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// This is collision detection. If you do another distance test for collision *response*,
// if might be useful to simply *skip* the test below completely, and report a collision.
// - if sphere-triangle overlap, result is ok
// - if they don't, we'll discard them during collision response with a similar test anyway
// Overall this approach should run faster.
// Original code by David Eberly in Magic.
BOOL SphereCollider::SphereTriOverlap(const Point& vert0, const Point& vert1, const Point& vert2)
{
// Stats
mNbVolumePrimTests++;
// Early exit if one of the vertices is inside the sphere
Point kDiff = vert2 - mCenter;
float fC = kDiff.SquareMagnitude();
if(fC <= mRadius2) return TRUE;
kDiff = vert1 - mCenter;
fC = kDiff.SquareMagnitude();
if(fC <= mRadius2) return TRUE;
kDiff = vert0 - mCenter;
fC = kDiff.SquareMagnitude();
if(fC <= mRadius2) return TRUE;
// Else do the full distance test
Point TriEdge0 = vert1 - vert0;
Point TriEdge1 = vert2 - vert0;
//Point kDiff = vert0 - mCenter;
float fA00 = TriEdge0.SquareMagnitude();
float fA01 = TriEdge0 | TriEdge1;
float fA11 = TriEdge1.SquareMagnitude();
float fB0 = kDiff | TriEdge0;
float fB1 = kDiff | TriEdge1;
//float fC = kDiff.SquareMagnitude();
float fDet = fabsf(fA00*fA11 - fA01*fA01);
float u = fA01*fB1-fA11*fB0;
float v = fA01*fB0-fA00*fB1;
float SqrDist;
if(u + v <= fDet)
{
if(u < 0.0f)
{
if(v < 0.0f) // region 4
{
if(fB0 < 0.0f)
{
// v = 0.0f;
if(-fB0>=fA00) { /*u = 1.0f;*/ SqrDist = fA00+2.0f*fB0+fC; }
else { u = -fB0/fA00; SqrDist = fB0*u+fC; }
}
else
{
// u = 0.0f;
if(fB1>=0.0f) { /*v = 0.0f;*/ SqrDist = fC; }
else if(-fB1>=fA11) { /*v = 1.0f;*/ SqrDist = fA11+2.0f*fB1+fC; }
else { v = -fB1/fA11; SqrDist = fB1*v+fC; }
}
}
else // region 3
{
// u = 0.0f;
if(fB1>=0.0f) { /*v = 0.0f;*/ SqrDist = fC; }
else if(-fB1>=fA11) { /*v = 1.0f;*/ SqrDist = fA11+2.0f*fB1+fC; }
else { v = -fB1/fA11; SqrDist = fB1*v+fC; }
}
}
else if(v < 0.0f) // region 5
{
// v = 0.0f;
if(fB0>=0.0f) { /*u = 0.0f;*/ SqrDist = fC; }
else if(-fB0>=fA00) { /*u = 1.0f;*/ SqrDist = fA00+2.0f*fB0+fC; }
else { u = -fB0/fA00; SqrDist = fB0*u+fC; }
}
else // region 0
{
// minimum at interior point
if(fDet==0.0f)
{
// u = 0.0f;
// v = 0.0f;
SqrDist = MAX_FLOAT;
}
else
{
float fInvDet = 1.0f/fDet;
u *= fInvDet;
v *= fInvDet;
SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
}
}
}
else
{
float fTmp0, fTmp1, fNumer, fDenom;
if(u < 0.0f) // region 2
{
fTmp0 = fA01 + fB0;
fTmp1 = fA11 + fB1;
if(fTmp1 > fTmp0)
{
fNumer = fTmp1 - fTmp0;
fDenom = fA00-2.0f*fA01+fA11;
if(fNumer >= fDenom)
{
// u = 1.0f;
// v = 0.0f;
SqrDist = fA00+2.0f*fB0+fC;
}
else
{
u = fNumer/fDenom;
v = 1.0f - u;
SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
}
}
else
{
// u = 0.0f;
if(fTmp1 <= 0.0f) { /*v = 1.0f;*/ SqrDist = fA11+2.0f*fB1+fC; }
else if(fB1 >= 0.0f) { /*v = 0.0f;*/ SqrDist = fC; }
else { v = -fB1/fA11; SqrDist = fB1*v+fC; }
}
}
else if(v < 0.0f) // region 6
{
fTmp0 = fA01 + fB1;
fTmp1 = fA00 + fB0;
if(fTmp1 > fTmp0)
{
fNumer = fTmp1 - fTmp0;
fDenom = fA00-2.0f*fA01+fA11;
if(fNumer >= fDenom)
{
// v = 1.0f;
// u = 0.0f;
SqrDist = fA11+2.0f*fB1+fC;
}
else
{
v = fNumer/fDenom;
u = 1.0f - v;
SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
}
}
else
{
// v = 0.0f;
if(fTmp1 <= 0.0f) { /*u = 1.0f;*/ SqrDist = fA00+2.0f*fB0+fC; }
else if(fB0 >= 0.0f) { /*u = 0.0f;*/ SqrDist = fC; }
else { u = -fB0/fA00; SqrDist = fB0*u+fC; }
}
}
else // region 1
{
fNumer = fA11 + fB1 - fA01 - fB0;
if(fNumer <= 0.0f)
{
// u = 0.0f;
// v = 1.0f;
SqrDist = fA11+2.0f*fB1+fC;
}
else
{
fDenom = fA00-2.0f*fA01+fA11;
if(fNumer >= fDenom)
{
// u = 1.0f;
// v = 0.0f;
SqrDist = fA00+2.0f*fB0+fC;
}
else
{
u = fNumer/fDenom;
v = 1.0f - u;
SqrDist = u*(fA00*u+fA01*v+2.0f*fB0) + v*(fA01*u+fA11*v+2.0f*fB1)+fC;
}
}
}
}
return fabsf(SqrDist) < mRadius2;
}
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