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");
}
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");
}