/// returns the normal vector
StaticVector<ctype,3> normal(int tri) const {
const StaticVector<ctype,3> a = vertices(triangles(tri).vertices[1]) - vertices(triangles(tri).vertices[0]);
const StaticVector<ctype,3> b = vertices(triangles(tri).vertices[2]) - vertices(triangles(tri).vertices[0]);
StaticVector<ctype,3> n = a.cross(b);
n.normalize();
return n;
}
ctype CircularPatch<ctype>::distanceTo(const StaticVector<ctype,3> &p) const
{
int i, j;
ctype bestDist = std::numeric_limits<ctype>::max();
// check point against triangles
for (j=0; j<size(); j++){
const DomainTriangle<ctype>& cT = par->triangles(triangles[j]);
StaticVector<ctype,3> triPoints[3];
triPoints[0] = par->vertices(cT.vertices[0]);
triPoints[1] = par->vertices(cT.vertices[1]);
triPoints[2] = par->vertices(cT.vertices[2]);
// local base
StaticVector<ctype,3> a = triPoints[1] - triPoints[0];
StaticVector<ctype,3> b = triPoints[2] - triPoints[0];
StaticVector<ctype,3> c = a.cross(b);
c.normalize();
StaticVector<ctype,3> x = p - triPoints[0];
// write x in the new base (Cramer's rule)
StaticMatrix<ctype,3> numerator(a, b, c);
StaticMatrix<ctype,3> alphaMat(x, b, c);
StaticMatrix<ctype,3> betaMat(a, x, c);
StaticMatrix<ctype,3> gammaMat(a, b, x);
ctype alpha = alphaMat.det()/numerator.det();
ctype beta = betaMat.det()/numerator.det();
ctype gamma = gammaMat.det()/numerator.det();
// check whether orthogonal projection onto the ab plane is in triangle
bool isIn = alpha>=0 && beta>=0 && (1-alpha-beta)>=0;
if (isIn && fabs(gamma)<bestDist){
// printf("a(%1.2f %1.2f %1.2f) b(%1.2f %1.2f %1.2f) c(%1.2f %1.2f %1.2f) x(%1.2f %1.2f %1.2f)\n",
// a.x, a.y, a.z, b.x, b.y, b.z, c.x, c.y, c.z, x.x, x.y, x.z);
// printf("tri: %d, alpha = %f, beta = %f, gamma = %f\n", j, alpha, beta, gamma);
bestDist = fabs(gamma);
}
}
// check point against edges
for (i=0; i<size(); i++){
for (j=0; j<3; j++){
const DomainTriangle<ctype>& cT = par->triangles(triangles[i]);
StaticVector<ctype,3> from = par->vertices(cT.vertices[j]);
StaticVector<ctype,3> to = par->vertices(cT.vertices[(j+1)%3]);
StaticVector<ctype,3> edge = to - from;
ctype projectLength = edge.dot(p - from)/edge.length();
StaticVector<ctype,3> projection = edge/edge.length() * projectLength;
ctype orthoDist = ((p-from) - projection).length();
if (projectLength>=0 && projectLength<=edge.length() && orthoDist<bestDist)
bestDist = orthoDist;
}
}
// check point against vertices
for (i=0; i<size(); i++){
for (j=0; j<3; j++){
ctype dist = (p - par->vertices(par->triangles(triangles[i]).vertices[j])).length();
if (dist < bestDist){
bestDist = dist;
}
}
}
return bestDist;
}
/// gives the surface area
ctype area(int tri) const {
StaticVector<ctype,3> a = vertices(triangles(tri).vertices[1]) - vertices(triangles(tri).vertices[0]);
StaticVector<ctype,3> b = vertices(triangles(tri).vertices[2]) - vertices(triangles(tri).vertices[0]);
return fabs(0.5 * (a.cross(b)).length());
}