public bool ClosestPtPointTriangle(ref Vector3 p, ref Vector3 a, ref Vector3 b, ref Vector3 c, ref SubSimplexClosestResult result)
{
result.m_usedVertices.SetAll(false);
// Check if P in vertex region outside A
Vector3 ab = b - a;
Vector3 ac = c - a;
Vector3 ap = p - a;
float d1 = Vector3.Dot(ab, ap);
float d2 = Vector3.Dot(ac, ap);
if (d1 <= 0f && d2 <= 0f)
{
result.m_closestPointOnSimplex = a;
result.m_usedVertices.Set(0, true);
result.SetBarycentricCoordinates(1, 0, 0, 0);
return true;// a; // barycentric coordinates (1,0,0)
}
// Check if P in vertex region outside B
Vector3 bp = p - b;
float d3 = Vector3.Dot(ab, bp);
float d4 = Vector3.Dot(ac, bp);
if (d3 >= 0f && d4 <= d3)
{
result.m_closestPointOnSimplex = b;
result.m_usedVertices.Set(1, true);
result.SetBarycentricCoordinates(0, 1, 0, 0);
return true; // b; // barycentric coordinates (0,1,0)
}
// Check if P in edge region of AB, if so return projection of P onto AB
float vc = d1 * d4 - d3 * d2;
if (vc <= 0f && d1 >= 0f && d3 <= 0f)
{
float v = d1 / (d1 - d3);
result.m_closestPointOnSimplex = a + v * ab;
result.m_usedVertices.Set(0, true);
result.m_usedVertices.Set(1, true);
result.SetBarycentricCoordinates(1 - v, v, 0, 0);
return true;
//return a + v * ab; // barycentric coordinates (1-v,v,0)
}
// Check if P in vertex region outside C
Vector3 cp = p - c;
float d5 = Vector3.Dot(ab, cp);
float d6 = Vector3.Dot(ac, cp);
if (d6 >= 0f && d5 <= d6)
{
result.m_closestPointOnSimplex = c;
result.m_usedVertices.Set(2, true);
result.SetBarycentricCoordinates(0, 0, 1, 0);
return true;//c; // barycentric coordinates (0,0,1)
}
// Check if P in edge region of AC, if so return projection of P onto AC
float vb = d5 * d2 - d1 * d6;
if (vb <= 0f && d2 >= 0f && d6 <= 0f)
{
float w = d2 / (d2 - d6);
result.m_closestPointOnSimplex = a + w * ac;
result.m_usedVertices.Set(0, true);
result.m_usedVertices.Set(2, true);
result.SetBarycentricCoordinates(1 - w, 0, w, 0);
return true;
//return a + w * ac; // barycentric coordinates (1-w,0,w)
}
// Check if P in edge region of BC, if so return projection of P onto BC
float va = d3 * d6 - d5 * d4;
if (va <= 0f && (d4 - d3) >= 0f && (d5 - d6) >= 0f)
{
float w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
result.m_closestPointOnSimplex = b + w * (c - b);
result.m_usedVertices.Set(1, true);
result.m_usedVertices.Set(2, true);
result.SetBarycentricCoordinates(0, 1 - w, w, 0);
return true;
// return b + w * (c - b); // barycentric coordinates (0,1-w,w)
}
// P inside face region. Compute Q through its barycentric coordinates (u,v,w)
float denom = 1f / (va + vb + vc);
float v1 = vb * denom;
float w1 = vc * denom;
result.m_closestPointOnSimplex = a + ab * v1 + ac * w1;
result.m_usedVertices.Set(0, true);
result.m_usedVertices.Set(1, true);
result.m_usedVertices.Set(2, true);
result.SetBarycentricCoordinates(1 - v1 - w1, v1, w1, 0);
return true;
// return a + ab * v + ac * w; // = u*a + v*b + w*c, u = va * denom = float(1.0) - v - w
}
public bool ClosestPtPointTetrahedron(ref Vector3 p, ref Vector3 a, ref Vector3 b, ref Vector3 c, ref Vector3 d, ref SubSimplexClosestResult finalResult)
{
SubSimplexClosestResult tempResult = new SubSimplexClosestResult();
// Start ref assuming point inside all halfspaces, so closest to itself
finalResult.m_closestPointOnSimplex = p;
finalResult.m_usedVertices.SetAll(true);
int pointOutsideABC = PointOutsideOfPlane(ref p, ref a, ref b, ref c, ref d);
int pointOutsideACD = PointOutsideOfPlane(ref p, ref a, ref c, ref d, ref b);
int pointOutsideADB = PointOutsideOfPlane(ref p, ref a, ref d, ref b, ref c);
int pointOutsideBDC = PointOutsideOfPlane(ref p, ref b, ref d, ref c, ref a);
if (pointOutsideABC < 0 || pointOutsideACD < 0 || pointOutsideADB < 0 || pointOutsideBDC < 0)
{
finalResult.m_degenerate = true;
return false;
}
if (pointOutsideABC == 0 && pointOutsideACD == 0 && pointOutsideADB == 0 && pointOutsideBDC == 0)
{
return false;
}
float bestSqDist = float.MaxValue;
// If point outside face abc then compute closest point on abc
if (pointOutsideABC != 0)
{
ClosestPtPointTriangle(ref p, ref a, ref b, ref c, ref tempResult);
Vector3 q = tempResult.m_closestPointOnSimplex;
float sqDist = (q - p).LengthSquared();
// Update best closest point if (squared) distance is less than current best
if (sqDist < bestSqDist)
{
bestSqDist = sqDist;
finalResult.m_closestPointOnSimplex = q;
//convert result bitmask!
finalResult.m_usedVertices.SetAll(false);
finalResult.m_usedVertices.Set(0, tempResult.m_usedVertices.Get(0));
finalResult.m_usedVertices.Set(1, tempResult.m_usedVertices.Get(1));
finalResult.m_usedVertices.Set(2, tempResult.m_usedVertices.Get(2));
finalResult.SetBarycentricCoordinates(
tempResult.m_barycentricCoords.X,
tempResult.m_barycentricCoords.Y,
tempResult.m_barycentricCoords.Z,
0
);
}
}
// Repeat test for face acd
if (pointOutsideACD != 0)
{
ClosestPtPointTriangle(ref p, ref a, ref c, ref d, ref tempResult);
Vector3 q = tempResult.m_closestPointOnSimplex;
float sqDist = (q - p).LengthSquared();
// Update best closest point if (squared) distance is less than current best
if (sqDist < bestSqDist)
{
bestSqDist = sqDist;
finalResult.m_closestPointOnSimplex = q;
//convert result bitmask!
finalResult.m_usedVertices.SetAll(false);
finalResult.m_usedVertices.Set(0, tempResult.m_usedVertices.Get(0));
finalResult.m_usedVertices.Set(2, tempResult.m_usedVertices.Get(1));
finalResult.m_usedVertices.Set(3, tempResult.m_usedVertices.Get(2));
finalResult.SetBarycentricCoordinates(
tempResult.m_barycentricCoords.X,
0,
tempResult.m_barycentricCoords.Y,
tempResult.m_barycentricCoords.Z);
}
}
// Repeat test for face adb
if (pointOutsideADB != 0)
{
ClosestPtPointTriangle(ref p, ref a, ref d, ref b, ref tempResult);
Vector3 q = tempResult.m_closestPointOnSimplex;
float sqDist = (q - p).LengthSquared();
// Update best closest point if (squared) distance is less than current best
if (sqDist < bestSqDist)
{
bestSqDist = sqDist;
finalResult.m_closestPointOnSimplex = q;
//convert result bitmask!
finalResult.m_usedVertices.SetAll(false);
finalResult.m_usedVertices.Set(0, tempResult.m_usedVertices.Get(0));
finalResult.m_usedVertices.Set(1, tempResult.m_usedVertices.Get(2));
finalResult.m_usedVertices.Set(3, tempResult.m_usedVertices.Get(1));
finalResult.SetBarycentricCoordinates(
tempResult.m_barycentricCoords.X,
tempResult.m_barycentricCoords.Z,
0,
tempResult.m_barycentricCoords.Y);
}
}
// Repeat test for face bdc
if (pointOutsideBDC != 0)
{
ClosestPtPointTriangle(ref p, ref b, ref d, ref c, ref tempResult);
Vector3 q = tempResult.m_closestPointOnSimplex;
float sqDist = (q - p).LengthSquared();
// Update best closest point if (squared) distance is less than current best
if (sqDist < bestSqDist)
{
bestSqDist = sqDist;
finalResult.m_closestPointOnSimplex = q;
//convert result bitmask!
finalResult.m_usedVertices.SetAll(false);
finalResult.m_usedVertices.Set(1, tempResult.m_usedVertices.Get(0));
finalResult.m_usedVertices.Set(2, tempResult.m_usedVertices.Get(2));
finalResult.m_usedVertices.Set(3, tempResult.m_usedVertices.Get(1));
finalResult.SetBarycentricCoordinates(
0,
tempResult.m_barycentricCoords.X,
tempResult.m_barycentricCoords.Z,
tempResult.m_barycentricCoords.Y);
}
}
//help! we ended up full !
if (finalResult.m_usedVertices.Get(0) &&
finalResult.m_usedVertices.Get(1) &&
finalResult.m_usedVertices.Get(2) &&
finalResult.m_usedVertices.Get(3))
{
return true;
}
return true;
}