bool Polygon::convertToInequalityConstraints(Eigen::MatrixXd& A, Eigen::VectorXd& b) const
{
Eigen::MatrixXd V(nVertices(), 2);
for (unsigned int i = 0; i < nVertices(); ++i)
V.row(i) = vertices_[i];
// Create k, a list of indices from V forming the convex hull.
// TODO: Assuming counter-clockwise ordered convex polygon.
// MATLAB: k = convhulln(V);
Eigen::MatrixXi k;
k.resizeLike(V);
for (unsigned int i = 0; i < V.rows(); ++i)
k.row(i) << i, (i+1) % V.rows();
Eigen::RowVectorXd c = V.colwise().mean();
V.rowwise() -= c;
A = Eigen::MatrixXd::Constant(k.rows(), V.cols(), NAN);
unsigned int rc = 0;
for (unsigned int ix = 0; ix < k.rows(); ++ix) {
Eigen::MatrixXd F(2, V.cols());
F.row(0) << V.row(k(ix, 0));
F.row(1) << V.row(k(ix, 1));
Eigen::FullPivLU<Eigen::MatrixXd> luDecomp(F);
if (luDecomp.rank() == F.rows()) {
A.row(rc) = F.colPivHouseholderQr().solve(Eigen::VectorXd::Ones(F.rows()));
++rc;
}
}
A = A.topRows(rc);
b = Eigen::VectorXd::Ones(A.rows());
b = b + A * c.transpose();
return true;
}
std::vector<carve::geom::vector<2> > Face<ndim>::projectedVertices() const {
p2_adapt_project<ndim> proj = projector();
std::vector<carve::geom::vector<2> > result;
result.reserve(nVertices());
for (size_t i = 0; i < nVertices(); ++i) {
result.push_back(proj(vertex(i)->v));
}
return result;
}
Face<ndim> *Face<ndim>::init(const Face<ndim> *base, iter_t vbegin, iter_t vend, bool flipped) {
CARVE_ASSERT(vbegin < vend);
vertices.reserve((size_t)std::distance(vbegin, vend));
if (flipped) {
std::reverse_copy(vbegin, vend, std::back_inserter(vertices));
plane_eqn = -base->plane_eqn;
} else {
std::copy(vbegin, vend, std::back_inserter(vertices));
plane_eqn = base->plane_eqn;
}
edges.clear();
edges.resize(nVertices(), NULL);
aabb.fit(vertices.begin(), vertices.end(), vec_adapt_vertex_ptr());
untag();
int da = carve::geom::largestAxis(plane_eqn.N);
project = getProjector(plane_eqn.N.v[da] > 0, da);
unproject = getUnprojector(plane_eqn.N.v[da] > 0, da);
return this;
}
void tDxfSpline::refresh()
{
hs->removeAllVertices();
/*
for (int i=0; i<nVertices(); i++){
hs->addVertex(vertex(i));
}*/
if (nVertices()>2){
UpdateControlPoints();
updateXX();
}
/*
if (data.degree<1 || data.degree>3) {
RS_DEBUG->print("RS_Spline::update: invalid degree: %d", data.degree);
return;
}
if (data.controlPoints.size() < data.degree+1) {
RS_DEBUG->print("RS_Spline::update: not enough control points");
return;
}
*/
// controlpoints berechnen.
}
void Mesh::addRow()
{
// Create new vertices 2d (temporary).
IndexVector2d newVertices2d;
resizeVertices2d(newVertices2d, nColumns(), nRows()+1);
// Top displacement of points already there.
qreal topMoveProp = 1.0f/(nRows()-1) - 1.0f/nRows();
// Add a point at each row.
int k = nVertices();
for (int x=0; x<nColumns(); x++)
{
// Get left and right vertices.
QPointF top = getVertex2d(x, 0);
QPointF bottom = getVertex2d(x, nRows()-1);
QPointF diff = bottom - top;
// First pass: move middle points.
for (int y=1; y<nRows()-1; y++)
{
QPointF p = getVertex2d(x, y);
p -= diff * y * topMoveProp;
_rawSetVertex( _vertices2d[x][y], p );
}
// Create and add new point.
QPointF newPoint = bottom - diff * 1.0f/nRows();
_addVertex(newPoint);
// Assign new vertices 2d.
for (int y=0; y<nRows()-1; y++)
newVertices2d[x][y] = _vertices2d[x][y];
// The new point.
newVertices2d[x][nRows()-1] = k;
// The rightmost point.
newVertices2d[x][nRows()] = _vertices2d[x][nRows()-1];
k++;
}
// Copy new mapping.
_vertices2d = newVertices2d;
// Increment number of columns.
_nRows++;
// Reorder.
_reorderVertices();
}
// vertices 0..3 = 4 corners
//
void Mesh::addColumn()
{
// Create new vertices 2d (temporary).
IndexVector2d newVertices2d;
resizeVertices2d(newVertices2d, nColumns()+1, nRows());
// Left displacement of points already there.
qreal leftMoveProp = 1.0f/(nColumns()-1) - 1.0f/nColumns();
// Add a point at each row.
int k = nVertices();
for (int y=0; y<nRows(); y++)
{
// Get left and right vertices.
QPointF left = getVertex2d( 0, y );
QPointF right = getVertex2d( nColumns()-1, y );
QPointF diff = right - left;
// First pass: move middle points.
for (int x=1; x<nColumns()-1; x++)
{
QPointF p = getVertex2d(x, y);
p -= diff * x * leftMoveProp;
_rawSetVertex( _vertices2d[x][y], p );
}
// Create and add new point.
QPointF newPoint = right - diff * 1.0f/nColumns();
_addVertex(newPoint);
// Assign new vertices 2d.
for (int x=0; x<nColumns()-1; x++)
newVertices2d[x][y] = _vertices2d[x][y];
// The new point.
newVertices2d[nColumns()-1][y] = k;
// The rightmost point.
newVertices2d[nColumns()][y] = _vertices2d[nColumns()-1][y];
k++;
}
// Copy new mapping.
_vertices2d = newVertices2d;
// Increment number of columns.
_nColumns++;
// Reorder.
_reorderVertices();
}
void MShape::write(QDomElement& obj)
{
// Write basic data.
Serializable::write(obj);
// Write vertices.
QDomElement verticesObj = obj.ownerDocument().createElement("vertices");
for (int i=0; i<nVertices(); i++)
{
QDomElement vertexObj = obj.ownerDocument().createElement("vertex");
vertexObj.setAttribute("x", QString::number(getVertex(i).x()));
vertexObj.setAttribute("y", QString::number(getVertex(i).y()));
verticesObj.appendChild(vertexObj);
}
obj.appendChild(verticesObj);
}
bool Polygon::offsetInward(const double margin)
{
// Create a list of indices of the neighbours of each vertex.
// TODO: Assuming counter-clockwise ordered convex polygon.
std::vector<Eigen::Array2i> neighbourIndices;
const unsigned int n = nVertices();
neighbourIndices.resize(n);
for (unsigned int i = 0; i < n; ++i) {
neighbourIndices[i] << (i > 0 ? (i-1)%n : n-1), (i + 1) % n;
}
std::vector<Position> copy(vertices_);
for (unsigned int i = 0; i < neighbourIndices.size(); ++i) {
Eigen::Vector2d v1 = vertices_[neighbourIndices[i](0)] - vertices_[i];
Eigen::Vector2d v2 = vertices_[neighbourIndices[i](1)] - vertices_[i];
v1.normalize();
v2.normalize();
const double angle = acos(v1.dot(v2));
copy[i] += margin / sin(angle) * (v1 + v2);
}
vertices_ = copy;
return true;
}
void MayaNurbsCurveWriter::write()
{
Alembic::AbcGeom::OCurvesSchema::Sample samp;
samp.setBasis(Alembic::AbcGeom::kBsplineBasis);
MStatus stat;
mCVCount = 0;
// if inheritTransform is on and the curve group is animated,
// bake the cv positions in the world space
MMatrix exclusiveMatrixInv = mRootDagPath.exclusiveMatrixInverse(&stat);
std::size_t numCurves = 1;
if (mIsCurveGrp)
numCurves = mNurbsCurves.length();
std::vector<Alembic::Util::int32_t> nVertices(numCurves);
std::vector<float> points;
std::vector<float> width;
std::vector<float> knots;
std::vector<Alembic::Util::uint8_t> orders(numCurves);
MMatrix transformMatrix;
bool useConstWidth = false;
MFnDependencyNode dep(mRootDagPath.transform());
MPlug constWidthPlug = dep.findPlug("width");
if (!constWidthPlug.isNull())
{
useConstWidth = true;
width.push_back(constWidthPlug.asFloat());
}
for (unsigned int i = 0; i < numCurves; i++)
{
MFnNurbsCurve curve;
if (mIsCurveGrp)
{
curve.setObject(mNurbsCurves[i]);
MMatrix inclusiveMatrix = mNurbsCurves[i].inclusiveMatrix(&stat);
transformMatrix = inclusiveMatrix*exclusiveMatrixInv;
}
else
{
curve.setObject(mRootDagPath.node());
}
if (i == 0)
{
if (curve.form() == MFnNurbsCurve::kOpen)
{
samp.setWrap(Alembic::AbcGeom::kNonPeriodic);
}
else
{
samp.setWrap(Alembic::AbcGeom::kPeriodic);
}
if (curve.degree() == 3)
{
samp.setType(Alembic::AbcGeom::kCubic);
}
else if (curve.degree() == 1)
{
samp.setType(Alembic::AbcGeom::kLinear);
}
else
{
samp.setType(Alembic::AbcGeom::kVariableOrder);
}
}
else
{
if (curve.form() == MFnNurbsCurve::kOpen)
{
samp.setWrap(Alembic::AbcGeom::kNonPeriodic);
}
if ((samp.getType() == Alembic::AbcGeom::kCubic &&
curve.degree() != 3) ||
(samp.getType() == Alembic::AbcGeom::kLinear &&
curve.degree() != 1))
{
samp.setType(Alembic::AbcGeom::kVariableOrder);
}
}
orders[i] = static_cast<Alembic::Util::uint8_t>(curve.degree() + 1);
Alembic::Util::int32_t numCVs = curve.numCVs(&stat);
MPointArray cvArray;
stat = curve.getCVs(cvArray, MSpace::kObject);
mCVCount += numCVs;
nVertices[i] = numCVs;
for (Alembic::Util::int32_t j = 0; j < numCVs; j++)
{
MPoint transformdPt;
if (mIsCurveGrp)
{
transformdPt = cvArray[j]*transformMatrix;
}
else
{
transformdPt = cvArray[j];
}
points.push_back(static_cast<float>(transformdPt.x));
points.push_back(static_cast<float>(transformdPt.y));
points.push_back(static_cast<float>(transformdPt.z));
}
MDoubleArray knotsArray;
curve.getKnots(knotsArray);
knots.reserve(knotsArray.length() + 2);
// need to add a knot to the start and end (M + 2N + 1)
if (knotsArray.length() > 1)
{
unsigned int knotsLength = knotsArray.length();
if (knotsArray[0] == knotsArray[knotsLength - 1] ||
knotsArray[0] == knotsArray[1])
{
knots.push_back(knotsArray[0]);
}
else
{
knots.push_back(2 * knotsArray[0] - knotsArray[1]);
}
for (unsigned int j = 0; j < knotsLength; ++j)
{
knots.push_back(knotsArray[j]);
}
if (knotsArray[0] == knotsArray[knotsLength - 1] ||
knotsArray[knotsLength - 1] == knotsArray[knotsLength - 2])
{
knots.push_back(knotsArray[knotsLength - 1]);
}
else
{
knots.push_back(2 * knotsArray[knotsLength - 1] -
knotsArray[knotsLength - 2]);
}
}
// width
MPlug widthPlug = curve.findPlug("width");
if (!useConstWidth && !widthPlug.isNull())
{
MObject widthObj;
MStatus status = widthPlug.getValue(widthObj);
MFnDoubleArrayData fnDoubleArrayData(widthObj, &status);
MDoubleArray doubleArrayData = fnDoubleArrayData.array();
Alembic::Util::int32_t arraySum = doubleArrayData.length();
if (arraySum == numCVs)
{
for (Alembic::Util::int32_t i = 0; i < arraySum; i++)
{
width.push_back(static_cast<float>(doubleArrayData[i]));
}
}
else if (status == MS::kSuccess)
{
MString msg = "Curve ";
msg += curve.partialPathName();
msg += " has incorrect size for the width vector.";
msg += "\nUsing default constant width of 0.1.";
MGlobal::displayWarning(msg);
width.clear();
width.push_back(0.1f);
useConstWidth = true;
}
else
{
width.push_back(widthPlug.asFloat());
useConstWidth = true;
}
}
else if (!useConstWidth)
{
// pick a default value
width.clear();
width.push_back(0.1f);
useConstWidth = true;
}
}
Alembic::AbcGeom::GeometryScope scope = Alembic::AbcGeom::kVertexScope;
if (useConstWidth)
scope = Alembic::AbcGeom::kConstantScope;
samp.setCurvesNumVertices(Alembic::Abc::Int32ArraySample(nVertices));
samp.setPositions(Alembic::Abc::V3fArraySample(
(const Imath::V3f *)&points.front(), points.size() / 3 ));
samp.setWidths(Alembic::AbcGeom::OFloatGeomParam::Sample(
Alembic::Abc::FloatArraySample(width), scope) );
if (samp.getType() == Alembic::AbcGeom::kVariableOrder)
{
samp.setOrders(Alembic::Abc::UcharArraySample(orders));
}
if (!knots.empty())
{
samp.setKnots(Alembic::Abc::FloatArraySample(knots));
}
mSchema.set(samp);
}
VertexIter HalfedgeMesh::collapseEdge( EdgeIter e )
{
// TODO This method should collapse the given edge and return an iterator to the new vertex created by the collapse.
//1. collect elements
EdgeIter e4 = e;
//Halfedges
HalfedgeIter h1 = e4->halfedge();
HalfedgeIter h5 = h1->twin();
//Faces
FaceIter f0 = h1->face();
FaceIter f1 = h5->face();
//Early Exit #1: Ignore requests to collapse boundary edges
if(f0->isBoundary() || f1->isBoundary())
return verticesEnd();
//Halfedges, cont'
HalfedgeIter h2 = h1->next();
HalfedgeIter h0 = h2->next();
HalfedgeIter h3 = h5->next();
HalfedgeIter h4 = h3->next();
HalfedgeIter h7 = h0->twin();
HalfedgeIter h12 = h3->twin();
HalfedgeIter h20 = h2->twin();
HalfedgeIter h15 = h4->twin();
//Edges
EdgeIter e0 = h0->edge();
EdgeIter e1 = h3->edge();
EdgeIter e2 = h4->edge();
EdgeIter e3 = h2->edge();
//EdgeIter e4
//Faces
//Vertices
VertexIter v0 = h0->vertex();
VertexIter v1 = h3->vertex();
VertexIter v2 = h4->vertex();
VertexIter v3 = h2->vertex();
//Early Exit #2: The number of the joint neighbor vertices of the two merging vertices
//must be EXACTLY TWO
std::vector<VertexIter> v1_neighbors;
std::vector<VertexIter> v3_neighbors;
HalfedgeIter h = h3;
do
{
h = h->twin();
if(h->vertex() != v1)
v1_neighbors.push_back(h->vertex());
h = h->next();
}
while(h != h3);
h = h2;
do
{
h = h->twin();
if(h->vertex() != v3)
v3_neighbors.push_back(h->vertex());
h = h->next();
}
while(h != h2);
std::sort(v1_neighbors.begin(), v1_neighbors.end());
std::sort(v3_neighbors.begin(), v3_neighbors.end());
std::vector<VertexIter> joint_neighbors;
std::set_intersection(v1_neighbors.begin(), v1_neighbors.end(),
v3_neighbors.begin(), v3_neighbors.end(),
std::back_inserter(joint_neighbors));
if(joint_neighbors.size() != 2)
return verticesEnd();
//Early Exit #3: mesh must have more than 4 vertices if neither v1 nor v3 is boundary vertex,
//and more than 3 vertices if either v1 or v3 is boundary vertex
if(!v1->isBoundary() && !v3->isBoundary() && nVertices() <= 4)
return verticesEnd();
if((v1->isBoundary() || v3->isBoundary()) && nVertices() <= 3)
return verticesEnd();
//Early Exit #4: v1, v3 cannot be both boundary vertex
if(v1->isBoundary() && v3->isBoundary())
return verticesEnd();
//Early Exit #5: boundary vertex needs at least one triangle
//By convention, Vertex::degree() returns the face degree
if(v0->isBoundary() && v0->degree() <= 1)
return verticesEnd();
if(v1->isBoundary() && v1->degree() <= 1)
return verticesEnd();
if(v2->isBoundary() && v2->degree() <= 1)
return verticesEnd();
if(v3->isBoundary() && v3->degree() <= 1)
return verticesEnd();
//Early Exit #6: degenerated case: v0/v1/v2/v3 are duplicated
if(v0 == v1 || v0 == v2 || v0 == v3 || v1 == v2 || v1 == v3 || v2 == v3)
return verticesEnd();
VertexIter output = verticesEnd();
if(v3->isBoundary())
{
std::vector<HalfedgeIter> v1_out;
HalfedgeIter h = v1->halfedge();
do
{
v1_out.push_back(h);
h = h->next()->next()->twin();
}
while(h != v1->halfedge());
//2. reassign elements
//Halfedges
h7->twin() = h20; h7->edge() = e3;
h20->twin() = h7;
h12->twin() = h15; h12->edge() = e2;
h15->twin() = h12;
for(auto h = v1_out.begin(); h!= v1_out.end(); ++h)
(*h)->vertex() = v3;
//Vertices
v0->halfedge() = h20;
v3->halfedge() = h15;
v3->position = 0.5f * (v1->position + v3->position);
v2->halfedge() = h12;
//Edges
e3->halfedge() = h20;
e2->halfedge() = h15;
//Faces
//3. delete elements
//Halfedges
deleteHalfedge(h0);
deleteHalfedge(h1);
deleteHalfedge(h2);
deleteHalfedge(h3);
deleteHalfedge(h4);
deleteHalfedge(h5);
//Vertices
deleteVertex(v1);
//Edges
deleteEdge(e0);
deleteEdge(e1);
deleteEdge(e4);
//Faces
deleteFace(f0);
deleteFace(f1);
output = v3;
}
else
{
std::vector<HalfedgeIter> v3_out;
HalfedgeIter h = v3->halfedge();
do
{
v3_out.push_back(h);
h = h->next()->next()->twin();
}
while(h != v3->halfedge());
//2. reassign elements
//Halfedges
h7->twin() = h20;
h20->twin() = h7; h20->edge() = e0;
h12->twin() = h15;
h15->twin() = h12; h15->edge() = e1;
for(auto h = v3_out.begin(); h!= v3_out.end(); ++h)
(*h)->vertex() = v1;
//Vertices
v0->halfedge() = h20;
v1->halfedge() = h15;
v1->position = 0.5f * (v1->position + v3->position);
v2->halfedge() = h12;
//Edges
e0->halfedge() = h20;
e1->halfedge() = h15;
//Faces
//3. delete elements
//Halfedges
deleteHalfedge(h0);
deleteHalfedge(h1);
deleteHalfedge(h2);
deleteHalfedge(h3);
deleteHalfedge(h4);
deleteHalfedge(h5);
//Vertices
deleteVertex(v3);
//Edges
deleteEdge(e2);
deleteEdge(e3);
deleteEdge(e4);
//Faces
deleteFace(f0);
deleteFace(f1);
output = v1;
}
return output;
}
void Face<ndim>::getVertexLoop(std::vector<const vertex_t *> &loop) const {
loop.resize(nVertices(), NULL);
std::copy(vbegin(), vend(), loop.begin());
}
void tDxfSpline::UpdateControlPoints()
{
controlPoints.clear();
//tList<tVector> controlPoints;
int n = nVertices();
if(isClosed && n < 3)
{
if(n > 0) controlPoints.append(vertex(0)->vector());
if(n > 1) controlPoints.append(vertex(1)->vector());
return;
}
if(isClosed && n < 4)
{
if(n > 0) controlPoints.append(vertex(0)->vector());
if(n > 2)
{
tVector x1 = vertex(0)->vector(),
x2 = vertex(1)->vector(),
x3 = vertex(2)->vector();
double dl1 = (x2 - x1).length();
double dl2 = (x3 - x2).length();
double dt = dl1/(dl1 + dl2);
if(dt < RS_TOLERANCE || dt > 1.0 - RS_TOLERANCE)
//return RS_Vector(false);
controlPoints.append((x2 - x1*(1.0 - dt)*(1.0 - dt) - x3*dt*dt)*(1./dt/(1 - dt)/2.0));
}
if(n > 1) {
controlPoints.append(vertex(n - 1)->vector());
}
return;
}
int iDim = 0;
if(isClosed) {
iDim = n;
} else {
iDim = n - 2;
}
double *dt = new double[iDim];
double dl1, dl2;
if(isClosed) {
dl1 = (vertex(n - 1)->vector() - vertex(0)->vector()).length();
dl2 = (vertex(1)->vector() - vertex(0)->vector()).length();
dt[0] = dl1/(dl1 + dl2);
for(int i = 1; i < iDim - 1; i++)
{
dl1 = dl2;
dl2 = (vertex(i + 1)->vector() - vertex(i)->vector()).length();
dt[i] = dl1/(dl1 + dl2);
}
dl1 = (vertex(n - 1)->vector() - vertex(n - 2)->vector()).length();
dl2 = (vertex(0)->vector() - vertex(n - 1)->vector()).length();
dt[iDim - 1] = dl1/(dl1 + dl2);
} else {
dl1 = (vertex(1)->vector() - vertex(0)->vector()).length();
dl2 = (vertex(2)->vector() - vertex(1)->vector()).length();
dt[0] = dl1/(dl1 + dl2/2.0);
for(int i = 1; i < iDim - 1; i++)
{
dl1 = dl2;
dl2 = (vertex(i + 2)->vector() - vertex(i + 1)->vector()).length();
dt[i] = dl1/(dl1 + dl2);
}
dl1 = dl2;
dl2 = (vertex(iDim)->vector() - vertex(iDim + 1)->vector()).length();
dt[iDim - 1] = dl1/(dl1 + 2.0*dl2);
}
double *pdMatrix = GetMatrix(n, dt);
if(!pdMatrix) return;
tVector *dx = new tVector[iDim],
*dx2 = new tVector[iDim];
/*double *dx = new double[iDim];
double *dy = new double[iDim];
double *dx2 = new double[iDim];
double *dy2 = new double[iDim];*/
if(isClosed)
{
double *pdDiag = pdMatrix;
double *pdDiag1 = &pdMatrix[n];
double *pdDiag2 = &pdMatrix[2*n - 1];
double *pdLastCol1 = &pdMatrix[3*n - 2];
double *pdLastCol2 = &pdMatrix[4*n - 4];
dx[0] = vertex(0)->vector() * (1./pdDiag[0]);
//dx[0] = vertex(0).x/pdDiag[0];
//dy[0] = vertex(0).y/pdDiag[0];
for(int i = 1; i < iDim - 1; i++)
{
dx[i] = (vertex(i)->vector() - dx[i-1]*pdDiag2[i-1])*(1./pdDiag[i]);
//dx[i] = (vertex(i).x - pdDiag2[i - 1]*dx[i - 1])/pdDiag[i];
//dy[i] = (vertex(i).y - pdDiag2[i - 1]*dy[i - 1])/pdDiag[i];
}
dx[iDim-1] = vertex(iDim - 1)->vector() - dx[iDim - 2]*pdDiag2[iDim - 2];
//dx[iDim - 1] = vertex(iDim - 1).x - pdDiag2[iDim - 2]*dx[iDim - 2];
//dy[iDim - 1] = vertex(iDim - 1).y - pdDiag2[iDim - 2]*dy[iDim - 2];
for(int i = 0; i < iDim - 2; i++)
{
dx[iDim-1] = dx[iDim-1] - (dx[i] * pdLastCol2[i]);
//dx[iDim - 1] -= (dx[i]*pdLastCol2[i]);
//dy[iDim - 1] -= (dy[i]*pdLastCol2[i]);
}
dx[iDim-1] = dx[iDim-1] * (1./pdDiag[iDim - 1]);
//dx[iDim - 1] /= pdDiag[iDim - 1];
//dy[iDim - 1] /= pdDiag[iDim - 1];
dx2[iDim-1] = dx[iDim-1]*(1./pdDiag[iDim-1]);
//dx2[iDim - 1] = dx[iDim - 1]/pdDiag[iDim - 1];
//dy2[iDim - 1] = dy[iDim - 1]/pdDiag[iDim - 1];
dx2[iDim-2] = (dx[iDim-2]-dx2[iDim-1]*pdDiag1[iDim-2])*(1./pdDiag[iDim - 2]);
//dx2[iDim - 2] = (dx[iDim - 2] - pdDiag1[iDim - 2]*dx2[iDim - 1])/pdDiag[iDim - 2];
//dy2[iDim - 2] = (dy[iDim - 2] - pdDiag1[iDim - 2]*dy2[iDim - 1])/pdDiag[iDim - 2];
for(int i = iDim - 3; i >= 0; i--)
{
dx2[i] = (dx[i] - dx2[i + 1]*pdDiag1[i] - dx2[iDim - 1]*pdLastCol1[i])*(1./pdDiag[i]);
//dx2[i] = (dx[i] - pdDiag1[i]*dx2[i + 1] - pdLastCol1[i]*dx2[iDim - 1])/pdDiag[i];
//dy2[i] = (dy[i] - pdDiag1[i]*dy2[i + 1] - pdLastCol1[i]*dy2[iDim - 1])/pdDiag[i];
}
for(int i = 0; i < iDim; i++)
{
controlPoints.append(dx2[i]);
}
}
else
{
double *pdDiag = pdMatrix;
double *pdDiag1 = &pdMatrix[n - 2];
double *pdDiag2 = &pdMatrix[2*n - 5];
dx[0] = (vertex(1)->vector() - vertex(0)->vector()*(1.0-dt[0]) * (1.0 - dt[0]))*(1./pdDiag[0]);
//dx[0] = (vertex(1).x - vertex(0).x*(1.0 - dt[0])*(1.0 - dt[0]))/pdDiag[0];
//dy[0] = (vertex(1).y - vertex(0).y*(1.0 - dt[0])*(1.0 - dt[0]))/pdDiag[0];
for(int i = 1; i < iDim - 1; i++)
{
dx[i] = (vertex(i + 1)->vector() - dx[i-1]*pdDiag2[i-1])*(1./pdDiag[i]);
//dx[i] = (vertex(i + 1).x - pdDiag2[i - 1]*dx[i - 1])/pdDiag[i];
//dy[i] = (vertex(i + 1).y - pdDiag2[i - 1]*dy[i - 1])/pdDiag[i];
}
dx[iDim-1] = ((vertex(iDim)->vector() - vertex(iDim + 1)->vector()*dt[n-3]*dt[n-3]) - dx[iDim-2]*pdDiag2[iDim-2])*(1./pdDiag[iDim-1]);
//dx[iDim - 1] = ((vertex(iDim).x - vertex(iDim + 1).x*dt[n - 3]*dt[n - 3]) -
// pdDiag2[iDim - 2]*dx[iDim - 2])/pdDiag[iDim - 1];
//dy[iDim - 1] = ((vertex(iDim).y - vertex(iDim + 1).y*dt[n - 3]*dt[n - 3]) -
// pdDiag2[iDim - 2]*dy[iDim - 2])/pdDiag[iDim - 1];
dx2[iDim-1] = dx[iDim-1]*(1./pdDiag[iDim - 1]);
//dx2[iDim - 1] = dx[iDim - 1]/pdDiag[iDim - 1];
//dy2[iDim - 1] = dy[iDim - 1]/pdDiag[iDim - 1];
for(int i = iDim - 2; i >= 0; i--)
{
dx2[i] = (dx[i]-dx2[i+1]*pdDiag1[i])*(1./pdDiag[i]);
//dx2[i] = (dx[i] - pdDiag1[i]*dx2[i + 1])/pdDiag[i];
//dy2[i] = (dy[i] - pdDiag1[i]*dy2[i + 1])/pdDiag[i];
}
controlPoints.append(vertex(0)->vector());
for(int i = 0; i < iDim; i++)
{
controlPoints.append(dx2[i]);
}
controlPoints.append(vertex(n - 1)->vector());
}
delete[] pdMatrix;
delete[] dt;
//delete[] dy2;
delete[] dx2;
//delete[] dy;
delete[] dx;
}