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geom Namespace Reference

All classes and functions in the computational geometry package are defined in the geom namespace. More...


Classes

class  RegularGrid
 A regular grid in N-D. More...
class  Ball
 A ball in N dimensional space. More...
class  BBox
 An axes-oriented bounding box in the specified dimension. More...
class  Circle3
 A circle in 3-dimensional space. More...
class  CircularArc3
 A circular arc in 3-dimensional space. More...
class  Interval
 An axes-oriented interval in the specified dimension. More...
class  Line_2
 A line in 2-D. More...
class  ParametrizedLine
 A parametrized line in N-D. More...
class  ParametrizedPlane
 A parametrized plane in N-D. More...
class  Plane
 A plane in 3 dimensions. More...
class  Segment
 A segment in N dimensional space. More...
class  SegmentMath
 A segment in N dimensional space designed for doing math operations. More...
class  SemiOpenInterval
 An axes-oriented semi-open interval in N dimensions. More...
class  Triangle
 A class for a triangle in N dimensions. More...
class  IndSimpSet
 Class for a mesh that stores vertices and indexed simplices. More...
class  IndSimpSetIncAdj
 An indexed simplex set that stores vertex-simplex incidences and simplex adjacencies. More...
class  ISS_Interpolate
 Interpolation for an indexed simplex set with fields at the vertices. More...
class  ISS_Distance
 Functor that returns the distance to a mesh. More...
class  ISS_SD_Distance
 Functor that returns the signed distance to an (N-1)-D mesh in N-D space. More...
class  ISS_SD_ClosestPoint
 Functor that returns the closest point to an (N-1)-D mesh in N-D space. More...
class  ISS_SD_ClosestPointDirection
 Functor that returns the closest point along a specified direction to an (N-1)-D mesh in N-D space. More...
class  ISS_SD_CloserPointDirection
 Functor that returns the closest point along a specified direction to an (N-1)-D mesh in N-D space. More...
class  ISS_SD_CloserPoint
 Functor that returns a closer point to an (N-1)-D mesh in N-D space. More...
class  ISS_SimplexQuery
 Simplex queries on an indexed simplex set. More...
class  ISS_VertexField
 Indexed simplex set with fields at the vertices. More...
class  SimplexAdj
 Simplex-simplex adjacencies in an M-D indexed simplex set. More...
class  VertexSimplexInc
 Vertex-simplex incidences in an M-D indexed simplex set. More...
class  ComplexWithFreeVertex
 A local simplicial complex with a free node at the center. More...
class  ComplexContentConstraint
 Functor that evaluates the content constraint for a local simplicial mesh. More...
class  ComplexNorm2
 Functor that evaluates the 2-norm of the quality metric for a local simplicial mesh. More...
class  ComplexNorm2Mod
 Functor that evaluates the 2-norm of the modified quality metric for a local simplicial mesh. More...
class  ComplexWithFreeVertexOnManifoldBase
 A base class for a local simplicial complex with a free node on a manifold. More...
class  ComplexWithFreeVertexOnManifold< QF, N, 1, _Manifold, T >
 A local simplicial complex with a free node on a manifold. More...
class  ComplexWithFreeVertexOnManifold< QF, N, 2, _Manifold, T >
 A local simplicial complex with a free node on a manifold. More...
class  ComplexManifoldNorm2
 Functor that evaluates the 2-norm of the quality metric for a local simplicial mesh. More...
class  ComplexManifoldNorm2Mod
 Functor that evaluates the 2-norm of the modified quality metric for a local simplicial mesh. More...
class  SimplexDeterminant
 Functor for the determinant of the Jacobian matrix. More...
class  SimplexContent
 Functor for the content of a simplex. More...
class  SimplexMinimumEdgeLength
 Functor for the minimum edge length of a simplex. More...
class  SimplexMaximumEdgeLength
 Functor for the minimum edge length of a simplex. More...
class  Simplex
 A simplex in N dimensions. More...
class  SimplexAdjJac
 Implements operations for the adjoint Jacobian matrix of a simplex. More...
class  SimplexAdjJacQF
 Quality function of the Jacobian and its adjoint. More...
class  SimplexCondNum
 Implements the condition number quality metric. More...
class  SimplexJac
 Implements operations for the Jacobian matrix of a simplex. More...
class  SimplexJacQF
 Simplex quality functions of the Jacobian matrix. More...
class  SimplexMeanRatio
 Implements the mean ratio quality metric. More...
class  SimplexModCondNum
 Implements the modified condition number quality metric. More...
class  SimplexModDet
 Implements operations for modifying the determinant of the Jacobian. More...
class  SimplexModMeanRatio
 Implements the mean ratio quality metric. More...
class  SimplexWithFreeVertex
 A simplex with a free vertex. More...
class  EdgeRemoval
 Edge removal in a tetrahedral mesh. More...
class  FaceRemoval
 Edge removal in a tetrahedral mesh. More...
class  IsNotSharpAngle
 Functor that returns true iff the boundary angle is not sharp. More...
class  Node_AllIncCells
 Node in a simplicial mesh that stores iterators to all incident cells. More...
class  Node_OneIncCell
 Vertex in a simplicial mesh that stores one cell incidence. More...
class  Node_VertSelf
 A node in a simplicial mesh that stores a vertex and an iterator to itself. More...
class  Node_VertSelfId
 A node in a simplicial mesh that stores a vertex, an iterator to itself, and an identifier. More...
class  SimpMeshRed
 A simplicial mesh data structure. More...
class  SmrCell
 Cell in a simplicial mesh that stores handles to the adjacent cells. More...
class  SmrNode
 Node in a simplicial mesh that stores iterators to all incident cells. More...
class  StructuredGrid
 Class for a structured grid. More...
class  CyclicIndex
 A class for a cyclic index. More...
class  IndexedEdgePolyhedron
 Class for an indexed edge polyhedron in 3-D. More...
class  Polygon
 Class for a polygon in 2-D. More...
class  ScanConversionPolygon
 Class for a polygon in 2-D. More...
class  ScanConversionPolyhedron
 A class for a polyhedron in 3-D designed for scan conversion. More...
class  BBoxTreeTypes
 Define types for a BBoxTree. More...
class  BBoxTreeNode
 Abstract base class for nodes in a BBoxTree. More...
class  BBoxTreeLeaf
 Class for a leaf in a BBoxTree. More...
class  BBoxTreeBranch
 Class for an internal node in a BBoxTree. More...
class  BBoxTree
 A bounding box tree in N-D. More...

Functions

template<int N, int M, typename T>
void readAscii (std::istream &in, IndSimpSet< N, M, true, T > *mesh)
 Read a mesh in ascii format.
template<int N, int M, typename T>
void writeAscii (std::ostream &out, const IndSimpSet< N, M, true, T > &mesh)
 Write a mesh in ascii format.
template<typename T>
void computeClosestPoint (const Circle3< T > &circle, typename Circle3< T >::Point x, typename Circle3< T >::Point *closestPoint)
 Compute the closest point on the circle.
template<typename T>
void computeClosestPoint (const Circle3< T > &circle, const typename Circle3< T >::Point &source, const typename Circle3< T >::Point &target, typename Circle3< T >::Point *closestPoint, T tolerance=std::sqrt(std::numeric_limits< T >::epsilon()), int maximumSteps=10)
 Compute the closest point on the circle to the edge.
template<typename T>
void computeClosestPoint (const CircularArc3< T > &circularArc, typename CircularArc3< T >::Point x, typename CircularArc3< T >::Point *closestPoint)
 Compute the closest point on the circular arc.
template<typename T>
void computeClosestPoint (const Circle3< T > &circle, const CircularArc3< T > &circularArc, typename CircularArc3< T >::Point *closestPoint, T tolerance=std::sqrt(std::numeric_limits< T >::epsilon()), int maximumSteps=10)
 Compute the closest point on the circle to the circular arc.
template<int N, typename T>
T computeDistance (const ads::FixedArray< N, T > &x, const ads::FixedArray< N, T > &y)
 Return the distance between the points x and y.
template<int N, typename T>
T computeDistance (const ads::FixedArray< 2, ads::FixedArray< N, T > > &x)
 Return the distance between the points x[0] and x[1].
template<int N, typename T>
T computeContent (const ads::FixedArray< N, T > &x, const ads::FixedArray< N, T > &y)
 Return the distance between the points x and y.
template<int N, typename T>
T computeContent (const ads::FixedArray< 2, ads::FixedArray< N, T > > &x)
 Return the distance between the points x[0] and x[1].
template<int N, typename T>
void computeGradientOfDistance (const ads::FixedArray< N, T > &x, const ads::FixedArray< N, T > &y, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to x) of the distance between the points x and y.
template<int N, typename T>
void computeGradientOfDistance (const ads::FixedArray< 2, ads::FixedArray< N, T > > &x, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to x[0]) of the distance between the points x[0] and x[1].
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< N, T > &x, const ads::FixedArray< N, T > &y, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to x) of the distance between the points x and y.
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< 2, ads::FixedArray< N, T > > &x, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to x[0]) of the distance between the points x[0] and x[1].
template<typename T>
T computeArea (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c)
 Return the area of the triangle with points a, b and c.
template<typename T>
T computeArea (const ads::FixedArray< 3, ads::FixedArray< 2, T > > &p)
 Return the area of the triangle with points p[0], p[1] and p[2].
template<typename T>
T computeArea (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c)
 Return the area of the triangle with points a, b and c.
template<typename T>
T computeArea (const ads::FixedArray< 3, ads::FixedArray< 3, T > > &p)
 Return the area of the triangle with points p[0], p[1] and p[2].
template<int N, typename T>
T computeContent (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b, const ads::FixedArray< N, T > &c)
 Return the area of the triangle with points a, b and c.
template<int N, typename T>
T computeContent (const ads::FixedArray< 3, ads::FixedArray< N, T > > &p)
 Return the area of the triangle with points p[0], p[1] and p[2].
template<typename T>
void computeGradientOfArea (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, ads::FixedArray< 2, T > *gradient)
 Calculate the gradient (with respect to a) of the area of the triangle with points a, b and c.
template<typename T>
void computeGradientOfArea (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c, ads::FixedArray< 3, T > *gradient)
 Calculate the gradient (with respect to a) of the area of the triangle with points a, b and c.
template<int N, typename T>
void computeGradientOfArea (const ads::FixedArray< 3, ads::FixedArray< N, T > > &p, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the area of the triangle with points p[0], p[1] and p[2].
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b, const ads::FixedArray< N, T > &c, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the area of the triangle with points a, b and c.
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< 3, ads::FixedArray< N, T > > &p, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the area of the triangle with points p[0], p[1] and p[2].
template<int N, typename T>
T computeVolume (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b, const ads::FixedArray< N, T > &c, const ads::FixedArray< N, T > &d)
 Return the volume of the tetrahedron with points a, b, c and d.
template<int N, typename T>
T computeVolume (const ads::FixedArray< 4, ads::FixedArray< N, T > > &p)
 Return the volume of the tetrahedron with points p[0], p[1], p[2] and p[3].
template<int N, typename T>
T computeContent (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b, const ads::FixedArray< N, T > &c, const ads::FixedArray< N, T > &d)
 Return the volume of the tetrahedron with points a, b, c and d.
template<int N, typename T>
T computeContent (const ads::FixedArray< 4, ads::FixedArray< N, T > > &p)
 Return the volume of the tetrahedron with points p[0], p[1], p[2] and p[3].
template<typename T>
void computeGradientOfVolume (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c, const ads::FixedArray< 3, T > &d, ads::FixedArray< 3, T > *gradient)
 Calculate the gradient (with respect to a) of the volume of the tetrahedron with points a, b, c and d.
template<int N, typename T>
void computeGradientOfVolume (const ads::FixedArray< 4, ads::FixedArray< N, T > > &p, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the volume of the tetrahedron with points p[0], p[1], p[2] and p[3].
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b, const ads::FixedArray< N, T > &c, const ads::FixedArray< N, T > &d, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the volume of the tetrahedron with points a, b, c and d.
template<int N, typename T>
void computeGradientOfContent (const ads::FixedArray< 4, ads::FixedArray< N, T > > &p, ads::FixedArray< N, T > *gradient)
 Calculate the gradient (with respect to a) of the volume of the tetrahedron with points p[0], p[1], p[2] and p[3].
template<int N, typename T>
T computeUpperBoundOnSignedDistance (const BBox< N, T > &box, const typename BBox< N, T >::Point &x)
 Return an upper bound on the signed distance from the point to the objects in the box.
template<int N, typename T>
T computeLowerBoundOnSignedDistance (const BBox< N, T > &box, const typename BBox< N, T >::Point &x)
 Return an lower bound on the signed distance from the point to the objects in the box.
template<int N, typename T>
T computeUpperBoundOnUnsignedDistance (const BBox< N, T > &box, const typename BBox< N, T >::Point &x)
 Return an upper bound on the signed distance.
template<int N, typename T>
T computeLowerBoundOnUnsignedDistance (const BBox< N, T > &box, const typename BBox< N, T >::Point &x)
 Return a lower bound on the signed distance.
template<typename T>
T computeOrientationDeterminant (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c)
 Compute the orientation determinant.
template<typename T>
T computeInCircleDeterminant (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, const ads::FixedArray< 2, T > &d)
 Compute the in-circle determinant.
template<typename T>
bool isInCircle (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, const ads::FixedArray< 2, T > &d)
 Return true if d is inside the circle with a, b, and c on its boundary.
template<int N, typename T>
T computeDotProduct (const ads::FixedArray< N, T > &x, const ads::FixedArray< N, T > &y)
 Return the dot product of x and y.
template<typename T>
ads::FixedArray< 3, T > computeCrossProduct (const ads::FixedArray< 3, T > &x, const ads::FixedArray< 3, T > &y)
 Return the cross product of x and y.
template<typename T>
void computeCrossProduct (const ads::FixedArray< 3, T > &x, const ads::FixedArray< 3, T > &y, ads::FixedArray< 3, T > *result)
 Compute the cross product of x and y.
template<typename T>
T computeTripleProduct (const ads::FixedArray< 3, T > &a, const ads::FixedArray< 3, T > &b, const ads::FixedArray< 3, T > &c)
 The scalar triple product of three vectors: $a \cdot b \times c$.
template<typename T>
T computeDiscriminant (const ads::FixedArray< 2, T > &p, const ads::FixedArray< 2, T > &q)
 Return the discriminant of the vectors.
template<typename T>
void computeAnOrthogonalVector (const ads::FixedArray< 3, T > &vector, ads::FixedArray< 3, T > *orthogonal)
 Compute an orthogonal vector.
template<int N, typename T>
T computeSquaredMagnitude (const ads::FixedArray< N, T > &x)
 Return the squared magnitude of this vector.
template<int N, typename T>
T computeMagnitude (const ads::FixedArray< N, T > &x)
 Return the magnitude of this vector.
template<int N, typename T>
void normalize (ads::FixedArray< N, T > *x)
 Normalize this vector so it has unit length.
template<int N, typename T>
T computeSquaredDistance (const ads::FixedArray< N, T > &p, const ads::FixedArray< N, T > &q)
 Return the squared distance between two points.
template<typename T>
int computeSignOfTurn (const ads::FixedArray< 2, T > &p, const ads::FixedArray< 2, T > &q, const ads::FixedArray< 2, T > &r)
 Positive turn: return 1. No turn: return 0. Negative turn: return -1.
template<typename T>
int computeApproximateSignOfTurn (const ads::FixedArray< 2, T > &p, const ads::FixedArray< 2, T > &q, const ads::FixedArray< 2, T > &r)
 Positive turn: return 1. No turn: return 0. Negative turn: return -1.
template<typename T>
T computePseudoAngle (const ads::FixedArray< 2, T > &vec)
 Return the pseudo-angle between vec and the x axis.
template<int N, typename T>
T computeAngle (const ads::FixedArray< N, T > &a, const ads::FixedArray< N, T > &b)
 Return the angle between the two vectors.
template<typename T>
void rotatePiOver2 (ads::FixedArray< 2, T > *p)
 Rotate the vector + pi / 2.
template<typename T>
void rotateMinusPiOver2 (ads::FixedArray< 2, T > &p)
 Rotate the vector - pi / 2.
template<bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< 2, 1, A, T, V, IS > *mesh, const ISS_SD_ClosestPoint< ISS > &condition, int n)
 Apply the closest point boundary condition at a vertex.
template<bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< 2, 1, A, T, V, IS > *mesh, const ISS_SD_ClosestPointDirection< ISS > &condition, int n)
 Apply the closest point in the normal direction boundary condition at a vertex.
template<bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< 3, 2, A, T, V, IS > *mesh, const ISS_SD_ClosestPoint< ISS > &condition, int n)
 Apply the closest point boundary condition at a vertex.
template<bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< 3, 2, A, T, V, IS > *mesh, const ISS_SD_ClosestPointDirection< ISS > &condition, int n)
 Apply the closest point in the normal direction boundary condition at a vertex.
template<int N, bool A, typename T, typename V, typename IS, class UnaryFunction>
void applyBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const UnaryFunction &condition, int n)
 Apply the condition at a vertex.
template<int N, bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const ISS_SD_ClosestPoint< ISS > &condition, int n)
 Apply the closest point boundary condition at a vertex.
template<int N, bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const ISS_SD_CloserPoint< ISS > &condition, int n)
 Apply the closer point boundary condition at a vertex.
template<int N, bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const ISS_SD_ClosestPointDirection< ISS > &condition, int n)
 Apply the closest point in the normal direction boundary condition at a vertex.
template<int N, bool A, typename T, typename V, typename IS, class ISS>
void applyBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const ISS_SD_CloserPointDirection< ISS > &condition, int n)
 Apply the closer point in the normal direction boundary condition at a vertex.
template<int M, typename T, typename VertRAIter, typename ISInIter, typename OutputIterator>
void computeMeanRatio (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, OutputIterator output)
 Calculate the mean ratio function for each simplex in the mesh.
template<int M, typename T, typename SimpInIter, typename OutputIterator>
void computeMeanRatio (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, OutputIterator output)
 Calculate the mean ratio function for each simplex in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter, typename OutputIterator>
void computeModifiedMeanRatio (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, OutputIterator output)
 Calculate the modified mean ratio function for each simplex in the mesh.
template<int M, typename T, typename SimpInIter, typename OutputIterator>
void computeModifiedMeanRatio (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, OutputIterator output)
 Calculate the modified mean ratio function for each simplex in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter, typename OutputIterator>
void computeConditionNumber (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, OutputIterator output)
 Calculate the condition number function for each simplex in the mesh.
template<int M, typename T, typename SimpInIter, typename OutputIterator>
void computeConditionNumber (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, OutputIterator output)
 Calculate the condition number function for each simplex in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter, typename OutputIterator>
void computeModifiedConditionNumber (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, OutputIterator output)
 Calculate the modified condition number function for each simplex in the mesh.
template<int M, typename T, typename SimpInIter, typename OutputIterator>
void computeModifiedConditionNumber (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, OutputIterator output)
 Calculate the modified condition number function for each simplex in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter, typename OutputIterator>
void computeContent (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, OutputIterator output)
 Calculate the content for each simplex in the mesh.
template<int M, typename T, typename SimpInIter, typename OutputIterator>
void computeContent (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, OutputIterator output)
 Calculate the content for each simplex in the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 2, 1, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS > &mesh, const ads::Array< 1, typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Number > &squaredHalfLengths, const typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Vertex &point, typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Vertex *closestPoint)
 Compute the signed distance to the mesh and closest point on the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 2, 1, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS > &mesh, const typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Vertex &point, typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Vertex *closestPoint)
 Compute the signed distance to the mesh and closest point on the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 2, 1, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS > &mesh, const typename IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS >::Vertex &point)
 Compute the signed distance to the mesh.
template<bool _A, typename _T, typename _V, typename _IS, typename InputIterator, typename NumberOutputIterator, typename PointOutputIterator>
void computeSignedDistance (const IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS > &mesh, InputIterator pointsBeginning, InputIterator pointsEnd, NumberOutputIterator distances, PointOutputIterator closestPoints)
 Compute the signed distances to the mesh and closest points on the mesh.
template<bool _A, typename _T, typename _V, typename _IS, typename InputIterator, typename NumberOutputIterator>
void computeSignedDistance (const IndSimpSetIncAdj< 2, 1, _A, _T, _V, _IS > &mesh, InputIterator pointsBeginning, InputIterator pointsEnd, NumberOutputIterator distances)
 Compute the signed distances to the mesh and closest points on the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 3, 2, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS > &mesh, const ads::Array< 1, typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Number > &squaredLongestEdgeLengths, const typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Vertex &point, typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Vertex *closestPoint)
 Compute the signed distance to the mesh and closest point on the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 3, 2, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS > &mesh, const typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Vertex &point, typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Vertex *closestPoint)
 Compute the signed distance to the mesh and closest point on the mesh.
template<bool _A, typename _T, typename _V, typename _IS>
IndSimpSetIncAdj< 3, 2, _A,
_T, _V, _IS >::Number 		computeSignedDistance (const IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS > &mesh, const typename IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS >::Vertex &point)
 Compute the signed distance to the mesh.
template<bool _A, typename _T, typename _V, typename _IS, typename InputIterator, typename NumberOutputIterator, typename PointOutputIterator>
void computeSignedDistance (const IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS > &mesh, InputIterator pointsBeginning, InputIterator pointsEnd, NumberOutputIterator distances, PointOutputIterator closestPoints)
 Compute the signed distances to the mesh and closest points on the mesh.
template<bool _A, typename _T, typename _V, typename _IS, typename InputIterator, typename NumberOutputIterator>
void computeSignedDistance (const IndSimpSetIncAdj< 3, 2, _A, _T, _V, _IS > &mesh, InputIterator pointsBeginning, InputIterator pointsEnd, NumberOutputIterator distances)
 Compute the signed distances to the mesh and closest points on the mesh.
template<int N, typename PtForIter, typename PtOutIter, typename IntOutIter, typename T>
void buildDistinctPoints (PtForIter pointsBeginning, PtForIter pointsEnd, PtOutIter distinctPointsOutput, IntOutIter indicesOutput, const T minDistance)
 From a set of points, generate an indexed set of distinct points.
template<int N, typename PtForIter, typename PtOutIter, typename IntOutIter>
void buildDistinctPoints (PtForIter pointsBeginning, PtForIter pointsEnd, PtOutIter distinctPoints, IntOutIter indices)
 From a set of points, generate an indexed set of distinct points.
template<int N, int M, bool A, typename T, typename V, typename IS>
void removeDuplicateVertices (IndSimpSet< N, M, A, T, V, IS > *x, T minDistance)
 Remove duplicate vertices.
template<int N, int M, bool A, typename T, typename V, typename IS>
void removeDuplicateVertices (IndSimpSet< N, M, A, T, V, IS > *x)
 Remove duplicate vertices.
template<int N, int M, typename VertForIter, typename ISForIter>
void writeIssAscii (std::ostream &out, VertForIter verticesBeginning, VertForIter verticesEnd, ISForIter indexedSimplicesBeginning, ISForIter indexedSimplicesEnd)
 Write an indexed simplex set in ascii format.
template<int N, int M, typename VertForIter, typename ISForIter>
void writeIssBinary (std::ostream &out, VertForIter verticesBeginning, VertForIter verticesEnd, ISForIter indexedSimplicesBeginning, ISForIter indexedSimplicesEnd)
 Write an indexed simplex set in binary format.
template<int N, int M, typename VertForIter, typename ISForIter, typename ContainerIter, typename StringIter>
void writeIssAndCellDataVtkXml (std::ostream &out, VertForIter verticesBeginning, VertForIter verticesEnd, ISForIter indexedSimplicesBeginning, ISForIter indexedSimplicesEnd, ContainerIter cellDataContainersBeginning, ContainerIter cellDataContainersEnd, StringIter dataNamesBeginning, StringIter dataNamesEnd)
 Write in VTK XML unstructured grid format with a cell field.
template<int N, int M, typename VertForIter, typename ISForIter>
void writeIssVtkXml (std::ostream &out, VertForIter verticesBeginning, VertForIter verticesEnd, ISForIter indexedSimplicesBeginning, ISForIter indexedSimplicesEnd)
 Write in VTK XML unstructured grid format.
template<int N, int M, typename VertForIter, typename ISForIter>
void writeIssVtkLegacy (std::ostream &out, VertForIter verticesBeginning, VertForIter verticesEnd, ISForIter indexedSimplicesBeginning, ISForIter indexedSimplicesEnd, std::string title="")
 Write in legacy VTK unstructured grid format.
template<bool A, typename T, typename V, typename IS>
IndSimpSetIncAdj< 2, 1, A,
T, V, IS >::Vertex 		computeVertexNormal (const IndSimpSetIncAdj< 2, 1, A, T, V, IS > &mesh, int n)
 Return the outward normal at the specified vertex.
template<bool A, typename T, typename V, typename IS>
void computeVertexNormal (const IndSimpSetIncAdj< 2, 1, A, T, V, IS > &mesh, int n, typename IndSimpSetIncAdj< 2, 1, A, T, V, IS >::Vertex *normal)
 Compute the outward normal at the specified vertex.
template<bool A, typename T, typename V, typename IS>
IndSimpSetIncAdj< 2, 2, A,
T, V, IS >::Vertex 		computeVertexNormal (const IndSimpSetIncAdj< 2, 2, A, T, V, IS > &mesh, int n)
 Return the outward normal at the specified boundary vertex.
template<bool A, typename T, typename V, typename IS>
void computeVertexNormal (const IndSimpSetIncAdj< 2, 2, A, T, V, IS > &mesh, int n, typename IndSimpSetIncAdj< 2, 2, A, T, V, IS >::Vertex *normal)
 Compute the outward normal at the specified boundary vertex.
template<bool A, typename T, typename V, typename IS>
IndSimpSetIncAdj< 3, 2, A,
T, V, IS >::Vertex 		computeVertexNormal (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, int n)
 Return the outward normal at the specified vertex.
template<bool A, typename T, typename V, typename IS>
void computeVertexNormal (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, int n, typename IndSimpSetIncAdj< 3, 2, A, T, V, IS >::Vertex *normal)
 Compute the outward normal at the specified vertex.
template<bool A, typename T, typename V, typename IS>
IndSimpSetIncAdj< 3, 3, A,
T, V, IS >::Vertex 		computeVertexNormal (const IndSimpSetIncAdj< 3, 3, A, T, V, IS > &mesh, int n)
 Return the outward normal at the specified boundary vertex.
template<bool A, typename T, typename V, typename IS>
void computeVertexNormal (const IndSimpSetIncAdj< 3, 3, A, T, V, IS > &mesh, int n, typename IndSimpSetIncAdj< 3, 3, A, T, V, IS >::Vertex *normal)
 Compute the outward normal at the specified boundary vertex.
template<bool A, typename T, typename V, typename IS>
void computeSimplexNormal (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, int simplexIndex, V *simplexNormal)
 Compute the outward normal for the specified simplex (triangle face).
template<bool A, typename T, typename V, typename IS, bool AA>
void computeSimplexNormals (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, ads::Array< 1, V, AA > *simplexNormals)
 Compute the outward normals for the simplices (triangle faces).
template<bool A, typename T, typename V, typename IS, bool AA>
void computeSimplexNormals (const IndSimpSetIncAdj< 2, 1, A, T, V, IS > &mesh, ads::Array< 1, V, AA > *simplexNormals)
 Compute the outward normals for the simplices (line segments).
template<bool A, typename T, typename V, typename IS, bool AA>
void computeVertexNormals (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, const ads::Array< 1, V, AA > &simplexNormals, ads::Array< 1, V, AA > *vertexNormals)
 Compute the outward normals for the vertices.
template<bool A, typename T, typename V, typename IS, bool A1, bool A2>
void computeSimplexAndVertexNormals (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, ads::Array< 1, V, A1 > *simplexNormals, ads::Array< 1, V, A2 > *vertexNormals)
 Compute the outward normals for the simplices and vertices.
template<int N, bool A, typename T, typename V, typename IS>
T computeCosineAngle (const IndSimpSetIncAdj< N, 1, A, T, V, IS > &mesh, int vertexIndex)
 Return the cosine of the interior angle at the specified vertex.
template<bool A, typename T, typename V, typename IS>
T computeCosineAngle (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, const typename IndSimpSetIncAdj< 3, 2, A, T, V, IS >::Face &face)
 Return the cosine of the interior angle at the specified 1-face.
template<bool A, typename T, typename V, typename IS>
T computeCosineBoundaryAngle (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, int vertexIndex)
 Return the cosine of the interior angle at the specified boundary vertex.
template<bool A, typename T, typename V, typename IS>
T computeAngle (const IndSimpSetIncAdj< 3, 2, A, T, V, IS > &mesh, int n)
 Return the solid interior angle at the specified vertex.
template<bool A, typename T, typename V, typename IS, typename OutputIterator>
void projectAndGetSimplices (const IndSimpSet< 2, 1, A, T, V, IS > &mesh, OutputIterator simplices)
 Project the line segments to 1-D and collect them.
template<bool A, typename T, typename V, typename IS, typename OutputIterator>
void projectAndGetSimplices (const IndSimpSet< 3, 2, A, T, V, IS > &mesh, OutputIterator simplices)
 Project the triangle simplices to 2-D and collect them.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS>
void geometricOptimizeInterior (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, int numSweeps=1)
 Optimize the position of the interior vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeInterior (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, int numSweeps=1)
 Make numSweeps optimization sweeps over the given interior vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS>
void geometricOptimizeInteriorUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const int numSweeps=1)
 Optimize the position of the interior vertices.
template<int N, bool A, typename T, typename V, typename IS>
void geometricOptimizeInteriorUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const int numSweeps=1)
 Optimize the position of the interior vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeBoundary (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, int numSweeps=1)
 Optimize the position of all boundary vertices.
template<template< int, typename > class QF, bool A, typename T, typename V, typename IS, typename IntForIter, int SD>
void geometricOptimizeBoundary (IndSimpSetIncAdj< 2, 2, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, PointsOnManifold< 2, 1, SD, T > *boundaryManifold, int numSweeps=1)
 Make numSweeps optimization sweeps over the given boundary vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeBoundaryUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all boundary vertices.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeBoundaryUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all boundary vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimize (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeWithBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeWithBoundaryConditionUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, int SD>
void geometricOptimizeWithBoundaryConditionUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of all vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, class BoundaryCondition>
void geometricOptimizeWithCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const BoundaryCondition &condition, int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, class BoundaryCondition>
void geometricOptimizeWithConditionUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const BoundaryCondition &condition, const int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS, class BoundaryCondition>
void geometricOptimizeWithConditionUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const BoundaryCondition &condition, const int numSweeps=1)
 Optimize the position of all vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS>
void geometricOptimize (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS>
void geometricOptimizeUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const int numSweeps=1)
 Optimize the position of all vertices.
template<int N, bool A, typename T, typename V, typename IS>
void geometricOptimizeUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, const int numSweeps=1)
 Optimize the position of all vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter, int SD>
void geometricOptimizeWithBoundaryCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, int numSweeps=1)
 Make numSweeps optimization sweeps over the given vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, int SD>
void geometricOptimizeWithBoundaryConditionUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of a set of vertices.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, int SD>
void geometricOptimizeWithBoundaryConditionUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, PointsOnManifold< N, N-1, SD, T > *boundaryManifold, const int numSweeps=1)
 Optimize the position of a set of vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithCondition (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, int numSweeps=1)
 Make numSweeps optimization sweeps over the given vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithConditionUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, int numSweeps=1)
 Optimize the position of a set of vertices.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithConditionUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, const int numSweeps=1)
 Optimize the position of a set of vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimize (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const int numSweeps=1)
 Make numSweeps optimization sweeps over the given vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const int numSweeps=1)
 Optimize the position of a set of vertices.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const int numSweeps=1)
 Optimize the position of a set of vertices.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithConditionConstrained (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, const T maxConstraintError, int numSweeps=1)
 Make numSweeps constrained optimization sweeps over the given vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithConditionConstrainedUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, const T maxConstraintError, int numSweeps=1)
 Optimize the position of a set of vertices subject to a constant content constraint.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter, class BoundaryCondition>
void geometricOptimizeWithConditionConstrainedUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const BoundaryCondition &condition, const T maxConstraintError, const int numSweeps=1)
 Optimize the position of a set of vertices subject to a constant content constraint.
template<template< int, typename > class QF, int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeConstrained (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const T maxConstraintError, const int numSweeps=1)
 Make numSweeps constrained optimization sweeps over the given vertices with the quality function given as a template parameter.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeConstrainedUsingMeanRatio (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const T maxConstraintError, const int numSweeps=1)
 Optimize the position of a set of vertices subject to a constant content constraint.
template<int N, bool A, typename T, typename V, typename IS, typename IntForIter>
void geometricOptimizeConstrainedUsingConditionNumber (IndSimpSetIncAdj< N, N, A, T, V, IS > *mesh, IntForIter begin, IntForIter end, const T maxConstraintError, const int numSweeps=1)
 Optimize the position of a set of vertices subject to a constant content constraint.
template<int M, typename SimpInIter, typename T>
void computeEdgeLengthStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumLength, T *maximumLength)
 Compute edge length statistics.
template<int M, typename VertRAIter, typename ISInIter, typename T>
void computeEdgeLengthStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumLength, T *maximumLength)
 Compute edge length statistics.
template<int N, bool A, typename T, typename V, typename IS>
void computeEdgeLengthStatistics (const IndSimpSetIncAdj< N, 2, A, T, V, IS > &mesh, T *minimumLength, T *maximumLength, T *meanLength)
 Compute edge length statistics.
template<int M, typename T, typename SimpInIter>
T computeMinimumEdgeLength (SimpInIter simplicesBeginning, SimpInIter simplicesEnd)
 Return the minimum edge length.
template<int M, typename T, typename SimpInIter>
T computeMaximumEdgeLength (SimpInIter simplicesBeginning, SimpInIter simplicesEnd)
 Return the maximum edge length.
template<int M, typename T, typename VertRAIter, typename ISInIter>
T computeContent (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd)
 Return the total content of the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
T computeContent (SimpInIter simplicesBeginning, SimpInIter simplicesEnd)
 Return the total content of the simplices in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter>
void computeContentStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumContent, T *maximumContent, T *meanContent)
 Calculate content (hypervolume) statistics for the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
void computeContentStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumContent, T *maximumContent, T *meanContent)
 Calculate content (hypervolume) statistics for the simplices in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter>
void computeDeterminantStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumDeterminant, T *maximumDeterminant, T *meanDeterminant)
 Calculate determinant statistics for the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
void computeDeterminantStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumDeterminant, T *maximumDeterminant, T *meanDeterminant)
 Calculate determinant statistics for the simplices in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter>
void computeModifiedMeanRatioStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumModMeanRatio, T *maximumModMeanRatio, T *meanModMeanRatio)
 Calculate modified mean ratio function statistics for the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
void computeModifiedMeanRatioStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumModMeanRatio, T *maximumModMeanRatio, T *meanModMeanRatio)
 Calculate modified mean ratio function statistics for the simplices in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter>
void computeModifiedConditionNumberStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumModCondNum, T *maximumModCondNum, T *meanModCondNum)
 Calculate modified condition number function statistics for the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
void computeModifiedConditionNumberStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumModCondNum, T *maximumModCondNum, T *meanModCondNum)
 Calculate modified condition number function statistics for the simplices in the mesh.
template<int M, typename T, typename VertRAIter, typename ISInIter>
void computeQualityStatistics (VertRAIter vertices, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd, T *minimumContent, T *maximumContent, T *meanContent, T *minimumDeterminant, T *maximumDeterminant, T *meanDeterminant, T *minimumModMeanRatio, T *maximumModMeanRatio, T *meanModMeanRatio, T *minimumModCondNum, T *maximumModCondNum, T *meanModCondNum)
 Calculate quality statistics for the simplices in the mesh.
template<int M, typename T, typename SimpInIter>
void computeQualityStatistics (SimpInIter simplicesBeginning, SimpInIter simplicesEnd, T *minimumContent, T *maximumContent, T *meanContent, T *minimumDeterminant, T *maximumDeterminant, T *meanDeterminant, T *minimumModMeanRatio, T *maximumModMeanRatio, T *meanModMeanRatio, T *minimumModCondNum, T *maximumModCondNum, T *meanModCondNum)
 Calculate quality statistics for the simplices in the mesh.
template<int N, int M, typename T, typename VertRAIter, typename ISInIter>
void printQualityStatistics (std::ostream &out, VertRAIter verticesBeginning, VertRAIter verticesEnd, ISInIter indexedSimplicesBeginning, ISInIter indexedSimplicesEnd)
 Print quality statistics for the simplices in the mesh.
template<int N, int M, typename T, typename SimpInIter>
void printQualityStatistics (std::ostream &out, SimpInIter simplicesBeginning, SimpInIter simplicesEnd)
 Print quality statistics for the simplices in the mesh.
template<typename IntForIter, typename IntOutIter>
void determineComplementSetOfIndices (const int upperBound, IntForIter beginning, IntForIter end, IntOutIter indexIterator)
 Make the complement set of indices.
template<int M>
std::ostream & operator<< (std::ostream &out, const SimplexAdj< M > &x)
 Write the simplex adjacencies.
template<int M>
std::ostream & operator<< (std::ostream &out, const VertexSimplexInc< M > &x)
 Write the vertex-simplex incidences.
template<int N, int M, typename T>
SimplexDeterminant< N, M, T > simplexDeterminant ()
 Convenience function for constructing a SimplexDeterminant.
template<int N, int M, typename T>
SimplexContent< N, M, T > simplexContent ()
 Convenience function for constructing a SimplexContent.
template<int N, int M, typename T>
SimplexMinimumEdgeLength<
N, M, T > 		simplexMinimumEdgeLength ()
 Convenience function for constructing a SimplexMinimumEdgeLength.
template<int N, int M, typename T>
SimplexMaximumEdgeLength<
N, M, T > 		simplexMaximumEdgeLength ()
 Convenience function for constructing a SimplexMaximumEdgeLength.
template<typename T>
void project (const Simplex< 1, ads::FixedArray< 2, T >, T > &s2, const ads::FixedArray< 2, T > &x2, Simplex< 1, ads::FixedArray< 1, T >, T > *s1, ads::FixedArray< 1, T > *x1)
 Project the simplex and the point in 2-D to 1-D.
template<typename T>
void project (const Simplex< 1, ads::FixedArray< 2, T >, T > &s2, const ads::FixedArray< 2, T > &x2, Simplex< 1, ads::FixedArray< 1, T >, T > *s1, ads::FixedArray< 1, T > *x1, ads::FixedArray< 1, T > *y1)
 Project the simplex and the point in 2-D to 1-D.
template<typename T>
void project (const Simplex< 2, ads::FixedArray< 3, T >, T > &s3, const ads::FixedArray< 3, T > &x3, Simplex< 2, ads::FixedArray< 2, T >, T > *s2, ads::FixedArray< 2, T > *x2)
 Project the simplex and the point in 3-D to 2-D.
template<typename T>
void project (const Simplex< 2, ads::FixedArray< 3, T >, T > &s3, const ads::FixedArray< 3, T > &x3, Simplex< 2, ads::FixedArray< 2, T >, T > *s2, ads::FixedArray< 2, T > *x2, ads::FixedArray< 1, T > *z1)
 Project the simplex and the point in 3-D to 2-D.
template<typename SMR, typename CellIteratorOutputIterator>
void getIncidentCells (const typename SMR::CellIterator cell, int i, int j, CellIteratorOutputIterator out)
 Get the incident cells of the edge.
template<class CellIterator, class NodeIterator>
int getFaceIndex (const CellIterator &cell, const NodeIterator &a, const NodeIterator &b)
 For a 2-simplex cell, a pair of nodes defines a 1-face. Return the index of this 1-face.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename ISSV, typename ISSIS>
void buildIndSimpSetFromSimpMeshRed (const SimpMeshRed< N, M, T, Node, Cell, Cont > &smr, IndSimpSet< N, M, true, T, ISSV, ISSIS > *iss)
 Make an indexed simplex set from the mesh.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int coarsen (SimpMeshRed< 2, 2, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, PointsOnManifold< 2, 1, SD, T > *manifold, int maxSweeps=0)
 Coarsen the mesh using the minimum edge length function.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int coarsen (SimpMeshRed< 2, 2, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, T cornerDeviation=-1, int maxSweeps=0)
 Coarsen the mesh using the min edge length function.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int coarsen (SimpMeshRed< 3, 2, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, PointsOnManifold< 3, 2, SD, T > *manifold, int maxSweeps=0)
 Coarsen the mesh using the min edge length function.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int coarsen (SimpMeshRed< 3, 2, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, T maxDihedralAngleDeviation=-1, T maxSolidAngleDeviation=-1, T maxBoundaryAngleDeviation=-1, int maxSweeps=0)
 Coarsen the mesh using the min edge length function.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int coarsen (SimpMeshRed< 3, 3, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, PointsOnManifold< 3, 2, SD, T > *manifold, int maxSweeps=0)
 Coarsen the mesh using the min edge length function.
template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int coarsen (SimpMeshRed< 3, 3, T, Node, Cell, Cont > *mesh, const MinEdgeLength &f, T minimumAllowedQuality, T qualityFactor, T maxDihedralAngleDeviation=-1, T maxSolidAngleDeviation=-1, T maxBoundaryAngleDeviation=-1, int maxSweeps=0)
 Coarsen the mesh using the min edge length function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInIter>
int coarsen (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, IntInIter begin, IntInIter end)
 Collapse edges to remove the specified cells.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void writeAscii (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &x)
 Write a mesh as an indexed simplex set in ascii format.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void print (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &x)
 Print detailed information about the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void writeBinary (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &x)
 Write a mesh as an indexed simplex set in binary format.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void readAscii (std::istream &in, SimpMeshRed< N, M, T, Node, Cell, Cont > *x)
 Read a mesh as an indexed simplex set in ascii format.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void readBinary (std::istream &in, SimpMeshRed< N, M, T, Node, Cell, Cont > *x)
 Read an indexed simplex set in binary format.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void writeVtkXml (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &x)
 Write in VTK XML unstructured grid format.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void writeVtkLegacy (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &x, std::string title="")
 Write in legacy VTK unstructured grid format.
template<class SMR>
SMR::Number computeIncidentCellsAngle (typename SMR::NodeConstIterator node)
 Return the solid angle accumulated from the incident cells.
template<class SMR>
SMR::Number computeDihedralAngle (typename SMR::ConstEdge edge)
 Compute the dihedral angle at the specified edge.
template<class SMR>
SMR::Number computeCosineAngle (typename SMR::FaceConstIterator face)
 Return the cosine of the interior angle at the specified 1-face.
template<class SMR>
void computeNodeNormal (typename SMR::NodeConstIterator node, typename SMR::Vertex *normal)
 Compute the normal to the surface.
template<class SMR>
SMR::Vertex computeNodeNormal (typename SMR::NodeConstIterator node)
 Return the normal to the surface.
template<class SMR>
void computeCellNormal (typename SMR::CellConstIterator cell, typename SMR::Vertex *normal)
 Compute the cell normal.
template<class SMR>
SMR::Vertex computeCellNormal (typename SMR::CellConstIterator cell)
 Return the normal to the surface.
template<class SMR>
void computeFaceNormal (typename SMR::CellConstIterator cell, int i, typename SMR::Vertex *x)
 Compute the face normal.
template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename OutputIterator>
void projectAndGetSimplices (const SimpMeshRed< 2, 1, T, Node, Cell, Cont > &mesh, OutputIterator simplices)
 Project the line segments to 1-D and collect them.
template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename OutputIterator>
void projectAndGetSimplices (const SimpMeshRed< 3, 2, T, Node, Cell, Cont > &mesh, OutputIterator simplices)
 Project the triangle simplices to 2-D and collect them.
template<int N, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
int incidenceOptimize (SimpMeshRed< N, 2, T, Node, Cell, Cont > *mesh, int norm, int numSweeps=0)
 Modify the topology to optimize the cell-node incidences.
template<int N, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
SimpMeshRed< N, 1, T, Node,
Cell, Cont >::CellIterator 		insertCell (SimpMeshRed< N, 1, T, Node, Cell, Cont > *mesh, const typename SimpMeshRed< N, 1, T, Node, Cell, Cont >::NodeIterator n0, const typename SimpMeshRed< N, 1, T, Node, Cell, Cont >::NodeIterator n1, const typename SimpMeshRed< N, 1, T, Node, Cell, Cont >::CellIterator c0=0, const typename SimpMeshRed< N, 1, T, Node, Cell, Cont >::CellIterator c1=0)
 Insert the specified cell into the 1-D mesh.
template<int N, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
SimpMeshRed< N, 2, T, Node,
Cell, Cont >::CellIterator 		insertCell (SimpMeshRed< N, 2, T, Node, Cell, Cont > *mesh, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::NodeIterator n0, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::NodeIterator n1, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::NodeIterator n2, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::CellIterator c0=0, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::CellIterator c1=0, const typename SimpMeshRed< N, 2, T, Node, Cell, Cont >::CellIterator c2=0)
 Insert the specified cell into the 2-D mesh.
template<int N, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
SimpMeshRed< N, 3, T, Node,
Cell, Cont >::CellIterator 		insertCell (SimpMeshRed< N, 3, T, Node, Cell, Cont > *mesh, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::NodeIterator n0, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::NodeIterator n1, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::NodeIterator n2, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::NodeIterator n3, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::CellIterator c0=0, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::CellIterator c1=0, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::CellIterator c2=0, const typename SimpMeshRed< N, 3, T, Node, Cell, Cont >::CellIterator c3=0)
 Insert the specified cell into the 3-D mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void orientPositive (SimpMeshRed< N, M, T, Node, Cell, Cont > *x)
 Orient each simplex so it has non-negative volume.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void eraseUnusedNodes (SimpMeshRed< N, M, T, Node, Cell, Cont > *x)
 Erase the nodes that do not have an incident cells.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void eraseCellsWithLowAdjacencies (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, int minimumAdjacencies)
 Erase cells until there are none with minimum adjacencies less than specified.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void renumberIdentifiers (SimpMeshRed< N, M, T, Node, Cell, Cont > *x)
 Re-number the node and cell identifiers so they start at 0 and are contiguous.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void countAdjacencies (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, ads::FixedArray< M+2, int > *counts)
 Calculate the adjacency counts for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
T computeContent (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh)
 Return the total content of the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeContentStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minContent, T *maxContent, T *meanContent)
 Calculate content (hypervolume) statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeEdgeLengthStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minLength, T *maxLength, T *meanLength)
 Calculate edge length statistics.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void printEdgeLengthStatistics (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh)
 Print edge length statistics.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeDeterminantStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minDeterminant, T *maxDeterminant, T *meanDeterminant)
 Calculate determinant statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeModifiedMeanRatioStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minModifiedMeanRatio, T *maxModifiedMeanRatio, T *meanModifiedMeanRatio)
 Calculate modified mean ratio function statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeModifiedConditionNumberStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minModifiedConditionNumber, T *maxModifiedConditionNumber, T *meanModifiedConditionNumber)
 Calculate modified condition number function statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void computeQualityStatistics (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, T *minContent, T *maxContent, T *meanContent, T *minDeterminant, T *maxDeterminant, T *meanDeterminant, T *minModifiedMeanRatio, T *maxModifiedMeanRatio, T *meanModifiedMeanRatio, T *minModifiedConditionNumber, T *maxModifiedConditionNumber, T *meanModifiedConditionNumber)
 Calculate quality statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void printQualityStatistics (std::ostream &out, const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh)
 Print quality statistics for the simplices in the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, class MaxEdgeLength>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, PointsOnManifold< N, MM, SD, T > *manifold, const MaxEdgeLength &f)
 Refine the mesh using the maximum edge length function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MaxEdgeLength>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, const MaxEdgeLength &f)
 Refine the mesh using the maximum edge length function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, typename IntInputIterator>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, PointsOnManifold< N, MM, SD, T > *manifold, IntInputIterator begin, IntInputIterator end)
 Refine the mesh by splitting the specified cells.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInputIterator>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, IntInputIterator begin, IntInputIterator end)
 Refine the mesh by splitting the specified cells.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, typename IntInputIterator, class MaxEdgeLength>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, PointsOnManifold< N, MM, SD, T > *manifold, IntInputIterator begin, IntInputIterator end, const MaxEdgeLength &f)
 Refine the specified cells using the maximum edge length function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInputIterator, class MaxEdgeLength>
int refine (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, IntInputIterator begin, IntInputIterator end, const MaxEdgeLength &f)
 Refine the specified cells using the maximum edge length function.
template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class ISS>
int refineBoundary (SimpMeshRed< 2, 2, T, Node, Cell, Cont > *x, const ISS &boundary, T maxAngle, T minEdgeLength, int maxSweeps=10)
 Refine the mesh to better fit the boundary.
template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class Distance, class ClosestPoint, class MaxAngle, class MinEdgeLength>
int refineBoundary (SimpMeshRed< 2, 2, T, Node, Cell, Cont > *x, const Distance &distance, const ClosestPoint &closestPoint, const MaxAngle &maxAngle, const MinEdgeLength &minEdgeLength, int maxSweeps=10)
 Refine the mesh to better fit the boundary.
template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MaxEdgeLength>
int refineAdjust (SimpMeshRed< 2, 2, T, Node, Cell, Cont > *mesh, const MaxEdgeLength &f)
 Refine and adjust the mesh using the maximum edge length function.
template<typename NodeInIter, class LSF, typename OutIter>
void determineNodesOutside (NodeInIter begin, NodeInIter end, const LSF &f, OutIter iter)
 Get the nodes that are outside the object.
template<typename CellInIter, class LSF, typename OutIter>
void determineCellsOutside (CellInIter begin, CellInIter end, const LSF &f, OutIter iter)
 Get the cells whose centroids are outside the object.
template<typename NodeInIter, typename OutIter>
void getNodes (NodeInIter begin, NodeInIter end, OutIter iter)
 Get the node iterators for the all of the nodes in the mesh.
template<typename NodeInIter, typename OutIter>
void determineInteriorNodes (NodeInIter begin, NodeInIter end, OutIter iter)
 Get the node iterators for the interior nodes.
template<typename NodeInIter, typename OutIter>
void determineBoundaryNodes (NodeInIter begin, NodeInIter end, OutIter iter)
 Get the node iterators for the boundary nodes.
template<typename CellInIter, typename OutIter>
void determineCellsWithRequiredAdjacencies (CellInIter begin, CellInIter end, int minimumRequiredAdjacencies, OutIter iter)
 Get the cell iterators with at least the specified number of adjacencies.
template<typename CellInIter, typename OutIter>
void determineCellsWithLowAdjacencies (CellInIter begin, CellInIter end, const int minimumRequiredAdjacencies, OutIter iter)
 Get the cell iterators with adjacencies less than specified.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void determineNeighbors (SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator node, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *neighbors)
 Get the neighboring nodes of a node.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void determineBoundaryNeighbors (SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator node, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *neighbors)
 Get the neighboring boundary nodes of a node.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void determineNeighbors (SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator node, int radius, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *neighbors)
 Get all the nodes within the specified radius of the specified node.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void determineFacesOfIncidentCells (SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator node, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::FaceSet *faces)
 Get the faces of the incident cells.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInIter>
void convertIdentifiersToIterators (SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh, IntInIter begin, IntInIter end, typename SimpMeshRed< N, M, T, Node, Cell, Cont >::CellIteratorSet *cells)
 Build a set of cell iterators from a range of cell identifiers.
int getNextNodeIndex (const int i, const int j)
 Get the next node index.
int getPreviousNodeIndex (const int i, const int j)
 Get the previous node index.
template<typename SMR>
int getNextNodeIndex (const typename SMR::CellConstIterator cell, const typename SMR::NodeConstIterator a, const typename SMR::NodeConstIterator b)
 Get the next node index.
template<typename SMR>
int getPreviousNodeIndex (const typename SMR::CellConstIterator cell, const typename SMR::NodeConstIterator a, const typename SMR::NodeConstIterator b)
 Get the previous node index.
template<int N, int M, typename T, template< class > class Vertex, template< class > class Cell, template< class, class > class Container>
void tile (const BBox< N, T > &domain, const T length, SimpMeshRed< N, M, T, Vertex, Cell, Container > *mesh)
 Tile the rectilinear region.
template<int N, int M, typename T, template< class > class Vertex, template< class > class Cell, template< class, class > class Container, class LSF>
void tile (const BBox< N, T > &domain, const T length, const LSF &f, SimpMeshRed< N, M, T, Vertex, Cell, Container > *mesh)
 Tile the object.
template<class _QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD>
int topologicalOptimize (SimpMeshRed< 3, 3, T, Node, Cell, Cont > *mesh, const PointsOnManifold< 3, 2, SD, T > *manifold, std::multiset< std::pair< int, int > > *edgeRemovalOperations=0, std::multiset< std::pair< int, int > > *faceRemovalOperations=0, int maximumSteps=std::numeric_limits< int >::max())
 Use edge and face removal to optimize the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD>
int topologicalOptimizeUsingMeanRatio (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, const PointsOnManifold< N, MM, SD, T > *manifold, std::multiset< std::pair< int, int > > *edgeRemovalOperations=0, std::multiset< std::pair< int, int > > *faceRemovalOperations=0, const int maximumSteps=std::numeric_limits< int >::max())
 Use edge and face removal to optimize the mesh.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD>
int topologicalOptimizeUsingConditionNumber (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, const PointsOnManifold< N, MM, SD, T > *manifold, std::multiset< std::pair< int, int > > *edgeRemovalOperations=0, std::multiset< std::pair< int, int > > *faceRemovalOperations=0, const int maximumSteps=std::numeric_limits< int >::max())
 Use edge and face removal to optimize the mesh.
template<class SMR>
bool doNodesShareACell (typename SMR::NodeConstIterator x, typename SMR::NodeConstIterator y)
 Return true if the nodes are incident to a common cell.
template<typename SMR, typename NodeIterInIter, class UnaryFunction>
void transformNodes (NodeIterInIter begin, NodeIterInIter end, const UnaryFunction &f)
 Transform each vertex in the range with the specified function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class UnaryFunction>
void transform (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, const UnaryFunction &f)
 Transform each vertex in the mesh with the specified function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class UnaryFunction>
void transformBoundary (SimpMeshRed< N, M, T, Node, Cell, Cont > *mesh, const UnaryFunction &f)
 Transform each boundary vertex in the mesh with the specified function.
template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
bool isValid (const SimpMeshRed< N, M, T, Node, Cell, Cont > &mesh)
 Return true if the mesh is valid.

Detailed Description

All classes and functions in the computational geometry package are defined in the geom namespace.

Function Documentation

template<int N, typename T>
T geom::computeUpperBoundOnSignedDistance ( const BBox< N, T > &  box,
const typename BBox< N, T >::Point &  x 
) [inline]

Return an upper bound on the signed distance from the point to the objects in the box.

Consider some objects contained in the bounding box: box. (Specifically, the objects form an N-D manifold. The distance from the point x to the manifold is signed; positive outside and negative inside.) This function returns an upper bound on the distance to the objects.

template<int N, typename T>
T geom::computeLowerBoundOnSignedDistance ( const BBox< N, T > &  box,
const typename BBox< N, T >::Point &  x 
) [inline]

Return an lower bound on the signed distance from the point to the objects in the box.

Consider some objects contained in the bounding box: box. (Specifically, the objects form an N-D manifold. The distance from the point x to the manifold is signed; positive outside and negative inside.) This function returns an lower bound on the distance to the objects.

template<typename T>
void geom::project ( const Simplex< 1, ads::FixedArray< 2, T >, T > &  s2,
const ads::FixedArray< 2, T > &  x2,
Simplex< 1, ads::FixedArray< 1, T >, T > *  s1,
ads::FixedArray< 1, T > *  x1 
)

Project the simplex and the point in 2-D to 1-D.

The first point in the 2-D simplex will be mapped to the origin; the second point will be mapped to the positive x axis. The 2-D point will be mapped to the x-axis.

Parameters:
s2 is the 1-simplex in 2-D.
x2 is the 2-D point.
s1 is the mapped simplex, a 1-simplex in 1-D.
x1 is the mapped point, a 1-D point.

template<typename T>
void geom::project ( const Simplex< 1, ads::FixedArray< 2, T >, T > &  s2,
const ads::FixedArray< 2, T > &  x2,
Simplex< 1, ads::FixedArray< 1, T >, T > *  s1,
ads::FixedArray< 1, T > *  x1,
ads::FixedArray< 1, T > *  y1 
)

Project the simplex and the point in 2-D to 1-D.

The first point in the 2-D simplex will be mapped to the origin; the second point will be mapped to the positive x axis. The 2-D point will be mapped to the x-axis.

Parameters:
s2 is the 1-simplex in 2-D.
x2 is the 2-D point.
s1 is the mapped simplex, a 1-simplex in 1-D.
x1 is the mapped point, a 1-D point.
y1 is the normal offset of x2 from s2.

template<typename T>
void geom::project ( const Simplex< 2, ads::FixedArray< 3, T >, T > &  s3,
const ads::FixedArray< 3, T > &  x3,
Simplex< 2, ads::FixedArray< 2, T >, T > *  s2,
ads::FixedArray< 2, T > *  x2 
)

Project the simplex and the point in 3-D to 2-D.

The first point in the 3-D simplex will be mapped to the origin; the second point will be mapped to the positive x axis. The triangle will have the positive orientation in the 2-D plane. The 3-D point will be mapped to the xy-plane.

Parameters:
s3 is the 2-simplex in 3-D.
x3 is the 3-D point.
s2 is the mapped simplex, a 2-simplex in 2-D.
x2 is the mapped point, a 2-D point.

template<typename T>
void geom::project ( const Simplex< 2, ads::FixedArray< 3, T >, T > &  s3,
const ads::FixedArray< 3, T > &  x3,
Simplex< 2, ads::FixedArray< 2, T >, T > *  s2,
ads::FixedArray< 2, T > *  x2,
ads::FixedArray< 1, T > *  z1 
)

Project the simplex and the point in 3-D to 2-D.

The first point in the 3-D simplex will be mapped to the origin; the second point will be mapped to the positive x axis. The triangle will have the positive orientation in the 2-D plane. The 3-D point will be mapped to the xy-plane.

Parameters:
s3 is the 2-simplex in 3-D.
x3 is the 3-D point.
s2 is the mapped simplex, a 2-simplex in 2-D.
x2 is the mapped point, a 2-D point.
z1 is the normal offset of x3 from s3.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename ISSV, typename ISSIS>
void geom::buildIndSimpSetFromSimpMeshRed ( const SimpMeshRed< N, M, T, Node, Cell, Cont > &  smr,
IndSimpSet< N, M, true, T, ISSV, ISSIS > *  iss 
)

Make an indexed simplex set from the mesh.

ISSV is the Indexed Simplex Set Vertex type. ISSIS is the Indexed Simplex Set Indexed Simplex type.

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 2, 2, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
PointsOnManifold< 2, 1, SD, T > *  manifold,
int  maxSweeps = 0 
)

Coarsen the mesh using the minimum edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
manifold The manifold data structure.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.
Only edges which are a common minimum edge are collapsed. Also, an edge may not be collapsed if its' endpoints are mirror nodes. (Doing so would tangle the mesh.) An interior edge may not be collapsed if both of its incident nodes lay on the boundary. (Doing so would change the topology of the mesh.)

A boundary edge may not be collapsed if both of its nodes are corner features. (Doing so would change the corner features.)

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 2, 2, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
T  cornerDeviation = -1,
int  maxSweeps = 0 
)

Coarsen the mesh using the min edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
cornerDeviation Any boundary node whose angle deviates from $ \pi $ more than this value will be considered a corner feature. If not specified, no vertices will be considered corner features.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 3, 2, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
PointsOnManifold< 3, 2, SD, T > *  manifold,
int  maxSweeps = 0 
)

Coarsen the mesh using the min edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
manifold The manifold data structure.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.
Only edges which are a common minimum edge are collapsed. Also, an edge may not be collapsed if its' endpoints are mirror nodes. (Doing so would tangle the mesh.) An interior edge may not be collapsed if both of its incident nodes lay on the boundary. (Doing so would change the topology of the mesh.)

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 3, 2, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
T  maxDihedralAngleDeviation = -1,
T  maxSolidAngleDeviation = -1,
T  maxBoundaryAngleDeviation = -1,
int  maxSweeps = 0 
)

Coarsen the mesh using the min edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
maxDihedralAngleDeviation The maximum dihedral angle deviation (from straight) for a surface feature. The rest are edge features. If not specified, all interior edges will be set as surface features.
maxSolidAngleDeviation Solid angles that deviate more than this value (from $2 \pi$) are corner features. If not specified, this criterion will not be used to identify corners.
maxBoundaryAngleDeviation If the angle deviation (from $\pi$) between two boundary edges exceeds this value, it will be set as a corner feature. If not specified, this criterion will not be used to identify corners on the boundary.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 3, 3, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
PointsOnManifold< 3, 2, SD, T > *  manifold,
int  maxSweeps = 0 
)

Coarsen the mesh using the min edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
manifold The manifold data structure.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.
Only edges which are a common minimum edge are collapsed. Also, an edge may not be collapsed if its' endpoints are mirror nodes. (Doing so would tangle the mesh.) An interior edge may not be collapsed if both of its incident nodes lay on the boundary. (Doing so would change the topology of the mesh.)

template<class QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MinEdgeLength>
int geom::coarsen ( SimpMeshRed< 3, 3, T, Node, Cell, Cont > *  mesh,
const MinEdgeLength &  f,
T  minimumAllowedQuality,
T  qualityFactor,
T  maxDihedralAngleDeviation = -1,
T  maxSolidAngleDeviation = -1,
T  maxBoundaryAngleDeviation = -1,
int  maxSweeps = 0 
)

Coarsen the mesh using the min edge length function.

Parameters:
mesh The simplicial mesh.
f The minimum edge length functor. The algorithm will try to collapse edges below this threshold.
minimumAllowedQuality A collapse is only allowed if the quality of the resulting elements is not less than this value.
qualityFactor A collapse is only allowed if the quality of the resulting elements is not less than the initial quality times this value.
maxDihedralAngleDeviation The maximum dihedral angle deviation (from straight) for a surface feature. The rest are edge features. If not specified, all interior edges will be set as surface features.
maxSolidAngleDeviation Solid angles that deviate more than this value (from $2 \pi$) are corner features. If not specified, this criterion will not be used to identify corners.
maxBoundaryAngleDeviation If the angle deviation (from $\pi$) between two boundary edges exceeds this value, it will be set as a corner feature. If not specified, this criterion will not be used to identify corners on the boundary.
maxSweeps The maximum number of sweeps over the vertices. By default, there is no limit on the number of sweeps.
Returns:
the number of edges collapsed.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInIter>
int geom::coarsen ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
IntInIter  begin,
IntInIter  end 
)

Collapse edges to remove the specified cells.

Parameters:
mesh The simplicial mesh.
begin The beginning of a range of cells.
end The end of a range of cells.
Returns:
the number of edges collapsed.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void geom::writeAscii ( std::ostream &  out,
const SimpMeshRed< N, M, T, Node, Cell, Cont > &  x 
)

Write a mesh as an indexed simplex set in ascii format.

First the space dimension and the simplex dimension are written. Then the vertex coordinates are written, followed by the tuples of vertex indices that comprise the simplices. The file format is: 

  space_dimension simplex_dimension
  num_vertices 
  vertex_0_coord_0 vertex_0_coord_1 ... vertex_0_coord_N-1
  vertex_1_coord_0 vertex_1_coord_1 ... vertex_1_coord_N-1
  ...
  num_simplices
  simplex_0_index_0 simplex_0_index_1 ... simplex_0_index_M
  simplex_1_index_0 simplex_1_index_1 ... simplex_1_index_M
  ..

template<class SMR>
SMR::Number geom::computeIncidentCellsAngle ( typename SMR::NodeConstIterator  node  ) 

Return the solid angle accumulated from the incident cells.

This function does not check if the node is in the interior or on the boundary. For the sake of efficiency, only call this function for boundary nodes.

template<class SMR>
SMR::Number geom::computeDihedralAngle ( typename SMR::ConstEdge  edge  ) 

Compute the dihedral angle at the specified edge.

The dihedral angle is accumulated from the incident cells.

template<class SMR>
SMR::Number geom::computeCosineAngle ( typename SMR::FaceConstIterator  face  ) 

Return the cosine of the interior angle at the specified 1-face.

Precondition:
The 1-face must have two incident simplices.

template<class SMR>
void geom::computeNodeNormal ( typename SMR::NodeConstIterator  node,
typename SMR::Vertex *  normal 
)

Compute the normal to the surface.

Parameters:
node Must be a boundary node.
normal Set to the node normal.

template<class SMR>
SMR::Vertex geom::computeNodeNormal ( typename SMR::NodeConstIterator  node  )  [inline]

Return the normal to the surface.

Parameters:
node Must be a boundary node.

template<class SMR>
void geom::computeCellNormal ( typename SMR::CellConstIterator  cell,
typename SMR::Vertex *  normal 
)

Compute the cell normal.

Note:
The space dimension must be one more than the simplex dimension, N == M + 1.

template<class SMR>
SMR::Vertex geom::computeCellNormal ( typename SMR::CellConstIterator  cell  )  [inline]

Return the normal to the surface.

Note:
The space dimension must be one more than the simplex dimension, N == M + 1.

template<class SMR>
void geom::computeFaceNormal ( typename SMR::CellConstIterator  cell,
int  i,
typename SMR::Vertex *  x 
)

Compute the face normal.

Note:
The space dimension must be equal to the simplex dimension, N == M.

template<int N, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
int geom::incidenceOptimize ( SimpMeshRed< N, 2, T, Node, Cell, Cont > *  mesh,
int  norm,
int  numSweeps = 0 
)

Modify the topology to optimize the cell-node incidences.

Parameters:
mesh The simplicial mesh.
norm The norm used in incidence optimization. May be 0, 1, or 2.
numSweeps The number of sweeps over the faces. By default, the number of sweeps is not limited.
Returns:
the number of edges flipped.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void geom::countAdjacencies ( const SimpMeshRed< N, M, T, Node, Cell, Cont > &  mesh,
ads::FixedArray< M+2, int > *  counts 
)

Calculate the adjacency counts for the simplices in the mesh.

Each simplex has between 0 and M+1 (inclusive) adjacent simplices.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, class MaxEdgeLength>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
PointsOnManifold< N, MM, SD, T > *  manifold,
const MaxEdgeLength &  f 
)

Refine the mesh using the maximum edge length function.

Parameters:
mesh The simplicial mesh.
manifold The manifold data structure.
f The maximum edge length functor. The algorithm will split edges above this threshold.
Returns:
the number of edges split.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MaxEdgeLength>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
const MaxEdgeLength &  f 
) [inline]

Refine the mesh using the maximum edge length function.

Parameters:
mesh The simplicial mesh.
f The maximum edge length functor. The algorithm will split edges above this threshold.
This simply calls the above function with a null pointer for the boundary manifold data structure.

Returns:
the number of edges split.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, typename IntInputIterator>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
PointsOnManifold< N, MM, SD, T > *  manifold,
IntInputIterator  begin,
IntInputIterator  end 
)

Refine the mesh by splitting the specified cells.

Parameters:
mesh The simplicial mesh.
manifold The boundary manifold data structure. By default it is null.
begin The beginning of a range of cell indices.
end The end of a range of cell indices.
Returns:
the number of edges split.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInputIterator>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
IntInputIterator  begin,
IntInputIterator  end 
) [inline]

Refine the mesh by splitting the specified cells.

Parameters:
mesh The simplicial mesh.
begin The beginning of a range of cell indices.
end The end of a range of cell indices.
This simply calls the above function with a null pointer for the boundary manifold data structure.

Returns:
the number of edges split.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD, typename IntInputIterator, class MaxEdgeLength>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
PointsOnManifold< N, MM, SD, T > *  manifold,
IntInputIterator  begin,
IntInputIterator  end,
const MaxEdgeLength &  f 
)

Refine the specified cells using the maximum edge length function.

Parameters:
mesh The simplicial mesh.
manifold The manifold data structure.
begin The beginning of a range of cell indices.
end The end of a range of cell indices.
f The maximum edge length functor. The algorithm will split edges above this threshold.
This function will refine the cells whose edge lengths exceed the maximum specified edge length.

Returns:
the number of edges split.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInputIterator, class MaxEdgeLength>
int geom::refine ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
IntInputIterator  begin,
IntInputIterator  end,
const MaxEdgeLength &  f 
) [inline]

Refine the specified cells using the maximum edge length function.

Parameters:
mesh The simplicial mesh.
begin The beginning of a range of cell indices.
end The end of a range of cell indices.
f The maximum edge length functor. The algorithm will split edges above this threshold.
This simply calls the above function with a null pointer for the boundary manifold data structure.

Returns:
the number of edges split.

template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class ISS>
int geom::refineBoundary ( SimpMeshRed< 2, 2, T, Node, Cell, Cont > *  x,
const ISS &  boundary,
T  maxAngle,
T  minEdgeLength,
int  maxSweeps = 10 
)

Refine the mesh to better fit the boundary.

Returns:
the number of edges split.

template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class Distance, class ClosestPoint, class MaxAngle, class MinEdgeLength>
int geom::refineBoundary ( SimpMeshRed< 2, 2, T, Node, Cell, Cont > *  x,
const Distance &  distance,
const ClosestPoint &  closestPoint,
const MaxAngle &  maxAngle,
const MinEdgeLength &  minEdgeLength,
int  maxSweeps = 10 
)

Refine the mesh to better fit the boundary.

Returns:
the number of edges split.

template<typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, class MaxEdgeLength>
int geom::refineAdjust ( SimpMeshRed< 2, 2, T, Node, Cell, Cont > *  mesh,
const MaxEdgeLength &  f 
)

Refine and adjust the mesh using the maximum edge length function.

Parameters:
mesh The simplicial mesh.
f The maximum edge length functor. The algorithm will split edges above this threshold.
When an edge is split, incidence optimization and Laplacian smoothing is performed to adjust the mesh.

Returns:
the number of edges split.

template<typename NodeInIter, class LSF, typename OutIter>
void geom::determineNodesOutside ( NodeInIter  begin,
NodeInIter  end,
const LSF &  f,
OutIter  iter 
)

Get the nodes that are outside the object.

Parameters:
begin is the beginning of a range of node input iterators.
end is the end of a range of node input iterators.
f is the level set function that describes the object. Points inside/outside the object have negative/positive values.
iter is an output iterator for the node const iterators.

template<typename CellInIter, class LSF, typename OutIter>
void geom::determineCellsOutside ( CellInIter  begin,
CellInIter  end,
const LSF &  f,
OutIter  iter 
)

Get the cells whose centroids are outside the object.

Parameters:
begin is the beginning of a range of cell input iterators.
end is the end of a range of cell input iterators.
f is the level set function that describes the object. Points inside/outside the object have negative/positive values.
iter is an output iterator for the cell const iterators.
This function calls the function of the same name with const iterators as the initial arguments.

template<typename NodeInIter, typename OutIter>
void geom::getNodes ( NodeInIter  begin,
NodeInIter  end,
OutIter  iter 
)

Get the node iterators for the all of the nodes in the mesh.

Parameters:
begin is the beginning of a range of node input iterators.
end is the end of a range of node input iterators.
iter is an output iterator for the node iterators.

template<typename NodeInIter, typename OutIter>
void geom::determineInteriorNodes ( NodeInIter  begin,
NodeInIter  end,
OutIter  iter 
)

Get the node iterators for the interior nodes.

Parameters:
begin is the beginning of a range of node input iterators.
end is the end of a range of node input iterators.
iter is an output iterator for the node iterators.

template<typename NodeInIter, typename OutIter>
void geom::determineBoundaryNodes ( NodeInIter  begin,
NodeInIter  end,
OutIter  iter 
)

Get the node iterators for the boundary nodes.

Parameters:
begin is the beginning of a range of node input iterators.
end is the end of a range of node input iterators.
iter is an output iterator for the node iterators.

template<typename CellInIter, typename OutIter>
void geom::determineCellsWithRequiredAdjacencies ( CellInIter  begin,
CellInIter  end,
int  minimumRequiredAdjacencies,
OutIter  iter 
)

Get the cell iterators with at least the specified number of adjacencies.

Parameters:
begin is the beginning of a range of cell input iterators.
end is the end of a range of cell input iterators.
minimumRequiredAdjacencies The minimum required adjacencies.
iter is an output iterator for the cell iterators.

template<typename CellInIter, typename OutIter>
void geom::determineCellsWithLowAdjacencies ( CellInIter  begin,
CellInIter  end,
const int  minimumRequiredAdjacencies,
OutIter  iter 
)

Get the cell iterators with adjacencies less than specified.

Parameters:
begin is the beginning of a range of cell input iterators.
end is the end of a range of cell input iterators.
minimumRequiredAdjacencies This function gets the cells that have fewer adjacencies than minimumRequiredAdjacencies.
iter is an output iterator for the cell iterators.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void geom::determineNeighbors ( SimpMeshRed< N, M, T, Node, Cell, Cont > &  mesh,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator  node,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *  neighbors 
)

Get the neighboring nodes of a node.

The set of nodes (not including the specified node) that share a cell with the specified node.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void geom::determineBoundaryNeighbors ( SimpMeshRed< N, M, T, Node, Cell, Cont > &  mesh,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator  node,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *  neighbors 
)

Get the neighboring boundary nodes of a node.

The set of boundary nodes (not including the specified node) that share a cell with the specified node.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont>
void geom::determineNeighbors ( SimpMeshRed< N, M, T, Node, Cell, Cont > &  mesh,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIterator  node,
int  radius,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::NodeIteratorSet *  neighbors 
)

Get all the nodes within the specified radius of the specified node.

The set includes the specified node.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, typename IntInIter>
void geom::convertIdentifiersToIterators ( SimpMeshRed< N, M, T, Node, Cell, Cont > &  mesh,
IntInIter  begin,
IntInIter  end,
typename SimpMeshRed< N, M, T, Node, Cell, Cont >::CellIteratorSet *  cells 
)

Build a set of cell iterators from a range of cell identifiers.

Parameters:
mesh The simplicial mesh. It is not modified, but because we are getting cell iterators (not cell const iterators) we pass it by reference (not const reference).
begin The beginning of the range of identifiers.
end The end of the range of identifiers.
cells The set of cell iterators.
The cell identifiers may not be the same as the cell indices. (Cell indices would be in the range [ 0 .. mesh.cells_size()).

template<int N, int M, typename T, template< class > class Vertex, template< class > class Cell, template< class, class > class Container>
void geom::tile ( const BBox< N, T > &  domain,
const T  length,
SimpMeshRed< N, M, T, Vertex, Cell, Container > *  mesh 
) [inline]

Tile the rectilinear region.

Parameters:
domain is the rectilinear domain to tile.
length is the maximum tetrahedron edge length.
mesh is the indexed simplex set.
In 2-D, tile the rectangular region with equilateral triangles. In 3-D, tile with a body-centered cubic lattice.

CONTINUE: draw a picture of the 2-D mesh and 3-D block.

The template parameters can be deduced from the arguments.

template<int N, int M, typename T, template< class > class Vertex, template< class > class Cell, template< class, class > class Container, class LSF>
void geom::tile ( const BBox< N, T > &  domain,
const T  length,
const LSF &  f,
SimpMeshRed< N, M, T, Vertex, Cell, Container > *  mesh 
) [inline]

Tile the object.

Parameters:
domain is the rectilinear domain to tile.
length is the maximum tetrahedron edge length.
f is the level set description of the object.
mesh is the indexed simplex set.
In 2-D, tile the rectangular region with equilateral triangles. In 3-D, tile with a body-centered cubic lattice.

The template parameters can be deduced from the arguments.

template<class _QualityMetric, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int SD>
int geom::topologicalOptimize ( SimpMeshRed< 3, 3, T, Node, Cell, Cont > *  mesh,
const PointsOnManifold< 3, 2, SD, T > *  manifold,
std::multiset< std::pair< int, int > > *  edgeRemovalOperations = 0,
std::multiset< std::pair< int, int > > *  faceRemovalOperations = 0,
int  maximumSteps = std::numeric_limits< int >::max() 
)

Use edge and face removal to optimize the mesh.

Parameters:
mesh The simplicial mesh.
manifold The manifold data structure. We pass this by const reference, because the topological optimization will not change the manifold data structure.
edgeRemovalOperations Multi-set to record the edge removal operations.
faceRemovalOperations Multi-set to record the face removal operations.
maximumSteps The maximum allowed number of steps.
Use the specified metric.

Returns:
The number of edge and face removal operations.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD>
int geom::topologicalOptimizeUsingMeanRatio ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
const PointsOnManifold< N, MM, SD, T > *  manifold,
std::multiset< std::pair< int, int > > *  edgeRemovalOperations = 0,
std::multiset< std::pair< int, int > > *  faceRemovalOperations = 0,
const int  maximumSteps = std::numeric_limits<int>::max() 
) [inline]

Use edge and face removal to optimize the mesh.

Parameters:
mesh The simplicial mesh.
manifold The manifold data structure.
edgeRemovalOperations Multi-set to record the edge removal operations.
faceRemovalOperations Multi-set to record the face removal operations.
maximumSteps The maximum allowed number of steps.
Use the modified mean ratio metric.

Returns:
The number of edge and face removal operations.

template<int N, int M, typename T, template< class > class Node, template< class > class Cell, template< class, class > class Cont, int MM, int SD>
int geom::topologicalOptimizeUsingConditionNumber ( SimpMeshRed< N, M, T, Node, Cell, Cont > *  mesh,
const PointsOnManifold< N, MM, SD, T > *  manifold,
std::multiset< std::pair< int, int > > *  edgeRemovalOperations = 0,
std::multiset< std::pair< int, int > > *  faceRemovalOperations = 0,
const int  maximumSteps = std::numeric_limits<int>::max() 
) [inline]

Use edge and face removal to optimize the mesh.

Parameters:
mesh The simplicial mesh.
manifold The manifold data structure.
edgeRemovalOperations Multi-set to record the edge removal operations.
faceRemovalOperations Multi-set to record the face removal operations.
maximumSteps The maximum allowed number of steps.
Use the modified mean ratio metric.

Returns:
The number of edge and face removal operations.

template<typename SMR, typename NodeIterInIter, class UnaryFunction>
void geom::transformNodes ( NodeIterInIter  begin,
NodeIterInIter  end,
const UnaryFunction &  f 
)

Transform each vertex in the range with the specified function.

The first template argument must be specified explicitly.

Generated on Fri Aug 24 12:56:00 2007 for Computational Geometry Package by  doxygen 1.4.7