez /= ez.Length();
ex = p2 - p1;
ex -= (ex * ez) * ez;
ex /= ex.Length();
ey = Cross (ez, ex);
}
void Sphere :: ToPlane (const Point<3> & p, Point<2> & pplane, double h, int & zone) const
{
Vec<3> p1p;
p1p = p - p1;
/*
if (p1p * ez < -r)
{
zone = -1;
pplane = Point<2> (1E8, 1E8);
}
else
{
zone = 0;
p1p /= h;
pplane(0) = p1p * ex;
pplane(1) = p1p * ey;
}
*/
Point<3> p1top = c + (c - p1);
Vec<3> p1topp = p - p1top;
Vec<3> p1topp1 = p1 - p1top;
Vec<3> lam;
// SolveLinearSystem (ex, ey, p1topp, p1topp1, lam);
Mat<3> m;
for (int i = 0; i < 3; i++)
{
m(i, 0) = ex(i);
m(i, 1) = ey(i);
m(i, 2) = p1topp(i);
}
m.Solve (p1topp1, lam);
pplane(0) = -lam(0) / h;
pplane(1) = -lam(1) / h;
if (lam(2) > 2)
zone = -1;
else
zone = 0;
}
void Sphere :: FromPlane (const Point<2> & pplane, Point<3> & p, double h) const
{
/*
// Vec<3> p1p;
double z;
Point<2> pplane2 (pplane);
pplane2(0) *= h;
pplane2(1) *= h;
z = -r + sqrt (sqr (r) - sqr (pplane2(0)) - sqr (pplane2(1)));
// p = p1;
p(0) = p1(0) + pplane2(0) * ex(0) + pplane2(1) * ey(0) + z * ez(0);
p(1) = p1(1) + pplane2(0) * ex(1) + pplane2(1) * ey(1) + z * ez(1);
p(2) = p1(2) + pplane2(0) * ex(2) + pplane2(1) * ey(2) + z * ez(2);
*/
Point<2> pplane2 (pplane);
pplane2(0) *= h;
pplane2(1) *= h;
p(0) = p1(0) + pplane2(0) * ex(0) + pplane2(1) * ey(0);
p(1) = p1(1) + pplane2(0) * ex(1) + pplane2(1) * ey(1);
p(2) = p1(2) + pplane2(0) * ex(2) + pplane2(1) * ey(2);
Project (p);
}
void Sphere :: Project (Point<3> & p) const
{
Vec<3> v;
v = p - c;
v *= (r / v.Length());
p = c + v;
}
INSOLID_TYPE Sphere :: BoxInSolid (const BoxSphere<3> & box) const
{
double dist;
dist = Dist (box.Center(), c);
if (dist - box.Diam()/2 > r) return IS_OUTSIDE;
if (dist + box.Diam()/2 < r) return IS_INSIDE;
return DOES_INTERSECT;
}
double Sphere :: HesseNorm () const
{
return 2 / r;
}
Point<3> Sphere :: GetSurfacePoint () const
{
return c + Vec<3> (r, 0, 0);
}
void Sphere :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int n = int(facets) + 1;
for (int j = 0; j <= n; j++)
for (int i = 0; i <= n; i++)
{
double lg = 2 * M_PI * double (i) / n;
double bg = M_PI * (double(j) / n - 0.5);
Point<3> p(c(0) + r * cos(bg) * sin (lg),
c(1) + r * cos(bg) * cos (lg),
c(2) + r * sin(bg));
tas.AddPoint (p);
}
for (int j = 0; j < n; j++)
for (int i = 0; i < n; i++)
{
int pi = i + (n+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+n+2));
tas.AddTriangle (TATriangle (0, pi, pi+n+2, pi+n+1));
}
}
Ellipsoid ::
Ellipsoid (const Point<3> & aa,
const Vec<3> & av1, const Vec<3> & av2, const Vec<3> & av3)
{
a = aa;
v1 = av1;
v2 = av2;
v3 = av3;
CalcData();
}
void Ellipsoid :: CalcData ()
{
// f = (x-a, vl)^2 / |vl|^2 + (x-a, vs)^2 / |vs|^2 -1
// f = sum_{i=1}^3 (x-a,v_i)^2 / |vi|^4 - 1 = sum (x-a,hv_i)^2
Vec<3> hv1, hv2, hv3;
double lv1 = v1.Length2 ();
if (lv1 < 1e-32) lv1 = 1;
double lv2 = v2.Length2 ();
if (lv2 < 1e-32) lv2 = 1;
double lv3 = v3.Length2 ();
if (lv3 < 1e-32) lv3 = 1;
rmin = sqrt (min3 (lv1, lv2, lv3));
hv1 = (1.0 / lv1) * v1;
hv2 = (1.0 / lv2) * v2;
hv3 = (1.0 / lv3) * v3;
cxx = hv1(0) * hv1(0) + hv2(0) * hv2(0) + hv3(0) * hv3(0);
cyy = hv1(1) * hv1(1) + hv2(1) * hv2(1) + hv3(1) * hv3(1);
czz = hv1(2) * hv1(2) + hv2(2) * hv2(2) + hv3(2) * hv3(2);
cxy = 2 * (hv1(0) * hv1(1) + hv2(0) * hv2(1) + hv3(0) * hv3(1));
cxz = 2 * (hv1(0) * hv1(2) + hv2(0) * hv2(2) + hv3(0) * hv3(2));
cyz = 2 * (hv1(1) * hv1(2) + hv2(1) * hv2(2) + hv3(1) * hv3(2));
Vec<3> va (a);
c1 = sqr(va * hv1) + sqr(va * hv2) + sqr(va * hv3) - 1;
Vec<3> v = -2 * (va * hv1) * hv1 - 2 * (va * hv2) * hv2 - 2 * (va * hv3) * hv3;
cx = v(0);
cy = v(1);
cz = v(2);
}
INSOLID_TYPE Ellipsoid :: BoxInSolid (const BoxSphere<3> & box) const
{
// double grad = 2.0 / rmin;
// double grad = 3*(box.Center()-a).Length() / (rmin*rmin*rmin);
double ggrad = 1.0 / (rmin*rmin);
Vec<3> g;
double val = CalcFunctionValue (box.Center());
CalcGradient (box.Center(), g);
double grad = g.Length();
double r = box.Diam() / 2;
double maxval = grad * r + ggrad * r * r;
// (*testout) << "box = " << box << ", val = " << val << ", maxval = " << maxval << endl;
if (val > maxval) return IS_OUTSIDE;
if (val < -maxval) return IS_INSIDE;
return DOES_INTERSECT;
}
double Ellipsoid :: HesseNorm () const
{
return 1.0/ (rmin * rmin);
}
double Ellipsoid :: MaxCurvature () const
{
const double a2 = v1.Length2();
const double b2 = v2.Length2();
const double c2 = v3.Length2();
return max3 ( sqrt(a2)/min2(b2,c2), sqrt(b2)/min2(a2,c2), sqrt(c2)/min2(a2,b2) );
}
Point<3> Ellipsoid :: GetSurfacePoint () const
{
return a + v1;
}
void Ellipsoid :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int n = int(facets) + 1;
for (int j = 0; j <= n; j++)
for (int i = 0; i <= n; i++)
{
double lg = 2 * M_PI * double (i) / n;
double bg = M_PI * (double(j) / n - 0.5);
Point<3> p(a +
sin (bg) * v1 +
cos (bg) * sin (lg) * v2 +
cos (bg) * cos (lg) * v3);
tas.AddPoint (p);
}
for (int j = 0; j < n; j++)
for (int i = 0; i < n; i++)
{
int pi = i + (n+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+n+2));
tas.AddTriangle (TATriangle (0, pi, pi+n+2, pi+n+1));
}
}
Cylinder :: Cylinder (Array<double> & coeffs)
{
SetPrimitiveData(coeffs);
}
Cylinder :: Cylinder (const Point<3> & aa, const Point<3> & ab, double ar)
{
a = aa;
b = ab;
vab = (b - a);
vab /= vab.Length();
r = ar;
// ( <x,x> - 2 <x,a> + <a,a>
// - <x,vab>^2 + 2 <x,vab> <a, vab> - <a, vab>^2
// - r^2) / (2r) = 0
double hv;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - a(0) / r;
cy = - a(1) / r;
cz = - a(2) / r;
c1 = (a(0) * a(0) + a(1) * a(1) + a(2) * a(2)) / (2 * r);
hv = a(0) * vab(0) + a(1) * vab(1) + a(2) * vab(2);
cxx -= vab(0) * vab(0) / (2 * r);
cyy -= vab(1) * vab(1) / (2 * r);
czz -= vab(2) * vab(2) / (2 * r);
cxy -= vab(0) * vab(1) / r;
cxz -= vab(0) * vab(2) / r;
cyz -= vab(1) * vab(2) / r;
cx += vab(0) * hv / r;
cy += vab(1) * hv / r;
cz += vab(2) * hv / r;
c1 -= hv * hv / (2 * r);
c1 -= r / 2;
// PrintCoeff ();
}
void Cylinder :: GetPrimitiveData (const char *& classname, Array<double> & coeffs) const
{
classname = "cylinder";
coeffs.SetSize (7);
coeffs.Elem(1) = a(0);
coeffs.Elem(2) = a(1);
coeffs.Elem(3) = a(2);
coeffs.Elem(4) = b(0);
coeffs.Elem(5) = b(1);
coeffs.Elem(6) = b(2);
coeffs.Elem(7) = r;
}
void Cylinder :: SetPrimitiveData (Array<double> & coeffs)
{
a(0) = coeffs.Elem(1);
a(1) = coeffs.Elem(2);
a(2) = coeffs.Elem(3);
b(0) = coeffs.Elem(4);
b(1) = coeffs.Elem(5);
b(2) = coeffs.Elem(6);
r = coeffs.Elem(7);
vab = (b - a);
vab /= vab.Length();
double hv;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - a(0) / r;
cy = - a(1) / r;
cz = - a(2) / r;
c1 = (a(0) * a(0) + a(1) * a(1) + a(2) * a(2)) / (2 * r);
hv = a(0) * vab(0) + a(1) * vab(1) + a(2) * vab(2);
cxx -= vab(0) * vab(0) / (2 * r);
cyy -= vab(1) * vab(1) / (2 * r);
czz -= vab(2) * vab(2) / (2 * r);
cxy -= vab(0) * vab(1) / r;
cxz -= vab(0) * vab(2) / r;
cyz -= vab(1) * vab(2) / r;
cx += vab(0) * hv / r;
cy += vab(1) * hv / r;
cz += vab(2) * hv / r;
c1 -= hv * hv / (2 * r);
c1 -= r / 2;
}
Primitive * Cylinder :: CreateDefault ()
{
return new Cylinder (Point<3> (0,0,0), Point<3> (1,0,0), 1);
}
Primitive * Cylinder :: Copy () const
{
return new Cylinder (a, b, r);
}
void Cylinder :: Print (ostream & ost) const
{
ost << "cylinder(" << a << "; " << b << "; " << r << ")";
}
int Cylinder :: IsIdentic (const Surface & s2, int & inv, double eps) const
{
const Cylinder * cyl2 = dynamic_cast<const Cylinder*> (&s2);
if (!cyl2) return 0;
if (fabs (cyl2->r - r) > eps) return 0;
Vec<3> v1 = b - a;
Vec<3> v2 = cyl2->a - a;
if ( fabs (v1 * v2) < (1-eps) * v1.Length() * v2.Length()) return 0;
v2 = cyl2->b - a;
if ( fabs (v1 * v2) < (1-eps) * v1.Length() * v2.Length()) return 0;
inv = 0;
return 1;
}
void Cylinder :: Transform (Transformation<3> & trans)
{
Point<3> hp;
trans.Transform (a, hp);
a = hp;
trans.Transform (b, hp);
b = hp;
vab = (b - a);
vab /= vab.Length();
// ( <x,x> - 2 <x,a> + <a,a>
// - <x,vab>^2 + 2 <x,vab> <a, vab> - <a, vab>^2
// - r^2) / (2r) = 0
double hv;
cxx = cyy = czz = 0.5 / r;
cxy = cxz = cyz = 0;
cx = - a(0) / r;
cy = - a(1) / r;
cz = - a(2) / r;
c1 = (a(0) * a(0) + a(1) * a(1) + a(2) * a(2)) / (2 * r);
hv = a(0) * vab(0) + a(1) * vab(1) + a(2) * vab(2);
cxx -= vab(0) * vab(0) / (2 * r);
cyy -= vab(1) * vab(1) / (2 * r);
czz -= vab(2) * vab(2) / (2 * r);
cxy -= vab(0) * vab(1) / r;
cxz -= vab(0) * vab(2) / r;
cyz -= vab(1) * vab(2) / r;
cx += vab(0) * hv / r;
cy += vab(1) * hv / r;
cz += vab(2) * hv / r;
c1 -= hv * hv / (2 * r);
c1 -= r / 2;
// PrintCoeff ();
}
void Cylinder :: DefineTangentialPlane (const Point<3> & ap1, const Point<3> & ap2)
{
Surface::DefineTangentialPlane (ap1, ap2);
ez = Center (p1, p2) - a;
ez -= (ez * vab) * vab;
ez /= ez.Length();
ex = p2 - p1;
ex -= (ex * ez) * ez;
ex /= ex.Length();
ey = Cross (ez, ex);
}
void Cylinder :: ToPlane (const Point<3> & p,
Point<2> & pplane,
double h, int & zone) const
{
Point<3> cp1p2 = Center (p1, p2);
Project (cp1p2);
Point<3> ccp1p2 = a + ( (cp1p2 - a) * vab ) * vab;
Vec<3> er = cp1p2 - ccp1p2;
er.Normalize();
Vec<3> ephi = Cross (vab, er);
double co, si;
Point<2> p1p, p2p, pp;
co = er * (p1 - ccp1p2);
si = ephi * (p1 - ccp1p2);
p1p(0) = r * atan2 (si, co);
p1p(1) = vab * (p1 - ccp1p2);
co = er * (p2 - ccp1p2);
si = ephi * (p2 - ccp1p2);
p2p(0) = r * atan2 (si, co);
p2p(1) = vab * (p2 - ccp1p2);
co = er * (p - ccp1p2);
si = ephi * (p - ccp1p2);
double phi = atan2 (si, co);
pp(0) = r * phi;
pp(1) = vab * (p - ccp1p2);
zone = 0;
if (phi > 1.57) zone = 1;
if (phi < -1.57) zone = 2;
Vec<2> e2x = p2p - p1p;
e2x /= e2x.Length();
Vec<2> e2y (-e2x(1), e2x(0));
Vec<2> p1pp = pp - p1p;
pplane(0) = (p1pp * e2x) / h;
pplane(1) = (p1pp * e2y) / h;
/*
(*testout) << "p1 = " << p1 << ", p2 = " << p2 << endl;
(*testout) << "p = " << p << ", pp = " << pp << ", pplane = " << pplane << endl;
*/
/*
Vec<3> p1p;
p1p = p - p1;
if (p1p * ez < -1 * r)
{
zone = -1;
pplane(0) = 1e8;
pplane(1) = 1e8;
}
else
{
zone = 0;
p1p /= h;
pplane(0) = p1p * ex;
pplane(1) = p1p * ey;
}
*/
}
void Cylinder :: FromPlane (const Point<2> & pplane, Point<3> & p, double h) const
{
Point<2> pplane2 (pplane);
pplane2(0) *= h;
pplane2(1) *= h;
p(0) = p1(0) + pplane2(0) * ex(0) + pplane2(1) * ey(0);
p(1) = p1(1) + pplane2(0) * ex(1) + pplane2(1) * ey(1);
p(2) = p1(2) + pplane2(0) * ex(2) + pplane2(1) * ey(2);
Project (p);
}
void Cylinder :: Project (Point<3> & p) const
{
Vec<3> v;
Point<3> c;
c = a + ((p - a) * vab) * vab;
v = p - c;
v *= (r / v.Length());
p = c + v;
}
/*
int Cylinder :: RootInBox (const BoxSphere<3> & box) const
{
double dist;
dist = sqrt (2 * CalcFunctionValue(box.Center()) * r + r * r);
if (fabs (dist - r) > box.Diam()/2) return 0;
return 2;
}
*/
INSOLID_TYPE Cylinder :: BoxInSolid (const BoxSphere<3> & box) const
{
double dist;
// dist = sqrt (2 * CalcFunctionValue(box.Center()) * r + r * r);
dist = (2 * CalcFunctionValue(box.Center()) * r + r * r);
if (dist <= 0) dist = 0;
else dist = sqrt (dist + 1e-16);
if (dist - box.Diam()/2 > r) return IS_OUTSIDE;
if (dist + box.Diam()/2 < r) return IS_INSIDE;
return DOES_INTERSECT;
}
double Cylinder :: HesseNorm () const
{
return 2 / r;
}
Point<3> Cylinder :: GetSurfacePoint () const
{
Vec<3> vr;
if (fabs (vab(0)) > fabs(vab(2)))
vr = Vec<3> (vab(1), -vab(0), 0);
else
vr = Vec<3> (0, -vab(2), vab(1));
vr *= (r / vr.Length());
return a + vr;
}
void Cylinder :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int n = int(facets) + 1;
Vec<3> lvab = b - a;
Vec<3> n1 = lvab.GetNormal();
Vec<3> n2 = Cross (lvab, n1);
n1.Normalize();
n2.Normalize();
for (int j = 0; j <= n; j++)
for (int i = 0; i <= n; i++)
{
double lg = 2 * M_PI * double (i) / n;
double bg = double(j) / n;
Point<3> p = a + (bg * lvab)
+ ((r * cos(lg)) * n1)
+ ((r * sin(lg)) * n2);
tas.AddPoint (p);
}
for (int j = 0; j < n; j++)
for (int i = 0; i < n; i++)
{
int pi = i + (n+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+n+2));
tas.AddTriangle (TATriangle (0, pi, pi+n+2, pi+n+1));
}
}
EllipticCylinder ::
EllipticCylinder (const Point<3> & aa,
const Vec<3> & avl, const Vec<3> & avs)
{
a = aa;
if(avl.Length2() > avs.Length2())
{
vl = avl;
vs = avs;
}
else
{
vl = avs;
vs = avl;
}
CalcData();
}
EllipticCylinder :: EllipticCylinder (Array<double> & coeffs)
{
SetPrimitiveData(coeffs);
}
void EllipticCylinder :: GetPrimitiveData (const char *& classname, Array<double> & coeffs) const
{
classname = "ellipticcylinder";
coeffs.SetSize (9);
coeffs[0] = a(0);
coeffs[1] = a(1);
coeffs[2] = a(2);
coeffs[3] = vl(0);
coeffs[4] = vl(1);
coeffs[5] = vl(2);
coeffs[6] = vs(0);
coeffs[7] = vs(1);
coeffs[8] = vs(2);
}
void EllipticCylinder :: SetPrimitiveData (Array<double> & coeffs)
{
a(0) = coeffs[0];
a(1) = coeffs[1];
a(2) = coeffs[2];
vl(0) = coeffs[3];
vl(1) = coeffs[4];
vl(2) = coeffs[5];
vs(0) = coeffs[6];
vs(1) = coeffs[7];
vs(2) = coeffs[8];
CalcData();
}
void EllipticCylinder :: CalcData ()
{
// f = (x-a, vl)^2 / |vl|^2 + (x-a, vs)^2 / |vs|^2 -1
Vec<3> hvl, hvs;
double lvl = vl.Length2 ();
if (lvl < 1e-32) lvl = 1;
double lvs = vs.Length2 ();
if (lvs < 1e-32) lvs = 1;
hvl = (1.0 / lvl) * vl;
hvs = (1.0 / lvs) * vs;
cxx = hvl(0) * hvl(0) + hvs(0) * hvs(0);
cyy = hvl(1) * hvl(1) + hvs(1) * hvs(1);
czz = hvl(2) * hvl(2) + hvs(2) * hvs(2);
cxy = 2 * (hvl(0) * hvl(1) + hvs(0) * hvs(1));
cxz = 2 * (hvl(0) * hvl(2) + hvs(0) * hvs(2));
cyz = 2 * (hvl(1) * hvl(2) + hvs(1) * hvs(2));
Vec<3> va (a);
c1 = pow(va * hvl,2) + pow(va * hvs,2) - 1;
Vec<3> v = -2 * (va * hvl) * hvl - 2 * (va * hvs) * hvs;
cx = v(0);
cy = v(1);
cz = v(2);
}
INSOLID_TYPE EllipticCylinder :: BoxInSolid (const BoxSphere<3> & box) const
{
double grad = 2.0 / vs.Length ();
double ggrad = 1.0 / vs.Length2 ();
double val = CalcFunctionValue (box.Center());
double r = box.Diam() / 2;
double maxval = grad * r + ggrad * r * r;
// (*testout) << "box = " << box << ", val = " << val << ", maxval = " << maxval << endl;
if (val > maxval) return IS_OUTSIDE;
if (val < -maxval) return IS_INSIDE;
return DOES_INTERSECT;
}
double EllipticCylinder :: HesseNorm () const
{
return 1.0/min(vs.Length2 (),vl.Length2());
}
double EllipticCylinder :: MaxCurvature () const
{
double aa = vs.Length();
double bb = vl.Length();
return max2(bb/(aa*aa),aa/(bb*bb));
}
double EllipticCylinder :: MaxCurvatureLoc (const Point<3> & /* c */,
double /* rad */) const
{
// saubere Loesung wird noch notwendig !!!
double aa = vs.Length();
double bb = vl.Length();
return max2(bb/(aa*aa),aa/(bb*bb));
}
Point<3> EllipticCylinder :: GetSurfacePoint () const
{
return a + vl;
}
void EllipticCylinder :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int n = int(facets) + 1;
Vec<3> axis = Cross (vl, vs);
for (int j = 0; j <= n; j++)
for (int i = 0; i <= n; i++)
{
double lg = 2 * M_PI * double (i) / n;
double bg = double(j) / n;
Point<3> p = a + (bg * axis)
+ cos(lg) * vl + sin(lg) * vs;
tas.AddPoint (p);
}
for (int j = 0; j < n; j++)
for (int i = 0; i < n; i++)
{
int pi = i + (n+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+n+2));
tas.AddTriangle (TATriangle (0, pi, pi+n+2, pi+n+1));
}
}
Cone :: Cone (const Point<3> & aa, const Point<3> & ab,
double ara, double arb)
{
a = aa;
b = ab;
ra = ara;
rb = arb;
CalcData();
// Print (cout);
}
Primitive * Cone :: CreateDefault ()
{
return new Cone (Point<3> (0,0,0), Point<3> (1,0,0), 0.5, 0.2);
}
void Cone :: GetPrimitiveData (const char *& classname, Array<double> & coeffs) const
{
classname = "cone";
coeffs.SetSize (8);
coeffs.Elem(1) = a(0);
coeffs.Elem(2) = a(1);
coeffs.Elem(3) = a(2);
coeffs.Elem(4) = b(0);
coeffs.Elem(5) = b(1);
coeffs.Elem(6) = b(2);
coeffs.Elem(7) = ra;
coeffs.Elem(8) = rb;
}
void Cone :: SetPrimitiveData (Array<double> & coeffs)
{
a(0) = coeffs.Elem(1);
a(1) = coeffs.Elem(2);
a(2) = coeffs.Elem(3);
b(0) = coeffs.Elem(4);
b(1) = coeffs.Elem(5);
b(2) = coeffs.Elem(6);
ra = coeffs.Elem(7);
rb = coeffs.Elem(8);
CalcData();
}
void Cone :: CalcData ()
{
minr = (ra < rb) ? ra : rb;
vab = b - a;
vabl = vab.Length();
Vec<3> va (a);
//
// f = r(P)^2 - R(z(P))^2
//
// z(P) = t0vec * P + t0 = (P-a, b-a)/(b-a,b-a)
// R(z(P)) = t1vec * P + t1 = rb * z + ra * (1-z)
// r(P)^2 =||P-a||^2 - ||a-b||^2 z^2k
cosphi = vabl / sqrt (vabl*vabl+sqr(ra-rb));
t0vec = vab;
t0vec /= (vabl * vabl);
t0 = -(va * vab) / (vabl * vabl);
t1vec = t0vec;
t1vec *= (rb - ra);
t1 = ra + (rb - ra) * t0;
cxx = cyy = czz = 1;
cxy = cxz = cyz = 0;
cxx = 1 - (vab*vab) * t0vec(0) * t0vec(0) - t1vec(0) * t1vec(0);
cyy = 1 - (vab*vab) * t0vec(1) * t0vec(1) - t1vec(1) * t1vec(1);
czz = 1 - (vab*vab) * t0vec(2) * t0vec(2) - t1vec(2) * t1vec(2);
cxy = -2 * (vab * vab) * t0vec(0) * t0vec(1) - 2 * t1vec(0) * t1vec(1);
cxz = -2 * (vab * vab) * t0vec(0) * t0vec(2) - 2 * t1vec(0) * t1vec(2);
cyz = -2 * (vab * vab) * t0vec(1) * t0vec(2) - 2 * t1vec(1) * t1vec(2);
cx = -2 * a(0) - 2 * (vab * vab) * t0 * t0vec(0) - 2 * t1 * t1vec(0);
cy = -2 * a(1) - 2 * (vab * vab) * t0 * t0vec(1) - 2 * t1 * t1vec(1);
cz = -2 * a(2) - 2 * (vab * vab) * t0 * t0vec(2) - 2 * t1 * t1vec(2);
c1 = va.Length2() - (vab * vab) * t0 * t0 - t1 * t1;
double maxr = max2(ra,rb);
cxx /= maxr; cyy /= maxr; czz /= maxr;
cxy /= maxr; cxz /= maxr; cyz /= maxr;
cx /= maxr; cy /= maxr; cz /= maxr;
c1 /= maxr;
// (*testout) << "t0vec = " << t0vec << " t0 = " << t0 << endl;
// (*testout) << "t1vec = " << t1vec << " t1 = " << t1 << endl;
// PrintCoeff (*testout);
}
INSOLID_TYPE Cone :: BoxInSolid (const BoxSphere<3> & box) const
{
Vec<3> cv(box.Center());
double rzp = cv * t1vec + t1;
double dist = sqrt (CalcFunctionValue(box.Center()) *max2(ra,rb) + rzp * rzp) - rzp;
dist *= cosphi;
INSOLID_TYPE res = DOES_INTERSECT;
if (dist - box.Diam() > 0) res = IS_OUTSIDE;
if (dist + box.Diam() < 0) res = IS_INSIDE;
return res;
}
double Cone :: HesseNorm () const
{
// cout << "2/minr = " << 2/minr << ", cxx .. = " << cxx << ", " << cyy << ", " << czz << endl;
return 2 / minr;
}
double Cone :: LocH (const Point<3> & p, double /* x */,
double /* c */,
const MeshingParameters & mparam, double hmax) const
{
//double bloch = Surface::LocH (p, x, c, hmax);
Vec<3> g;
CalcGradient (p, g);
double lam = Abs(g);
double meancurv =
-( 2 * g(0)*g(1)*cxy - 2 * czz * (g(0)*g(0)+g(1)*g(1))
+2 * g(1)*g(2)*cyz - 2 * cxx * (g(1)*g(1)+g(2)*g(2))
+2 * g(0)*g(2)*cxz - 2 * cyy * (g(0)*g(0)+g(2)*g(2))) / (3*lam*lam*lam);
// cout << "type = " << typeid(*this).name() << ", baseh = " << bloch << ", meancurv = " << meancurv << endl;
// return bloch;
meancurv = fabs (meancurv);
if (meancurv < 1e-20) meancurv = 1e-20;
// cout << "c = " << c << ", safety = " << mparam.curvaturesafety << endl;
double hcurv = 1.0/(4*meancurv*mparam.curvaturesafety);
return min2 (hmax, hcurv);
}
Point<3> Cone :: GetSurfacePoint () const
{
Vec<3> vr = vab.GetNormal ();
vr *= (ra / vr.Length());
return a + vr;
}
void Cone :: GetTriangleApproximation
(TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int i, j;
double lg, bg;
int n = int(facets) + 1;
Vec<3> lvab = b - a;
Vec<3> n1 = lvab.GetNormal();
Vec<3> n2 = Cross (lvab, n1);
n1.Normalize();
n2.Normalize();
for (j = 0; j <= n; j++)
for (i = 0; i <= n; i++)
{
lg = 2 * M_PI * double (i) / n;
bg = double(j) / n;
Point<3> p = a + (bg * lvab)
+ (( (ra+(rb-ra)*bg) * cos(lg)) * n1)
+ (( (ra+(rb-ra)*bg) * sin(lg)) * n2);
tas.AddPoint (p);
}
for (j = 0; j < n; j++)
for (i = 0; i < n; i++)
{
int pi = i + (n+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+n+2));
tas.AddTriangle (TATriangle (0, pi, pi+n+2, pi+n+1));
}
}
/// Torus
/// Lorenzo Codecasa (codecasa@elet.polimi.it)
/// April 27th, 2005
///
Torus :: Torus (const Point<3> & ac, const Vec<3> & an, double aR, double ar)
{
c = ac;
n = an;
n.Normalize();
R = aR;
r = ar;
}
void Torus :: GetPrimitiveData (const char *& classname, Array<double> & coeffs) const
{
classname = "torus";
coeffs.SetSize (8);
coeffs.Elem(1) = c(0);
coeffs.Elem(2) = c(1);
coeffs.Elem(3) = c(2);
coeffs.Elem(4) = n(0);
coeffs.Elem(5) = n(1);
coeffs.Elem(6) = n(2);
coeffs.Elem(7) = R;
coeffs.Elem(8) = r;
}
void Torus :: SetPrimitiveData (Array<double> & coeffs)
{
c(0) = coeffs.Elem(1);
c(1) = coeffs.Elem(2);
c(2) = coeffs.Elem(3);
n(0) = coeffs.Elem(4);
n(1) = coeffs.Elem(5);
n(2) = coeffs.Elem(6);
R = coeffs.Elem(7);
r = coeffs.Elem(8);
}
Primitive * Torus :: CreateDefault ()
{
return new Torus (Point<3> (0,0,0), Vec<3> (0,0,1), 2, 1);
}
Primitive * Torus :: Copy () const
{
return new Torus (c, n, R, r);
}
void Torus :: Transform (Transformation<3> & trans)
{
Point<3> hc;
trans.Transform (c, hc);
c = hc;
Vec<3> hn;
trans.Transform (n, hn);
n = hn;
}
int Torus :: IsIdentic (const Surface & s2, int & inv, double eps) const
{
const Torus * torus2 = dynamic_cast<const Torus*> (&s2);
if (!torus2) return 0;
if (fabs (torus2->R - R) > eps) return 0;
if (fabs (torus2->r - r) > eps) return 0;
Vec<3> v2 = torus2->n - n;
if ( v2 * v2 > eps ) return 0;
v2 = torus2->c - c;
if ( v2 * v2 > eps ) return 0;
inv = 0;
return 1;
}
double Torus :: CalcFunctionValue (const Point<3> & point) const
{
/*
// original version
Vec<3> v1 = point - c;
double a1 = Abs2 (v1); // v1(0) * v1(0) + v1(1) * v1(1) + v1(2) * v1(2);
double a2 = n * v1; // n(0) * v1(0) + n(1) * v1(1) + n(2) * v1(2);
double a3 = a1 + R * R - r * r;
double a4 = Abs2 (n); // n(0) * n(0) + n(1) * n(1) + n(2) * n(2);
return ( a3 * a3 -4 * R * R * ( a1 - a2 * a2 / a4 ) ) / ( R * R * R );
*/
// JS, April 2011
Vec<3> v1 = point-c;
double abs2 = Abs2(v1);
double tau = v1 * n;
double rho = sqrt (abs2 - tau*tau);
return sqr (R - rho) + tau*tau - r*r;
// double val2 = sqr (tau*tau + sqr (R - rho) -r*r) / (R*R*R);
}
void Torus :: CalcGradient (const Point<3> & point, Vec<3> & grad) const
{
/*
Vec<3> v1 = point - c;
double a1 = v1(0) * v1(0) + v1(1) * v1(1) + v1(2) * v1(2);
double a2 = n(0) * v1(0) + n(1) * v1(1) + n(2) * v1(2);
double a3 = a1 - R * R - r * r;
double a4 = n(0) * n(0) + n(1) * n(1) + n(2) * n(2);
grad(0) = ( 4 * a3 * v1(0) + 8 * R * R * a2 / a4 * n(0) ) / ( R * R * R );
grad(1) = ( 4 * a3 * v1(1) + 8 * R * R * a2 / a4 * n(1) ) / ( R * R * R );
grad(2) = ( 4 * a3 * v1(2) + 8 * R * R * a2 / a4 * n(2) ) / ( R * R * R );
*/
Vec<3> v1 = point-c;
double abs2 = Abs2(v1);
double tau = v1 * n;
double rho = sqrt (abs2 - tau*tau);
// double func = sqr (R - rho) + tau*tau - r*r;
Vec<3> gradabs2 = 2 * v1;
Vec<3> gradtau = n;
Vec<3> gradrho = 0.5 / rho * (gradabs2 - 2 * tau * gradtau);
grad = -2 * (R - rho) * gradrho + 2 * tau * gradtau;
}
void Torus :: CalcHesse (const Point<3> & point, Mat<3> & hesse) const
{
Surface::CalcHesse (point, hesse);
return;
Vec<3> v1 = point - c;
double a1 = v1(0) * v1(0) + v1(1) * v1(1) + v1(2) * v1(2);
double a3 = a1 - R * R - r * r;
double a4 = n(0) * n(0) + n(1) * n(1) + n(2) * n(2);
hesse(0,0) = ( 4 * a3 + 8 * (v1(0) * v1(0) + (R * n(0)) * (R * n(0)) / a4 ) ) / ( R * R * R );
hesse(1,1) = ( 4 * a3 + 8 * (v1(1) * v1(1) + (R * n(1)) * (R * n(1)) / a4 ) ) / ( R * R * R );
hesse(2,2) = ( 4 * a3 + 8 * (v1(2) * v1(2) + (R * n(2)) * (R * n(2)) / a4 ) ) / ( R * R * R );
hesse(0,1) = hesse(1,0) = 8 * (v1(0) * v1(1) + (R * n(0)) * (R * n(1)) / a4 ) / ( R * R * R );
hesse(1,2) = hesse(2,1) = 8 * (v1(1) * v1(2) + (R * n(1)) * (R * n(2)) / a4) / ( R * R * R );
hesse(0,2) = hesse(2,0) = 8 * (v1(0) * v1(2) + (R * n(0)) * (R * n(2)) / a4) / ( R * R * R );
}
double Torus :: HesseNorm () const
{
return 4/(r*r);
// return ( 2 / r + 2 / ( R - r ) );
}
Point<3> Torus :: GetSurfacePoint () const
{
Vec<3> vn = n.GetNormal();
return c + ( R + r ) * vn.Normalize();
}
/// void Torus :: DefineTangentialPlane (const Point<3> & ap1, const Point<3> & ap2)
/// {
/// }
/// void Torus :: ToPlane (const Point<3> & p,
/// Point<2> & pplane,
/// double h, int & zone) const
/// {
/// }
/// void Torus :: FromPlane (const Point<2> & pplane, Point<3> & p, double h) const
/// {
/// }
/// void Torus :: Project (Point<3> & p) const
/// {
/// }
INSOLID_TYPE Torus :: BoxInSolid (const BoxSphere<3> & box) const
{
Vec<3> v1 = box.Center() - c;
double a1 = Abs2(v1); // v1(0) * v1(0) + v1(1) * v1(1) + v1(2) * v1(2);
double a2 = n * v1; // n(0) * v1(0) + n(1) * v1(1) + n(2) * v1(2);
double a4 = Abs2(n); // n(0) * n(0) + n(1) * n(1) + n(2) * n(2);
double dist = sqrt( a1 + R * R - 2 * R * sqrt( a1 - a2 * a2 / a4) );
if (dist - box.Diam()/2 > r) return IS_OUTSIDE;
if (dist + box.Diam()/2 < r) return IS_INSIDE;
return DOES_INTERSECT;
}
void Torus :: GetTriangleApproximation (TriangleApproximation & tas,
const Box<3> & /* boundingbox */, double facets) const
{
int N = int(facets) + 1;
Vec<3> lvab = n ;
lvab.Normalize();
Vec<3> n1 = lvab.GetNormal();
n1.Normalize();
Vec<3> n2 = Cross(lvab, n1);
n2.Normalize();
for (int j = 0; j <= N; j++)
for (int i = 0; i <= N; i++)
{
double lg = 2 * M_PI * double (i) / N;
double bg = 2 * M_PI * double(j) / N;
Point<3> p = c + ( R + r * cos(lg) ) * ( cos(bg) * n1 + sin(bg) * n2 ) + r * sin(lg) * n;
tas.AddPoint (p);
}
for (int j = 0; j < N; j++)
for (int i = 0; i < N; i++)
{
int pi = i + (N+1) * j;
tas.AddTriangle (TATriangle (0, pi, pi+1, pi+N+2));
tas.AddTriangle (TATriangle (0, pi, pi+N+2, pi+N+1));
}
}
void Torus :: Read (istream & ist)
{
ist >> c(0) >> c(1) >> c(2) >> n(0) >> n(1) >> n(2) >> R >> r;
}
void Torus :: Print (ostream & ost) const
{
ost << c(0) << " " << c(1) << " " << c(2) << " "
<< n(0) << " " << n(1) << " " << n(2) << " "
<< R << " " << r << endl;
}
}
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