void ConvexPolyhedron3<Real>::Create (const V3Array& rakPoint,
const IArray& raiConnect)
{
assert( rakPoint.size() >= 4 && raiConnect.size() >= 4 );
int iVQuantity = (int)rakPoint.size();
int iTQuantity = (int)raiConnect.size()/3;
int iEQuantity = iVQuantity + iTQuantity - 2;
Reset(iVQuantity,iEQuantity,iTQuantity);
m_akPoint = rakPoint;
// Copy polyhedron points into vertex array. Compute centroid for use in
// making sure the triangles are counterclockwise oriented when viewed
// from the outside.
ComputeCentroid();
// get polyhedron edge and triangle information
for (int iT = 0, iIndex = 0; iT < iTQuantity; iT++)
{
// get vertex indices for triangle
int iV0 = raiConnect[iIndex++];
int iV1 = raiConnect[iIndex++];
int iV2 = raiConnect[iIndex++];
// make sure triangle is counterclockwise
Vector3<Real>& rkV0 = m_akPoint[iV0];
Vector3<Real>& rkV1 = m_akPoint[iV1];
Vector3<Real>& rkV2 = m_akPoint[iV2];
Vector3<Real> kDiff = m_kCentroid - rkV0;
Vector3<Real> kE1 = rkV1 - rkV0;
Vector3<Real> kE2 = rkV2 - rkV0;
Vector3<Real> kNormal = kE1.Cross(kE2);
Real fLength = kNormal.Length();
if ( fLength > Math<Real>::EPSILON )
{
kNormal /= fLength;
}
else
{
kNormal = kDiff;
kNormal.Normalize();
}
Real fDistance = kNormal.Dot(kDiff);
if ( fDistance < (Real)0.0 )
{
// triangle is counterclockwise
Insert(iV0,iV1,iV2);
}
else
{
// triangle is clockwise
Insert(iV0,iV2,iV1);
}
}
UpdatePlanes();
}
//----------------------------------------------------------------------------
void ExtractTrilinear::MakeUnique (V3Array& rkVA, T3Array& rkTA)
{
int iVQuantity = (int)rkVA.size(), iTQuantity = (int)rkTA.size();
if ( iVQuantity == 0 || iTQuantity == 0 )
return;
// use a hash table to generate unique storage
V3Map kVMap;
V3MapIterator pkVIter;
for (int iV = 0, iNextVertex = 0; iV < iVQuantity; iV++)
{
// keep only unique vertices
pair<V3MapIterator,bool> kResult = kVMap.insert(
make_pair(rkVA[iV],iNextVertex));
if ( kResult.second == true )
iNextVertex++;
}
// use a hash table to generate unique storage
T3Map kTMap;
T3MapIterator pkTIter;
for (int iT = 0, iNextTriangle = 0; iT < iTQuantity; iT++)
{
// replace old vertex indices by new ones
Triangle3& rkTri = rkTA[iT];
pkVIter = kVMap.find(rkVA[rkTri.i0]);
assert( pkVIter != kVMap.end() );
rkTri.i0 = pkVIter->second;
pkVIter = kVMap.find(rkVA[rkTri.i1]);
assert( pkVIter != kVMap.end() );
rkTri.i1 = pkVIter->second;
pkVIter = kVMap.find(rkVA[rkTri.i2]);
assert( pkVIter != kVMap.end() );
rkTri.i2 = pkVIter->second;
// keep only unique triangles
pair<T3MapIterator,bool> kResult = kTMap.insert(
make_pair(rkTri,iNextTriangle));
if ( kResult.second == true )
iNextTriangle++;
}
// pack the vertices
rkVA.resize(kVMap.size());
for (pkVIter = kVMap.begin(); pkVIter != kVMap.end(); pkVIter++)
rkVA[pkVIter->second] = pkVIter->first;
// pack the triangles
rkTA.resize(kTMap.size());
for (pkTIter = kTMap.begin(); pkTIter != kTMap.end(); pkTIter++)
rkTA[pkTIter->second] = pkTIter->first;
}
bool ConvexPolyhedron3<Real>::ComputeSilhouette (V3Array& rkTerminator,
const Vector3<Real>& rkEye, const Plane3<Real>& rkPlane,
const Vector3<Real>& rkU, const Vector3<Real>& rkV,
V2Array& rkSilhouette)
{
Real fEDist = rkPlane.DistanceTo(rkEye); // assert: fEDist > 0
// closest planar point to E is K = E-dist*N
Vector3<Real> kClosest = rkEye - fEDist*rkPlane.GetNormal();
// project polyhedron points onto plane
for (int i = 0; i < (int)rkTerminator.size(); i++)
{
Vector3<Real>& 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<Real> kProjected = rkEye + fRatio*(rkPoint - rkEye);
// compute (x,y) so that Q = K+x*U+y*V+z*N
Vector3<Real> kDiff = kProjected - kClosest;
rkSilhouette.push_back(Vector2<Real>(rkU.Dot(kDiff),rkV.Dot(kDiff)));
}
return true;
}
//----------------------------------------------------------------------------
void ExtractTrilinear::ExtractContour (float fLevel, V3Array& rkVA,
T3Array& rkTA)
{
rkVA.clear();
rkTA.clear();
for (int iZ = 0; iZ < m_iZBound-1; iZ++)
{
for (int iY = 0; iY < m_iYBound-1; iY++)
{
for (int iX = 0; iX < m_iXBound-1; iX++)
{
// get vertices on edges of box (if any)
VETable kTable;
int iType = GetVertices(fLevel,iX,iY,iZ,kTable);
if ( iType != 0 )
{
// get edges on faces of box
GetXMinEdges(iX,iY,iZ,iType,kTable);
GetXMaxEdges(iX,iY,iZ,iType,kTable);
GetYMinEdges(iX,iY,iZ,iType,kTable);
GetYMaxEdges(iX,iY,iZ,iType,kTable);
GetZMinEdges(iX,iY,iZ,iType,kTable);
GetZMaxEdges(iX,iY,iZ,iType,kTable);
// ear-clip the wireframe mesh
kTable.RemoveTriangles(rkVA,rkTA);
}
}
}
}
}
//----------------------------------------------------------------------------
void VETable::RemoveTriangles (V3Array& rkVA, T3Array& rkTA)
{
// ear-clip the wireframe to get the triangles
Triangle3 kTri;
while ( Remove(kTri) )
{
int iV0 = (int)rkVA.size(), iV1 = iV0+1, iV2 = iV1+1;
rkTA.push_back(Triangle3(iV0,iV1,iV2));
const Vertex& rkV0 = m_akVertex[kTri.i0];
const Vertex& rkV1 = m_akVertex[kTri.i1];
const Vertex& rkV2 = m_akVertex[kTri.i2];
rkVA.push_back(Vertex3(rkV0.m_fX,rkV0.m_fY,rkV0.m_fZ));
rkVA.push_back(Vertex3(rkV1.m_fX,rkV1.m_fY,rkV1.m_fZ));
rkVA.push_back(Vertex3(rkV2.m_fX,rkV2.m_fY,rkV2.m_fZ));
}
}
void ConvexPolyhedron3<Real>::Create (const V3Array& rakPoint,
const IArray& raiConnect, const PArray& rakPlane)
{
assert( rakPoint.size() >= 4 && raiConnect.size() >= 4 );
int iVQuantity = (int)rakPoint.size();
int iTQuantity = (int)raiConnect.size()/3;
int iEQuantity = iVQuantity + iTQuantity - 2;
Reset(iVQuantity,iEQuantity,iTQuantity);
m_akPoint = rakPoint;
m_akPlane = rakPlane;
// Copy polyhedron points into vertex array. Compute centroid for use in
// making sure the triangles are counterclockwise oriented when viewed
// from the outside.
ComputeCentroid();
// get polyhedron edge and triangle information
for (int iT = 0, iIndex = 0; iT < iTQuantity; iT++)
{
// get vertex indices for triangle
int iV0 = raiConnect[iIndex++];
int iV1 = raiConnect[iIndex++];
int iV2 = raiConnect[iIndex++];
Real fDistance = m_akPlane[iT].DistanceTo(m_kCentroid);
if ( fDistance > (Real)0.0 )
{
// triangle is counterclockwise
Insert(iV0,iV1,iV2);
}
else
{
// triangle is clockwise
Insert(iV0,iV2,iV1);
}
}
}
void ConvexPolyhedron3<Real>::ComputeTerminator (const Vector3<Real>& rkEye,
V3Array& rkTerminator)
{
// temporary storage for signed distances from eye to triangles
int iTQuantity = m_akTriangle.GetQuantity();
vector<Real> afDistance(iTQuantity);
int i, j;
for (i = 0; i < iTQuantity; i++)
afDistance[i] = Math<Real>::MAX_REAL;
// Start a search for a front-facing triangle that has an adjacent
// back-facing triangle or for a back-facing triangle that has an
// adjacent front-facing triangle.
int iTCurrent = 0;
MTTriangle* pkTCurrent = &m_akTriangle[iTCurrent];
Real fTriDist = GetDistance(rkEye,iTCurrent,afDistance);
int iEFirst = -1;
for (i = 0; i < iTQuantity; i++)
{
// Check adjacent neighbors for edge of terminator. Such an
// edge occurs if the signed distance changes sign.
int iMinIndex = -1;
Real fMinAbsDist = Math<Real>::MAX_REAL;
Real afAdjDist[3];
for (j = 0; j < 3; j++)
{
afAdjDist[j] = GetDistance(rkEye,pkTCurrent->Adjacent(j),
afDistance);
if ( IsNegativeProduct(fTriDist,afAdjDist[j]) )
{
iEFirst = pkTCurrent->Edge(j);
break;
}
Real fAbsDist = Math<Real>::FAbs(afAdjDist[j]);
if ( fAbsDist < fMinAbsDist )
{
fMinAbsDist = fAbsDist;
iMinIndex = j;
}
}
if ( j < 3 )
break;
// First edge not found during this iteration. Move to adjacent
// triangle whose distance is smallest of all adjacent triangles.
iTCurrent = pkTCurrent->Adjacent(iMinIndex);
pkTCurrent = &m_akTriangle[iTCurrent];
fTriDist = afAdjDist[iMinIndex];
}
assert( i < iTQuantity );
MTEdge& rkEFirst = m_akEdge[iEFirst];
rkTerminator.push_back(m_akPoint[GetVLabel(rkEFirst.Vertex(0))]);
rkTerminator.push_back(m_akPoint[GetVLabel(rkEFirst.Vertex(1))]);
// walk along the terminator
int iVFirst = rkEFirst.Vertex(0);
int iV = rkEFirst.Vertex(1);
int iE = iEFirst;
int iEQuantity = m_akEdge.GetQuantity();
for (i = 0; i < iEQuantity; i++)
{
// search all edges sharing the vertex for another terminator edge
int j, jMax = m_akVertex[iV].GetEdgeQuantity();
for (j = 0; j < m_akVertex[iV].GetEdgeQuantity(); j++)
{
int iENext = m_akVertex[iV].GetEdge(j);
if ( iENext == iE )
continue;
Real fDist0 = GetDistance(rkEye,m_akEdge[iENext].GetTriangle(0),
afDistance);
Real fDist1 = GetDistance(rkEye,m_akEdge[iENext].GetTriangle(1),
afDistance);
if ( IsNegativeProduct(fDist0,fDist1) )
{
if ( m_akEdge[iENext].GetVertex(0) == iV )
{
iV = m_akEdge[iENext].GetVertex(1);
rkTerminator.push_back(m_akPoint[GetVLabel(iV)]);
if ( iV == iVFirst )
return;
}
else
{
iV = m_akEdge[iENext].GetVertex(0);
rkTerminator.push_back(m_akPoint[GetVLabel(iV)]);
if ( iV == iVFirst )
return;
}
iE = iENext;
break;
}
}
assert( j < jMax );
}
assert( i < iEQuantity );
}
//----------------------------------------------------------------------------
void ExtractTrilinear::ComputeNormals (const V3Array& rkVA,
const T3Array& rkTA, V3Array& rkNA)
{
// maintain a running sum of triangle normals at each vertex
int iVQuantity = (int)rkVA.size(), iTQuantity = (int)rkTA.size();
rkNA.resize(iVQuantity);
int i, j;
for (i = 0; i < iVQuantity; i++)
{
rkNA[i].x = 0.0f;
rkNA[i].y = 0.0f;
rkNA[i].z = 0.0f;
}
for (i = 0, j = 0; i < iTQuantity; i++)
{
const Triangle3& rkT = rkTA[i];
Vertex3 kV0 = rkVA[rkT.i0];
Vertex3 kV1 = rkVA[rkT.i1];
Vertex3 kV2 = rkVA[rkT.i2];
// construct triangle normal
float fEX1 = kV1.x - kV0.x;
float fEY1 = kV1.y - kV0.y;
float fEZ1 = kV1.z - kV0.z;
float fEX2 = kV2.x - kV0.x;
float fEY2 = kV2.y - kV0.y;
float fEZ2 = kV2.z - kV0.z;
float fNX = fEY1*fEZ2 - fEY2*fEZ1;
float fNY = fEZ1*fEX2 - fEZ2*fEX1;
float fNZ = fEX1*fEY2 - fEX2*fEY1;
// maintain the sum of normals at each vertex
rkNA[rkT.i0].x += fNX;
rkNA[rkT.i0].y += fNY;
rkNA[rkT.i0].z += fNZ;
rkNA[rkT.i1].x += fNX;
rkNA[rkT.i1].y += fNY;
rkNA[rkT.i1].z += fNZ;
rkNA[rkT.i2].x += fNX;
rkNA[rkT.i2].y += fNY;
rkNA[rkT.i2].z += fNZ;
}
// The normal vector storage was used to accumulate the sum of
// triangle normals. Now these vectors must be rescaled to be
// unit length.
for (i = 0; i < iVQuantity; i++)
{
Vertex3& rkV = rkNA[i];
float fLength = sqrtf(rkV.x*rkV.x + rkV.y*rkV.y + rkV.z*rkV.z);
if ( fLength > 1e-08f )
{
float fInvLength = 1.0f/fLength;
rkV.x *= fInvLength;
rkV.y *= fInvLength;
rkV.z *= fInvLength;
}
else
{
rkV.x = 0.0f;
rkV.y = 0.0f;
rkV.z = 0.0f;
}
}
}