netgen/libsrc/csg/extrusion.cpp

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#include <mystdlib.h>
#include <linalg.hpp>
#include <csg.hpp>
namespace netgen
{
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NgArray<Point<3> > project1, project2;
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void ExtrusionFace :: Init(void)
{
p0.SetSize(path->GetNSplines());
x_dir.SetSize(path->GetNSplines());
y_dir.SetSize(path->GetNSplines());
z_dir.SetSize(path->GetNSplines());
loc_z_dir.SetSize(path->GetNSplines());
spline3_path.SetSize(path->GetNSplines());
line_path.SetSize(path->GetNSplines());
for(int i=0; i<path->GetNSplines(); i++)
{
spline3_path[i] = dynamic_cast < const SplineSeg3<3>* >(&path->GetSpline(i));
line_path[i] = dynamic_cast < const LineSeg<3>* >(&path->GetSpline(i));
if(line_path[i])
{
y_dir[i] = line_path[i]->EndPI() - line_path[i]->StartPI();
y_dir[i].Normalize();
z_dir[i] = glob_z_direction;
Orthogonalize(y_dir[i],z_dir[i]);
x_dir[i] = Cross(y_dir[i],z_dir[i]);
loc_z_dir[i] = z_dir[i];
}
else
{
z_dir[i] = glob_z_direction;
loc_z_dir[i] = glob_z_direction;
}
}
profile->GetCoeff(profile_spline_coeff);
latest_point3d = -1.111e30;
}
ExtrusionFace :: ExtrusionFace(const SplineSeg<2> * profile_in,
const SplineGeometry<3> * path_in,
const Vec<3> & z_direction) :
profile(profile_in), path(path_in), glob_z_direction(z_direction)
{
deletable = false;
Init();
}
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ExtrusionFace :: ExtrusionFace(const NgArray<double> & raw_data)
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{
deletable = true;
int pos=0;
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NgArray< Point<2> > p(3);
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int ptype = int(raw_data[pos]); pos++;
for(int i=0; i<ptype; i++)
{
p[i](0) = raw_data[pos]; pos++;
p[i](1) = raw_data[pos]; pos++;
}
if(ptype == 2)
{
profile = new LineSeg<2>(GeomPoint<2>(p[0],1),
GeomPoint<2>(p[1],1));
}
else if(ptype == 3)
{
profile = new SplineSeg3<2>(GeomPoint<2>(p[0],1),
GeomPoint<2>(p[1],1),
GeomPoint<2>(p[2],1));
}
path = new SplineGeometry<3>;
pos = const_cast< SplineGeometry<3> *>(path)->Load(raw_data,pos);
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for(int i = 0; i < 3; i++)
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{
glob_z_direction(i) = raw_data[pos];
pos++;
}
Init();
}
ExtrusionFace :: ~ExtrusionFace()
{
if(deletable)
{
delete profile;
delete path;
}
}
int ExtrusionFace :: IsIdentic (const Surface & s2, int & inv, double eps) const
{
const ExtrusionFace * ext2 = dynamic_cast<const ExtrusionFace*>(&s2);
if(!ext2) return 0;
if(ext2 == this)
return 1;
return 0;
}
void ExtrusionFace :: Orthogonalize(const Vec<3> & v1, Vec<3> & v2) const
{
v2 -= (v1*v2)*v1;
v2.Normalize();
}
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void ExtrusionFace :: CalcProj(const Point<3> & point3d, Point<2> & point2d,
int & seg, double & t) const
{
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if (Dist2 (point3d, latest_point3d) <
1e-25 * Dist2(path->GetSpline(0).StartPI(), path->GetSpline(0).EndPI()))
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{
point2d = latest_point2d;
seg = latest_seg;
t = latest_t;
return;
}
latest_point3d = point3d;
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double cutdist = -1;
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NgArray<double> mindist(path->GetNSplines());
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for(int i = 0; i < path->GetNSplines(); i++)
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{
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double auxcut = -1;
double auxmin = -1;
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if(spline3_path[i])
{
Point<3> startp(path->GetSpline(i).StartPI());
Point<3> endp(path->GetSpline(i).EndPI());
Point<3> tanp(spline3_path[i]->TangentPoint());
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// lower bound for dist
auxmin = sqrt (MinDistTP2 (startp, endp, tanp, point3d));
// upper bound for dist
auxcut = min2 (Dist (startp, point3d), Dist (endp, point3d));
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}
else if(line_path[i])
{
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auxmin = auxcut = sqrt (MinDistLP2 (path->GetSpline(i).StartPI(),
path->GetSpline(i).EndPI(),
point3d));
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}
mindist[i] = auxmin;
if(i==0 || auxcut < cutdist)
cutdist = auxcut;
}
Point<2> testpoint2d;
Point<3> testpoint3d;
double minproj(-1);
bool minproj_set(false);
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for(int i=0; i<path->GetNSplines(); i++)
{
if(mindist[i] > cutdist*(1+1e-10)) continue;
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double thist = CalcProj(point3d,testpoint2d,i);
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testpoint3d = p0[i] + testpoint2d(0)*x_dir[i] + testpoint2d(1)*loc_z_dir[i];
double d = Dist2(point3d,testpoint3d);
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if(!minproj_set || d < minproj)
{
minproj_set = true;
minproj = d;
point2d = testpoint2d;
t = thist;
seg = i;
latest_seg = i;
latest_t = t;
latest_point2d = point2d;
}
}
}
double ExtrusionFace :: CalcProj(const Point<3> & point3d, Point<2> & point2d,
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int seg) const
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{
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double t = -1;
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if(line_path[seg])
{
point2d(0) = (point3d-line_path[seg]->StartPI())*x_dir[seg];
point2d(1) = (point3d-line_path[seg]->StartPI())*z_dir[seg];
double l = Dist(line_path[seg]->StartPI(),
line_path[seg]->EndPI());
t = min2(max2((point3d - line_path[seg]->StartPI()) * y_dir[seg],0.),
l);
p0[seg] = line_path[seg]->StartPI() + t*y_dir[seg];
t *= 1./l;
}
else if(spline3_path[seg])
{
spline3_path[seg]->Project(point3d,p0[seg],t);
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y_dir[seg] = spline3_path[seg]->GetTangent(t);
y_dir[seg].Normalize();
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loc_z_dir[seg] = z_dir[seg];
Orthogonalize(y_dir[seg],loc_z_dir[seg]);
x_dir[seg] = Cross(y_dir[seg],loc_z_dir[seg]);
Vec<3> dir = point3d-p0[seg];
point2d(0) = x_dir[seg]*dir;
point2d(1) = loc_z_dir[seg]*dir;
}
return t;
}
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double ExtrusionFace :: CalcFunctionValue (const Point<3> & point) const
{
Point<2> p;
double dummyd;
int dummyi;
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CalcProj(point, p, dummyi, dummyd);
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return
profile_spline_coeff(0)*p(0)*p(0) +
profile_spline_coeff(1)*p(1)*p(1) +
profile_spline_coeff(2)*p(0)*p(1) +
profile_spline_coeff(3)*p(0) +
profile_spline_coeff(4)*p(1) +
profile_spline_coeff(5);
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}
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void ExtrusionFace :: CalcGradient (const Point<3> & point, Vec<3> & grad) const
{
Point<2> p2d;
double t_path;
int seg;
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CalcProj (point, p2d, seg, t_path);
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Point<3> phi;
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Vec<3> phip, phipp, phi_minus_point;
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path->GetSpline(seg).GetDerivatives(t_path, phi, phip, phipp);
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phi_minus_point = phi-point;
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Vec<3> grad_t = (1.0/(phipp*phi_minus_point + phip*phip)) * phip;
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Vec<3> grad_xbar, grad_ybar;
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Vec<3> hex, hey, hez, dex, dey, dez;
CalcLocalCoordinatesDeriv (seg, t_path, hex, hey, hez, dex, dey, dez);
grad_xbar = hex - (phi_minus_point*dex + hex*phip) * grad_t;
grad_ybar = hez - (phi_minus_point*dez + hez*phip) * grad_t;
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double dFdxbar = 2.*profile_spline_coeff(0)*p2d(0) +
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profile_spline_coeff(2)*p2d(1) + profile_spline_coeff(3);
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double dFdybar = 2.*profile_spline_coeff(1)*p2d(1) +
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profile_spline_coeff(2)*p2d(0) + profile_spline_coeff(4);
grad = dFdxbar * grad_xbar + dFdybar * grad_ybar;
}
void ExtrusionFace :: CalcHesse (const Point<3> & point, Mat<3> & hesse) const
{
const double eps = 1e-7*Dist(path->GetSpline(0).StartPI(),path->GetSpline(0).EndPI());
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Point<3> auxpoint1(point),auxpoint2(point);
Vec<3> auxvec,auxgrad1,auxgrad2;
for(int i=0; i<3; i++)
{
auxpoint1(i) -= eps;
auxpoint2(i) += eps;
CalcGradient(auxpoint1,auxgrad1);
CalcGradient(auxpoint2,auxgrad2);
auxvec = (1./(2.*eps)) * (auxgrad2-auxgrad1);
for(int j=0; j<3; j++)
hesse(i,j) = auxvec(j);
auxpoint1(i) = point(i);
auxpoint2(i) = point(i);
}
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/*
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Vec<3> grad;
CalcGradient(point,grad);
Point<3> auxpoint(point);
Vec<3> auxvec,auxgrad;
for(int i=0; i<3; i++)
{
auxpoint(i) -= eps;
CalcGradient(auxpoint,auxgrad);
auxvec = (1./eps) * (grad-auxgrad);
for(int j=0; j<3; j++)
hesse(i,j) = auxvec(j);
auxpoint(i) = point(i);
}
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*/
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for(int i=0; i<3; i++)
for(int j=i+1; j<3; j++)
hesse(i,j) = hesse(j,i) = 0.5*(hesse(i,j)+hesse(j,i));
}
double ExtrusionFace :: HesseNorm () const
{
return fabs(profile_spline_coeff(0) + profile_spline_coeff(1)) +
sqrt(pow(profile_spline_coeff(0)+profile_spline_coeff(1),2)+4.*pow(profile_spline_coeff(2),2));
}
double ExtrusionFace :: MaxCurvature () const
{
double retval,actmax;
retval = profile->MaxCurvature();
for(int i=0; i<path->GetNSplines(); i++)
{
actmax = path->GetSpline(i).MaxCurvature();
if(actmax > retval)
retval = actmax;
}
return 2.*retval;
}
void ExtrusionFace :: Project (Point<3> & p) const
{
double dummyt;
int seg;
Point<2> p2d;
CalcProj(p,p2d,seg,dummyt);
profile->Project(p2d,p2d,profile_par);
p = p0[seg] + p2d(0)*x_dir[seg] + p2d(1)*loc_z_dir[seg];
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Vec<2> tangent2d = profile->GetTangent(profile_par);
profile_tangent = tangent2d(0)*x_dir[seg] + tangent2d(1)*y_dir[seg];
}
Point<3> ExtrusionFace :: GetSurfacePoint () const
{
p0[0] = path->GetSpline(0).GetPoint(0.5);
if(!line_path[0])
{
y_dir[0] = path->GetSpline(0).GetTangent(0.5);
y_dir[0].Normalize();
loc_z_dir[0] = z_dir[0];
Orthogonalize(y_dir[0],loc_z_dir[0]);
x_dir[0] = Cross(y_dir[0],loc_z_dir[0]);
}
Point<2> locpoint = profile->GetPoint(0.5);
return p0[0] + locpoint(0)*x_dir[0] + locpoint(1)*loc_z_dir[0];
}
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bool ExtrusionFace :: BoxIntersectsFace(const Box<3> & box) const
{
Point<3> center = box.Center();
Project(center);
//(*testout) << "box.Center() " << box.Center() << " projected " << center << " diam " << box.Diam()
// << " dist " << Dist(box.Center(),center) << endl;
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return (Dist(box.Center(),center) < 0.5*box.Diam());
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}
bool ExtrusionFace :: PointInFace (const Point<3> & p, const double eps) const
{
Point<3> hp = p;
Project(hp);
return Dist2(p,hp) < sqr(eps);
}
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void ExtrusionFace :: LineIntersections ( const Point<3> & p,
const Vec<3> & v,
const double eps,
int & before,
int & after,
bool & intersecting ) const
{
Point<2> p2d;
Vec<2> v2d;
intersecting = false;
double segt;
int seg;
CalcProj(p,p2d,seg,segt);
if(seg == 0 && segt < 1e-20)
{
Vec<3> v1,v2;
v1 = path->GetSpline(0).GetTangent(0);
v2 = p-p0[seg];
if(v1*v2 < -eps)
return;
}
if(seg == path->GetNSplines()-1 && 1.-segt < 1e-20)
{
Vec<3> v1,v2;
v1 = path->GetSpline(seg).GetTangent(1);
v2 = p-p0[seg];
if(v1*v2 > eps)
return;
}
v2d(0) = v * x_dir[seg];
v2d(1) = v * loc_z_dir[seg];
Vec<2> n(v2d(1),-v2d(0));
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NgArray < Point<2> > ips;
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profile->LineIntersections(v2d(1),
-v2d(0),
-v2d(1)*p2d(0) + v2d(0)*p2d(1),
ips,eps);
int comp;
if(fabs(v2d(0)) >= fabs(v2d(1)))
comp = 0;
else
comp = 1;
//(*testout) << "p2d " << p2d;
for(int i=0; i<ips.Size(); i++)
{
//(*testout) << " ip " << ips[i];
double t = (ips[i](comp)-p2d(comp))/v2d(comp);
if(t < -eps)
before++;
else if(t > eps)
after++;
else
intersecting = true;
}
//(*testout) << endl;
}
void ExtrusionFace :: Print (ostream & str) const{}
INSOLID_TYPE ExtrusionFace :: VecInFace ( const Point<3> & p,
const Vec<3> & v,
const double eps ) const
{
Vec<3> normal1;
CalcGradient(p,normal1); normal1.Normalize();
double d1 = normal1*v;
if(d1 > eps)
return IS_OUTSIDE;
if(d1 < -eps)
return IS_INSIDE;
return DOES_INTERSECT;
/*
Point<2> p2d;
double t_path;
int seg;
CalcProj(p,p2d,seg,t_path);
double t;
profile.Project(p2d,p2d,t);
Vec<2> profile_tangent = profile.GetTangent(t);
double d;
Vec<3> normal1;
CalcGradient(p,normal1); normal1.Normalize();
double d1 = normal1*v;
Vec<2> v2d;
v2d(0) = v*x_dir[seg];
v2d(1) = v*loc_z_dir[seg];
Vec<2> normal(-profile_tangent(1),profile_tangent(0));
//d = normal*v2d;
d = d1;
if(d > eps)
return IS_OUTSIDE;
if(d < -eps)
return IS_INSIDE;
return DOES_INTERSECT;
*/
}
void ExtrusionFace :: GetTriangleApproximation (TriangleApproximation & tas,
const Box<3> & boundingbox,
double facets) const
{
int n = int(facets) + 1;
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for(int k = 0; k < path -> GetNSplines(); k++)
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{
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for(int i = 0; i <= n; i++)
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{
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Point<3> origin = path -> GetSpline(k).GetPoint(double(i)/double(n));
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if(!line_path[k])
{
y_dir[k] = path->GetSpline(k).GetTangent(double(i)/double(n));
y_dir[k].Normalize();
}
loc_z_dir[k] = z_dir[k];
Orthogonalize(y_dir[k],loc_z_dir[k]);
if(!line_path[k])
x_dir[k] = Cross(y_dir[k],loc_z_dir[k]);
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for(int j = 0; j <= n; j++)
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{
Point<2> locp = profile->GetPoint(double(j)/double(n));
tas.AddPoint(origin + locp(0)*x_dir[k] + locp(1)*loc_z_dir[k]);
}
}
}
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for(int k = 0; k < path->GetNSplines(); k++)
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
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{
int pi = k*(n+1)*(n+1) + (n+1)*i +j;
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tas.AddTriangle( TATriangle (0, pi,pi+1,pi+n+1) );
tas.AddTriangle( TATriangle (0, pi+1,pi+n+1,pi+n+2) );
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}
}
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void ExtrusionFace :: GetRawData(NgArray<double> & data) const
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{
data.DeleteAll();
profile->GetRawData(data);
path->GetRawData(data);
for(int i=0; i<3; i++)
data.Append(glob_z_direction[i]);
}
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void ExtrusionFace ::
CalcLocalCoordinates (int seg, double t,
Vec<3> & ex, Vec<3> & ey, Vec<3> & ez) const
{
ey = path->GetSpline(seg).GetTangent(t);
ey /= ey.Length();
ex = Cross (ey, glob_z_direction);
ex /= ex.Length();
ez = Cross (ex, ey);
}
void ExtrusionFace ::
CalcLocalCoordinatesDeriv (int seg, double t,
Vec<3> & ex, Vec<3> & ey, Vec<3> & ez,
Vec<3> & dex, Vec<3> & dey, Vec<3> & dez) const
{
Point<3> point;
Vec<3> first, second;
path->GetSpline(seg).GetDerivatives (t, point, first, second);
ey = first;
ex = Cross (ey, glob_z_direction);
ez = Cross (ex, ey);
dey = second;
dex = Cross (dey, glob_z_direction);
dez = Cross (dex, ey) + Cross (ex, dey);
double lenx = ex.Length();
double leny = ey.Length();
double lenz = ez.Length();
ex /= lenx;
ey /= leny;
ez /= lenz;
dex /= lenx;
dex -= (dex * ex) * ex;
dey /= leny;
dey -= (dey * ey) * ey;
dez /= lenz;
dez -= (dez * ez) * ez;
}
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Extrusion :: Extrusion(const SplineGeometry<3> & path_in,
const SplineGeometry<2> & profile_in,
const Vec<3> & z_dir) :
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path(&path_in), profile(&profile_in), z_direction(z_dir)
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{
surfaceactive.SetSize(0);
surfaceids.SetSize(0);
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for(int j=0; j<profile->GetNSplines(); j++)
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{
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ExtrusionFace * face = new ExtrusionFace(&((*profile).GetSpline(j)),
path,
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z_direction);
faces.Append(face);
surfaceactive.Append(true);
surfaceids.Append(0);
}
}
Extrusion :: ~Extrusion()
{
for(int i=0; i<faces.Size(); i++)
delete faces[i];
}
INSOLID_TYPE Extrusion :: BoxInSolid (const BoxSphere<3> & box) const
{
for(int i=0; i<faces.Size(); i++)
{
if(faces[i]->BoxIntersectsFace(box))
return DOES_INTERSECT;
}
return PointInSolid(box.Center(),0);
}
INSOLID_TYPE Extrusion :: PointInSolid (const Point<3> & p,
const double eps,
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NgArray<int> * const facenums) const
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{
Vec<3> random_vec(-0.4561,0.7382,0.4970247);
int before(0), after(0);
bool intersects(false);
bool does_intersect(false);
for(int i=0; i<faces.Size(); i++)
{
faces[i]->LineIntersections(p,random_vec,eps,before,after,intersects);
//(*testout) << "intersects " << intersects << " before " << before << " after " << after << endl;
if(intersects)
{
if(facenums)
{
facenums->Append(i);
does_intersect = true;
}
else
return DOES_INTERSECT;
}
}
if(does_intersect)
return DOES_INTERSECT;
if(before % 2 == 0)
return IS_OUTSIDE;
return IS_INSIDE;
}
INSOLID_TYPE Extrusion :: PointInSolid (const Point<3> & p,
double eps) const
{
return PointInSolid(p,eps,NULL);
}
void Extrusion :: GetTangentialSurfaceIndices (const Point<3> & p,
NgArray<int> & surfind, double eps) const
{
for (int j = 0; j < faces.Size(); j++)
if (faces[j] -> PointInFace(p, eps))
if (!surfind.Contains (GetSurfaceId(j)))
surfind.Append (GetSurfaceId(j));
}
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INSOLID_TYPE Extrusion :: VecInSolid (const Point<3> & p,
const Vec<3> & v,
double eps) const
{
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NgArray<int> facenums;
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INSOLID_TYPE pInSolid = PointInSolid(p,eps,&facenums);
if(pInSolid != DOES_INTERSECT)
return pInSolid;
double d(0);
if(facenums.Size() == 1)
{
Vec<3> normal;
faces[facenums[0]]->CalcGradient(p,normal);
normal.Normalize();
d = normal*v;
latestfacenum = facenums[0];
}
else if (facenums.Size() == 2)
{
Vec<3> checkvec;
Point<3> dummy(p);
faces[facenums[0]]->Project(dummy);
if(fabs(faces[facenums[0]]->GetProfilePar()) < 0.1)
{
int aux = facenums[0];
facenums[0] = facenums[1]; facenums[1] = aux;
}
checkvec = faces[facenums[0]]->GetYDir();
Vec<3> n0, n1;
faces[facenums[0]]->CalcGradient(p,n0);
faces[facenums[1]]->CalcGradient(p,n1);
n0.Normalize();
n1.Normalize();
Vec<3> t = Cross(n0,n1);
if(checkvec*t < 0) t*= (-1.);
Vec<3> t0 = Cross(n0,t);
Vec<3> t1 = Cross(t,n1);
t0.Normalize();
t1.Normalize();
const double t0v = t0*v;
const double t1v = t1*v;
if(t0v > t1v)
{
latestfacenum = facenums[0];
d = n0*v;
}
else
{
latestfacenum = facenums[1];
d = n1*v;
}
if(fabs(t0v) < eps && fabs(t1v) < eps)
latestfacenum = -1;
}
else
{
cerr << "WHY ARE THERE " << facenums.Size() << " FACES?" << endl;
}
if(d > eps)
return IS_OUTSIDE;
if(d < -eps)
return IS_INSIDE;
return DOES_INTERSECT;
}
// checks if lim s->0 lim t->0 p + t(v1 + s v2) in solid
INSOLID_TYPE Extrusion :: VecInSolid2 (const Point<3> & p,
const Vec<3> & v1,
const Vec<3> & v2,
double eps) const
{
INSOLID_TYPE retval;
retval = VecInSolid(p,v1,eps);
// *testout << "extr, vecinsolid=" << int(retval) << endl;
if(retval != DOES_INTERSECT)
return retval;
if(latestfacenum >= 0)
return faces[latestfacenum]->VecInFace(p,v2,0);
else
return VecInSolid(p,v2,eps);
}
int Extrusion :: GetNSurfaces() const
{
return faces.Size();
}
Surface & Extrusion :: GetSurface (int i)
{
return *faces[i];
}
const Surface & Extrusion :: GetSurface (int i) const
{
return *faces[i];
}
void Extrusion :: Reduce (const BoxSphere<3> & box)
{
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for(int i = 0; i < faces.Size(); i++)
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surfaceactive[i] = faces[i]->BoxIntersectsFace(box);
}
void Extrusion :: UnReduce ()
{
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for(int i = 0; i < faces.Size(); i++)
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surfaceactive[i] = true;
}
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RegisterClassForArchive<ExtrusionFace, Surface> regexf;
RegisterClassForArchive<Extrusion, Primitive> regextr;
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}