//===== Compute Surface Curvature Metrics Given U W =====//
void Surf::CompCurvature( double u, double w, double& k1, double& k2, double& ka, double& kg )
{
double tol = 1e-10;
double bump = 1e-3;
// First derivative vectors
vec3d S_u = CompTanU( u, w );
vec3d S_w = CompTanW( u, w );
double E = dot( S_u, S_u );
double G = dot( S_w, S_w );
if( E < tol && G < tol )
{
double umid = m_MaxU / 2.0;
double wmid = m_MaxW / 2.0;
u = u + ( umid - u ) * bump;
w = w + ( wmid - w ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
else if( E < tol) // U direction degenerate
{
double wmid = m_MaxW / 2.0;
w = w + ( wmid - w ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
else if( G < tol ) // W direction degenerate
{
double umid = m_MaxU / 2.0;
u = u + ( umid - u ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
// Second derivative vectors
vec3d S_uu = CompTanUU( u, w );
vec3d S_uw = CompTanUW( u, w );
vec3d S_ww = CompTanWW( u, w );
// Unit normal vector
vec3d Q = cross( S_u, S_w );
Q.normalize();
double F = dot( S_u, S_w );
double L = dot( S_uu, Q );
double M = dot( S_uw, Q );
double N = dot( S_ww, Q );
// Mean curvature
ka = (E*N + G*L - 2.0*F*M)/(2.0*(E*G - F*F));
// Gaussian curvature
kg = (L*N - M*M)/(E*G - F*F);
double b = sqrt( ka*ka - kg );
// Principal curvatures
double kmax = ka + b;
double kmin = ka - b;
// Ensure k1 has largest magnitude
if( fabs(kmax) > fabs(kmin) )
{
k1 = kmax;
k2 = kmin;
}
else
{
k1 = kmin;
k2 = kmax;
}
}
//===== Compute Surface Curvature Metrics Given U W =====//
void SurfCore::CompCurvature( double u, double w, double& k1, double& k2, double& ka, double& kg ) const
{
double umn = m_Surface.get_u0();
double wmn = m_Surface.get_v0();
double umx = m_Surface.get_umax();
double wmx = m_Surface.get_vmax();
double slop = 1e-3;
if( u < (umn - slop) || w < (wmn - slop) || u > (umx + slop) || w > (wmx + slop) )
{
printf("BAD parameter in SurfCore::CompCurvature! %f %f\n", u, w );
assert(false);
}
if ( u < umn )
u = umn;
if ( w < wmn )
w = wmn;
if ( u > umx )
u = umx;
if ( w > wmx )
w = wmx;
double tol = 1e-10;
double bump = 1e-3;
// First derivative vectors
vec3d S_u = CompTanU( u, w );
vec3d S_w = CompTanW( u, w );
double E = dot( S_u, S_u );
double G = dot( S_w, S_w );
if( E < tol && G < tol )
{
double umid = GetMidU();
double wmid = GetMidW();
u = u + ( umid - u ) * bump;
w = w + ( wmid - w ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
else if( E < tol ) // U direction degenerate
{
double wmid = GetMidW();
w = w + ( wmid - w ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
else if( G < tol ) // W direction degenerate
{
double umid = GetMidU();
u = u + ( umid - u ) * bump;
S_u = CompTanU( u, w );
S_w = CompTanW( u, w );
E = dot( S_u, S_u );
G = dot( S_w, S_w );
}
// Second derivative vectors
vec3d S_uu = CompTanUU( u, w );
vec3d S_uw = CompTanUW( u, w );
vec3d S_ww = CompTanWW( u, w );
// Unit normal vector
vec3d Q = cross( S_u, S_w );
Q.normalize();
double F = dot( S_u, S_w );
double L = dot( S_uu, Q );
double M = dot( S_uw, Q );
double N = dot( S_ww, Q );
// Mean curvature
ka = ( E * N + G * L - 2.0 * F * M ) / ( 2.0 * ( E * G - F * F ) );
// Gaussian curvature
kg = ( L * N - M * M ) / ( E * G - F * F );
double b = sqrt( ka * ka - kg );
// Principal curvatures
double kmax = ka + b;
double kmin = ka - b;
// Ensure k1 has largest magnitude
if( std::abs( kmax ) > std::abs( kmin ) )
{
k1 = kmax;
k2 = kmin;
}
else
{
k1 = kmin;
k2 = kmax;
}
}
//===== Compute Second Derivative W,W =====//
vec3d Surf::CompTanWW01(double u01, double w01)
{
return CompTanWW( u01*m_MaxU, w01*m_MaxW );
}