CGAL::Poisson_reconstruction_function< Gt > Class Template Reference

#include <CGAL/Poisson_reconstruction_function.h>

Definition

Implementation of the Poisson Surface Reconstruction method.

Given a set of 3D points with oriented normals sampled on the boundary of a 3D solid, the Poisson Surface Reconstruction method [2] solves for an approximate indicator function of the inferred solid, whose gradient best matches the input normals. The output scalar function, represented in an adaptive octree, is then iso-contoured using an adaptive marching cubes.

Poisson_reconstruction_function implements a variant of this algorithm which solves for a piecewise linear function on a 3D Delaunay triangulation instead of an adaptive octree.

Template Parameters

Gt	Geometric traits class.

Is Model Of:

ImplicitFunction

Examples:

Surface_reconstruction_points_3/poisson_reconstruction_example.cpp.

Types
typedef Gt	Geom_traits
	Geometric traits class.
typedef Triangulation::Cell_handle	Cell_handle
typedef Geom_traits::FT	FT
	number type.
typedef Geom_traits::Point_3	Point
	point type.
typedef Geom_traits::Vector_3	Vector
	vector type.
typedef Geom_traits::Sphere_3	Sphere

Creation
template<typename InputIterator , typename PointPMap , typename NormalPMap >
	Poisson_reconstruction_function (InputIterator first, InputIterator beyond, PointPMap point_pmap, NormalPMap normal_pmap)
	Creates a Poisson implicit function from the range of points [first, beyond). More...

Operations
Sphere	bounding_sphere () const
	Returns a sphere bounding the inferred surface.
template<class SparseLinearAlgebraTraits_d >
bool	compute_implicit_function (SparseLinearAlgebraTraits_d solver, bool smoother_hole_filling=false)
	This function must be called after the insertion of oriented points. More...
FT	operator() (const Point &p) const
	ImplicitFunction interface: evaluates the implicit function at a given 3D query point. More...
Point	get_inner_point () const
	Returns a point located inside the inferred surface.

Constructor & Destructor Documentation

template<class Gt >

template<typename InputIterator , typename PointPMap , typename NormalPMap >

CGAL::Poisson_reconstruction_function< Gt >::Poisson_reconstruction_function	(	InputIterator	first,
		InputIterator	beyond,
		PointPMap	point_pmap,
		NormalPMap	normal_pmap
	)

Creates a Poisson implicit function from the range of points [first, beyond).

Template Parameters

InputIterator	iterator over input points.
PointPMap	is a model of ReadablePropertyMap with a value_type = Point. It can be omitted if InputIterator value_type is convertible to Point.
NormalPMap	is a model of ReadablePropertyMap with a value_type = Vector.

Parameters

first	iterator over the first input point.
beyond	past-the-end iterator over the input points.
point_pmap	property map: value_type of InputIterator -> Point (the position of an input point).
normal_pmap	property map: value_type of InputIterator -> Vector (the oriented normal of an input point).

Member Function Documentation

template<class Gt >

template<class SparseLinearAlgebraTraits_d >

bool CGAL::Poisson_reconstruction_function< Gt >::compute_implicit_function	(	SparseLinearAlgebraTraits_d	solver,
		bool	smoother_hole_filling = false
	)

This function must be called after the insertion of oriented points.

It computes the piecewise linear scalar function operator() by: applying Delaunay refinement, solving for operator() at each vertex of the triangulation with a sparse linear solver, and shifting and orienting operator() such that it is 0 at all input points and negative inside the inferred surface.

Template Parameters

SparseLinearAlgebraTraits_d

Symmetric definite positive sparse linear solver. If Eigen 3.1 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, an overload with Eigen_solver_traits<Eigen::ConjugateGradient<Eigen_sparse_symmetric_matrix<double>::EigenType> > as default solver is provided.

Parameters

solver	sparse linear solver.
smoother_hole_filling	controls if the Delaunay refinement is done for the input points, or for an approximation of the surface obtained from a first pass of the algorithm on a sample of the points.

Returns

false if the linear solver fails.

template<class Gt >

FT CGAL::Poisson_reconstruction_function< Gt >::operator()

(

const Point &

p)

const

ImplicitFunction interface: evaluates the implicit function at a given 3D query point.

The function compute_implicit_function() must be called before the first call to operator().