Changes in src/tesselation.cpp [b998c3:fad93c]

File:

• src/tesselation.cpp (modified) (19 diffs)

src/tesselation.cpp

@@ -879 +879 @@
 CandidateForTesselation::CandidateForTesselation (TesselPoint *candidate, BoundaryLineSet* line, Vector OptCandidateCenter, Vector OtherOptCandidateCenter) :
     BaseLine(line),
-    IsDegenerated(false),
     ShortestAngle(2.*M_PI),
     OtherShortestAngle(2.*M_PI)
@@ -1588 +1587 @@
   bool insertNewLine = true;
 
-  LineMap::iterator FindLine = a->lines.find(b->node->nr);
-  if (FindLine != a->lines.end()) {
-    Log() << Verbose(1) << "INFO: There is at least one line between " << *a << " and " << *b << ": " << *(FindLine->second) << "." << endl;
-
+  if (a->lines.find(b->node->nr) != a->lines.end()) {
+    LineMap::iterator FindLine = a->lines.find(b->node->nr);
     pair<LineMap::iterator,LineMap::iterator> FindPair;
     FindPair = a->lines.equal_range(b->node->nr);
+    Log() << Verbose(1) << "INFO: There is at least one line between " << *a << " and " << *b << ": " << *(FindLine->second) << "." << endl;
 
     for (FindLine = FindPair.first; FindLine != FindPair.second; FindLine++) {
@@ -1917 +1915 @@
   double maxCoordinate[NDIM];
   BoundaryLineSet BaseLine;
+  Vector Oben;
   Vector helper;
   Vector Chord;
   Vector SearchDirection;
-  Vector CircleCenter;  // center of the circle, i.e. of the band of sphere's centers
-  Vector CirclePlaneNormal; // normal vector defining the plane this circle lives in
-  Vector SphereCenter;
-  Vector NormalVector;
-
-  NormalVector.Zero();
+
+  Oben.Zero();
 
   for (i = 0; i < 3; i++) {
@@ -1960 +1955 @@
   BTS = NULL;
   for (int k=0;k<NDIM;k++) {
-    NormalVector.Zero();
-    NormalVector.x[k] = 1.;
+    Oben.Zero();
+    Oben.x[k] = 1.;
     BaseLine.endpoints[0] = new BoundaryPointSet(MaxPoint[k]);
     Log() << Verbose(0) << "Coordinates of start node at " << *BaseLine.endpoints[0]->node << "." << endl;
@@ -1968 +1963 @@
     ShortestAngle = 999999.; // This will contain the angle, which will be always positive (when looking for second point), when looking for third point this will be the quadrant.
 
-    FindSecondPointForTesselation(BaseLine.endpoints[0]->node, NormalVector, Temporary, &ShortestAngle, RADIUS, LC); // we give same point as next candidate as its bonds are looked into in find_second_...
+    FindSecondPointForTesselation(BaseLine.endpoints[0]->node, Oben, Temporary, &ShortestAngle, RADIUS, LC); // we give same point as next candidate as its bonds are looked into in find_second_...
     if (Temporary == NULL)  // have we found a second point?
       continue;
     BaseLine.endpoints[1] = new BoundaryPointSet(Temporary);
 
-    // construct center of circle
-    CircleCenter.CopyVector(BaseLine.endpoints[0]->node->node);
-    CircleCenter.AddVector(BaseLine.endpoints[1]->node->node);
-    CircleCenter.Scale(0.5);
-
-    // construct normal vector of circle
-    CirclePlaneNormal.CopyVector(BaseLine.endpoints[0]->node->node);
-    CirclePlaneNormal.SubtractVector(BaseLine.endpoints[1]->node->node);
-
-    double radius = CirclePlaneNormal.NormSquared();
+    helper.CopyVector(BaseLine.endpoints[0]->node->node);
+    helper.SubtractVector(BaseLine.endpoints[1]->node->node);
+    helper.Normalize();
+    Oben.ProjectOntoPlane(&helper);
+    Oben.Normalize();
+    helper.VectorProduct(&Oben);
+    ShortestAngle = 2.*M_PI; // This will indicate the quadrant.
+
+    Chord.CopyVector(BaseLine.endpoints[0]->node->node); // bring into calling function
+    Chord.SubtractVector(BaseLine.endpoints[1]->node->node);
+    double radius = Chord.ScalarProduct(&Chord);
     double CircleRadius = sqrt(RADIUS*RADIUS - radius/4.);
-
-    NormalVector.ProjectOntoPlane(&CirclePlaneNormal);
-    NormalVector.Normalize();
-    ShortestAngle = 2.*M_PI; // This will indicate the quadrant.
-
-    SphereCenter.CopyVector(&NormalVector);
-    SphereCenter.Scale(CircleRadius);
-    SphereCenter.AddVector(&CircleCenter);
-    // Now, NormalVector and SphereCenter are two orthonormalized vectors in the plane defined by CirclePlaneNormal (not normalized)
+    helper.CopyVector(&Oben);
+    helper.Scale(CircleRadius);
+    // Now, oben and helper are two orthonormalized vectors in the plane defined by Chord (not normalized)
 
     // look in one direction of baseline for initial candidate
-    SearchDirection.MakeNormalVector(&CirclePlaneNormal, &NormalVector);  // whether we look "left" first or "right" first is not important ...
+    SearchDirection.MakeNormalVector(&Chord, &Oben);  // whether we look "left" first or "right" first is not important ...
 
     // adding point 1 and point 2 and add the line between them
@@ -2003 +1993 @@
     //Log() << Verbose(1) << "INFO: OldSphereCenter is at " << helper << ".\n";
     CandidateForTesselation OptCandidates(&BaseLine);
-    FindThirdPointForTesselation(NormalVector, SearchDirection, SphereCenter, OptCandidates, NULL, RADIUS, LC);
+    FindThirdPointForTesselation(Oben, SearchDirection, helper, OptCandidates, NULL, RADIUS, LC);
     Log() << Verbose(0) << "List of third Points is:" << endl;
     for (TesselPointList::iterator it = OptCandidates.pointlist.begin(); it != OptCandidates.pointlist.end(); it++) {
@@ -2177 +2167 @@
   Vector CircleCenter;
   Vector CirclePlaneNormal;
-  Vector RelativeSphereCenter;
+  Vector OldSphereCenter;
   Vector SearchDirection;
   Vector helper;
@@ -2184 +2174 @@
   double radius, CircleRadius;
 
+  Log() << Verbose(0) << "Current baseline is " << *CandidateLine.BaseLine << " of triangle " << T << "." << endl;
   for (int i=0;i<3;i++)
-    if ((T.endpoints[i]->node != CandidateLine.BaseLine->endpoints[0]->node) && (T.endpoints[i]->node != CandidateLine.BaseLine->endpoints[1]->node)) {
+    if ((T.endpoints[i]->node != CandidateLine.BaseLine->endpoints[0]->node) && (T.endpoints[i]->node != CandidateLine.BaseLine->endpoints[1]->node))
       ThirdNode = T.endpoints[i]->node;
-      break;
-    }
-  Log() << Verbose(0) << "Current baseline is " << *CandidateLine.BaseLine << " with ThirdNode " << *ThirdNode << " of triangle " << T << "." << endl;
 
   // construct center of circle
@@ -2203 +2191 @@
   radius = CirclePlaneNormal.ScalarProduct(&CirclePlaneNormal);
   if (radius/4. < RADIUS*RADIUS) {
-    // construct relative sphere center with now known CircleCenter
-    RelativeSphereCenter.CopyVector(&T.SphereCenter);
-    RelativeSphereCenter.SubtractVector(&CircleCenter);
-
     CircleRadius = RADIUS*RADIUS - radius/4.;
     CirclePlaneNormal.Normalize();
     Log() << Verbose(1) << "INFO: CircleCenter is at " << CircleCenter << ", CirclePlaneNormal is " << CirclePlaneNormal << " with circle radius " << sqrt(CircleRadius) << "." << endl;
 
-    Log() << Verbose(1) << "INFO: OldSphereCenter is at " << T.SphereCenter << "." << endl;
-
-    // construct SearchDirection and an "outward pointer"
-    SearchDirection.MakeNormalVector(&RelativeSphereCenter, &CirclePlaneNormal);
-    helper.CopyVector(&CircleCenter);
+    // construct old center
+    GetCenterofCircumcircle(&OldSphereCenter, *T.endpoints[0]->node->node, *T.endpoints[1]->node->node, *T.endpoints[2]->node->node);
+    helper.CopyVector(&T.NormalVector);  // normal vector ensures that this is correct center of the two possible ones
+    radius = CandidateLine.BaseLine->endpoints[0]->node->node->DistanceSquared(&OldSphereCenter);
+    helper.Scale(sqrt(RADIUS*RADIUS - radius));
+    OldSphereCenter.AddVector(&helper);
+    OldSphereCenter.SubtractVector(&CircleCenter);
+    Log() << Verbose(1) << "INFO: OldSphereCenter is at " << OldSphereCenter << "." << endl;
+
+    // construct SearchDirection
+    SearchDirection.MakeNormalVector(&T.NormalVector, &CirclePlaneNormal);
+    helper.CopyVector(CandidateLine.BaseLine->endpoints[0]->node->node);
     helper.SubtractVector(ThirdNode->node);
     if (helper.ScalarProduct(&SearchDirection) < -HULLEPSILON)// ohoh, SearchDirection points inwards!
       SearchDirection.Scale(-1.);
+    SearchDirection.ProjectOntoPlane(&OldSphereCenter);
+    SearchDirection.Normalize();
     Log() << Verbose(1) << "INFO: SearchDirection is " << SearchDirection << "." << endl;
-    if (fabs(RelativeSphereCenter.ScalarProduct(&SearchDirection)) > HULLEPSILON) {
+    if (fabs(OldSphereCenter.ScalarProduct(&SearchDirection)) > HULLEPSILON) {
       // rotated the wrong way!
       eLog() << Verbose(1) << "SearchDirection and RelativeOldSphereCenter are still not orthogonal!" << endl;
@@ -2226 +2219 @@
 
     // add third point
-    FindThirdPointForTesselation(T.NormalVector, SearchDirection, T.SphereCenter, CandidateLine, ThirdNode, RADIUS, LC);
+    FindThirdPointForTesselation(T.NormalVector, SearchDirection, OldSphereCenter, CandidateLine, ThirdNode, RADIUS, LC);
 
   } else {
@@ -2357 +2350 @@
     AddTesselationPoint((*Sprinter), 2);
 
-
+    Center.CopyVector(&CandidateLine.OptCenter);
     // add the lines
     AddTesselationLine(TPS[0], TPS[1], 0);
@@ -2366 +2359 @@
     BTS = new class BoundaryTriangleSet(BLS, TrianglesOnBoundaryCount);
     AddTesselationTriangle();
-    BTS->GetCenter(&Center);
-    Center.SubtractVector(&CandidateLine.OptCenter);
-    BTS->SphereCenter.CopyVector(&CandidateLine.OptCenter);
+    Center.Scale(-1.);
     BTS->GetNormalVector(Center);
 
@@ -2775 +2766 @@
   Vector NewNormalVector;   // normal vector of the Candidate's triangle
   Vector helper, OptCandidateCenter, OtherOptCandidateCenter;
-  Vector RelativeOldSphereCenter;
-  Vector NewPlaneCenter;
   double CircleRadius; // radius of this circle
   double radius;
-  double otherradius;
   double alpha, Otheralpha; // angles (i.e. parameter for the circle).
-  bool IsDegenerated;
   int N[NDIM], Nlower[NDIM], Nupper[NDIM];
   TesselPoint *Candidate = NULL;
-  TesselPoint *CandidateTriangle[3];
 
   Log() << Verbose(1) << "INFO: NormalVector of BaseTriangle is " << NormalVector << "." << endl;
@@ -2797 +2783 @@
   CirclePlaneNormal.SubtractVector(CandidateLine.BaseLine->endpoints[1]->node->node);
 
-  RelativeOldSphereCenter.CopyVector(&OldSphereCenter);
-  RelativeOldSphereCenter.SubtractVector(&CircleCenter);
-
-  CandidateTriangle[0] = CandidateLine.BaseLine->endpoints[0]->node;
-  CandidateTriangle[1] = CandidateLine.BaseLine->endpoints[1]->node;
-
   // calculate squared radius TesselPoint *ThirdNode,f circle
-  radius = CirclePlaneNormal.NormSquared()/4.;
-  if (radius < RADIUS*RADIUS) {
-    CircleRadius = RADIUS*RADIUS - radius;
+  radius = CirclePlaneNormal.ScalarProduct(&CirclePlaneNormal);
+  if (radius/4. < RADIUS*RADIUS) {
+    CircleRadius = RADIUS*RADIUS - radius/4.;
     CirclePlaneNormal.Normalize();
-    Log() << Verbose(1) << "INFO: CircleCenter is at " << CircleCenter << ", CirclePlaneNormal is " << CirclePlaneNormal << " with circle radius " << sqrt(CircleRadius) << "." << endl;
+    //Log() << Verbose(1) << "INFO: CircleCenter is at " << CircleCenter << ", CirclePlaneNormal is " << CirclePlaneNormal << " with circle radius " << sqrt(CircleRadius) << "." << endl;
 
     // test whether old center is on the band's plane
-    if (fabs(RelativeOldSphereCenter.ScalarProduct(&CirclePlaneNormal)) > HULLEPSILON) {
-      eLog() << Verbose(1) << "Something's very wrong here: RelativeOldSphereCenter is not on the band's plane as desired by " << fabs(RelativeOldSphereCenter.ScalarProduct(&CirclePlaneNormal)) << "!" << endl;
-      RelativeOldSphereCenter.ProjectOntoPlane(&CirclePlaneNormal);
-    }
-    radius = RelativeOldSphereCenter.NormSquared();
+    if (fabs(OldSphereCenter.ScalarProduct(&CirclePlaneNormal)) > HULLEPSILON) {
+      eLog() << Verbose(1) << "Something's very wrong here: OldSphereCenter is not on the band's plane as desired by " << fabs(OldSphereCenter.ScalarProduct(&CirclePlaneNormal)) << "!" << endl;
+      OldSphereCenter.ProjectOntoPlane(&CirclePlaneNormal);
+    }
+    radius = OldSphereCenter.ScalarProduct(&OldSphereCenter);
     if (fabs(radius - CircleRadius) < HULLEPSILON) {
-      Log() << Verbose(1) << "INFO: RelativeOldSphereCenter is at " << RelativeOldSphereCenter << "." << endl;
+      //Log() << Verbose(1) << "INFO: OldSphereCenter is at " << OldSphereCenter << "." << endl;
 
       // check SearchDirection
-      Log() << Verbose(1) << "INFO: SearchDirection is " << SearchDirection << "." << endl;
-      if (fabs(RelativeOldSphereCenter.ScalarProduct(&SearchDirection)) > HULLEPSILON) {  // rotated the wrong way!
+      //Log() << Verbose(1) << "INFO: SearchDirection is " << SearchDirection << "." << endl;
+      if (fabs(OldSphereCenter.ScalarProduct(&SearchDirection)) > HULLEPSILON) {  // rotated the wrong way!
         eLog() << Verbose(1) << "SearchDirection and RelativeOldSphereCenter are not orthogonal!" << endl;
       }
@@ -2852 +2832 @@
 
                 // check for three unique points
-                Log() << Verbose(2) << "INFO: Current Candidate is " << *Candidate << " for BaseLine " << *CandidateLine.BaseLine << " with OldSphereCenter " << OldSphereCenter << "." << endl;
+                Log() << Verbose(2) << "INFO: Current Candidate is " << *Candidate << " at " << *(Candidate->node) << "." << endl;
                 if ((Candidate != CandidateLine.BaseLine->endpoints[0]->node) && (Candidate != CandidateLine.BaseLine->endpoints[1]->node) ){
 
-                  // find center on the plane
-                  GetCenterofCircumcircle(&NewPlaneCenter, *CandidateLine.BaseLine->endpoints[0]->node->node, *CandidateLine.BaseLine->endpoints[1]->node->node, *Candidate->node);
-                  Log() << Verbose(1) << "INFO: NewPlaneCenter is " << NewPlaneCenter << "." << endl;
+                  // construct both new centers
+                  GetCenterofCircumcircle(&NewSphereCenter, *CandidateLine.BaseLine->endpoints[0]->node->node, *CandidateLine.BaseLine->endpoints[1]->node->node, *Candidate->node);
+                  OtherNewSphereCenter.CopyVector(&NewSphereCenter);
 
                   if ((NewNormalVector.MakeNormalVector(CandidateLine.BaseLine->endpoints[0]->node->node, CandidateLine.BaseLine->endpoints[1]->node->node, Candidate->node))
-                  && (fabs(NewNormalVector.NormSquared()) > HULLEPSILON)
+                  && (fabs(NewNormalVector.ScalarProduct(&NewNormalVector)) > HULLEPSILON)
                   ) {
+                    helper.CopyVector(&NewNormalVector);
                     Log() << Verbose(1) << "INFO: NewNormalVector is " << NewNormalVector << "." << endl;
-                    radius = CandidateLine.BaseLine->endpoints[0]->node->node->DistanceSquared(&NewPlaneCenter);
-                    Log() << Verbose(1) << "INFO: CircleCenter is at " << CircleCenter << ", CirclePlaneNormal is " << CirclePlaneNormal << " with circle radius " << sqrt(CircleRadius) << "." << endl;
-                    Log() << Verbose(1) << "INFO: SearchDirection is " << SearchDirection << "." << endl;
-                    Log() << Verbose(1) << "INFO: Radius of CircumCenterCircle is " << radius << "." << endl;
+                    radius = CandidateLine.BaseLine->endpoints[0]->node->node->DistanceSquared(&NewSphereCenter);
                     if (radius < RADIUS*RADIUS) {
-                      otherradius = CandidateLine.BaseLine->endpoints[1]->node->node->DistanceSquared(&NewPlaneCenter);
-                      if (fabs(radius - otherradius) > HULLEPSILON) {
-                        eLog() << Verbose(1) << "Distance to center of circumcircle is not the same from each corner of the triangle: " << fabs(radius-otherradius) << endl;
-                      }
-                      // construct both new centers
-                      NewSphereCenter.CopyVector(&NewPlaneCenter);
-                      OtherNewSphereCenter.CopyVector(&NewPlaneCenter);
-                      helper.CopyVector(&NewNormalVector);
                       helper.Scale(sqrt(RADIUS*RADIUS - radius));
-                      Log() << Verbose(2) << "INFO: Distance of NewPlaneCenter " << NewPlaneCenter << " to either NewSphereCenter is " << helper.Norm() << " of vector " << helper << " with sphere radius " << RADIUS << "." << endl;
+                      Log() << Verbose(2) << "INFO: Distance of NewCircleCenter to NewSphereCenter is " << helper.Norm() << " with sphere radius " << RADIUS << "." << endl;
                       NewSphereCenter.AddVector(&helper);
+                      NewSphereCenter.SubtractVector(&CircleCenter);
                       Log() << Verbose(2) << "INFO: NewSphereCenter is at " << NewSphereCenter << "." << endl;
+
                       // OtherNewSphereCenter is created by the same vector just in the other direction
                       helper.Scale(-1.);
                       OtherNewSphereCenter.AddVector(&helper);
+                      OtherNewSphereCenter.SubtractVector(&CircleCenter);
                       Log() << Verbose(2) << "INFO: OtherNewSphereCenter is at " << OtherNewSphereCenter << "." << endl;
 
@@ -2888 +2861 @@
                       Otheralpha = GetPathLengthonCircumCircle(CircleCenter, CirclePlaneNormal, CircleRadius, OtherNewSphereCenter, OldSphereCenter, NormalVector, SearchDirection);
                       alpha = min(alpha, Otheralpha);
-
-                      CandidateTriangle[2] = Candidate;
-                      // the idea of the IsDegenerated flag is not to put a penalty on degenerated triangles, but to push them to the
-                      // very end of the Tesselation::OpenLines list.
-                      IsDegenerated = (CheckPresenceOfTriangle(CandidateTriangle) >= 3);
-                      if (!IsDegenerated && CandidateLine.IsDegenerated) {  // if current is not, but old one was, comparison would be unfair
-                        // if there is a better candidate, drop the current list and add the new candidate
-                        // otherwise ignore the new candidate and keep the list
-                        if (CandidateLine.ShortestAngle-2.*M_PI > (alpha - HULLEPSILON)) {
-                          if (fabs(alpha - Otheralpha) > MYEPSILON) {
-                            CandidateLine.OptCenter.CopyVector(&NewSphereCenter);
-                            CandidateLine.OtherOptCenter.CopyVector(&OtherNewSphereCenter);
-                          } else {
-                            CandidateLine.OptCenter.CopyVector(&OtherNewSphereCenter);
-                            CandidateLine.OtherOptCenter.CopyVector(&NewSphereCenter);
-                          }
-                          // if there is an equal candidate, add it to the list without clearing the list
-                          if ((CandidateLine.ShortestAngle-2.*M_PI - HULLEPSILON) < alpha) {
-                            CandidateLine.pointlist.push_back(Candidate);
-                            Log() << Verbose(0) << "ACCEPT: We have found an equally good candidate: " << *(Candidate) << " with "
-                              << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
-                          } else {
-                            // remove all candidates from the list and then the list itself
-                            CandidateLine.pointlist.clear();
-                            CandidateLine.pointlist.push_back(Candidate);
-                            Log() << Verbose(0) << "ACCEPT: We have found a better candidate: " << *(Candidate) << " with "
-                              << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
-                          }
-                          CandidateLine.ShortestAngle = alpha;
-                          CandidateLine.IsDegenerated = IsDegenerated;
-                          if (IsDegenerated)
-                            CandidateLine.ShortestAngle += 2.*M_PI;
-                          Log() << Verbose(0) << "INFO: There are " << CandidateLine.pointlist.size() << " candidates in the list now." << endl;
+                      // if there is a better candidate, drop the current list and add the new candidate
+                      // otherwise ignore the new candidate and keep the list
+                      if (CandidateLine.ShortestAngle > (alpha - HULLEPSILON)) {
+                        if (fabs(alpha - Otheralpha) > MYEPSILON) {
+                          CandidateLine.OptCenter.CopyVector(&NewSphereCenter);
+                          CandidateLine.OtherOptCenter.CopyVector(&OtherNewSphereCenter);
                         } else {
-                          if ((Candidate != NULL) && (CandidateLine.pointlist.begin() != CandidateLine.pointlist.end())) {
-                            Log() << Verbose(1) << "REJECT: Old candidate " << *(Candidate) << " with " << CandidateLine.ShortestAngle << " is better than new one " << *Candidate << " with " << alpha << " ." << endl;
-                          } else {
-                            Log() << Verbose(1) << "REJECT: Candidate " << *Candidate << " with " << alpha << " was rejected." << endl;
-                          }
+                          CandidateLine.OptCenter.CopyVector(&OtherNewSphereCenter);
+                          CandidateLine.OtherOptCenter.CopyVector(&NewSphereCenter);
                         }
+                        // if there is an equal candidate, add it to the list without clearing the list
+                        if ((CandidateLine.ShortestAngle - HULLEPSILON) < alpha) {
+                          CandidateLine.pointlist.push_back(Candidate);
+                          Log() << Verbose(0) << "ACCEPT: We have found an equally good candidate: " << *(Candidate) << " with "
+                            << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
+                        } else {
+                          // remove all candidates from the list and then the list itself
+                          CandidateLine.pointlist.clear();
+                          CandidateLine.pointlist.push_back(Candidate);
+                          Log() << Verbose(0) << "ACCEPT: We have found a better candidate: " << *(Candidate) << " with "
+                            << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
+                        }
+                        CandidateLine.ShortestAngle = alpha;
+                        Log() << Verbose(0) << "INFO: There are " << CandidateLine.pointlist.size() << " candidates in the list now." << endl;
                       } else {
-                        // if there is a better candidate, drop the current list and add the new candidate
-                        // otherwise ignore the new candidate and keep the list
-                        if (CandidateLine.ShortestAngle > (alpha - HULLEPSILON)) {
-                          if (fabs(alpha - Otheralpha) > MYEPSILON) {
-                            CandidateLine.OptCenter.CopyVector(&NewSphereCenter);
-                            CandidateLine.OtherOptCenter.CopyVector(&OtherNewSphereCenter);
-                          } else {
-                            CandidateLine.OptCenter.CopyVector(&OtherNewSphereCenter);
-                            CandidateLine.OtherOptCenter.CopyVector(&NewSphereCenter);
-                          }
-                          // if there is an equal candidate, add it to the list without clearing the list
-                          if ((CandidateLine.ShortestAngle - HULLEPSILON) < alpha) {
-                            CandidateLine.pointlist.push_back(Candidate);
-                            Log() << Verbose(0) << "ACCEPT: We have found an equally good candidate: " << *(Candidate) << " with "
-                              << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
-                          } else {
-                            // remove all candidates from the list and then the list itself
-                            CandidateLine.pointlist.clear();
-                            CandidateLine.pointlist.push_back(Candidate);
-                            Log() << Verbose(0) << "ACCEPT: We have found a better candidate: " << *(Candidate) << " with "
-                              << alpha << " and circumsphere's center at " << CandidateLine.OptCenter << "." << endl;
-                          }
-                          CandidateLine.ShortestAngle = alpha;
-                          Log() << Verbose(0) << "INFO: There are " << CandidateLine.pointlist.size() << " candidates in the list now." << endl;
+                        if ((Candidate != NULL) && (CandidateLine.pointlist.begin() != CandidateLine.pointlist.end())) {
+                          Log() << Verbose(1) << "REJECT: Old candidate " << *(Candidate) << " with " << CandidateLine.ShortestAngle << " is better than new one " << *Candidate << " with " << alpha << " ." << endl;
                         } else {
-                          if ((Candidate != NULL) && (CandidateLine.pointlist.begin() != CandidateLine.pointlist.end())) {
-                            Log() << Verbose(1) << "REJECT: Old candidate " << *(Candidate) << " with " << CandidateLine.ShortestAngle << " is better than new one " << *Candidate << " with " << alpha << " ." << endl;
-                          } else {
-                            Log() << Verbose(1) << "REJECT: Candidate " << *Candidate << " with " << alpha << " was rejected." << endl;
-                          }
+                          Log() << Verbose(1) << "REJECT: Candidate " << *Candidate << " with " << alpha << " was rejected." << endl;
                         }
                       }
@@ -4197 +4128 @@
 
   /// 2. Go through all BoundaryPointSet's, check their triangles' NormalVector
-  map <int, int> *DegeneratedTriangles = FindAllDegeneratedTriangles();
   set < BoundaryPointSet *> EndpointCandidateList;
   pair < set < BoundaryPointSet *>::iterator, bool > InsertionTester;
@@ -4208 +4138 @@
     for (LineMap::const_iterator LineRunner = (Runner->second)->lines.begin(); LineRunner != (Runner->second)->lines.end(); LineRunner++)
       for (TriangleMap::const_iterator TriangleRunner = (LineRunner->second)->triangles.begin(); TriangleRunner != (LineRunner->second)->triangles.end(); TriangleRunner++) {
-        if (DegeneratedTriangles->find(TriangleRunner->second->Nr) == DegeneratedTriangles->end()) {
-          TriangleInsertionTester = TriangleVectors.insert( pair< int, Vector *> ((TriangleRunner->second)->Nr, &((TriangleRunner->second)->NormalVector)) );
-          if (TriangleInsertionTester.second)
-            Log() << Verbose(1) << " Adding triangle " << *(TriangleRunner->second) << " to triangles to check-list." << endl;
-        } else {
-          Log() << Verbose(1) << " NOT adding triangle " << *(TriangleRunner->second) << " as it's a simply degenerated one." << endl;
-        }
+        TriangleInsertionTester = TriangleVectors.insert( pair< int, Vector *> ((TriangleRunner->second)->Nr, &((TriangleRunner->second)->NormalVector)) );
+        if (TriangleInsertionTester.second)
+          Log() << Verbose(1) << " Adding triangle " << *(TriangleRunner->second) << " to triangles to check-list." << endl;
       }
     // check whether there are two that are parallel
@@ -4287 +4213 @@
     /// 4a. Gather all triangles of this polygon
     TriangleSet *T = (*PolygonRunner)->GetAllContainedTrianglesFromEndpoints();
-
-    if (T->size() == 2) {
-      Log() << Verbose(1) << " Skipping degenerated polygon, is just a (already simply degenerated) triangle." << endl;
-      delete(T);
-      continue;
-    }
 
     TriangleSet::iterator TriangleWalker = T->begin();  // is the inner iterator