/// <summary>
/// Gets the point triangle intersection, return null if it can't find correct solution.
/// </summary>
/// <returns>The point triangle intersection.</returns>
/// <param name="v1">V1.</param>
/// <param name="v2">V2.</param>
/// <param name="v3">V3.</param>
/// <param name="p">P.</param>
/// <param name="t0">T0.</param>
/// <param name="t1">T1.</param>
public static Vector3d?GetPointTriangleIntersection(
Vector3d v1,
Vector3d v2,
Vector3d v3,
Vector3d p,
ref double t0,
ref double t1)
{
Vector3d diff = p - v1;
Vector3d edge0 = v2 - v1;
Vector3d edge1 = v3 - v1;
double a00 = edge0.Dot(edge0);
double a01 = edge0.Dot(edge1);
double a11 = edge1.Dot(edge1);
double b0 = -diff.Dot(edge0);
double b1 = -diff.Dot(edge1);
double det = a00 * a11 - a01 * a01;
t0 = a01 * b1 - a11 * b0;
t1 = a01 * b0 - a00 * b1;
if (t0 + t1 <= det)
{
if (t0 < 0.0)
{
if (t1 < 0.0) // region 4
{
if (b0 < 0.0)
{
t1 = 0.0;
if (-b0 >= a00) // V0
{
t0 = 1.0;
}
else // E01
{
t0 = -b0 / a00;
}
}
else
{
t0 = 0.0;
if (b1 >= 0.0) // V0
{
t1 = 0.0;
}
else if (-b1 >= a11) // V2
{
t1 = 1.0;
}
else // E20
{
t1 = -b1 / a11;
}
}
}
else // region 3
{
t0 = 0.0;
if (b1 >= 0.0) // V0
{
t1 = 0.0;
}
else if (-b1 >= a11) // V2
{
t1 = 1.0;
}
else // E20
{
t1 = -b1 / a11;
}
}
}
else if (t1 < 0.0) // region 5
{
t1 = 0.0;
if (b0 >= 0.0) // V0
{
t0 = 0.0;
}
else if (-b0 >= a00) // V1
{
t0 = 1.0;
}
else // E01
{
t0 = -b0 / a00;
}
}
else // region 0, interior
{
if (Math.Abs(det) > 1E-100)
{
double invDet = 1.0 / det;
t0 *= invDet;
t1 *= invDet;
}
else
{
return(null);
}
}
}
else
{
double tmp0, tmp1, numer, denom;
if (t0 < 0.0) // region 2
{
tmp0 = a01 + b0;
tmp1 = a11 + b1;
if (tmp1 > tmp0)
{
numer = tmp1 - tmp0;
denom = a00 - 2.0 * a01 + a11;
if (numer >= denom) // V1
{
t0 = 1.0;
t1 = 0.0;
}
else // E12
{
t0 = numer / denom;
t1 = 1.0 - t0;
}
}
else
{
t0 = 0.0;
if (tmp1 <= 0.0) // V2
{
t1 = 1.0;
}
else if (b1 >= 0.0) // V0
{
t1 = 0.0;
}
else // E20
{
t1 = -b1 / a11;
}
}
}
else if (t1 < 0.0) // region 6
{
tmp0 = a01 + b1;
tmp1 = a00 + b0;
if (tmp1 > tmp0)
{
numer = tmp1 - tmp0;
denom = a00 - 2.0 * a01 + a11;
if (numer >= denom) // V2
{
t1 = 1.0;
t0 = 0.0;
}
else // E12
{
t1 = numer / denom;
t0 = 1.0 - t1;
}
}
else
{
t1 = 0.0;
if (tmp1 <= 0.0) // V1
{
t0 = 1.0;
}
else if (b0 >= 0.0) // V0
{
t0 = 0.0;
}
else // E01
{
t0 = -b0 / a00;
}
}
}
else // region 1
{
numer = a11 + b1 - a01 - b0;
if (numer <= 0.0) // V2
{
t0 = 0.0;
t1 = 1.0;
}
else
{
denom = a00 - 2.0 * a01 + a11;
if (numer >= denom) // V1
{
t0 = 1.0;
t1 = 0.0;
}
else // 12
{
t0 = numer / denom;
t1 = 1.0 - t0;
}
}
}
}
return(v1 + t0 * edge0 + t1 * edge1);
}
