//----------------------------------------------------------------------------
bool ConvexPolyhedron::ComputeSilhouette (vector<Vector3>& rkTerminator,
const Vector3& rkEye, const Plane& rkPlane, const Vector3& rkU,
const Vector3& rkV, vector<Vector2>& rkSilhouette)
{
Real fEDist = rkPlane.DistanceTo(rkEye); // assert: fEDist > 0
// closest planar point to E is K = E-dist*N
Vector3 kClosest = rkEye - fEDist*rkPlane.Normal();
// project polyhedron points onto plane
for (int i = 0; i < (int)rkTerminator.size(); i++)
{
Vector3& rkPoint = rkTerminator[i];
Real fVDist = rkPlane.DistanceTo(rkPoint);
if ( fVDist >= fEDist )
{
// cannot project vertex onto plane
return false;
}
// compute projected point Q
Real fRatio = fEDist/(fEDist-fVDist);
Vector3 kProjected = rkEye + fRatio*(rkPoint - rkEye);
// compute (x,y) so that Q = K+x*U+y*V+z*N
Vector3 kDiff = kProjected - kClosest;
rkSilhouette.push_back(Vector2(rkU.Dot(kDiff),rkV.Dot(kDiff)));
}
return true;
}
// Works for either side of a plane; this wasn't always the case
bool Segment::Intersects( const Plane& p, CollisionInfo* const pInfo /*=NULL*/ ) const
{
Vector ab = m_Point2 - m_Point1;
float d = ab.Dot( p.m_Normal );
if( Abs( d ) > EPSILON ) // Is segment not parallel to the plane?
{
// Test the t-value where the line crosses the plane to see if the
// segment intersects or lies completely on one side (accounting
// for the possibility that the segment faces the other way now).
float t = -p.DistanceTo( m_Point1 ) / d;
if( t >= 0.0f && t <= 1.0f )
{
if( pInfo )
{
pInfo->m_Collision = true;
pInfo->m_Intersection = m_Point1 + t * ab;
pInfo->m_Plane = p;
pInfo->m_HitT = t;
}
return true;
}
}
return false;
}
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
//
int
MLRIndexedPolyMesh::FindBackFace(const Point3D& u)
{
Check_Object(this);
int i, numPrimitives = GetNumPrimitives();
int ret = 0, len = lengths.GetLength();
unsigned char *iPtr;
Plane *p;
if(len <= 0)
{
visible = 0;
return 0;
}
p = &facePlanes[0];
iPtr = &testList[0];
if(state.GetBackFaceMode() == MLRState::BackFaceOffMode)
{
ResetTestList();
ret = 1;
}
else
{
for(i=0;i<numPrimitives;i++,p++,iPtr++)
{
// Scalar s = p->DistanceTo(u);
// *iPtr = !Get_Sign_Bit(s);
*iPtr = (p->DistanceTo(u) >= 0.0f) ? (unsigned char)1: (unsigned char)0;
ret += *iPtr;
}
visible = ret ? (unsigned char)1 : (unsigned char)0;
}
visible = ret ? (unsigned char)1 : (unsigned char)0;
FindVisibleVertices();
return ret;
}
//----------------------------------------------------------------------------
static void SplitAndDecompose (Tetrahedron kTetra, const Plane& rkPlane,
vector<Tetrahedron>& rkInside)
{
// determine on which side of the plane the points of the tetrahedron lie
Real afC[4];
int i, aiP[4], aiN[4], aiZ[4];
int iPositive = 0, iNegative = 0, iZero = 0;
for (i = 0; i < 4; i++)
{
afC[i] = rkPlane.DistanceTo(kTetra[i]);
if ( afC[i] > 0.0f )
aiP[iPositive++] = i;
else if ( afC[i] < 0.0f )
aiN[iNegative++] = i;
else
aiZ[iZero++] = i;
}
// For a split to occur, one of the c_i must be positive and one must
// be negative.
if ( iNegative == 0 )
{
// tetrahedron is completely on the positive side of plane, full clip
return;
}
if ( iPositive == 0 )
{
// tetrahedron is completely on the negative side of plane
rkInside.push_back(kTetra);
return;
}
// Tetrahedron is split by plane. Determine how it is split and how to
// decompose the negative-side portion into tetrahedra (6 cases).
Real fW0, fW1, fInvCDiff;
Vector3 akIntp[4];
if ( iPositive == 3 )
{
// +++-
for (i = 0; i < iPositive; i++)
{
fInvCDiff = 1.0f/(afC[aiP[i]] - afC[aiN[0]]);
fW0 = -afC[aiN[0]]*fInvCDiff;
fW1 = +afC[aiP[i]]*fInvCDiff;
kTetra[aiP[i]] = fW0*kTetra[aiP[i]] + fW1*kTetra[aiN[0]];
}
rkInside.push_back(kTetra);
}
else if ( iPositive == 2 )
{
if ( iNegative == 2 )
{
// ++--
for (i = 0; i < iPositive; i++)
{
fInvCDiff = 1.0f/(afC[aiP[i]]-afC[aiN[0]]);
fW0 = -afC[aiN[0]]*fInvCDiff;
fW1 = +afC[aiP[i]]*fInvCDiff;
akIntp[i] = fW0*kTetra[aiP[i]] + fW1*kTetra[aiN[0]];
}
for (i = 0; i < iNegative; i++)
{
fInvCDiff = 1.0f/(afC[aiP[i]]-afC[aiN[1]]);
fW0 = -afC[aiN[1]]*fInvCDiff;
fW1 = +afC[aiP[i]]*fInvCDiff;
akIntp[i+2] = fW0*kTetra[aiP[i]] + fW1*kTetra[aiN[1]];
}
kTetra[aiP[0]] = akIntp[2];
kTetra[aiP[1]] = akIntp[1];
rkInside.push_back(kTetra);
rkInside.push_back(Tetrahedron(kTetra[aiN[1]],akIntp[3],akIntp[2],
akIntp[1]));
rkInside.push_back(Tetrahedron(kTetra[aiN[0]],akIntp[0],akIntp[1],
akIntp[2]));
}
else
{
// ++-0
for (i = 0; i < iPositive; i++)
{
fInvCDiff = 1.0f/(afC[aiP[i]]-afC[aiN[0]]);
fW0 = -afC[aiN[0]]*fInvCDiff;
fW1 = +afC[aiP[i]]*fInvCDiff;
kTetra[aiP[i]] = fW0*kTetra[aiP[i]] + fW1*kTetra[aiN[0]];
}
rkInside.push_back(kTetra);
}
}
else if ( iPositive == 1 )
{
if ( iNegative == 3 )
{
// +---
for (i = 0; i < iNegative; i++)
{
fInvCDiff = 1.0f/(afC[aiP[0]]-afC[aiN[i]]);
fW0 = -afC[aiN[i]]*fInvCDiff;
fW1 = +afC[aiP[0]]*fInvCDiff;
akIntp[i] = fW0*kTetra[aiP[0]] + fW1*kTetra[aiN[i]];
}
kTetra[aiP[0]] = akIntp[0];
rkInside.push_back(kTetra);
rkInside.push_back(Tetrahedron(akIntp[0],kTetra[aiN[1]],
kTetra[aiN[2]],akIntp[1]));
rkInside.push_back(Tetrahedron(kTetra[aiN[2]],akIntp[1],akIntp[2],
akIntp[0]));
}
else if ( iNegative == 2 )
{
// +--0
for (i = 0; i < iNegative; i++)
{
fInvCDiff = 1.0f/(afC[aiP[0]]-afC[aiN[i]]);
fW0 = -afC[aiN[i]]*fInvCDiff;
fW1 = +afC[aiP[0]]*fInvCDiff;
akIntp[i] = fW0*kTetra[aiP[0]] + fW1*kTetra[aiN[i]];
}
kTetra[aiP[0]] = akIntp[0];
rkInside.push_back(kTetra);
rkInside.push_back(Tetrahedron(akIntp[1],kTetra[aiZ[0]],
kTetra[aiN[1]],akIntp[0]));
}
else
{
// +-00
fInvCDiff = 1.0f/(afC[aiP[0]]-afC[aiN[0]]);
fW0 = -afC[aiN[0]]*fInvCDiff;
fW1 = +afC[aiP[0]]*fInvCDiff;
kTetra[aiP[0]] = fW0*kTetra[aiP[0]] + fW1*kTetra[aiN[0]];
rkInside.push_back(kTetra);
}
}
}
//----------------------------------------------------------------------------
int ConvexClipper::Clip (const Plane& rkPlane)
{
// compute signed distances from vertices to plane
int iPositive = 0, iNegative = 0;
for (int iV = 0; iV < (int)m_akVertex.size(); iV++)
{
Vertex& rkV = m_akVertex[iV];
if ( rkV.m_bVisible )
{
rkV.m_fDistance = rkPlane.DistanceTo(rkV.m_kPoint);
if ( rkV.m_fDistance >= m_fEpsilon )
{
iPositive++;
}
else if ( rkV.m_fDistance <= -m_fEpsilon )
{
iNegative++;
rkV.m_bVisible = false;
}
else
{
// The point is on the plane (within floating point
// tolerance).
rkV.m_fDistance = 0.0f;
}
}
}
if ( iPositive == 0 )
{
// mesh is in negative half-space, fully clipped
return Plane::NEGATIVE_SIDE;
}
if ( iNegative == 0 )
{
// mesh is in positive half-space, fully visible
return Plane::POSITIVE_SIDE;
}
// clip the visible edges
for (int iE = 0; iE < (int)m_akEdge.size(); iE++)
{
Edge& rkE = m_akEdge[iE];
if ( rkE.m_bVisible )
{
int iV0 = rkE.m_aiVertex[0], iV1 = rkE.m_aiVertex[1];
int iF0 = rkE.m_aiFace[0], iF1 = rkE.m_aiFace[1];
Face& rkF0 = m_akFace[iF0];
Face& rkF1 = m_akFace[iF1];
Real fD0 = m_akVertex[iV0].m_fDistance;
Real fD1 = m_akVertex[iV1].m_fDistance;
if ( fD0 <= 0.0f && fD1 <= 0.0f )
{
// The edge is culled. If the edge is exactly on the clip
// plane, it is possible that a visible triangle shares it.
// The edge will be re-added during the face loop.
rkF0.m_akEdge.erase(iE);
if ( rkF0.m_akEdge.empty() )
rkF0.m_bVisible = false;
rkF1.m_akEdge.erase(iE);
if ( rkF1.m_akEdge.empty() )
rkF1.m_bVisible = false;
rkE.m_bVisible = false;
continue;
}
if ( fD0 >= 0.0f && fD1 >= 0.0f )
{
// face retains the edge
continue;
}
// The edge is split by the plane. Compute the point of
// intersection. If the old edge is <V0,V1> and I is the
// intersection point, the new edge is <V0,I> when d0 > 0 or
// <I,V1> when d1 > 0.
int iNV = m_akVertex.size();
m_akVertex.push_back(Vertex());
Vertex& rkNV = m_akVertex[iNV];
Vector3& rkP0 = m_akVertex[iV0].m_kPoint;
Vector3& rkP1 = m_akVertex[iV1].m_kPoint;
rkNV.m_kPoint = rkP0+(fD0/(fD0-fD1))*(rkP1-rkP0);
if ( fD0 > 0.0f )
rkE.m_aiVertex[1] = iNV;
else
rkE.m_aiVertex[0] = iNV;
}
}
// The mesh straddles the plane. A new convex polygonal face will be
// generated. Add it now and insert edges when they are visited.
int iNF = m_akFace.size();
m_akFace.push_back(Face());
Face& rkNF = m_akFace[iNF];
rkNF.m_kPlane = rkPlane;
// process the faces
for (int iF = 0; iF < iNF; iF++)
{
Face& rkF = m_akFace[iF];
if ( rkF.m_bVisible )
{
// Determine if the face is on the negative side, the positive
// side, or split by the clipping plane. The m_iOccurs members
// are set to zero to help find the end points of the polyline
// that results from clipping a face.
assert( rkF.m_akEdge.size() >= 2 );
set<int>::iterator pkIter = rkF.m_akEdge.begin();
while ( pkIter != rkF.m_akEdge.end() )
{
int iE = *pkIter++;
Edge& rkE = m_akEdge[iE];
assert( rkE.m_bVisible );
m_akVertex[rkE.m_aiVertex[0]].m_iOccurs = 0;
m_akVertex[rkE.m_aiVertex[1]].m_iOccurs = 0;
}
int iVStart, iVFinal;
if ( GetOpenPolyline(rkF,iVStart,iVFinal) )
{
// polyline is open, close it up
int iNE = m_akEdge.size();
m_akEdge.push_back(Edge());
Edge& rkNE = m_akEdge[iNE];
rkNE.m_aiVertex[0] = iVStart;
rkNE.m_aiVertex[1] = iVFinal;
rkNE.m_aiFace[0] = iF;
rkNE.m_aiFace[1] = iNF;
// add new edge to polygons
rkF.m_akEdge.insert(iNE);
rkNF.m_akEdge.insert(iNE);
}
}
}
// Process face rkNF to make sure it is a simple polygon (theoretically
// convex, but numerically may be slightly not convex). Floating point
// round-off errors can cause the new face from the last loop to be
// needle-like with a collapse of two edges into a single edge. This
// block guarantees the invariant "face always a simple polygon".
PostProcess(iNF,rkNF);
int iESize = rkNF.m_akEdge.size();
if ( iESize < 3 )
{
// face is completely degenerate, remove it from mesh
m_akFace.pop_back();
}
return Plane::NO_SIDE;
}