mirror of
https://github.com/NGSolve/netgen.git
synced 2024-11-11 16:49:16 +05:00
rational spline weights to obtain circles
This commit is contained in:
Joachim Schoeberl
parent
63022fe1b9
commit
cc81dab63e
@ -33,6 +33,109 @@ namespace netgen
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
template<int D>
|
||||
SplineSeg3<D> :: SplineSeg3 (const GeomPoint<D> & ap1,
|
||||
const GeomPoint<D> & ap2,
|
||||
const GeomPoint<D> & ap3)
|
||||
: p1(ap1), p2(ap2), p3(ap3)
|
||||
{
|
||||
weight = Dist (p1, p3) / sqrt (0.5 * (Dist2 (p1, p2) + Dist2 (p2, p3)));
|
||||
// weight = sqrt(2);
|
||||
// cout << "weight = " << weight << endl;
|
||||
proj_latest_t = 0.5;
|
||||
}
|
||||
|
||||
template<int D>
|
||||
inline Point<D> SplineSeg3<D> :: GetPoint (double t) const
|
||||
{
|
||||
double x, y, w;
|
||||
double b1, b2, b3;
|
||||
|
||||
b1 = (1-t)*(1-t);
|
||||
b2 = weight * t * (1-t);
|
||||
b3 = t * t;
|
||||
|
||||
x = p1(0) * b1 + p2(0) * b2 + p3(0) * b3;
|
||||
y = p1(1) * b1 + p2(1) * b2 + p3(1) * b3;
|
||||
w = b1 + b2 + b3;
|
||||
|
||||
if(D==3)
|
||||
{
|
||||
double z = p1(2) * b1 + p2(2) * b2 + p3(2) * b3;
|
||||
return Point<D> (x/w, y/w, z/w);
|
||||
}
|
||||
else
|
||||
return Point<D> (x/w, y/w);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
template<int D>
|
||||
Vec<D> SplineSeg3<D> :: GetTangent (const double t) const
|
||||
{
|
||||
const double b1 = (1.-t)*((weight-2.)*t-weight);
|
||||
const double b2 = weight*(1.-2.*t);
|
||||
const double b3 = t*((weight-2)*t+2.);
|
||||
|
||||
|
||||
Vec<D> retval;
|
||||
for(int i=0; i<D; i++)
|
||||
retval(i) = b1*p1(i) + b2*p2(i) + b3*p3(i);
|
||||
|
||||
return retval;
|
||||
|
||||
}
|
||||
|
||||
|
||||
template<int D>
|
||||
void SplineSeg3<D> :: GetCoeff (Vector & u) 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)
|
||||
{
|
||||
Point<D> p = GetPoint (t);
|
||||
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 = 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;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
template<int D>
|
||||
@ -208,20 +311,20 @@ namespace netgen
|
||||
Vec<D> v1(p1), v2(p2), v3(p3);
|
||||
|
||||
double b1 = (1.-t)*(1.-t);
|
||||
double b2 = sqrt(2.)*t*(1.-t);
|
||||
double b2 = weight*t*(1.-t);
|
||||
double b3 = t*t;
|
||||
double w = b1+b2+b3;
|
||||
b1 *= 1./w; b2 *= 1./w; b3 *= 1./w;
|
||||
|
||||
double b1p = 2.*(t-1.);
|
||||
double b2p = sqrt(2.)*(1.-2.*t);
|
||||
double b2p = weight*(1.-2.*t);
|
||||
double b3p = 2.*t;
|
||||
const double wp = b1p+b2p+b3p;
|
||||
const double fac1 = wp/w;
|
||||
b1p *= 1./w; b2p *= 1./w; b3p *= 1./w;
|
||||
|
||||
const double b1pp = 2.;
|
||||
const double b2pp = -2.*sqrt(2.);
|
||||
const double b2pp = -2.*weight;
|
||||
const double b3pp = 2.;
|
||||
const double wpp = b1pp+b2pp+b3pp;
|
||||
const double fac2 = (wpp*w-2.*wp*wp)/(w*w);
|
||||
@ -278,10 +381,10 @@ namespace netgen
|
||||
|
||||
double t;
|
||||
|
||||
const double c1 = a*p1(0) - sqrt(2.)*a*p2(0) + a*p3(0)
|
||||
+ b*p1(1) - sqrt(2.)*b*p2(1) + b*p3(1)
|
||||
+ (2.-sqrt(2.))*c;
|
||||
const double c2 = -2.*a*p1(0) + sqrt(2.)*a*p2(0) -2.*b*p1(1) + sqrt(2.)*b*p2(1) + (sqrt(2.)-2.)*c;
|
||||
const double c1 = a*p1(0) - weight*a*p2(0) + a*p3(0)
|
||||
+ b*p1(1) - weight*b*p2(1) + b*p3(1)
|
||||
+ (2.-weight)*c;
|
||||
const double c2 = -2.*a*p1(0) + weight*a*p2(0) -2.*b*p1(1) + weight*b*p2(1) + (weight-2.)*c;
|
||||
const double c3 = a*p1(0) + b*p1(1) + c;
|
||||
|
||||
if(fabs(c1) < 1e-20)
|
||||
|
||||
@ -141,7 +141,7 @@ namespace netgen
|
||||
{
|
||||
///
|
||||
GeomPoint<D> p1, p2, p3;
|
||||
|
||||
double weight;
|
||||
mutable double proj_latest_t;
|
||||
public:
|
||||
///
|
||||
@ -406,101 +406,6 @@ namespace netgen
|
||||
|
||||
|
||||
|
||||
template<int D>
|
||||
SplineSeg3<D> :: SplineSeg3 (const GeomPoint<D> & ap1,
|
||||
const GeomPoint<D> & ap2,
|
||||
const GeomPoint<D> & ap3)
|
||||
: p1(ap1), p2(ap2), p3(ap3)
|
||||
{
|
||||
proj_latest_t = 0.5;
|
||||
}
|
||||
|
||||
template<int D>
|
||||
inline Point<D> SplineSeg3<D> :: GetPoint (double t) const
|
||||
{
|
||||
double x, y, w;
|
||||
double b1, b2, b3;
|
||||
|
||||
b1 = (1-t)*(1-t);
|
||||
b2 = sqrt(2.0) * t * (1-t);
|
||||
b3 = t * t;
|
||||
|
||||
x = p1(0) * b1 + p2(0) * b2 + p3(0) * b3;
|
||||
y = p1(1) * b1 + p2(1) * b2 + p3(1) * b3;
|
||||
w = b1 + b2 + b3;
|
||||
|
||||
if(D==3)
|
||||
{
|
||||
double z = p1(2) * b1 + p2(2) * b2 + p3(2) * b3;
|
||||
return Point<D> (x/w, y/w, z/w);
|
||||
}
|
||||
else
|
||||
return Point<D> (x/w, y/w);
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
template<int D>
|
||||
Vec<D> SplineSeg3<D> :: GetTangent (const double t) const
|
||||
{
|
||||
const double b1 = (1.-t)*((sqrt(2.)-2.)*t-sqrt(2.));
|
||||
const double b2 = sqrt(2.)*(1.-2.*t);
|
||||
const double b3 = t*((sqrt(2.)-2)*t+2.);
|
||||
|
||||
|
||||
Vec<D> retval;
|
||||
for(int i=0; i<D; i++)
|
||||
retval(i) = b1*p1(i) + b2*p2(i) + b3*p3(i);
|
||||
|
||||
return retval;
|
||||
|
||||
}
|
||||
|
||||
|
||||
template<int D>
|
||||
void SplineSeg3<D> :: GetCoeff (Vector & u) 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)
|
||||
{
|
||||
Point<D> p = GetPoint (t);
|
||||
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 = 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;
|
||||
}
|
||||
|
||||
/*
|
||||
template<int D>
|
||||
double SplineSeg3<D> :: MaxCurvature(void) const
|
||||
|
||||
Loading…
Reference in New Issue
Block a user