private bool IntersectsSharedEdge(TopoVertex[] shared, TopoVertex a, TopoVertex b, TopoTriangle tri)
{
// Test if coplanar. If not no intersection is possible
if (Math.Abs(DistanceToPlane(b.pos)) > epsilonZero)
{
return(false);
}
int idx2, idx1;
DominantAxis(out idx1, out idx2);
if (InPlanePointInside(idx1, idx2, b.pos))
{
return(true);
}
if (tri.InPlanePointInside(idx1, idx2, a.pos))
{
return(true);
}
return(false);
}
public bool Intersects(TopoTriangle tri)
{
// First detect shared edges for more reliable and faster tests
TopoVertex[] shared = new TopoVertex[3];
TopoVertex[] uniqueA = new TopoVertex[3];
TopoVertex[] uniqueB = new TopoVertex[3];
int nShared = 0, nUniqueA = 0, nUniqueB = 0;
for (int i = 0; i < 3; i++)
{
bool isDouble = false;
for (int j = 0; j < 3; j++)
{
if (vertices[i] == tri.vertices[j])
{
shared[nShared++] = vertices[i];
isDouble = true;
break;
}
}
if (!isDouble)
{
uniqueA[nUniqueA++] = vertices[i];
}
}
if (nShared > 0)
{
for (int i = 0; i < 3; i++)
{
bool isDouble = false;
for (int j = 0; j < nShared; j++)
{
if (tri.vertices[i] == shared[j])
{
isDouble = true;
break;
}
}
if (!isDouble)
{
uniqueB[nUniqueB++] = tri.vertices[i];
}
}
if (nShared == 1)
{
return(IntersectsSharedVertex(shared[0], uniqueA, uniqueB, tri));
}
if (nShared == 2)
{
return(IntersectsSharedEdge(shared, uniqueA[0], uniqueB[0], tri));
}
return(true);
}
// Nice to read but unoptimized intersection computation
RHMatrix3 A = new RHMatrix3();
RHVector3 p1 = vertices[1].pos.Subtract(vertices[0].pos);
RHVector3 p2 = vertices[2].pos.Subtract(vertices[0].pos);
A.SetXColumn(p1);
A.SetYColumn(p2);
RHVector3 P = new RHVector3(vertices[0].pos);
RHVector3 q1 = tri.vertices[1].pos.Subtract(tri.vertices[0].pos);
RHVector3 q2 = tri.vertices[2].pos.Subtract(tri.vertices[0].pos);
RHVector3 r1 = tri.vertices[0].pos.Subtract(P); // r2 == r1!
RHVector3 r3 = tri.vertices[2].pos.Subtract(P);
A.SetZColumn(q1);
double detAq1 = A.Determinant;
A.SetZColumn(q2);
double detAq2 = A.Determinant;
//A.SetZColumn(q3);
double detAq3 = detAq1 - detAq2; // A.Determinant;
A.SetZColumn(r1);
double detAr1 = A.Determinant;
//A.SetZColumn(r3);
double detAr3 = detAr1 + detAq2; // A.Determinant;
int intersect = 0;
if (detAq1 == 0 && detAq2 == 0 && detAq3 == 0) // same plane case
{
if (detAr1 != 0)
{
return(false); // other parallel plance
}
// Select plane for computation x-y or x-z based on normal
int idx1, idx2;
DominantAxis(out idx1, out idx2);
if (InPlaneIntersectLine(idx1, idx2, vertices[0].pos, vertices[1].pos, tri.vertices[0].pos, tri.vertices[1].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[0].pos, vertices[1].pos, tri.vertices[1].pos, tri.vertices[2].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[0].pos, vertices[1].pos, tri.vertices[2].pos, tri.vertices[0].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[1].pos, vertices[2].pos, tri.vertices[0].pos, tri.vertices[1].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[1].pos, vertices[2].pos, tri.vertices[1].pos, tri.vertices[2].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[1].pos, vertices[2].pos, tri.vertices[2].pos, tri.vertices[0].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[2].pos, vertices[0].pos, tri.vertices[0].pos, tri.vertices[1].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[2].pos, vertices[0].pos, tri.vertices[1].pos, tri.vertices[2].pos))
{
return(true);
}
if (InPlaneIntersectLine(idx1, idx2, vertices[2].pos, vertices[0].pos, tri.vertices[2].pos, tri.vertices[0].pos))
{
return(true);
}
// Test if point inside. 1 test per triangle is enough
if (InPlanePointInside(idx1, idx2, tri.vertices[0].pos))
{
return(true);
}
if (InPlanePointInside(idx1, idx2, tri.vertices[1].pos))
{
return(true);
}
if (InPlanePointInside(idx1, idx2, tri.vertices[2].pos))
{
return(true);
}
if (tri.InPlanePointInside(idx1, idx2, vertices[0].pos))
{
return(true);
}
if (tri.InPlanePointInside(idx1, idx2, vertices[1].pos))
{
return(true);
}
if (tri.InPlanePointInside(idx1, idx2, vertices[2].pos))
{
return(true);
}
return(false);
}
double beta1 = -1, beta2 = -1, beta3 = -1;
if (detAq1 != 0)
{
beta1 = -detAr1 / detAq1;
if (beta1 >= epsilonZeroMinus && beta1 <= epsilonOnePlus)
{
intersect = 1;
}
}
if (detAq2 != 0)
{
beta2 = -detAr1 / detAq2;
if (beta2 >= epsilonZeroMinus && beta2 <= epsilonOnePlus)
{
intersect |= 2;
}
}
if (detAq3 != 0)
{
beta3 = -detAr3 / detAq3;
if (beta3 >= epsilonZeroMinus && beta3 <= epsilonOnePlus)
{
intersect |= 4;
}
}
if (intersect == 7)
{ // Special case intersection in one point caused 3 valid betas
if (Math.Abs(beta1) < epsilonZero)
{
intersect = 6;
}
else if (Math.Abs(beta3) < epsilonZero)
{
intersect = 3;
}
else
{
intersect = 5;
}
}
//if (intersect == 0) return false; // Lies on wrong side
RHVector3 T = null, t = null;
if ((intersect & 1) == 1)
{
T = new RHVector3(q1);
T.Scale(beta1);
T.AddInternal(tri.vertices[0].pos);
}
if ((intersect & 2) == 2)
{
if (T == null)
{
T = new RHVector3(q2);
T.Scale(beta2);
T.AddInternal(tri.vertices[0].pos);
}
else
{
q2.Scale(beta2);
q2.AddInternal(tri.vertices[0].pos);
t = q2.Subtract(T);
}
}
if ((intersect & 4) == 4 && T != null && (t == null || t.Length < epsilonZero))
{
RHVector3 q3 = tri.vertices[1].pos.Subtract(tri.vertices[2].pos);
q3.Scale(beta3);
q3.AddInternal(tri.vertices[2].pos);
t = q3.Subtract(T);
}
if (t == null)
{
return(false);
}
if (t.Length < epsilonZero)
{ // Only one point touches the plane
int idx1, idx2;
DominantAxis(out idx1, out idx2);
return(InPlanePointInside(idx1, idx2, T));
}
// Compute intersection points with this triangle
double d1 = p1.x * t.y - p1.y * t.x;
double d2 = p1.x * t.z - p1.z * t.x;
double delta1 = -1, delta2 = -1, delta3 = -1, gamma1 = -1, gamma2 = -1, gamma3 = -1;
if (Math.Abs(d1) > epsilonZero || Math.Abs(d2) > epsilonZero)
{
if (Math.Abs(d1) > Math.Abs(d2))
{
delta1 = -(t.x * T.y - t.y * T.x + P.x * t.y - P.y * t.x) / d1;
gamma1 = -(p1.x * T.y - p1.y * T.x - p1.x * P.y + p1.y * P.x) / d1;
}
else
{
delta1 = -(t.x * T.z - t.z * T.x + P.x * t.z - P.z * t.x) / d2;
gamma1 = -(p1.x * T.z - p1.z * T.x - p1.x * P.z + p1.z * P.x) / d2;
}
}
d1 = p2.x * t.y - p2.y * t.x;
d2 = p2.x * t.z - p2.z * t.x;
if (Math.Abs(d1) > epsilonZero || Math.Abs(d2) > epsilonZero)
{
if (Math.Abs(d1) > Math.Abs(d2))
{
delta2 = -(t.x * T.y - t.y * T.x + P.x * t.y - P.y * t.x) / d1;
gamma2 = -(p2.x * T.y - p2.y * T.x - p2.x * P.y + p2.y * P.x) / d1;
}
else
{
delta2 = -(t.x * T.z - t.z * T.x + P.x * t.z - P.z * t.x) / d2;
gamma2 = -(p2.x * T.z - p2.z * T.x - p2.x * P.z + p2.z * P.x) / d2;
}
}
P.AddInternal(p1);
p2.SubtractInternal(p1); // p2 is now p3!
d1 = p2.x * t.y - p2.y * t.x;
d2 = p2.x * t.z - p2.z * t.x;
if (Math.Abs(d1) > epsilonZero || Math.Abs(d2) > epsilonZero)
{
if (Math.Abs(d1) > Math.Abs(d2))
{
delta3 = -(t.x * T.y - t.y * T.x + P.x * t.y - P.y * t.x) / d1;
gamma3 = -(p2.x * T.y - p2.y * T.x - p2.x * P.y + p2.y * P.x) / d1;
}
else
{
delta3 = -(t.x * T.z - t.z * T.x + P.x * t.z - P.z * t.x) / d2;
gamma3 = -(p2.x * T.z - p2.z * T.x - p2.x * P.z + p2.z * P.x) / d2;
}
}
// Check for line intersection inside the line. Hits at the vertices to not count!
if (delta1 >= epsilonZero && delta1 <= epsilonOneMinus && gamma1 >= epsilonZero && gamma1 <= epsilonOneMinus)
{
return(true);
}
if (delta2 >= epsilonZero && delta2 <= epsilonOneMinus && gamma2 >= epsilonZero && gamma2 <= epsilonOneMinus)
{
return(true);
}
if (delta3 >= epsilonZero && delta3 <= epsilonOneMinus && gamma3 >= epsilonZero && gamma3 <= epsilonOneMinus)
{
return(true);
}
// Test if intersection is inside triangle
intersect = 0;
if (delta1 >= epsilonZeroMinus && delta1 <= epsilonOnePlus)
{
intersect |= 1;
}
if (delta2 >= epsilonZeroMinus && delta2 <= epsilonOnePlus)
{
intersect |= 2;
}
if (delta3 >= epsilonZeroMinus && delta3 <= epsilonOnePlus)
{
intersect |= 4;
}
/* if (gamma1 == 0) gamma1 = -1;
* if (gamma2 == 0) gamma2 = -1;
* if (gamma3 == 0) gamma3 = -1;*/
if (gamma1 == 0)
{
intersect &= ~1;
}
if (gamma2 == 0)
{
intersect &= ~2;
}
if (gamma3 == 0)
{
intersect &= ~4;
}
/* if ((intersect & 3) == 3) return gamma1 * gamma2 < 0;
* if ((intersect & 5) == 5) return gamma1 * gamma3 < 0;
* if ((intersect & 6) == 6) return gamma3 * gamma2 < 0;*/
if ((intersect & 3) == 3)
{
if (gamma1 * gamma2 < 0)
{
return(true);
}
else
{
return(false);
}
}
if ((intersect & 5) == 5)
{
if (gamma1 * gamma3 < 0)
{
return(true);
}
else
{
return(false);
}
}
if ((intersect & 6) == 6)
{
if (gamma3 * gamma2 < 0)
{
return(true);
}
else
{
return(false);
}
}
// if (intersect!=0) happens only with numeric problems
// return true;
return(false); // No intersection found :-)
}
