bool ray4::hitsTriangle(const float4 *points, float &length) const
{
const float4 p0p1(points[1] - points[0]);
const float4 p0p2(points[2] - points[0]);
const float4 normal = float4(p0p1.cross(p0p2));
// n * p = n * (s + t*d) = n*s + n*d*t
// n(p-s) = ndt
// (n(p-s))/(n*d) = t
float4 dir = direction();
float4 outFactor = float4(-1.0f);
float4 normalTimesDirection = normal.prod(dir);
outFactor = (normalTimesDirection != float4(0.0f)).select(normal.prod(points[0] - start()) / normalTimesDirection, outFactor);
if((outFactor < float4(0.0f)).all())
return false;
if(outFactor.max() > 1.0f)
return false;
const float4 location = this->point(outFactor.max());
length = outFactor.max();
return location.isOnTriangle(points);
}
bool float4::isOnTriangle(const float4 *points) const
{
const float4 zero(0.0f);
const float4 one(1.0f);
const float4 p0p1(points[1] - points[0]);
const float4 p0p2(points[2] - points[0]);
const float4 normal(p0p1.cross(p0p2));
if(std::abs((normal * *this) - (normal * points[0])) >= 0.001f)
return false;
const float4 p0hp(*this - points[0]);
// dot00 = dot(v0, v0)
// dot01 = dot(v0, v1)
// dot02 = dot(v0, v2)
// dot11 = dot(v1, v1)
// dot12 = dot(v1, v2)
//
// // Compute barycentric coordinates
// invDenom = 1 / (dot00 * dot11 - dot01 * dot01)
// u = (dot11 * dot02 - dot01 * dot12) * invDenom
// v = (dot00 * dot12 - dot01 * dot02) * invDenom
//
// // Check if point is in triangle
// return (u > 0) && (v > 0) && (u + v < 1)
const float4 dot00(p0p1.vdot(p0p1));
const float4 dot01(p0p1.vdot(p0p2));
const float4 dot02(p0p1.vdot(p0hp));
const float4 dot11(p0p2.vdot(p0p2));
const float4 dot12(p0p2.vdot(p0hp));
const float4 invDenom = one / (dot00.prod(dot11) - dot01.prod(dot01));
const float4 u = (dot11.prod(dot02) - dot01.prod(dot12)).prod(invDenom);
const float4 v = (dot00.prod(dot12) - dot01.prod(dot02)).prod(invDenom);
return (u >= zero).all() && (v >= zero).all() && (u + v <= one).all();
}
