/*******************************************************************************
*
* Initialize Function
*
*******************************************************************************/
void initialize() {
/**************************************************
* Setting up for Clock (PLL, M, N1, N2)
* for 32 MHz and Fcy = 16 MHz
*************************************************/
// Fosc = Fin(M/(N1*N2)) = 8 MHz (32/(2*4)) = 32 MHz
PLLFBD = 30; // M = 32
// N1 default is 2
// N2 default is 4
// Fcy = Fosc/2 by default
// Setting up RD6 and RD7
_TRISD6 = 1;
_TRISD7 = 1; // Set RD6 & 7 to inputs
// Initialize LCD
Init_LCD();
lcd_cmd(0xD);
// Making sure that we are starting at line 1, column 0
home_it();
// Print the LcdData1
puts_lcd(LcdData1, sizeof(LcdData1)-1);
// Move to next line
line_2();
// Print the LCDData2
puts_lcd(LcdData2, sizeof(LcdData2)-1);
}
void LinkStatusWidget::initLines(){
lines.clear();
int lineLeft=this->left_left+this->left_width+this->left_space;
int lineRight=this->width()-this->right_right;
int centerHeight=this->right_top+this->right_height+this->right_space/2;
QPoint p_left_left(lineLeft,centerHeight);
QPoint p_left_right(lineRight,centerHeight);
QLine line_1(p_left_left,p_left_right);
int lineRightRight=this->width()-this->right_right+this->right_space;
int lineRightTop=centerHeight- this->right_space/2-this->right_height/2;
int lineRightBottom= centerHeight+this->right_space/2+this->right_height/2;
QPoint p_right_top_left(lineRightRight,lineRightTop);
QPoint p_right_top_right(lineRightRight,lineRightBottom);
QLine line_2(p_right_top_left,p_right_top_right);
lines.append(line_1);
lines.append(line_2);
}
bool ParametricCurveTests::testProjectionBasedInterpolation()
{
bool success = true;
// to start with, project a line onto a linear basis
shards::CellTopology line_2(shards::getCellTopologyData<shards::Line<2> >() );
/////////////////// TEST LINEAR CURVES RECOVERED //////////////////////
BasisPtr linearBasis = BasisFactory::basisFactory()->getBasis(1, line_2.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
double x0=3, y0=-3, x1=5, y1=4;
// double dist = sqrt((x1-x0)*(x1-x0) + (y1-y0)*(y1-y0));
double dist = 1; // the length of the parametric space
BasisCachePtr basisCache = BasisCache::basisCache1D(0, dist, linearBasis->getDegree()*2);
ParametricCurvePtr myLine = ParametricCurve::line(x0, y0, x1, y1);
bool useH1 = true;
double lengthScale = 1.0;
FieldContainer<double> basisCoefficients_x, basisCoefficients_y;
myLine->projectionBasedInterpolant(basisCoefficients_x, linearBasis, 0, lengthScale, useH1);
myLine->projectionBasedInterpolant(basisCoefficients_y, linearBasis, 1, lengthScale, useH1);
if ( ! basisSumInterpolatesCurveEndPoints(basisCoefficients_x,basisCoefficients_y, linearBasis, myLine))
{
cout << "testProjectionBasedInterpolation() failed: projection-based interpolant doesn't interpolate line endpoints.\n";
cout << "basisCoefficients_x:\n" << basisCoefficients_x;
cout << "basisCoefficients_y:\n" << basisCoefficients_y;
success = false;
}
// in fact, we should recover the line in x and y:
if ( !basisSumEqualsFunction(basisCoefficients_x, linearBasis, myLine->x()) )
{
cout << "testProjectionBasedInterpolation() failed: projection-based interpolant doesn't recover the line in the x component.\n";
success = false;
}
if ( !basisSumEqualsFunction(basisCoefficients_y, linearBasis, myLine->y()) )
{
cout << "testProjectionBasedInterpolation() failed: projection-based interpolant doesn't recover the line in the y component.\n";
success = false;
}
/////////////////// TEST CUBIC CURVES RECOVERED //////////////////////
FunctionPtr t = Function::xn(1);
// define x and y as functions of t:
FunctionPtr x_t = t*t*t-2*t;
FunctionPtr y_t = t*t*t+8*t*t;
ParametricCurvePtr myCurve = ParametricCurve::curve(x_t,y_t);
BasisPtr cubicBasis = BasisFactory::basisFactory()->getBasis(3, line_2.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
myCurve->projectionBasedInterpolant(basisCoefficients_x, cubicBasis, 0, lengthScale, useH1);
myCurve->projectionBasedInterpolant(basisCoefficients_y, cubicBasis, 1, lengthScale, useH1);
// we should again recover the curve exactly:
if ( !basisSumEqualsFunction(basisCoefficients_x, cubicBasis, myCurve->x()) )
{
cout << "testProjectionBasedInterpolation() failed: projection-based interpolant doesn't recover the cubic curve in the x component.\n";
success = false;
}
if ( !basisSumEqualsFunction(basisCoefficients_y, cubicBasis, myCurve->y()) )
{
cout << "testProjectionBasedInterpolation() failed: projection-based interpolant doesn't recover the cubic curve in the y component.\n";
success = false;
}
/////////////////// TEST UNRECOVERABLE CURVE INTERPOLATED //////////////////////
// finally, project the cubic curve onto a quadratic basis, and check that it interpolates the endpoints
BasisPtr quadraticBasis = BasisFactory::basisFactory()->getBasis(2, line_2.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
myCurve->projectionBasedInterpolant(basisCoefficients_x, quadraticBasis, 0, lengthScale, useH1);
myCurve->projectionBasedInterpolant(basisCoefficients_y, quadraticBasis, 1, lengthScale, useH1);
if ( ! basisSumInterpolatesCurveEndPoints(basisCoefficients_x,basisCoefficients_y, quadraticBasis, myCurve))
{
cout << "testProjectionBasedInterpolation() failed: quadratic projection-based interpolant doesn't interpolate cubic curve endpoints.\n";
cout << "basisCoefficients_x:\n" << basisCoefficients_x;
cout << "basisCoefficients_y:\n" << basisCoefficients_y;
success = false;
}
return success;
}
bool ParametricCurveTests::testCircularArc()
{
bool success = true;
// the arc details are copied from CurvilinearMeshTests -- motivation is to diagnose test failure there with a more granular test here
double radius = 1.0;
double meshWidth = sqrt(2);
ParametricCurvePtr circle = ParametricCurve::circle(radius, meshWidth / 2.0, meshWidth / 2.0);
ParametricCurvePtr circularArc = ParametricCurve::subCurve(circle, 5.0/8.0, 7.0/8.0);
BasisCachePtr basisCache = BasisCache::parametric1DCache(15); // overintegrate to be safe
FunctionPtr cos_part = Teuchos::rcp( new Cos_ax(PI/2, 1.25*PI));
FunctionPtr sin_part = Teuchos::rcp( new Sin_ax(PI/2, 1.25*PI));
FunctionPtr x_t = meshWidth / 2 + cos_part;
FunctionPtr y_t = meshWidth / 2 + sin_part;
FunctionPtr dx_dt = (- PI / 2) * sin_part;
FunctionPtr dy_dt = (PI / 2) * cos_part;
double arcIntegral_x = circularArc->x()->integrate(basisCache);
double x_t_integral = x_t->integrate(basisCache);
// check that we have the right idea for all those functions:
if (! x_t->equals(circularArc->x(),basisCache))
{
double x1_expected = Function::evaluate(x_t,1);
double x1_actual;
circularArc->xPart()->value(1,x1_actual);
cout << "expected x(0) = " << x1_expected;
cout << "; actual = " << x1_actual << endl;
cout << "x part of circularArc doesn't match expected.\n";
success = false;
}
if (! y_t->equals(circularArc->y(),basisCache))
{
double y1_actual;
circularArc->yPart()->value(1,y1_actual);
cout << "expected y(1) = " << Function::evaluate(y_t,1);
cout << "; actual = " << y1_actual << endl;
cout << "y part of circularArc doesn't match expected.\n";
success = false;
}
if (! dx_dt->equals(circularArc->dt_parametric()->x(),basisCache))
{
cout << "dx/dt of circularArc doesn't match expected.\n";
success = false;
}
if (! dy_dt->equals(circularArc->dt_parametric()->y(),basisCache))
{
cout << "dy/dt of circularArc doesn't match expected.\n";
success = false;
}
// test exact curve at t=0.5
double tol=1e-14;
double t = 0.5;
double x_expected = meshWidth / 2;
double y_expected = meshWidth / 2 - radius;
double x,y,xErr,yErr;
// check value
circularArc->value(t, x, y);
xErr = abs(x-x_expected);
yErr = abs(y-y_expected);
if (xErr > tol)
{
cout << "exact arc x at t=0.5 is incorrect.\n";
success = false;
}
if (yErr > tol)
{
cout << "exact arc y at t=0.5 is incorrect.\n";
success = false;
}
// check derivatives
// figuring out what the x derivative should be is a bit of work, I think,
// but the y value is at a minimum, so its derivative should be zero
y_expected = 0;
circularArc->dt_parametric()->value(t, x, y);
yErr = abs(y-y_expected);
if (yErr > tol)
{
cout << "exact arc dy/dt at t=0.5 is nonzero.\n";
success = false;
}
shards::CellTopology line_2(shards::getCellTopologyData<shards::Line<2> >() );
BasisPtr quadraticBasis = BasisFactory::basisFactory()->getBasis(2, line_2.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
// figure out what the weights for the quadratic "middle node" basis function should be:
double expected_H1_weight_x, expected_H1_weight_y;
double expected_L2_weight_x, expected_L2_weight_y;
FunctionPtr middleBasis;
{
FunctionPtr t = Function::xn(1);
middleBasis = 4 * t * (1-t);
}
double middleBasisL2_squared = (middleBasis*middleBasis)->integrate(basisCache);
double middleBasisH1_squared = ( middleBasis->dx() * middleBasis->dx() )->integrate(basisCache) + middleBasisL2_squared;
ParametricCurvePtr circularArcBubble = ParametricCurve::bubble(circularArc);
FunctionPtr bubble_x = circularArcBubble->x();
FunctionPtr bubble_y = circularArcBubble->y();
double x_against_middle_L2 = (bubble_x * middleBasis)->integrate(basisCache);
double x_against_middle_H1 = (bubble_x->dx() * middleBasis->dx())->integrate(basisCache) + x_against_middle_L2;
double y_against_middle_L2 = (bubble_y * middleBasis)->integrate(basisCache);
double y_against_middle_H1 = (bubble_y->dx() * middleBasis->dx())->integrate(basisCache) + y_against_middle_L2;
expected_L2_weight_x = x_against_middle_L2 / middleBasisL2_squared;
expected_H1_weight_x = x_against_middle_H1 / middleBasisH1_squared;
expected_L2_weight_y = y_against_middle_L2 / middleBasisL2_squared;
expected_H1_weight_y = y_against_middle_H1 / middleBasisH1_squared;
int middleBasisOrdinal = quadraticBasis->getDofOrdinal(1,0,0);
FieldContainer<double> basisCoefficients_x, basisCoefficients_y;
bool useH1 = false; // just trying to diagnose whether the issue is in derivatives or values (most likely derivatives)
double lengthScale = 1.0;
circularArcBubble->projectionBasedInterpolant(basisCoefficients_x, quadraticBasis, 0, lengthScale, useH1);
circularArcBubble->projectionBasedInterpolant(basisCoefficients_y, quadraticBasis, 1, lengthScale, useH1);
double weightError_x = abs(expected_L2_weight_x-basisCoefficients_x[middleBasisOrdinal]);
double weightError_y = abs(expected_L2_weight_y-basisCoefficients_y[middleBasisOrdinal]);
if (weightError_x > tol)
{
success = false;
cout << "testCircularArc(): L2 projection doesn't match expected basis weight in x.\n";
cout << "expected " << expected_L2_weight_x << ", was " << basisCoefficients_x[middleBasisOrdinal] << endl;
}
if (weightError_y > tol)
{
success = false;
cout << "testCircularArc(): L2 projection doesn't match expected basis weight in y.\n";
cout << "expected " << expected_L2_weight_y << ", was " << basisCoefficients_y[middleBasisOrdinal] << endl;
}
useH1 = true;
circularArcBubble->projectionBasedInterpolant(basisCoefficients_x, quadraticBasis, 0, lengthScale, useH1);
circularArcBubble->projectionBasedInterpolant(basisCoefficients_y, quadraticBasis, 1, lengthScale, useH1);
weightError_x = abs(expected_H1_weight_x-basisCoefficients_x[middleBasisOrdinal]);
weightError_y = abs(expected_H1_weight_y-basisCoefficients_y[middleBasisOrdinal]);
if (weightError_x > tol)
{
success = false;
cout << "testCircularArc(): H1 projection doesn't match expected basis weight in x.\n";
cout << "expected " << expected_H1_weight_x << ", was " << basisCoefficients_x[middleBasisOrdinal] << endl;
}
if (weightError_y > tol)
{
success = false;
cout << "testCircularArc(): H1 projection doesn't match expected basis weight in y.\n";
cout << "expected " << expected_H1_weight_y << ", was " << basisCoefficients_y[middleBasisOrdinal] << endl;
}
/*
FunctionPtr projection_x = BasisSumFunction::basisSumFunction(quadraticBasis, basisCoefficients_x);
FunctionPtr projection_y = BasisSumFunction::basisSumFunction(quadraticBasis, basisCoefficients_y);
FieldContainer<double> parametricPoint(1,1);
parametricPoint[0] = t;
FieldContainer<double> refPoint = basisCache->getRefCellPointsForPhysicalPoints(parametricPoint);
basisCache->setRefCellPoints(refPoint);
FieldContainer<double> value(1,1);
projection_x->values(value, basisCache);
x = value[0];
projection_y->values(value, basisCache);
y = value[0];
// same expectations at the beginning, except of course now we don't expect to nail it.
// but we do expect to be closer than the linear interpolation of the vertices
x_expected = meshWidth / 2;
y_expected = meshWidth / 2 - radius;
double linearErr_x = 0; // linear interpolant nails the x value
double linearErr_y = abs(y_expected);
xErr = abs(x-x_expected);
yErr = abs(y-y_expected);
if (xErr > linearErr_x + tol) {
cout << "quadratic projection-based interpolant has greater error in x than linear interpolant.\n";
success = false;
}
if (yErr > linearErr_y + tol) {
cout << "quadratic projection-based interpolant has greater error in y than linear interpolant.\n";
success = false;
}*/
return success;
}
/*******************************************************************************
*
* Main Function
*
*******************************************************************************/
int main() {
// setting up everything
initialize();
int LcdCounter = 0;
int LcdFlag = 0, LcdLine = 1;
/*************** Main Loop ***********************************/
while (1) {
// Next press of RD6 = the printing of one char
if ((_RD6 == 0) && (LcdFlag == 1))
{
if (LcdCounter < (sizeof(LcdData1)-1))
{
puts_lcd(&LcdData1[LcdCounter], 1);
LcdCounter++;
}
if (LcdCounter >= (sizeof(LcdData1)- 1))
{
if ((LcdCounter == (sizeof(LcdData1) - 1 )) && (LcdLine = 1))
{
line_2();
LcdLine = 2;
}
else if (LcdCounter <= ((sizeof(LcdData1) + sizeof(LcdData2)) -2))
{
puts_lcd(&LcdData2[(LcdCounter - sizeof(LcdData1))], 1);
LcdCounter++;
}
}
Delay_Us(1000); // Debouncing
}
// First press of RD6 = clear the screen
if ((_RD6 == 0) && (LcdFlag == 0))
{
home_clr();
home_it();
LcdFlag = 1;
Delay_Us(1000); // Debouncing
}
// If RD7 was pressed
if ((_RD7 == 0))
{
if ((LcdCounter == sizeof(LcdData1)) && (LcdLine == 2))
{
lcd_cmd(0x8F);
puts_lcd(&LcdSpace, 1);
lcd_cmd(0x8F);
LcdCounter--;
// LcdLine = 1;
}
else
{
cursor_left();
puts_lcd(&LcdSpace, 1);
cursor_left();
LcdCounter--;
}
Delay_Us(1000); // Debouncing
}
} // End of the infinite While loop
return 1;
}
//
// removes the given vertex and retriangulates the hole which would be made
//
// The method returns true if the vertex has been removed and false if the vertex has been retained.
//
bool MeshEx::removeVertexAndReTriangulateNeighbourhood( Vertex *v )
{
std::vector<MeshEx::Edge *> boundaryEdges; // boundary edges which form the polygon which has to be triangulated
std::vector<MeshEx::Edge *> criticalEdges; // edges which are not only connected to other vertices of the vertexring through boundary edges
std::map<MeshEx::Vertex *, EdgeInfoHelper> boundaryRing; // maps incomming and outgoing edge to each vertex of the boundary vertex-ring
// gather and prepare information ------------------------------------------------
for( std::vector<Triangle *>::iterator it = v->triangleRing.begin(); it != v->triangleRing.end(); ++it )
{
Triangle *t = (*it);
Edge *boundaryEdge = t->getOtherEdge( v );
boundaryRing[boundaryEdge->v1].registerEdge( boundaryEdge );
boundaryRing[boundaryEdge->v2].registerEdge( boundaryEdge );
boundaryEdges.push_back( boundaryEdge );
}
// align the edges so that for each vertex e1 is the incomming and e2 is the outgoing edge
Vertex *first = boundaryRing.begin()->first;
Vertex *current = first;
Vertex *next = 0;
Vertex *prev = 0;
do
{
// we have to be sure that each boundaryRing Vertex has an incomming and outgoing edge
if( !boundaryRing[current].e1 || !boundaryRing[current].e2 )
{
printf( "error : edge ring around vertex not closed boundary vertex has less than 2 edges (polygon hole?)\n" );
//++g_iterations;
return false;
}
boundaryRing[current].setVertex( current );
next = boundaryRing[current].next;
if( boundaryRing[next].e1 != boundaryRing[current].e2 )
boundaryRing[next].swap();
current = next;
}while( current != first );
// we have to collect all edges going out from the vertex-ring vertices which are connected to
// other vertices of the vertex ring - these will later be used for consistency check #2 (see chapter 4.4 of the paper)
// for each vertex of the vertex Ring V
for( std::map<Vertex *, EdgeInfoHelper>::iterator it = boundaryRing.begin(); it != boundaryRing.end(); ++it )
{
Vertex *rv = it->first; // current vertex of the vertex ring
// for each triangle referencing rv...
for( std::vector<Triangle *>::iterator tit = rv->triangleRing.begin(); tit != rv->triangleRing.end(); ++tit )
{
Triangle *rv_tri = *tit;
// ... which doesnt belong to the triangleRing of v
if( std::find( v->triangleRing.begin(), v->triangleRing.end(), rv_tri ) == v->triangleRing.end() )
{
// collect the edges containing rv...
for( size_t i=0; i<3; ++i )
if( rv_tri->e[i]->contains(rv) )
// ...and dont belong to the edgeRing list
if( std::find( boundaryEdges.begin(), boundaryEdges.end(), rv_tri->e[i] ) == boundaryEdges.end() )
// store the edge if the node on the other side references another vertex of the vertex-ring
if( boundaryRing.find( rv_tri->e[i]->getOtherVertex(rv) ) != boundaryRing.end() )
criticalEdges.push_back( rv_tri->e[i] );
}
}
}
// remove duplicate entries
std::sort( criticalEdges.begin(), criticalEdges.end() );
criticalEdges.erase( std::unique(criticalEdges.begin(), criticalEdges.end()), criticalEdges.end() );
// Now we will project the neighbourhood of v onto a plane so that we can employ the greedy
// triangulation. For this we will have to find a projection of the neighbourhood of v so that
// no edges intersect on that plane. If they would, then the greedy triangulation would introduce
// folds which means that the topology would be destroyed.
// Looking for a working projection may lead to a number of projection-trials. For the first try
// we will take the plane to be the plane defined by the normal of v and (its distance to the origin).
// This will do the job most of the time.
math::Vec3f normal; // direction of the projection plane
math::Vec3f base1; // base vector which builds the 2d-coordinate system
math::Vec3f base2; // base vector which builds the 2d-coordinate system
float distance; // distance of the plane to the origin
CGAL::Orientation boundaryPolygonOrientation; // orientation (clockwise/counterclockwise of the boundary polyon)
distance = -math::dotProduct( v->position, normal );
size_t trialCount = 13; // only one trial for now
size_t currentTrial = 0;
bool success = true;
do
{
// we assume that we will be successfull
success = true;
switch(currentTrial)
{
case 0:
// first trial: we take the plane defined by the normal of v
normal = v->normal;
break;
// for all other trials we will try one of 12 different directions
case 1:normal = math::normalize( math::Vec3f( .8507f, .4472f, .2764f ));break;
case 2:normal = math::normalize( math::Vec3f( -.8507f, .4472f, .2764f ));break;
case 3:normal = math::normalize( math::Vec3f( .8507f, -.4472f, -.2764f ));break;
case 4:normal = math::normalize( math::Vec3f( -.8507f, -.4472f, -.2764f ));break;
case 5:normal = math::normalize( math::Vec3f( .5257f, -.4472f, .7236f ));break;
case 6:normal = math::normalize( math::Vec3f( .5257f, .4472f, -.7236f ));break;
case 7:normal = math::normalize( math::Vec3f( -.5257f, -.4472f, .7236f ));break;
case 8:normal = math::normalize( math::Vec3f( -.5257f, .4472f, -.7236f ));break;
case 9:normal = math::normalize( math::Vec3f( .0f, .4472f, .8944f ));break;
case 10:normal = math::normalize( math::Vec3f( .0f, -1.0f, .0f ));break;
case 11:normal = math::normalize( math::Vec3f( .0f, 1.0f, .0f ));break;
case 12:normal = math::normalize( math::Vec3f( .0f, -.4472f, -.8944f ));break;
};
// compute the basis of the 2d-coordinate system of the plane defined by current normal
base1 = math::normalize( math::projectPointOnPlane( normal, distance, boundaryRing.begin()->first->position ) - v->position );
base2 = math::normalize( math::crossProduct( normal, base1 ) );
// project neighbours into the given plane
for( std::map<Vertex *, EdgeInfoHelper>::iterator it = boundaryRing.begin(); it != boundaryRing.end(); ++it )
it->second.projected = _get2d( base1, base2, math::projectPointOnPlane( normal, distance, it->first->position ) );
// topologic constistency check #1 (see chapter 4.4 of the paper)
// now do the consistency check: test if all edges dont intersect and dont lie over each other
// if any edge between the projected vertices intersect -> success = false
// test each projected edge of the edge ring against each other edge
for( std::vector<Edge *>::iterator it1 = boundaryEdges.begin(); it1 != boundaryEdges.end() - 1; ++it1 )
{
for( std::vector<Edge *>::iterator it2 = it1+1; it2 != boundaryEdges.end(); ++it2 )
{
Edge *e1 = *it1;
Edge *e2 = *it2;
math::Vec3f intersectionPoint;
// skip if the 2 lines share a common vertex
if( e2->contains(e1->v1) || e2->contains(e1->v2) )
continue;
math::Vec2f e1_v1_projected = boundaryRing[e1->v1].projected;
math::Vec2f e1_v2_projected = boundaryRing[e1->v2].projected;
math::Vec2f e2_v1_projected = boundaryRing[e2->v1].projected;
math::Vec2f e2_v2_projected = boundaryRing[e2->v2].projected;
CGAL::Segment_2<K> line_1( Point( e1_v1_projected.x, e1_v1_projected.y ), Point(e1_v2_projected.x, e1_v2_projected.y) );
CGAL::Segment_2<K> line_2( Point( e2_v1_projected.x, e2_v1_projected.y ), Point(e2_v2_projected.x, e2_v2_projected.y) );
if( CGAL::do_intersect( line_1, line_2 ) )
{
success = false;
break;
}
}
if( !success )
break;
}
if( success )
{
//
// now we do the topology consistency check #2 (see chapter 4.4 of the paper)
// this is done by checking all critical edges whether they cross the interior of the
// polygon boundary which is formed by the projected vertex ring vertices
// to do this we create the 2 polygongs which can be made by using the edge as a divider
// the line crosses the interior if both polgons have a counterclockwise orientation
//
for( std::vector<Edge *>::iterator it = criticalEdges.begin(); it != criticalEdges.end(); ++it )
{
Edge *criticalEdge = *it;
// setup left polygon
// start from v1 and go to v2
Polygon leftPoly;
prev = 0;
current = criticalEdge->v1;
do
{
leftPoly.push_back( current, boundaryRing[current].projected );
prev = current;
current = boundaryRing[current].next;
}while( current != criticalEdge->v2 );
leftPoly.push_back( current, boundaryRing[current].projected );
// setup right polygon
// start from v2 and go to v1
Polygon rightPoly;
prev = 0;
current = criticalEdge->v2;
do
{
rightPoly.push_back( current, boundaryRing[current].projected );
prev = current;
current = boundaryRing[current].next;
}while( current != criticalEdge->v1 );
rightPoly.push_back( current, boundaryRing[current].projected );
// if orientations of both polygons are the same then the critical edge crosses the bounding polygon interior
if( leftPoly.orientation() == rightPoly.orientation() )
{
printf( "info : unable to triangulate since critical edge(es) would cross the polygon interior - vertex is not removed\n" );
success = false;
break;
}
}
}
}while( (++currentTrial < trialCount)&&(!success) );
if( !success )
{
// we dont remove the vertex since we didnt managed to find a planar
// projection of the neighbourhood which would not destroy the topology
printf( "info : unable to find planar projection for vertex remove and retriangulation - vertex is not removed\n" );
//++g_iterations;
return false;
}
boundaryPolygonOrientation = CGAL::orientation( Point_3( v->position ), Point_3( v->position + base1 ), Point_3( v->position + base2 ), Point_3( v->position + normal ) );
// execute the result ------------------------------------------------------------
// remove vertex v and the triangle ring around v
removeVertex( v );
// compute squared distances
// compute the squared distances of all point pairs
std::vector<DistanceHelper> sqDistances; // sorted distances of each pair of points
for( std::map<Vertex *, EdgeInfoHelper>::iterator it1 = boundaryRing.begin(); it1 != boundaryRing.end(); ++it1 )
for( std::map<Vertex *, EdgeInfoHelper>::iterator it2 = it1; it2 != boundaryRing.end(); ++it2 )
{
Vertex *v1 = it1->first;
Vertex *v2 = it2->first;
if( v1 == v2 )
continue;
// we dont want to add pairs, which would build a boundary edge, since those
// already exist -> simply check for next or prev vertex in boundaryRing
if( (boundaryRing[v1].next == v2)||(boundaryRing[v1].prev == v2) )
continue;
sqDistances.push_back( DistanceHelper( it1->first, it2->first ) );
}
// sort
std::sort( sqDistances.begin(), sqDistances.end() );
//
std::list<Polygon *> polygons; // polygons which have to be triangulated
std::vector<Edge *> edges( boundaryEdges.begin(), boundaryEdges.end() ); // created edges
// create polygon which is made by the boundary edges and put it on polygon list
Polygon *boundaryPolygon = new Polygon();
first = boundaryRing.begin()->first;
current = first;
prev = 0;
do
{
boundaryPolygon->push_back( current, boundaryRing[current].projected );
prev = current;
current = boundaryRing[current].next;
}while( current != first );
if( boundaryPolygon->orientation() != boundaryPolygonOrientation )
boundaryPolygon->flip();
polygons.push_back( boundaryPolygon );
// for each entry in the sqDistance list
// find the polygon on the polygon list which contains h->v1 and h->v2
// check if edge is outside the polygon by checking the orientations of the left and right sides (build left and right polygons)
// check if edge intersects with any other existing edge which dont have a point in h->v1 or h->v2
// if checks pass:
// create edge -> assign it to the left and right polygons | add it to the list of edges
// split the polygon by removing the polygon from polygon list and putting the left and right polygons on the list if it is not a triangle
//
// if the any polygon remains on the polygon list, throw an error that the triangulation has created a hole in the mesh
//std::vector<Edge *> edges( edgeRing.begin(), edgeRing.end() );
// when the mother polygon is already a triangle, then we have sqDistances.size() == 0
// and we have to handle the polygon
if( boundaryPolygon->isTriangle() )
{
createTriangle( boundaryPolygon->vertices[0], boundaryPolygon->vertices[1], boundaryPolygon->vertices[2], edges );
polygons.clear();
delete boundaryPolygon;
//++g_iterations;
return true;
}
for( std::vector<DistanceHelper>::iterator it=sqDistances.begin(); it != sqDistances.end(); ++it )
{
DistanceHelper *h = &(*it);
Polygon *poly = 0; // polygon which contains both vertices of h
std::list<Polygon *>::iterator pit;
// find the polygon which contains both vertices of h
for( pit = polygons.begin(); pit != polygons.end(); ++pit )
{
Polygon *p = *pit;
if( p->contains( h->v1 ) && p->contains( h->v2 ) )
{
poly = p;
break;
}
}
// if no polygon could be found which contains both vertices of h, then
// we can skip this one
if( !poly )
continue;
// test for intersection with all existing edges
bool intersection = false;
for( std::vector<Edge *>::iterator eit = edges.begin(); eit != edges.end(); ++eit)
{
Edge *e = (*eit);
math::Vec3f intersectionPoint;
// ---- test for intersection of the edges projected into 2d plane using cgal ----
// skip if the 2 lines share a common vertex
if( e->contains(h->v1) || e->contains(h->v2) )
continue;
CGAL::Segment_2<K> line_1( Point( boundaryRing[e->v1].projected.x, boundaryRing[e->v1].projected.y ), Point(boundaryRing[e->v2].projected.x, boundaryRing[e->v2].projected.y) );
CGAL::Segment_2<K> line_2( Point( boundaryRing[h->v1].projected.x, boundaryRing[h->v1].projected.y ), Point(boundaryRing[h->v2].projected.x, boundaryRing[h->v2].projected.y) );
if( CGAL::do_intersect( line_1, line_2 ) )
{
intersection = true;
break;
}
}
// if there was an intersection, then we can skip this one
// since a non-compatible edge would be introduced
if( intersection )
continue;
// no intersection, get the 2 polygons which would be created from dividing the mother polyon along the edge
Polygon *left, *right;
left = right = 0;
poly->split( left, right, h->v1, h->v2 );
// if the 2 polygons have the same orientation, then we can be sure that
// the edge goes through the interior of the polygon
if( left->orientation() == right->orientation() )
{
// remove the current polygon from the list of polygons
polygons.erase( pit );
delete poly;
// create the edge h->v1 -> h->v2
Edge *edge = createEdge( h->v1, h->v2 );
edges.push_back( edge );
// and add the left and righ polygon to the list if they are not triangles
if( left->isTriangle() )
{
// add triangle to the mesh
createTriangle( left->vertices[0], left->vertices[1], left->vertices[2], edges );
// remove polygon helper structure
delete left;
}else
polygons.push_back( left );
if( right->isTriangle() )
{
// add triangle to the mesh
createTriangle( right->vertices[0], right->vertices[1], right->vertices[2], edges );
// remove polygon helper structure
delete right;
}else
polygons.push_back( right );
}else
{
delete left;
delete right;
}
}
if( !polygons.empty() )
printf( "error : hole created during retriangulation\n" );
for( std::list<Polygon *>::iterator pit = polygons.begin(); pit != polygons.end(); ++pit )
delete *pit;
polygons.clear();
//++g_iterations;
return true;
}
