float3 Triangle::RandomPointInside(LCG &rng) const
{
float epsilon = 1e-3f;
///@todo rng.Float() returns [0,1[, but to be completely uniform, we'd need [0,1] here.
float s = rng.Float(epsilon, 1.f - epsilon);//1e-2f, 1.f - 1e-2f);
float t = rng.Float(epsilon, 1.f - epsilon);//1e-2f, 1.f - 1e-2f
if (s + t >= 1.f)
{
s = 1.f - s;
t = 1.f - t;
}
#ifdef MATH_ASSERT_CORRECTNESS
float3 pt = Point(s, t);
float2 uv = BarycentricUV(pt);
assert(uv.x >= 0.f);
assert(uv.y >= 0.f);
assert(uv.x + uv.y <= 1.f);
float3 uvw = BarycentricUVW(pt);
assert(uvw.x >= 0.f);
assert(uvw.y >= 0.f);
assert(uvw.z >= 0.f);
assert(EqualAbs(uvw.x + uvw.y + uvw.z, 1.f));
#endif
return Point(s, t);
}
bool Triangle::Contains(const float3 &point, float triangleThickness) const
{
if (PlaneCCW().Distance(point) > triangleThickness) // The winding order of the triangle plane does not matter.
return false; ///@todo The plane-point distance test is omitted in Real-Time Collision Detection. p. 25. A bug in the book?
float3 br = BarycentricUVW(point);
return br.y >= 0.f && br.z >= 0.f && (br.y + br.z) <= 1.f;
}
bool Triangle::Contains(const float3 &point, float triangleThickness) const
{
if (PlaneCCW().Distance(point) > triangleThickness) // The winding order of the triangle plane does not matter.
return false; ///@todo The plane-point distance test is omitted in Real-Time Collision Detection. p. 25. A bug in the book?
float3 br = BarycentricUVW(point);
return br.x >= -1e-3f && br.y >= -1e-3f && br.z >= -1e-3f; // Allow for a small epsilon to properly account for points very near the edges of the triangle.
}
float2 Triangle::BarycentricUV(const float3 &point) const
{
float3 uvw = BarycentricUVW(point);
return float2(uvw.y, uvw.z);
}
