//--------------------------------------------------------------------------------------------------
// Compute barycentric coordinates (area coordinates) (u, v, w) for
// point p with respect to triangle (t0, t1, t2)
// These can be used as weights for interpolating scalar values across the triangle
// Based on section 3.4 in "Real Time collision detection" by Christer Ericson
//--------------------------------------------------------------------------------------------------
cvf::Vec3d GeometryTools::barycentricCoords(const cvf::Vec3d& t0, const cvf::Vec3d& t1, const cvf::Vec3d& t2, const cvf::Vec3d& p)
{
// Unnormalized triangle normal
cvf::Vec3d m = (t1 - t0 ^ t2 - t0);
// Absolute components for determining projection plane
int X = 0, Y = 1;
int Z = findClosestAxis(m);
switch (Z)
{
case 0: X = 1; Y = 2; break; // x is largest, project to the yz plane
case 1: X = 0; Y = 2; break; // y is largest, project to the xz plane
case 2: X = 0; Y = 1; break; // z is largest, project to the xy plane
}
// Compute areas in plane of largest projection
// Nominators and one-over-denominator for u and v ratios
double nu, nv, ood;
nu = TriArea2D(p[X], p[Y], t1[X], t1[Y], t2[X], t2[Y]); // Area of PBC in yz plane
nv = TriArea2D(p[X], p[Y], t2[X], t2[Y], t0[X], t0[Y]); // Area of PCA in yz plane
ood = 1.0f / m[Z]; // 1/(2*area of ABC in yz plane)
if (Z == 1) ood = -ood; // For some reason not explained
// Normalize
m[0] = nu * ood;
m[1] = nv * ood;
m[2] = 1.0f - m[0] - m[1];
return m;
}
float3 Triangle::BarycentricUVW(const float3 &point) const
{
// Implementation from Christer Ericson's Real-Time Collision Detection, pp. 51-52.
// Unnormalized triangle normal.
float3 m = Cross(b-a, c-a);
// Nominators and one-over-denominator for u and v ratios.
float nu, nv, ood;
// Absolute components for determining projection plane.
float x = Abs(m.x);
float y = Abs(m.y);
float z = Abs(m.z);
if (x >= y && x >= z)
{
// Project to the yz plane.
nu = TriArea2D(point.y, point.z, b.y, b.z, c.y, c.z); // Area of PBC in yz-plane.
nv = TriArea2D(point.y, point.z, c.y, c.z, a.y, a.z); // Area OF PCA in yz-plane.
ood = 1.f / m.x; // 1 / (2*area of ABC in yz plane)
}
else if (y >= z) // Note: The book has a redundant 'if (y >= x)' comparison
{
// y is largest, project to the xz-plane.
nu = TriArea2D(point.x, point.z, b.x, b.z, c.x, c.z);
nv = TriArea2D(point.x, point.z, c.x, c.z, a.x, a.z);
ood = 1.f / -m.y;
}
else // z is largest, project to the xy-plane.
{
nu = TriArea2D(point.x, point.y, b.x, b.y, c.x, c.y);
nv = TriArea2D(point.x, point.y, c.x, c.y, a.x, a.y);
ood = 1.f / m.z;
}
float u = nu * ood;
float v = nv * ood;
float w = 1.f - u - v;
return float3(u,v,w);
#if 0 // TODO: This version should be more SIMD-friendly, but for some reason, it doesn't return good values for all points inside the triangle.
float3 v0 = b - a;
float3 v1 = c - a;
float3 v2 = point - a;
float d00 = Dot(v0, v0);
float d01 = Dot(v0, v1);
float d02 = Dot(v0, v2);
float d11 = Dot(v1, v1);
float d12 = Dot(v1, v2);
float denom = 1.f / (d00 * d11 - d01 * d01);
float v = (d11 * d02 - d01 * d12) * denom;
float w = (d00 * d12 - d01 * d02) * denom;
float u = 1.0f - v - w;
return float3(u, v, w);
#endif
}
