public bool DoesBoxOverlap(BoundingBox box)
{
/// We are using separating axis theorem
/// We have to test 4 planes from tetrahedron, 3 planes from BB (trivial) and 6 * 3 planes from cross product of edges
///
/// First early out on box planes - trivial world space bounding box
///
if (!BoundingBox.Intersects(m_BoundingBox, box))
{
return(false);
}
Vector3[] corners = box.GetCorners();
Vector4 baryCentricBoundsMin = new Vector4(float.MaxValue, float.MaxValue, float.MaxValue, float.MaxValue);
Vector4 baryCentricBoundsMax = new Vector4(float.MinValue, float.MinValue, float.MinValue, float.MinValue);
/// Second check tetrahedron planes, easy due to barycentric matrices
foreach (var vert in corners)
{
float b0, b1, b2, b3;
CalculateBarycentricCoordinates(vert, out b0, out b1, out b2, out b3);
baryCentricBoundsMin = Vector4.Minimize(baryCentricBoundsMin, new Vector4(b0, b1, b2, b3));
baryCentricBoundsMax = Vector4.Maximize(baryCentricBoundsMax, new Vector4(b0, b1, b2, b3));
}
if (baryCentricBoundsMin.X > 1.0f || baryCentricBoundsMin.Y > 1.0f || baryCentricBoundsMin.Z > 1.0f || baryCentricBoundsMin.W > 1.0f)
{
return(false);
}
if (baryCentricBoundsMax.X < 0.0f || baryCentricBoundsMax.Y < 0.0f || baryCentricBoundsMax.Z < 0.0f || baryCentricBoundsMax.W < 0.0f)
{
return(false);
}
// Finally, more difficult part - planes between the edges of both
Vector3[] boxVectors = { new Vector3(1, 0, 0), new Vector3(0, 1, 0), new Vector3(0, 0, 1) };
Vector3[] tetEdgeVectors = new Vector3[6];
// Note: not necessary to normalize, we are interested in axis limits overlap
// And those vectors cannot be 0 (degenerated tetrahedron)
tetEdgeVectors[0] = m_Vertices[1] - m_Vertices[0];
tetEdgeVectors[1] = m_Vertices[2] - m_Vertices[0];
tetEdgeVectors[2] = m_Vertices[3] - m_Vertices[0];
tetEdgeVectors[3] = m_Vertices[2] - m_Vertices[1];
tetEdgeVectors[4] = m_Vertices[3] - m_Vertices[2];
tetEdgeVectors[5] = m_Vertices[1] - m_Vertices[3];
foreach (var tetEdge in tetEdgeVectors)
{
foreach (var boxEdge in boxVectors)
{
// Normal of plane constructed by those 2 edges
var planeNormal = Vector3.Cross(tetEdge, boxEdge);
if (planeNormal.LengthSquared() > 0.0001f)
{
Vector2 tetLimits = GeometricsAlgorithms.GetAxisProjectionLimits(m_Vertices, planeNormal);
Vector2 boxLimits = GeometricsAlgorithms.GetAxisProjectionLimits(corners, planeNormal);
if (tetLimits.X > boxLimits.Y || tetLimits.Y < boxLimits.X)
{
return(false);
}
}
}
}
return(true);
}
public static Vector4 FindTwoTetrahedronsSplittingPlane(Tetrahedron first, Tetrahedron second)
{
List <Vector3> potentialSplitPlanes = new List <Vector3>();
potentialSplitPlanes.Add(new Vector3(first.m_TetPlanes[0].X, first.m_TetPlanes[0].Y, first.m_TetPlanes[0].Z));
potentialSplitPlanes.Add(new Vector3(first.m_TetPlanes[1].X, first.m_TetPlanes[1].Y, first.m_TetPlanes[1].Z));
potentialSplitPlanes.Add(new Vector3(first.m_TetPlanes[2].X, first.m_TetPlanes[2].Y, first.m_TetPlanes[2].Z));
potentialSplitPlanes.Add(new Vector3(first.m_TetPlanes[3].X, first.m_TetPlanes[3].Y, first.m_TetPlanes[3].Z));
potentialSplitPlanes.Add(new Vector3(second.m_TetPlanes[0].X, second.m_TetPlanes[0].Y, second.m_TetPlanes[0].Z));
potentialSplitPlanes.Add(new Vector3(second.m_TetPlanes[1].X, second.m_TetPlanes[1].Y, second.m_TetPlanes[1].Z));
potentialSplitPlanes.Add(new Vector3(second.m_TetPlanes[2].X, second.m_TetPlanes[2].Y, second.m_TetPlanes[2].Z));
potentialSplitPlanes.Add(new Vector3(second.m_TetPlanes[3].X, second.m_TetPlanes[3].Y, second.m_TetPlanes[3].Z));
Vector3[] tetEdgeVectorsFirst = new Vector3[6];
Vector3[] tetEdgeVectorsSecond = new Vector3[6];
tetEdgeVectorsFirst[0] = first.m_Vertices[1] - first.m_Vertices[0];
tetEdgeVectorsFirst[1] = first.m_Vertices[2] - first.m_Vertices[0];
tetEdgeVectorsFirst[2] = first.m_Vertices[3] - first.m_Vertices[0];
tetEdgeVectorsFirst[3] = first.m_Vertices[2] - first.m_Vertices[1];
tetEdgeVectorsFirst[4] = first.m_Vertices[3] - first.m_Vertices[2];
tetEdgeVectorsFirst[5] = first.m_Vertices[1] - first.m_Vertices[3];
tetEdgeVectorsSecond[0] = second.m_Vertices[1] - second.m_Vertices[0];
tetEdgeVectorsSecond[1] = second.m_Vertices[2] - second.m_Vertices[0];
tetEdgeVectorsSecond[2] = second.m_Vertices[3] - second.m_Vertices[0];
tetEdgeVectorsSecond[3] = second.m_Vertices[2] - second.m_Vertices[1];
tetEdgeVectorsSecond[4] = second.m_Vertices[3] - second.m_Vertices[2];
tetEdgeVectorsSecond[5] = second.m_Vertices[1] - second.m_Vertices[3];
foreach (var tetEdgeFirst in tetEdgeVectorsFirst)
{
foreach (var tetEdgeSecond in tetEdgeVectorsSecond)
{
// Normal of plane constructed by those 2 edges
var planeNormal = Vector3.Cross(tetEdgeFirst, tetEdgeSecond);
if (planeNormal.LengthSquared() > 0.001f)
{
planeNormal.Normalize();
potentialSplitPlanes.Add(planeNormal);
}
}
}
const float epsilon = 0.001f;// fixed 1mm
foreach (var splittingPlaneNormal in potentialSplitPlanes)
{
Vector2 tetOneLimits = GeometricsAlgorithms.GetAxisProjectionLimits(first.m_Vertices, splittingPlaneNormal);
Vector2 tetTwoLimits = GeometricsAlgorithms.GetAxisProjectionLimits(second.m_Vertices, splittingPlaneNormal);
if ((tetOneLimits.X + epsilon) > tetTwoLimits.Y)
{
return(new Vector4(splittingPlaneNormal, -(tetOneLimits.X + tetTwoLimits.Y) / 2.0f));
}
if (tetOneLimits.Y < (tetTwoLimits.X + epsilon))
{
return(new Vector4(splittingPlaneNormal, -(tetOneLimits.Y + tetTwoLimits.X) / 2.0f));
}
}
throw new Exception("no splitting plane found");
}