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stable evaluation of implizit spline-curve representation

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This commit is contained in:
Joachim Schöberl 2016-09-29 11:03:00 +02:00
parent d7a5f44c39
commit b7a869b77f
4 changed files with 117 additions and 7 deletions
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55
libsrc/csg/revolution.cpp
View File

@ -156,25 +156,42 @@ namespace netgen
{
if(spline_coefficient.Size() == 0)
spline->GetCoeff(spline_coefficient);
if(spline_coefficient_shifted.Size() == 0)
spline->GetCoeff(spline_coefficient_shifted, spline->StartPI());
Point<2> p;
CalcProj(point,p);
return spline_coefficient(0)*p(0)*p(0) + spline_coefficient(1)*p(1)*p(1)
double val = spline_coefficient(0)*p(0)*p(0) + spline_coefficient(1)*p(1)*p(1)
+ spline_coefficient(2)*p(0)*p(1) + spline_coefficient(3)*p(0)
+ spline_coefficient(4)*p(1) + spline_coefficient(5);
Vec<2> pr = p-spline->StartPI();
// cout << "spline_coefficinet = " << spline_coefficient << endl;
// cout << "shifted = " << spline_coefficient_shifted << endl;
double val2 = spline_coefficient_shifted(0)*pr(0)*pr(0) + spline_coefficient_shifted(1)*pr(1)*pr(1)
+ spline_coefficient_shifted(2)*pr(0)*pr(1) + spline_coefficient_shifted(3)*pr(0)
+ spline_coefficient_shifted(4)*pr(1) + spline_coefficient_shifted(5);
// cout << "val = " << val << " =?= " << val2 << endl;
return val2;
}
void RevolutionFace :: CalcGradient (const Point<3> & point, Vec<3> & grad) const
{
if(spline_coefficient.Size() == 0)
spline->GetCoeff(spline_coefficient);
if(spline_coefficient_shifted.Size() == 0)
spline->GetCoeff(spline_coefficient_shifted, spline->StartPI());
Vec<3> point_minus_p0 = point-p0;
Point<2> p;
CalcProj0(point_minus_p0,p);
/*
const double dFdxbar = 2.*spline_coefficient(0)*p(0) + spline_coefficient(2)*p(1) + spline_coefficient(3);
if(fabs(p(1)) > 1e-10)
@ -193,6 +210,27 @@ namespace netgen
grad(2) = dFdxbar*v_axis(2);
//(*testout) << "grad2("<<point<<") = " << grad << endl;
}
*/
Vec<2> pr = p-spline->StartPI();
const double dFdxbar = 2.*spline_coefficient_shifted(0)*pr(0) + spline_coefficient_shifted(2)*pr(1) + spline_coefficient_shifted(3);
if(fabs(p(1)) > 1e-10)
{
const double dFdybar = 2.*spline_coefficient_shifted(1)*pr(1) + spline_coefficient_shifted(2)*pr(0) + spline_coefficient_shifted(4);
grad(0) = dFdxbar*v_axis(0) + dFdybar * ( point_minus_p0(0)-v_axis(0)*p(0) )/p(1);
grad(1) = dFdxbar*v_axis(1) + dFdybar * ( point_minus_p0(1)-v_axis(1)*p(0) )/p(1);
grad(2) = dFdxbar*v_axis(2) + dFdybar * ( point_minus_p0(2)-v_axis(2)*p(0) )/p(1);
//(*testout) << "grad1("<<point<<") = " << grad << endl;
}
else
{
grad(0) = dFdxbar*v_axis(0);
grad(1) = dFdxbar*v_axis(1);
grad(2) = dFdxbar*v_axis(2);
//(*testout) << "grad2("<<point<<") = " << grad << endl;
}
}
@ -558,10 +596,19 @@ namespace netgen
CalcProj(p,p2d);
if (!spline -> InConvexHull(p2d, eps)) return false;
/*
double val = spline_coefficient(0)*p2d(0)*p2d(0) + spline_coefficient(1)*p2d(1)*p2d(1) + spline_coefficient(2)*p2d(0)*p2d(1) +
spline_coefficient(3)*p2d(0) + spline_coefficient(4)*p2d(1) + spline_coefficient(5);
*/
Vec<2> pr = p2d - spline->StartPI();
double val = spline_coefficient_shifted(0)*pr(0)*pr(0)
+ spline_coefficient_shifted(1)*pr(1)*pr(1)
+ spline_coefficient_shifted(2)*pr(0)*pr(1)
+ spline_coefficient_shifted(3)*pr(0)
+ spline_coefficient_shifted(4)*pr(1)
+ spline_coefficient_shifted(5);
return (fabs(val) < eps);
/*
if(val > eps)

4
libsrc/csg/revolution.hpp
View File

@ -17,8 +17,10 @@ namespace netgen
Vec<3> v_axis;
int id;
// coefficient for implicizt polynomial
mutable Vector spline_coefficient;
mutable Vector spline_coefficient_shifted;
Array < Vec<2>* > checklines_vec;

45
libsrc/gprim/spline.cpp
View File

@ -189,6 +189,51 @@ namespace netgen
if (tang * gradn < 0) u *= -1;
}
template<int D>
void SplineSeg3<D> :: GetCoeff (Vector & u, Point<D> pref) const
{
DenseMatrix a(6, 6);
DenseMatrix ata(6, 6);
Vector f(6);
u.SetSize(6);
// ata.SetSymmetric(1);
double t = 0;
for (int i = 0; i < 5; i++, t += 0.25)
{
Vec<D> p = GetPoint (t)-pref;
a(i, 0) = p(0) * p(0);
a(i, 1) = p(1) * p(1);
a(i, 2) = p(0) * p(1);
a(i, 3) = p(0);
a(i, 4) = p(1);
a(i, 5) = 1;
}
a(5, 0) = 1;
CalcAtA (a, ata);
u = 0;
u(5) = 1;
a.MultTrans (u, f);
ata.Solve (f, u);
// the sign
Point<D> p0 = GetPoint(0);
Vec<D> ht = GetTangent(0);
Vec<2> tang(ht(0), ht(1));
double gradx = u(3);
double grady = u(4);
// double gradx = 2.*u(0)*p0(0) + u(2)*p0(1) + u(3);
// double grady = 2.*u(1)*p0(1) + u(2)*p0(0) + u(4);
Vec<2> gradn (grady, -gradx);
if (tang * gradn < 0) u *= -1;
}

20
libsrc/gprim/spline.hpp
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@ -85,6 +85,7 @@ namespace netgen
void PrintCoeff (ostream & ost) const;
virtual void GetCoeff (Vector & coeffs) const = 0;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const { ; }
virtual void GetPoints (int n, Array<Point<D> > & points) const;
@ -138,7 +139,8 @@ namespace netgen
virtual const GeomPoint<D> & EndPI () const { return p2; }
///
virtual void GetCoeff (Vector & coeffs) const;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const;
virtual string GetType(void) const {return "line";}
virtual void LineIntersections (const double a, const double b, const double c,
@ -186,7 +188,8 @@ namespace netgen
virtual const GeomPoint<D> & EndPI () const { return p3; }
///
virtual void GetCoeff (Vector & coeffs) const;
virtual void GetCoeff (Vector & coeffs, Point<D> p0) const;
virtual string GetType(void) const {return "spline3";}
const GeomPoint<D> & TangentPoint (void) const { return p2; }
@ -394,6 +397,19 @@ namespace netgen
coeffs[5] = -dx * p1(1) + dy * p1(0);
}
template<int D>
void LineSeg<D> :: GetCoeff (Vector & coeffs, Point<D> p) const
{
coeffs.SetSize(6);
double dx = p2(0) - p1(0);
double dy = p2(1) - p1(1);
coeffs[0] = coeffs[1] = coeffs[2] = 0;
coeffs[3] = -dy;
coeffs[4] = dx;
coeffs[5] = -dx * (p1(1)-p(1)) + dy * (p1(0)-p(0));
}
template<int D>