double OGRCompoundCurve::get_Area() const
{
if( IsEmpty() || !get_IsClosed() )
return 0;
// Optimization for convex rings.
if( IsConvex() )
{
// Compute area of shape without the circular segments.
OGRPointIterator* poIter = getPointIterator();
OGRLineString oLS;
oLS.setNumPoints( getNumPoints() );
OGRPoint p;
for( int i = 0; poIter->getNextPoint(&p); i++ )
{
oLS.setPoint( i, p.getX(), p.getY() );
}
double dfArea = oLS.get_Area();
delete poIter;
// Add the area of the spherical segments.
dfArea += get_AreaOfCurveSegments();
return dfArea;
}
OGRLineString* poLS = CurveToLine();
double dfArea = poLS->get_Area();
delete poLS;
return dfArea;
}
bool Polygon::DiagonalExists(int i, int j) const
{
assume(p.size() >= 3);
assume(i >= 0);
assume(j >= 0);
assume(i < (int)p.size());
assume(j < (int)p.size());
#ifndef MATH_ENABLE_INSECURE_OPTIMIZATIONS
if (p.size() < 3 || i < 0 || j < 0 || i >= (int)p.size() || j >= (int)p.size())
return false;
#endif
assume(IsPlanar());
assume(i != j);
if (i == j) // Degenerate if i == j.
return false;
if (i > j)
Swap(i, j);
assume(i+1 != j);
if (i+1 == j) // Is this LineSegment an edge of this polygon?
return false;
Plane polygonPlane = PlaneCCW();
LineSegment diagonal = polygonPlane.Project(LineSegment(p[i], p[j]));
// First check that this diagonal line is not intersected by an edge of this polygon.
for(int k = 0; k < (int)p.size(); ++k)
if (!(k == i || k+1 == i || k == j))
if (polygonPlane.Project(LineSegment(p[k], p[k+1])).Intersects(diagonal))
return false;
return IsConvex();
}
double OGRCircularString::get_Area() const
{
if( IsEmpty() || !get_IsClosed() )
return 0;
double cx = 0.0;
double cy = 0.0;
double square_R = 0.0;
if( IsFullCircle(cx, cy, square_R) )
{
return M_PI * square_R;
}
// Optimization for convex rings.
if( IsConvex() )
{
// Compute area of shape without the circular segments.
double dfArea = get_LinearArea();
// Add the area of the spherical segments.
dfArea += get_AreaOfCurveSegments();
return dfArea;
}
OGRLineString* poLS = CurveToLine();
const double dfArea = poLS->get_Area();
delete poLS;
return dfArea;
}
bool Polyhedron::ContainsConvex(const float3 &point) const
{
assume(IsConvex());
for(int i = 0; i < NumFaces(); ++i)
if (FacePlane(i).SignedDistance(point) > 0.f)
return false;
return true;
}
Polygon::Polygon(std::vector<sf::Vector2f> points, sf::Color color, sf::Vector2f position)
{
//No points = nothing to do
if (points.size() < 0)
return;
//Check if shape is concave or convex
if (IsConvex(points))
{
//If it is convex, we only have 1 shape in m_shapes
CreateConvexPolygon(points, color);
}
m_shape.setPosition(position);
}
bool Polyhedron::ClipLineSegmentToConvexPolyhedron(const float3 &ptA, const float3 &dir,
float &tFirst, float &tLast) const
{
assume(IsConvex());
// Intersect line segment against each plane.
for(int i = 0; i < NumFaces(); ++i)
{
/* Denoting the dot product of vectors a and b with <a,b>, we have:
The points P on the plane p satisfy the equation <P, p.normal> == p.d.
The points P on the line have the parametric equation P = ptA + dir * t.
Solving for the distance along the line for intersection gives
t = (p.d - <p.normal, ptA>) / <p.normal, dir>.
*/
Plane p = FacePlane(i);
float denom = Dot(p.normal, dir);
float dist = p.d - Dot(p.normal, ptA);
// Avoid division by zero. In this case the line segment runs parallel to the plane.
if (Abs(denom) < 1e-5f)
{
// If <P, p.normal> < p.d, then the point lies in the negative halfspace of the plane, which is inside the polyhedron.
// If <P, p.normal> > p.d, then the point lies in the positive halfspace of the plane, which is outside the polyhedron.
// Therefore, if p.d - <ptA, p.normal> == dist < 0, then the whole line is outside the polyhedron.
if (dist < 0.f)
return false;
}
else
{
float t = dist / denom;
if (denom < 0.f) // When entering halfspace, update tFirst if t is larger.
tFirst = Max(t, tFirst);
else // When exiting halfspace, updeate tLast if t is smaller.
tLast = Min(t, tLast);
if (tFirst > tLast)
return false; // We clipped the whole line segment.
}
}
return true;
}
float3 Polyhedron::ClosestPointConvex(const float3 &point) const
{
assume(IsConvex());
if (ContainsConvex(point))
return point;
float3 closestPoint = float3::nan;
float closestDistance = FLT_MAX;
for(int i = 0; i < NumFaces(); ++i)
{
float3 closestOnPoly = FacePolygon(i).ClosestPoint(point);
float d = closestOnPoly.DistanceSq(point);
if (d < closestDistance)
{
closestPoint = closestOnPoly;
closestDistance = d;
}
}
return closestPoint;
}
void VoronoiPolygonSite::DrawSiteFilled()
{
// DETERMINE WINDING ORDER (ONLY DRAW CAP ON CCW, "OUTSIDE" IS REALLY OUTSIDE)
if (OrderingIsCCW(Pts,NumPts))
{
// DETERMINE IF POLYGON IS CONVEX OR NONCONVEX
if (IsConvex(Pts,NumPts))
{
glBegin(GL_POLYGON);
for (int k=0; k<(NumPts*2); k+=2)
glVertex2fv(&(Pts[k]));
glEnd();
}
else // NONCONVEX POLYGONS MUST BE TRIANGULATED (OPENGL DOES NOT HANDLE NONCONVEX)
{
//DrawNonconvexPoly(Pts,NumPts);
DrawSiteFilledWithTessPoly(Pts, NumPts);
}
} else {
DrawSiteFilledWithTessPoly(Pts, NumPts);
}
}
TriangulateEC<Real>::TriangulateEC (int iQuantity,
const Vector2<Real>* akPosition, Query::Type eQueryType, Real fEpsilon,
int*& raiIndex)
{
assert(iQuantity >= 3 && akPosition);
if (eQueryType == Query::QT_FILTERED)
{
assert((Real)0.0 <= fEpsilon && fEpsilon <= (Real)1.0);
}
Vector2<Real>* akSPosition = 0;
Vector2<Real> kMin, kMax, kRange;
Real fScale;
int i;
switch (eQueryType)
{
case Query::QT_INT64:
// Transform the vertices to the square [0,2^{20}]^2.
Vector2<Real>::ComputeExtremes(iQuantity,akPosition,kMin,kMax);
kRange = kMax - kMin;
fScale = (kRange[0] >= kRange[1] ? kRange[0] : kRange[1]);
fScale *= (Real)(1 << 20);
akSPosition = WM4_NEW Vector2<Real>[iQuantity];
for (i = 0; i < iQuantity; i++)
{
akSPosition[i] = (akPosition[i] - kMin)*fScale;
}
m_pkQuery = WM4_NEW Query2Int64<Real>(iQuantity,akSPosition);
break;
case Query::QT_INTEGER:
// Transform the vertices to the square [0,2^{24}]^2.
Vector2<Real>::ComputeExtremes(iQuantity,akPosition,kMin,kMax);
kRange = kMax - kMin;
fScale = (kRange[0] >= kRange[1] ? kRange[0] : kRange[1]);
fScale *= (Real)(1 << 24);
akSPosition = WM4_NEW Vector2<Real>[iQuantity];
for (i = 0; i < iQuantity; i++)
{
akSPosition[i] = (akPosition[i] - kMin)*fScale;
}
m_pkQuery = WM4_NEW Query2TInteger<Real>(iQuantity,akSPosition);
break;
case Query::QT_REAL:
// Transform the vertices to the square [0,1]^2.
Vector2<Real>::ComputeExtremes(iQuantity,akPosition,kMin,kMax);
kRange = kMax - kMin;
fScale = (kRange[0] >= kRange[1] ? kRange[0] : kRange[1]);
akSPosition = WM4_NEW Vector2<Real>[iQuantity];
for (i = 0; i < iQuantity; i++)
{
akSPosition[i] = (akPosition[i] - kMin)*fScale;
}
m_pkQuery = WM4_NEW Query2<Real>(iQuantity,akSPosition);
break;
case Query::QT_RATIONAL:
// No transformation of the input data.
m_pkQuery = WM4_NEW Query2TRational<Real>(iQuantity,akPosition);
break;
case Query::QT_FILTERED:
// No transformation of the input data.
m_pkQuery = WM4_NEW Query2Filtered<Real>(iQuantity,akPosition,
fEpsilon);
break;
}
int iQm1 = iQuantity - 1;
raiIndex = WM4_NEW int[3*iQm1];
int* piIndex = raiIndex;
m_akVertex = WM4_NEW Vertex[iQuantity];
m_iCFirst = -1;
m_iCLast = -1;
m_iRFirst = -1;
m_iRLast = -1;
m_iEFirst = -1;
m_iELast = -1;
// Create a circular list of the polygon vertices for dynamic removal of
// vertices. Keep track of two linear sublists, one for the convex
// vertices and one for the reflex vertices. This is an O(N) process
// where N is the number of polygon vertices.
for (i = 0; i <= iQm1; i++)
{
// link the vertices
Vertex& rkV = V(i);
rkV.VPrev = (i > 0 ? i-1 : iQm1);
rkV.VNext = (i < iQm1 ? i+1 : 0);
// link the convex/reflex vertices
if (IsConvex(i))
{
InsertAfterC(i);
}
else
{
InsertAfterR(i);
}
}
if (m_iRFirst == -1)
{
// polygon is convex, just triangle fan it
for (i = 1; i < iQm1; i++)
{
*piIndex++ = 0;
*piIndex++ = i;
*piIndex++ = i+1;
}
return;
}
// Identify the ears and build a circular list of them. Let V0, V1, and
// V2 be consecutive vertices forming a triangle T. The vertex V1 is an
// ear if no other vertices of the polygon lie inside T. Although it is
// enough to show that V1 is not an ear by finding at least one other
// vertex inside T, it is sufficient to search only the reflex vertices.
// This is an O(C*R) process where C is the number of convex vertices and
// R is the number of reflex vertices, N = C+R. The order is O(N^2), for
// example when C = R = N/2.
for (i = m_iCFirst; i != -1; i = V(i).SNext)
{
if (IsEar(i))
{
InsertEndE(i);
}
}
V(m_iEFirst).EPrev = m_iELast;
V(m_iELast).ENext = m_iEFirst;
// Remove the ears, one at a time.
while (true)
{
// add triangle of ear to output
int iVPrev = V(m_iEFirst).VPrev;
int iVNext = V(m_iEFirst).VNext;
*piIndex++ = iVPrev;
*piIndex++ = m_iEFirst;
*piIndex++ = iVNext;
// remove the vertex corresponding to the ear
RemoveV(m_iEFirst);
if (--iQuantity == 3)
{
// Only one triangle remains, just remove the ear and copy it.
RemoveE();
iVPrev = V(m_iEFirst).VPrev;
iVNext = V(m_iEFirst).VNext;
*piIndex++ = iVPrev;
*piIndex++ = m_iEFirst;
*piIndex++ = iVNext;
break;
}
// removal of the ear can cause an adjacent vertex to become an ear
bool bWasReflex;
Vertex& rkVPrev = V(iVPrev);
if (!rkVPrev.IsEar)
{
bWasReflex = !rkVPrev.IsConvex;
if (IsConvex(iVPrev))
{
if (bWasReflex)
{
RemoveR(iVPrev);
}
if (IsEar(iVPrev))
{
InsertBeforeE(iVPrev);
}
}
}
Vertex& rkVNext = V(iVNext);
if (!rkVNext.IsEar)
{
bWasReflex = !rkVNext.IsConvex;
if (IsConvex(iVNext))
{
if (bWasReflex)
{
RemoveR(iVNext);
}
if (IsEar(iVNext))
{
InsertAfterE(iVNext);
}
}
}
// remove the ear
RemoveE();
}
WM4_DELETE[] akSPosition;
WM4_DELETE m_pkQuery;
}