Geometry Namespace Reference

Contains all definitions in the Geometry package. More...

Classes
struct	Angular2DOrdering
class	AnyCollisionGeometry3D
	An AnyGeometry with collision detection information. More...
class	AnyCollisionQuery
	A class that stores information regarding a collision query. May be slightly faster than running individual queries. More...
class	AnyContactsQueryResult
class	AnyContactsQuerySettings
class	AnyDistanceQueryResult
class	AnyDistanceQuerySettings
class	AnyGeometry3D
	A class that stores any kind of geometry we've defined. More...
class	ApproximatePenetrationDepth
	Uses a propagation method to calculate an approximate penetration distance of mesh m1 inside m2. More...
class	Arrangement1D
	An arrangement of 1-D intervals. Intervals identified by an integer ID. More...
class	BallTree
class	BallTreeNode
	A node of a ball-tree point location data structure. More...
struct	ClosestPointCallback
class	CollisionConvexHull3D
	The collision data class for ConvexHull3D that contains the solid3 data structure moved by some rigid transform. More...
class	CollisionImplicitSurface
	An implicit surface (usually signed-distance function) with a fast collision detection data structure. More...
class	CollisionMesh
	A triangle mesh along with PQP bounding volume structures that enable fast collision and other proximity queries. More...
class	CollisionMeshQuery
	A general-purpose distance querying class. More...
class	CollisionMeshQueryEnhanced
class	CollisionPointCloud
	A point cloud with a fast collision detection data structure. More...
class	ConvexHull3D
	A 3D convex hull class. More...
class	DenseTSDFReconstruction
	Performs a kinect-fusion-like dense TSDF reconstruction. More...
class	Grid
	A gridding of n-dimensional space. More...
class	GridHash
	An ND grid containing objects (referenced by void pointers) More...
class	GridHash3D
	A grid containing objects (referenced by void pointers) More...
class	GridSubdivision
	An ND grid with a list of arbitrary objects (given by void pointers) More...
class	GridSubdivision3D
	A grid with a list of arbitrary objects (given by void pointers) More...
class	GridTable
	A table with entry T on a gridding of n-dimensional space. More...
class	ICPParameters
struct	IndexHash
class	KDTree
	A kd-tree or a node of one. More...
class	LPSolvePointCallback
	Helper callback used in PolytopeProjection2D. More...
class	MultiVolumeGrid
	A 3D array over an axis-aligned 3D volume, containing one or more channels. More...
class	Octree
struct	OctreeNode
class	OctreePointSet
	Stores a point set P on an octree grid. Allows for O(d) adding, O(d h) range queries and pseudo-O(d) nearest neighbor queries. More...
class	OctreeScalarField
	Stores a function f(x) on an octree grid. Allows for O(d) setting, sub O(d) testing of f(x) in range [a,b], O(d h) selection of nodes with values in range [a,b]. More...
struct	Point2DWithID
class	PointPointCollider
struct	PointRay2D
	A 2D point or infinite ray. Note: rays should be normalized unit vectors. More...
struct	PointRay2DWithID
struct	PointRay3D
	A 3D point or infinite ray. Note: rays should be normalized unit vectors. More...
class	PolytopeProjection2D
	A method for projecting a polytope defined by the feasible set of a linear program lp onto a 2D subspace. Handles unbounded and infeasible problems. More...
struct	RayCastCallback
class	SegmentOverlay
	Computes the overlay of a set of segments using a sweep line algorithm. More...
class	SparseTSDFReconstruction
	Performs a kinect-fusion-like sparse TSDF reconstruction. A hash grid is used to build multiple TSDFs across an infinite domain. More...
class	SparseVolumeGrid
	A 3D array over a sparse, axis aligned 3D volume. Has a similar interface as VolumeGrid, but uses a hash grid data structure to achieve better performance in large grids with infinite domain. More...
struct	UnboundedPolytope2D
	A representation of a possibly unbounded polytope in the 2d plane. More...
struct	XMonotoneChain
	A polyline with vertices ordered in nondecreasing order. More...

Functions
void	RigidTransformToPQP (const RigidTransform &f, PQP_REAL R[3][3], PQP_REAL T[3])
void	GetMinMax (const Meshing::VolumeGrid *mingrid, const Meshing::VolumeGrid *maxgrid, const AABB3D &bb, Real &vmin, Real &vmax)
Real	Distance (const CollisionImplicitSurface &s, const Vector3 &pt)
Real	Distance (const CollisionImplicitSurface &s, const Vector3 &pt, Vector3 &surfacePt, Vector3 &direction)
Real	Distance (const CollisionImplicitSurface &grid, const GeometricPrimitive3D &a, Vector3 &gridclosest, Vector3 &geomclosest, Vector3 &direction)
bool	Collides (const CollisionImplicitSurface &s, const CollisionPointCloud &pc, Real margin, vector< int > &collidingPoints, size_t maxContacts)
Real	DistanceLowerBound (const CollisionImplicitSurface &s, const CollisionPointCloud &pc, int nindex, const Matrix4 &Mpc_s)
Real	Distance (const CollisionImplicitSurface &s, const CollisionPointCloud &pc, int &closestPoint, Real upperBound=Inf)
	Returns the distance and closest point to a CollisionPointCloud.
Real	RayGridCellIntersect (const Ray3D &ray, const Meshing::VolumeGrid &grid, const IntTriple &c, Real umin, Real umax, Real levelSet, Real vtol=1e-3)
Real	RayCast (const Meshing::VolumeGrid &grid, const Ray3D &ray, Real levelSet, Real tmax)
Real	RayCast (const CollisionImplicitSurface &s, const Ray3D &rayWorld, Real levelSet, Real tmax)
bool	Collides (const CollisionImplicitSurface &s, const CollisionPointCloud &pc, Real margin, std::vector< int > &collidingPoints, size_t maxContacts=1)
void	PQPToRigidTransform (const PQP_REAL R[3][3], const PQP_REAL T[3], RigidTransform &f)
void	ConvertTriToPQP (const TriMesh &tri, PQP_Model &pqp)
void	CopyPQPModel (const PQP_Model *source, PQP_Model *dest)
bool	OverlappingTriangleCollision (const CollisionMesh *m1, const CollisionMesh *m2, int a, int b, Vector3 &p1, Vector3 &p2)
void	VEC3_COPY (PQP_REAL *res, const PQP_REAL *in)
Real	distance (const Segment3D &s, const Point3D &p)
bool	Collide (const Meshing::TriMesh &m1, const Meshing::TriMesh &m2)
bool	WithinDistance (const Meshing::TriMesh &m1, const Meshing::TriMesh &m2, Real tol)
Real	Distance (const Meshing::TriMesh &m1, const Meshing::TriMesh &m2, Real absErr, Real relErr)
Real	ClosestPoints (const Meshing::TriMesh &m1, const Meshing::TriMesh &m2, Real absErr, Real relErr, Vector3 &p1, Vector3 &p2)
void	Copy (const PQP_REAL p[3], Vector3 &x)
void	Copy (const Vector3 &x, PQP_REAL p[3])
void	BVToBox (const BV &b, Box3D &box)
void	BoxToBV (const Box3D &box, BV &b)
int	aabb_sphere_disjoint (const PQP_REAL box_dims[3], const PQP_REAL c[3], PQP_REAL r)
Real	aabb_ray_collide (const PQP_REAL box_dims[3], const PQP_REAL s[3], const PQP_REAL d[3])
void	ToLocal (const BV &b, const PQP_REAL p[3], PQP_REAL ploc[3])
void	ToLocal (const BV &b, const Vector3 &in, Vector3 &out)
bool	CollideBV (const PQP_REAL d[3], const Vector3 &pt)
void	DistanceLimitsBV (const PQP_REAL d[3], const Vector3 &pt, Real &dmin, Real &dmax)
void	ToLocal (const BV &bv, const Segment3D &in, Segment3D &out)
bool	CollideBV (const PQP_REAL d[3], const Segment3D &s)
bool	Collide (const Triangle3D &tri, const Segment3D &s, Vector3 &pt)
void	ToLocal (const BV &bv, const Sphere3D &in, Sphere3D &out)
bool	CollideBV (const PQP_REAL d[3], const Sphere3D &s)
bool	Collide (const Triangle3D &tri, const Sphere3D &s, Vector3 &pt)
void	ToLocal (const BV &bv, const BV &in, BV &out)
bool	CollideBV (const PQP_REAL d[3], BV &bv)
bool	Collide (const Triangle3D &tri, const BV &b, Vector3 &pt)
template<class Geom >
int	CollideRecurse (const Geom &g, const PQP_Model &m, int b, Vector3 &pt)
template<class Geom >
void	CollideAllRecurse (const Geom &g, const PQP_Model &m, int b, vector< int > &tris, size_t max)
int	ClosestPoint (const CollisionMesh &mesh, const Vector3 &p, Vector3 &cp, Real bound)
int	Collide (const CollisionMesh &m, const Segment3D &s, Vector3 &pt)
bool	Collide (const CollisionMesh &m, const Sphere3D &s)
	Returns true if m intersects the given geometry.
bool	Collide (const CollisionMesh &m, const AABB3D &bb)
bool	Collide (const CollisionMesh &m, const Box3D &b)
bool	Collide (const CollisionMesh &m, const GeometricPrimitive3D &g)
bool	WithinDistance (const CollisionMesh &c, const GeometricPrimitive3D &a, Real d)
bool	Collide (const CollisionMesh &m1, const CollisionMesh &m2)
void	CollideAll (const CollisionMesh &m, const Sphere3D &s, vector< int > &tris, int max)
	Computes a list of triangles that overlap the geometry.
void	CollideAll (const CollisionMesh &m, const Segment3D &s, vector< int > &tris, int max)
void	CollideAll (const CollisionMesh &m, const AABB3D &bb, vector< int > &tris, int max)
void	CollideAll (const CollisionMesh &m, const Box3D &bb, vector< int > &tris, int max)
void	CollideAll (const CollisionMesh &m, const GeometricPrimitive3D &g, std::vector< int > &tris, int max)
bool	WithinDistance (const CollisionMesh &m, const Vector3 &p, Real d)
	Returns true if p is within distance d of m using the PQP bounding heirarchy. More...
void	NearbyTriangles (const CollisionMesh &m, const Vector3 &p, Real d, vector< int > &tris, int max)
	Computes the triangles in m within distance d to p on m. More...
void	FitBox (const GeometricPrimitive3D &g, Box3D &box)
void	NearbyTriangles (const CollisionMesh &m, const GeometricPrimitive3D &g, Real d, vector< int > &tris, int max)
void	NearbyTriangles (const CollisionMesh &m1, const CollisionMesh &m2, Real d, vector< int > &tris1, vector< int > &tris2, int max)
Real	Distance (const CollisionMesh &c, const Vector3 &pt, Real bound)
Real	Distance (const CollisionMesh &c, const Vector3 &pt, int &closestTri, Vector3 &cp, Vector3 &dir, Real bound)
Real	Distance (const CollisionMesh &c, const GeometricPrimitive3D &a, Real bound)
Real	Distance (const CollisionMesh &c, const GeometricPrimitive3D &a, int &closestTri, Vector3 &cp, Vector3 &dir, Real bound)
int	ClosestPointAndNormal (const TriMesh &m, Real pWeight, Real nWeight, const Vector3 &p, const Vector3 &n, Vector3 &cp)
int	ClosestPointAndNormal (const CollisionMesh &mesh, Real nWeight, const Vector3 &p, const Vector3 &n, Vector3 &cp)
Real	BVRayCollision (const BV &bv, const Ray3D &r)
int	RayCast (const CollisionMesh &mesh, const Ray3D &r, Vector3 &pt)
int	RayCastLocal (const CollisionMesh &mesh, const Ray3D &r, Vector3 &pt)
void	GetBB (const CollisionMesh &m, Box3D &bb)
	Returns the bounding box containing m. More...
PQP_REAL	TriDistance (PQP_REAL R[3][3], PQP_REAL T[3], Tri *t1, Tri *t2, PQP_REAL p[3], PQP_REAL q[3])
void	CollideAll (const CollisionMesh &m, const Sphere3D &s, std::vector< int > &tris, int max=INT_MAX)
	Computes a list of triangles that overlap the geometry.
void	CollideAll (const CollisionMesh &m, const Segment3D &s, std::vector< int > &tris, int max=INT_MAX)
void	CollideAll (const CollisionMesh &m, const AABB3D &bb, std::vector< int > &tris, int max=INT_MAX)
void	CollideAll (const CollisionMesh &m, const Box3D &b, std::vector< int > &tris, int max=INT_MAX)
bool	WithinDistance (const CollisionMesh &m1, const CollisionMesh &m2, Real d)
void	NearbyTriangles (const CollisionMesh &m, const Vector3 &p, Real d, std::vector< int > &tris, int max=INT_MAX)
	Computes the triangles in m within distance d to p on m. More...
void	NearbyTriangles (const CollisionMesh &m, const GeometricPrimitive3D &g, Real d, std::vector< int > &tris, int max=INT_MAX)
void	NearbyTriangles (const CollisionMesh &m1, const CollisionMesh &m2, Real d, std::vector< int > &tris1, std::vector< int > &tris2, int max=INT_MAX)
Real	Distance (const CollisionMesh &m1, const CollisionMesh &m2, Real absErr, Real relErr, Real bound=Inf)
	Checks distance between two meshes (convenience function, equivalent to m1.Distance(m2))
void	ClosestPoints (const CollisionMesh &m1, const CollisionMesh &m2, Real absErr, Real relErr, Vector3 &v1local, Vector3 &v2local, Real bound=Inf)
void	GetBB (const CollisionPointCloud &pc, Box3D &b)
	Returns the oriented bounding box of the point cloud.
bool	withinDistanceTest (void *obj)
bool	WithinDistance (const CollisionPointCloud &pc, const GeometricPrimitive3D &g, Real tol)
bool	distanceTest (void *obj)
Real	Distance (const CollisionPointCloud &pc, const Vector3 &pt)
	Returns the nearest distance from any point in pc to g. O(log n) running time.
Real	Distance (const CollisionPointCloud &pc, const Vector3 &pt, int &closestPoint, Real upperBound)
Real	Distance (const CollisionPointCloud &pc, const GeometricPrimitive3D &g)
Real	Distance (const CollisionPointCloud &pc, const GeometricPrimitive3D &g, int &closestPoint, Real upperBound)
Real	Distance (const CollisionPointCloud &pc1, const CollisionPointCloud &pc2, int &closestPoint1, int &closestPoint2, Real upperBound)
bool	nearbyTest (void *obj)
void	NearbyPoints (const CollisionPointCloud &pc, const GeometricPrimitive3D &g, Real tol, std::vector< int > &pointIds, size_t maxContacts)
int	RayCast (const CollisionPointCloud &pc, Real rad, const Ray3D &r, Vector3 &pt)
int	RayCastLocal (const CollisionPointCloud &pc, Real rad, const Ray3D &r, Vector3 &pt)
Real	Volume (const AABB3D &bb)
Real	Volume (const OctreeNode &n)
bool	Collides (const CollisionPointCloud &a, const CollisionPointCloud &b, Real margin, std::vector< int > &apoints, std::vector< int > &bpoints, size_t maxContacts)
void	SubdivideAdd (const Triangle3D &t, Meshing::PointCloud3D &pc, Real maxDispersion2)
void	MeshToPointCloud (const Meshing::TriMesh &mesh, Meshing::PointCloud3D &pc, Real maxDispersion=Inf, bool wantNormals=false)
	Places points on the vertices of a mesh. If any triangle has vertices farther away than maxDispersion, the triangle is subdivided until all triangles are covered by balls of radius maxDispersion.
void	PointCloudToMesh (const Meshing::PointCloud3D &pc, Meshing::TriMesh &mesh, GLDraw::GeometryAppearance &appearance, Real depthDiscontinuity=Inf)
	Same as normal PointCloudToMesh, but colors and UV coordinates are extracted.
void	PointCloudToMesh (const Meshing::PointCloud3D &pc, Meshing::TriMesh &mesh, Real depthDiscontinuity=Inf)
	If a point cloud is structured, this creates a uniform mesh out of it. If depthDiscontinuity is provided, the mesh is split at the points where the relative depth of adjacent points is greater than depthDiscontinuity * average depth. (A decent value is 0.02 for typical depth sensors.)
void	PrimitiveToMesh (const GeometricPrimitive3D &primitive, Meshing::TriMesh &mesh, int numDivs)
	Creates a mesh for a geometric primitive. If the primitive has curved surfaces, they are split into numDivs strips.
void	FitGridToBB (const AABB3D &bb, Meshing::VolumeGrid &grid, Real resolution, Real expansion=0.5)
void	PrimitiveToImplicitSurface (const GeometricPrimitive3D &primitive, Meshing::VolumeGrid &grid, Real resolution, Real expansion=0)
	Creates an implicit surface for a geometric primitive. The grid has resolution no more than resolution on each axis.
void	Extrema (const AABB3D &bb, const Vector3 &dir, Real &a, Real &b)
void	SpaceCarving (const CollisionMesh &mesh, const Vector3 &d, const Vector3 &x, const Vector3 &y, Meshing::VolumeGrid &grid, Array3D< Real > &occupancy, Real resolution, bool firstPass=true)
void	SaveSliceCSV (const Array3D< Real > &values, const char *fn)
void	MeshToImplicitSurface_FMM (const CollisionMesh &mesh, Meshing::VolumeGrid &grid, Real resolution)
	Creates an implicit surface for a mesh using a Fast Marching Method. More...
void	MeshToImplicitSurface_SpaceCarving (const CollisionMesh &mesh, Meshing::VolumeGrid &grid, Real resolution, int numViews=20)
	Creates an implicit surface for a mesh using a space-carving technique. The grid has resolution no less than resolution on each axis. numViews views (6 orthographic, numViews-6 random) are taken of the mesh to create the space carving. More...
void	ImplicitSurfaceToMesh (const Meshing::VolumeGrid &grid, Meshing::TriMesh &mesh, Real levelSet=0.0)
	Creates a mesh from an implicit surface via Marching Cubes. This assumes the values of the grid are defined at the cell centers, unlike the methods in MarchingCubes.h which assume the array defines values at the cell corners... this performs the necessary correction.
void	MeshToConvexHull (const Meshing::TriMesh &mesh, ConvexHull3D &ch)
	Creates a convex hull from a mesh.
void	PointCloudToConvexHull (const Meshing::PointCloud3D &pc, ConvexHull3D &ch)
	Creates a convex hull from a point cloud.
void	_HACD_CallBack (const char *msg, double progress, double concavity, size_t nVertices)
void	MeshConvexDecomposition (const Meshing::TriMesh &mesh, ConvexHull3D &ch, Real concavity)
	Computes a convex decomposition of the mesh. concavity can be set to > 0 to compute an approximate convex decomposition using the HACD algorithm. More...
void	AppendPoints (const ConvexHull3D &ch, vector< Vector3 > &points)
void	ConvexHullToMesh (const ConvexHull3D &ch, Meshing::TriMesh &mesh)
template<typename Point , typename OrientFunc >
int	ConvexHull2D_ChainTemplate (const Point P[], int n, Point H[], OrientFunc Orient)
int	ConvexHull2D_Chain (const Point2D P[], int n, Point2D H[])
	Compute the convex hull of a set of sorted points (or point-rays) More...
int	ConvexHull2D_Chain (const PointRay2D P[], int n, PointRay2D H[])
int	ConvexHull2D_Chain (const Point2D P[], int n, Point2D H[], int Hindex[])
int	ConvexHull2D_Chain (const PointRay2D P[], int n, PointRay2D H[], int Hindex[])
int	ConvexHull2D_Chain_Unsorted (Point2D P[], int n, Point2D H[])
	Same as above, but unsorted input. Upon exit, the contents of P are rearranged in lexicographical order.
int	ConvexHull2D_Chain_Unsorted (PointRay2D P[], int n, PointRay2D H[])
int	ConvexHull2D_Chain_Unsorted (Point2D P[], int n, Point2D H[], int Hindex[])
int	ConvexHull2D_Chain_Unsorted (PointRay2D P[], int n, PointRay2D H[], int Hindex[])
void	Point2DListToPlanes (const Point2D P[], int n, Plane2D H[])
	Given a list of points on a convex hull, return a list of planes along edges with normals pointing outward. More...
int	Point2DListToPlanes (const PointRay2D P[], int n, Plane2D H[])
bool	ConvexHull3D_Qhull (const vector< Vector3 > &points, vector< vector< int > > &facets)
	Computes the convex hull of the point set using the Qhull library. More...
bool	ConvexHull3D_Qhull (const vector< double > &points, vector< vector< int > > &facets)
bool	ConvexHull3D_Qhull (const std::vector< Vector3 > &points, std::vector< IntTriple > &tris)
	Computes the convex hull of the point set using the Qhull library. More...
DT_ShapeHandle	_MakePolytope (const vector< double > &points)
std::tuple< Real, Vector3, Vector3 >	dist_func (DT_ObjectHandle object1, DT_ObjectHandle object2)
std::ostream &	operator<< (std::ostream &out, const ConvexHull3D &b)
std::istream &	operator>> (std::istream &in, ConvexHull3D &b)
bool	ConvexHull3D_Qhull (const std::vector< Vector3 > &points, std::vector< std::vector< int > > &facets)
	Computes the convex hull of the point set using the Qhull library. More...
bool	ConvexHull3D_Qhull (const std::vector< double > &points, std::vector< std::vector< int > > &facets)
void	Rank1Update (Matrix2 &m, const Vector2 &x, const Vector2 &y)
void	Rank1Update (Matrix3 &m, const Vector3 &x, const Vector3 &y)
Vector2	GetMean (const vector< Vector2 > &pts)
Vector3	GetMean (const vector< Vector3 > &pts)
void	GetCovariance (const vector< Vector2 > &pts, Matrix2 &C)
void	GetCovariance (const vector< Vector3 > &pts, Matrix3 &C)
bool	FitGaussian (const vector< Vector2 > &pts, Vector2 &mean, Matrix2 &R, Vector2 &axes)
bool	FitGaussian (const vector< Vector3 > &pts, Vector3 &mean, Matrix3 &R, Vector3 &axes)
bool	FitLine (const vector< Vector2 > &pts, Line2D &l)
bool	FitLine (const vector< Vector3 > &pts, Line3D &l)
bool	FitPlane (const vector< Vector3 > &pts, Plane3D &p)
bool	FitCircle (const std::vector< Vector2 > &pts, Circle2D &c)
Vector2	GetMean (const std::vector< Vector2 > &pts)
Vector3	GetMean (const std::vector< Vector3 > &pts)
void	GetCovariance (const std::vector< Vector2 > &pts, Matrix2 &C)
void	GetCovariance (const std::vector< Vector3 > &pts, Matrix3 &C)
bool	FitGaussian (const std::vector< Vector2 > &pts, Vector2 &center, Matrix2 &R, Vector2 &axes)
bool	FitGaussian (const std::vector< Vector3 > &pts, Vector3 &center, Matrix3 &R, Vector3 &axes)
bool	FitLine (const std::vector< Vector2 > &pts, Line2D &l)
bool	FitLine (const std::vector< Vector3 > &pts, Line3D &l)
bool	FitPlane (const std::vector< Vector3 > &pts, Plane3D &p)
void	NeighborGraph (const Meshing::PointCloud3D &pc, Real R, Graph::UndirectedGraph< int, int > &G)
void	NeighborGraph (const vector< Vector3 > &pc, Real R, Graph::UndirectedGraph< int, int > &G)
void	NearestNeighborGraph (const Meshing::PointCloud3D &pc, int k, Graph::Graph< int, int > &G)
void	NearestNeighborGraph (const vector< Vector3 > &pc, int k, Graph::Graph< int, int > &G)
bool	Lexical2DOrder (const Point2D &p1, const Point2D &p2)
	Lexical < order on 2D points.
bool	Lexical3DOrder (const Point3D &p1, const Point3D &p2)
	Lexical < order on 3D points.
Real	Orient2D (const Point2D &p0, const Point2D &p1, const Point2D &p2)
	Orientation of p2 relative to p1, relative to p0. More...
Real	HomogeneousCmp (Real a, bool awZero, Real b, bool bwZero)
	Comparison of 1D points in homogeneous coordinates. More...
Real	HomogeneousSub (Real a, bool awZero, Real b, bool bwZero)
	Subtraction of 1D points in homogeneous coordinates.
bool	LexicalRay2DOrder (const PointRay2D &p1, const PointRay2D &p2)
bool	LexicalRay3DOrder (const PointRay3D &p1, const PointRay3D &p2)
Real	OrientRay2D (const PointRay2D &p0, const PointRay2D &p1, const PointRay2D &p2)
bool	SweepLineOrder (const Point2D &a, const Point2D &b)

Detailed Description

Contains all definitions in the Geometry package.

Function Documentation

int Geometry::ClosestPoint	(	const CollisionMesh &	m,
		const Vector3 &	p,
		Vector3 &	cplocal,
		Real	bound = Inf
	)

Finds the closest point pt to p on m and returns the triangle index. The closest point is cplocal, given in the mesh's local frame If bound is given, this will quit and return -1 if the closest point is known to be farther than bound.

References ClosestPoint(), and Math3D::RigidTransform::mulInverse().

Referenced by ClosestPoint(), Distance(), Geometry::AnyCollisionGeometry3D::SetTransform(), and Geometry::BallTree::TreeSize().

int Geometry::ClosestPointAndNormal	(	const Meshing::TriMesh &	m,
		Real	pWeight,
		Real	nWeight,
		const Vector3 &	p,
		const Vector3 &	n,
		Vector3 &	cp
	)

Returns the point on the mesh that minimizes pWeight||p-x||^2 + nWeight||n-nx||^2. The point x is returned in cp, and the triangle index is the return value.

References ClosestPointAndNormal(), and Meshing::TriMesh::GetTriangle().

Referenced by ClosestPointAndNormal().

int Geometry::ClosestPointAndNormal	(	const CollisionMesh &	mesh,
		Real	nWeight,
		const Vector3 &	p,
		const Vector3 &	n,
		Vector3 &	cplocal
	)

Same as above, but uses the PQP bounding heirarchy and assumes pWeight = 1.

p and n are assumed given in world coordinates, with the mesh's current transform taken into account.

The closest point is cplocal, which is given in mesh-local coordinates

References ClosestPointAndNormal(), Math3D::RigidTransform::mulInverse(), and Math3D::Matrix3::mulTranspose().

void Geometry::ClosestPoints	(	const CollisionMesh &	m1,
		const CollisionMesh &	m2,
		Real	absErr,
		Real	relErr,
		Vector3 &	v1local,
		Vector3 &	v2local,
		Real	bound = Inf
	)

Convenience function to compute closest points between two meshes. v1 and v2 are in their respective mesh's local coordinates If bound is given, this will quit and return far away points if the closest points is known to be farther than bound.

int Geometry::Collide	(	const CollisionMesh &	m,
		const Segment3D &	s,
		Vector3 &	pt
	)

Checks for collision between s and m. Returns the index of the tri, or -1 if none, and computes the intersecting point pt.

References Math3D::RigidTransform::mulInverse().

bool Geometry::Collides	(	const CollisionImplicitSurface &	s,
		const CollisionPointCloud &	pc,
		Real	margin,
		std::vector< int > &	collidingPoints,
		size_t	maxContacts = 1
	)

Returns true if the point cloud is within margin distance of the geometry represented by s. One or more colliding points can also be returned in collidingPoints.

References Geometry::CollisionImplicitSurface::baseGrid, Geometry::CollisionImplicitSurface::currentTransform, Geometry::CollisionPointCloud::currentTransform, GET_LOGGER, GetBB(), Math3D::Box3D::intersectsApprox(), Geometry::CollisionPointCloud::maxRadius, Math3D::Matrix4::mulPoint(), Geometry::CollisionPointCloud::radiusIndex, and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

Referenced by Geometry::AnyCollisionGeometry3D::SetTransform().

bool Geometry::Collides	(	const CollisionImplicitSurface &	s,
		const CollisionPointCloud &	pc,
		Real	margin,
		std::vector< int > &	collidingPoints,
		size_t	maxContacts = 1
	)

Returns true if the point cloud is within margin distance of the geometry represented by s. One or more colliding points can also be returned in collidingPoints.

References Geometry::CollisionImplicitSurface::baseGrid, Geometry::CollisionImplicitSurface::currentTransform, Geometry::CollisionPointCloud::currentTransform, GET_LOGGER, GetBB(), Math3D::Box3D::intersectsApprox(), Geometry::CollisionPointCloud::maxRadius, Math3D::Matrix4::mulPoint(), Geometry::CollisionPointCloud::radiusIndex, and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

Referenced by Geometry::AnyCollisionGeometry3D::SetTransform().

bool Geometry::Collides	(	const CollisionPointCloud &	pc1,
		const CollisionPointCloud &	pc2,
		Real	margin,
		std::vector< int > &	points1,
		std::vector< int > &	points2,
		size_t	maxContacts = 1
	)

Returns true if the point clouds are within margin distance of one another. points1 and points2 return one or more pairs of close-by points. maxContacts controls how many pairs are computed.

void Geometry::ConvexHullToMesh	(	const ConvexHull3D &	ch,
		Meshing::TriMesh &	mesh
	)

Computes a mesh from a ConvexHull. Uses Qhull.

References ConvexHull3D_Qhull().

Referenced by GLDraw::GeometryAppearance::Refresh().

Real Geometry::Distance	(	const CollisionImplicitSurface &	s,
		const Vector3 &	pt
	)

Returns the distance between s and pt, assuming it's a signed distance field. Negative values indicate interior points. Input is in world coordinates.

References Geometry::CollisionImplicitSurface::baseGrid, Geometry::CollisionImplicitSurface::currentTransform, Math3D::RigidTransform::mulInverse(), and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

Referenced by Geometry::KDTree::ClosePoints(), Geometry::KDTree::Select(), and Geometry::AnyCollisionGeometry3D::SetTransform().

Real Geometry::Distance	(	const CollisionImplicitSurface &	s,
		const Vector3 &	pt,
		Vector3 &	surfacePt,
		Vector3 &	direction
	)

Returns the distance between s and pt, assuming s is a signed distance field. Negative values indicate interior points.

Outputs:

• surfacePt is the closest point on the surface
• direction is the unit normal in the direction of decreasing signed distance. If pt is outside, this points toward surfacePt, but if pt is inside, this points further into s.

Inputs and outputs are all in world coordinates.

References Geometry::CollisionImplicitSurface::baseGrid, Geometry::CollisionImplicitSurface::currentTransform, Meshing::VolumeGridTemplate< T >::Gradient(), Math3D::RigidTransform::mulInverse(), and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

Real Geometry::Distance	(	const CollisionImplicitSurface &	s,
		const GeometricPrimitive3D &	geom,
		Vector3 &	surfacePt,
		Vector3 &	geomPt,
		Vector3 &	direction
	)

Same as above, except that:

• geomPt is the closest/deepest point on geom.
• direction is the unit normal of decreasing distance, in that if geom is moved in this direction, the distance decreases.

Only points and spheres are currently supported

References GET_LOGGER.

Real Geometry::Distance	(	const CollisionPointCloud &	pc,
		const Vector3 &	pt,
		int &	closestPoint,
		Real	upperBound
	)

Returns the nearest distance from any point in pc to g. O(log n) running time. Saves the closest point index into ClosestPoint. If upperBound is given, and if no point is closer than upperBound, this may return upperBound as the return value and closestPoint=-1.

References Geometry::CollisionPointCloud::currentTransform, and Math3D::RigidTransform::mulInverse().

Real Geometry::Distance	(	const CollisionPointCloud &	pc,
		const GeometricPrimitive3D &	g
	)

Returns the nearest distance from any point in pc to g. O(log n) running time for points and spheres, O(n) running time for everythign else.

Real Geometry::Distance	(	const CollisionPointCloud &	pc,
		const GeometricPrimitive3D &	g,
		int &	closestPoint,
		Real	upperBound = Inf
	)

Returns the nearest distance from any point in pc to g. O(log n) running time for points and spheres, O(n) running time for everything else. Saves the closest point index into closestPoint. If upperBound is given, and if no point is closer than upperBound, this may return upperBound as the return value and closestPoint=-1.

References Geometry::CollisionPointCloud::bblocal, Geometry::CollisionPointCloud::currentTransform, Math::IsInf(), and Geometry::CollisionPointCloud::radiusIndex.

Real Geometry::Distance	(	const CollisionPointCloud &	pc1,
		const CollisionPointCloud &	pc2,
		int &	closestPoint1,
		int &	closestPoint2,
		Real	upperBound = Inf
	)

Returns the nearest distance from any point in pc1 to any point in pc2. O(n log n) running time. Saves the closest point pair into closestPoint1 and closestPoint2. If upperBound is given, then if no pair of points is closer than upperBound, this may return upperBound as the return distance and closestPoint1=closestPoint2=-1.

References Geometry::CollisionPointCloud::currentTransform, and Geometry::CollisionPointCloud::radiusIndex.

Real Geometry::Distance	(	const CollisionMesh &	m,
		const Vector3 &	p,
		Real	bound = Inf
	)

Returns the nearest distance from any point in m to g. O(log n) running time. If the distance is > bound, then this terminates early and returns bound.

References ClosestPoint().

Real Geometry::Distance	(	const CollisionMesh &	m,
		const Vector3 &	p,
		int &	closestTri,
		Vector3 &	surfacePt,
		Vector3 &	direction,
		Real	bound = Inf
	)

Same as the above, but with additional outputs

Outputs

• surfacePt is the closest point on the surface, in world coordinates
• direction is the unit normal from the surface to p, in world coordinates

References ClosestPoint(), Math::FuzzyZero(), and Meshing::TriMesh::TriangleNormal().

Real Geometry::Distance	(	const CollisionMesh &	m,
		const GeometricPrimitive3D &	g,
		Real	bound = Inf
	)

Returns the nearest distance from any point in m to g. O(log n) running time for point / sphere, O(n) otherwise. If the distance is > bound, then this terminates early and returns bound.

Real Geometry::Distance	(	const CollisionMesh &	m,
		const GeometricPrimitive3D &	g,
		int &	closestTri,
		Vector3 &	surfacePt,
		Vector3 &	direction,
		Real	bound = Inf
	)

Same as the above, but with additional outputs

Outputs

• surfacePt is the closest point on the surface, in world coordinates
• direction is the unit normal from the surface to the closest / deepest point on g, in world coordinates

References GET_LOGGER, and Meshing::TriMesh::GetTriangle().

void Geometry::FitBox	(	const GeometricPrimitive3D &	g,
		Box3D &	box
	)

fits an oriented bounding box to the geometry. TODO: do a better job on triangles, segments

References CollideAll(), FitBox(), GET_LOGGER, Meshing::TriMesh::GetTriangle(), NearbyTriangles(), Geometry::CollisionMeshQuery::TolerancePair(), Geometry::CollisionMeshQuery::TolerancePairs(), and Geometry::CollisionMeshQuery::WithinDistance().

Referenced by FitBox().

void Geometry::GetBB	(	const CollisionMesh &	m,
		Box3D &	bb
	)

Returns the bounding box containing m.

@{

References GET_LOGGER, and GetBB().

Referenced by Geometry::AnyCollisionGeometry3D::ClearCollisionData(), Collides(), Geometry::AnyCollisionGeometry3D::GetAABB(), Geometry::AnyCollisionGeometry3D::GetBB(), GetBB(), NearbyPoints(), and WithinDistance().

void Geometry::NearbyPoints	(	const CollisionPointCloud &	pc,
		const GeometricPrimitive3D &	g,
		Real	tol,
		std::vector< int > &	points,
		size_t	maxContacts = std::numeric_limits< size_t >::max()
	)

Computes the set of points in the pc that are within tol distance of the primitive g. O(min(n,c)) running time, where c is the number of grid cells within distance tol of the bounding box of g.

References Geometry::CollisionPointCloud::bblocal, Geometry::CollisionPointCloud::currentTransform, GetBB(), Geometry::CollisionPointCloud::maxRadius, and Geometry::CollisionPointCloud::radiusIndex.

Referenced by Geometry::AnyCollisionGeometry3D::SetTransform().

void Geometry::NearbyTriangles	(	const CollisionMesh &	m,
		const Vector3 &	p,
		Real	d,
		vector< int > &	tris,
		int	max
	)

Computes the triangles in m within distance d to p on m.

Finds the triangles within distance d to p on m using the PQP bounding heirarchy

References CollideAll(), and NearbyTriangles().

Referenced by FitBox(), NearbyTriangles(), and Geometry::AnyCollisionGeometry3D::SetTransform().

void Geometry::NearbyTriangles	(	const CollisionMesh &	m,
		const Vector3 &	p,
		Real	d,
		vector< int > &	tris,
		int	max
	)

Computes the triangles in m within distance d to p on m.

Finds the triangles within distance d to p on m using the PQP bounding heirarchy

References CollideAll(), and NearbyTriangles().

Referenced by FitBox(), NearbyTriangles(), and Geometry::AnyCollisionGeometry3D::SetTransform().

void Geometry::NearestNeighborGraph	(	const Meshing::PointCloud3D &	pc,
		int	k,
		Graph::Graph< int, int > &	G
	)

Computes a graph where each node is an index of a point in the point cloud and each edge connects points (i,j) for which j is a k-nearest neighbor (in Euclidean space)

void Geometry::NearestNeighborGraph	(	const vector< Vector3 > &	pc,
		int	k,
		Graph::Graph< int, int > &	G
	)

Computes a graph where each node is an index of a point in the point cloud and each edge connects points (i,j) for which j is a k-nearest neighbor (in Euclidean space)

References ArrayUtils::copy(), Geometry::KDTree::Create(), and Geometry::KDTree::KClosestPoints().

void Geometry::NeighborGraph	(	const Meshing::PointCloud3D &	pc,
		Real	R,
		Graph::UndirectedGraph< int, int > &	G
	)

Computes a graph where each node is an index of a point in the point cloud and each edge connects points within distance R (in Euclidean space)

void Geometry::NeighborGraph	(	const vector< Vector3 > &	pc,
		Real	R,
		Graph::UndirectedGraph< int, int > &	G
	)

Computes a graph where each node is an index of a point in the point cloud and each edge connects points within distance R (in Euclidean space)

References Geometry::GridSubdivision::Insert().

int Geometry::RayCast	(	const CollisionPointCloud &	pc,
		Real	rad,
		const Ray3D &	r,
		Vector3 &	pt
	)

Casts a ray at the point cloud (where each point is fattened by radius rad). Returns index of the first point hit (-1 if none) and the colliding point in pt.

References Geometry::CollisionPointCloud::currentTransform, Math3D::RigidTransform::mulInverse(), Math3D::Matrix3::mulTranspose(), and RayCastLocal().

Real Geometry::RayCast	(	const Meshing::VolumeGrid &	grid,
		const Ray3D &	ray,
		Real	levelSet,
		Real	tmax
	)

Returns the distance to the closest point on the implicit surface defined at the given level set. The algorithm marches along cells intersected by the ray until a zero-crossing is met (O(n)) where n is the resolution of the grid.

Returns the distance to the closest point on the implicit surface defined at the given level set. tmax will be returned if no collision is found.

The algorithm marches along cells intersected by the ray until a zero-crossing is met (O(n)) where n is the resolution of the grid.

References Meshing::GetSegmentCells(), RayCast(), and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

Referenced by Geometry::AnyCollisionGeometry3D::ClearCollisionData(), PrimitiveToImplicitSurface(), and RayCast().

Real Geometry::RayCast	(	const CollisionImplicitSurface &	s,
		const Ray3D &	rayWorld,
		Real	levelSet,
		Real	tmax
	)

Returns the distance to the closest point on the implicit surface defined at the given level set. The algorithm uses the collision hierarchy (O(log n) where n is the resolution of the grid.

Returns the distance to the closest point on the implicit surface defined at the given level set. tmax will be returned if no collision is found.

The algorithm uses the collision hierarchy (O(log n) where n is the resolution of the grid.

References Geometry::CollisionImplicitSurface::baseGrid, Geometry::CollisionImplicitSurface::currentTransform, Meshing::VolumeGridTemplate< T >::GetIndexRange(), Meshing::VolumeGridTemplate< T >::GetIndexRangeClamped(), Meshing::GetSegmentCells(), Geometry::CollisionImplicitSurface::minHierarchy, Math3D::RigidTransform::mulInverse(), Math3D::Matrix3::mulTranspose(), RayCast(), and Meshing::VolumeGridTemplate< T >::TrilinearInterpolate().

int Geometry::RayCast	(	const CollisionMesh &	m,
		const Ray3D &	r,
		Vector3 &	pt
	)

Casts a ray at the mesh. Returns the index of the first triangle hit (-1 if none) and stores the colliding point in pt (given in world coordinates).

References RayCast().

int Geometry::RayCastLocal	(	const CollisionPointCloud &	pc,
		Real	rad,
		const Ray3D &	r,
		Vector3 &	pt
	)

Same as RayCast, but the ray (and colliding point) are in the local frame of the point cloud

References Geometry::CollisionPointCloud::bblocal.

int Geometry::RayCastLocal	(	const CollisionMesh &	m,
		const Ray3D &	r,
		Vector3 &	pt
	)

Same as RayCast, but the ray (and colliding point) are in the local frame of the mesh

References RayCastLocal().

Referenced by RayCast(), and RayCastLocal().

bool Geometry::WithinDistance	(	const CollisionPointCloud &	pc,
		const GeometricPrimitive3D &	g,
		Real	tol
	)

Computes whether any point in the pc is within tol distance of the primitive g. O(min(n,c)) running time, where c is the number of grid cells within distance tol of the bounding box of g.

References Geometry::CollisionPointCloud::bblocal, Geometry::CollisionPointCloud::currentTransform, GetBB(), Geometry::CollisionPointCloud::maxRadius, and Geometry::CollisionPointCloud::radiusIndex.

bool Geometry::WithinDistance	(	const CollisionMesh &	m,
		const Vector3 &	p,
		Real	d
	)

Returns true if p is within distance d of m using the PQP bounding heirarchy.

Returns true if m is within distance d of the geometry.