Swept ray test for character->world ledge hang intersection checks

ParallelogramTriangle.cpp

// | = dot product, ^ = cross product. Please forgive my younger self for his sins.

void UpdateMinMax(float value, float& min, float& max)
{
  if (value < min)
    min = value;
  else if (value > max)
    max = value;
}

void ProjectTriangleOntoAxis(const cVector3 points[3], const cVector3& axis, float& min_t, float& max_t)
{
	// Initial projection of first point
	min_t = points[0] | axis;
	max_t = min_t;

	// Project remaining points and adjust projection range
	UpdateMinMax(points[1] | axis, min_t, max_t);
	UpdateMinMax(points[2] | axis, min_t, max_t);
}

void ProjectParallelogramOntoAxis(const cVector3& pos, const cVector3 edges[2], const cVector3& axis, float& min_t, float& max_t)
{
	// Initial projection of first point
	min_t = pos | axis;
	max_t = min_t;

	// Project remaining points and adjust projection range
	UpdateMinMax((pos + edges[0]) | axis, min_t, max_t);
	UpdateMinMax((pos + edges[1]) | axis, min_t, max_t);
	UpdateMinMax((pos + edges[0] + edges[1]) | axis, min_t, max_t);
}

bool TestParallelogramTriangle(const cVector3& pos, const cVector3 edges[2], const cVector3 points[3], const cVector3& normal)
{
	float d, min0, max0, min1, max1;

	// Big list of SATs. Only need to test for Fa + Fb + Ea * Eb axes, which in this case
	// is 1 + 1 + 2 * 3 = 8.
	// In all cases both objects are being projected onto the same axes. Since the only required
	// result of these comparisons is an overlap test we can ignore normalisation of vectors. Of course,
	// this might include numerical errors for very large or small objects but we need to see how big
	// or small this is before we can make any decisions as to how to efficiently solve the problem.

	// Check axis of triangle normal
	d = points[0] | normal;
	min0 = d;
	max0 = min0;
	ProjectParallelogramOntoAxis(pos, edges, normal, min1, max1);
	if (max1 < min0 || max0 < min1)
		return (false);

	// Check axis of parallelogram normal
	cVector3 pn = edges[0] ^ edges[1];
	min0 = pos | pn;
	max0 = min0;
	ProjectTriangleOntoAxis(points, pn, min1, max1);
	if (max1 < min0 || max0 < min1)
		return (false);

	cVector3 tri_edges[] =
	{
		points[1] - points[0],
		points[2] - points[1],
		points[0] - points[2]
	};

	// Check permutations of edge cross products
	for (int i = 0; i < 2; i++)
	{
		for (int j = 0; j < 3; j++)
		{
			cVector3 axis = edges[i] ^ tri_edges[j];
			ProjectTriangleOntoAxis(points, axis, min0, max0);
			ProjectParallelogramOntoAxis(pos, edges, axis, min1, max1);
			if (max1 < min0 || max0 < min1)
				return (false);
		}
	}

	return (true);
}