Aim: model of a CEuclideanOrientedShape from an implicit function from an oriented point cloud. The implicit function is given by the generalized winding number of the oriented point cloud [10] . We use the libIGL implementation. More...

#include <DGtal/shapes/WindingNumbersShape.h>

Public Types
using	Space = TSpace
	Types.
using	RealPoint = typename Space::RealPoint
using	RealVector = typename Space::RealVector
using	Orientation = DGtal::Orientation

Public Member Functions
	WindingNumbersShape ()=delete
	WindingNumbersShape (ConstAlias< Eigen::MatrixXd > points, ConstAlias< Eigen::MatrixXd > normals, bool skipPointAreas=false)
	WindingNumbersShape (ConstAlias< Eigen::MatrixXd > points, ConstAlias< Eigen::MatrixXd > normals, const Eigen::VectorXd &areas)
void	setPointAreas (ConstAlias< Eigen::VectorXd > areas)
Orientation	orientation (const RealPoint aPoint, const double threshold=0.3) const
std::vector< Orientation >	orientationBatch (const Eigen::MatrixXd &queries, const double threshold=0.3) const
void	rawWindingNumberBatch (const Eigen::MatrixXd &queries, Eigen::VectorXd &W) const

Data Fields
CountedConstPtrOrConstPtr< Eigen::MatrixXd >	myPoints
	Const alias to the points.
CountedConstPtrOrConstPtr< Eigen::MatrixXd >	myNormals
	Const alias to the normals.
Eigen::VectorXd	myPointAreas
	Const alias to point area measure.
std::vector< std::vector< int > >	myO_PI
	libIGL octree for fast queries data structure
Eigen::MatrixXi	myO_CH
	libIGL octree for fast queries data structure
Eigen::MatrixXd	myO_CN
	libIGL octree for fast queries data structure
Eigen::VectorXd	myO_W
	libIGL octree for fast queries data structure

Detailed Description

template<typename TSpace>
struct DGtal::WindingNumbersShape< TSpace >

Aim: model of a CEuclideanOrientedShape from an implicit function from an oriented point cloud. The implicit function is given by the generalized winding number of the oriented point cloud [10] . We use the libIGL implementation.

Description of template class 'WindingNumbersShape'

See also: testWindingNumberShape, windingNumberShape

Template Parameters

TSPace the digital space type (a model of CSpace)

Definition at line 77 of file WindingNumbersShape.h.

Member Typedef Documentation

◆ Orientation

template<typename TSpace>

using DGtal::WindingNumbersShape< TSpace >::Orientation = DGtal::Orientation

Definition at line 83 of file WindingNumbersShape.h.

◆ RealPoint

template<typename TSpace>

using DGtal::WindingNumbersShape< TSpace >::RealPoint = typename Space::RealPoint

Definition at line 81 of file WindingNumbersShape.h.

◆ RealVector

template<typename TSpace>

using DGtal::WindingNumbersShape< TSpace >::RealVector = typename Space::RealVector

Definition at line 82 of file WindingNumbersShape.h.

◆ Space

template<typename TSpace>

using DGtal::WindingNumbersShape< TSpace >::Space = TSpace

Types.

Definition at line 80 of file WindingNumbersShape.h.

Constructor & Destructor Documentation

◆ WindingNumbersShape() [1/3]

template<typename TSpace>

DGtal::WindingNumbersShape< TSpace >::WindingNumbersShape ( )

delete

◆ WindingNumbersShape() [2/3]

template<typename TSpace>

DGtal::WindingNumbersShape< TSpace >::WindingNumbersShape	(	ConstAlias< Eigen::MatrixXd >	points,
		ConstAlias< Eigen::MatrixXd >	normals,
		bool	skipPointAreas = false )

inline

Construct a WindingNumberShape Euclidean shape from an oriented point cloud. This constructor estimates the area of each point using CGAL.

If the number of points is greater than 20, CGAL is used to estimate the per-sample area (if skipPointAreas is set to false).

Parameters

points	a "nx3" matrix with the sample coordinates.
normals	a "nx3" matrix for the normal vectors.
skipPointAreas	if true, we do not estimate the point areas using CGAL (default: false)

Definition at line 97 of file WindingNumbersShape.h.

    {
      myPoints  = points;
      myNormals = normals;
      myPointAreas = Eigen::VectorXd::Ones(myPoints->rows());
      // Build octree, from libIGL tutorials
      igl::octree(*myPoints,myO_PI,myO_CH,myO_CN,myO_W);
      if (skipPointAreas)
        trace.warning()<<"[WindingNumberShape] Skipping the CGAL point area estimation. By default, point areas are set to 1.0"<<std::endl;
      else
        if (points->rows()> 20)
        {
          Eigen::MatrixXi I;
          igl::knn(*myPoints,(int)points->rows(),myO_PI,myO_CH,myO_CN,myO_W,I);
          // CGAL is only used to help get point areas
          igl::copyleft::cgal::point_areas(*myPoints,I,*myNormals,myPointAreas);
          trace.info()<<"[WindingNumberShape] Min/max point area : "<<myPointAreas.minCoeff()<<" -- "<<myPointAreas.maxCoeff()<<std::endl;
        }
        else
        {
          trace.warning()<<"[WindingNumberShape] Too few points to use CGAL point_areas. Using the constant area setting."<<std::endl;
        }
    }

References myNormals, myO_CH, myO_CN, myO_PI, myO_W, myPointAreas, myPoints, and DGtal::trace.

◆ WindingNumbersShape() [3/3]

template<typename TSpace>

DGtal::WindingNumbersShape< TSpace >::WindingNumbersShape	(	ConstAlias< Eigen::MatrixXd >	points,
		ConstAlias< Eigen::MatrixXd >	normals,
		const Eigen::VectorXd &	areas )

inline

Construct a WindingNumberShape Euclidean shape from an oriented point cloud. For this constructor, the area of each point is given by the user.

Parameters

points	a "nx3" matrix with the sample coordinates.
normals	a "nx3" matrix for the normal vectors.
areas	a "n" vector with the area of each point.

Definition at line 129 of file WindingNumbersShape.h.

    {
      myPoints  = points;
      myNormals = normals;
      myPointAreas = areas;
      igl::octree(*myPoints,myO_PI,myO_CH,myO_CN,myO_W);
    }

References myNormals, myO_CH, myO_CN, myO_PI, myO_W, myPointAreas, and myPoints.

Member Function Documentation

◆ orientation()

template<typename TSpace>

Orientation DGtal::WindingNumbersShape< TSpace >::orientation	(	const RealPoint	aPoint,
		const double	threshold = 0.3 ) const

inline

Orientation of a point using the winding number value from an oriented pointcloud.

Note: For multiple queries, orientationBatch() should be used.

Parameters

aPoint	[in] a point in space
threshold	[in] the iso-value of the surface of the winding number implicit map (default = 0.3).

Returns: a DGtal::Orientation value

Definition at line 155 of file WindingNumbersShape.h.

    {
      Eigen::MatrixXd queries(1,3);
      queries << aPoint(0) , aPoint(1) , aPoint(2);
      auto singlePoint = orientationBatch(queries, threshold);
      return singlePoint[0];
    }

References aPoint, and orientationBatch().

◆ orientationBatch()

template<typename TSpace>

std::vector< Orientation > DGtal::WindingNumbersShape< TSpace >::orientationBatch	(	const Eigen::MatrixXd &	queries,
		const double	threshold = 0.3 ) const

inline

Orientation of a set of points (queries) using the winding number value from an oriented pointcloud.

Parameters

queries	[in] a "nx3" matrix with the query points in space.
threshold	[in] the iso-value of the surface of the winding number implicit map (default = 0.3).

Returns: a DGtal::Orientation value vector for each query point.

Definition at line 170 of file WindingNumbersShape.h.

    {
      Eigen::VectorXd W;
      std::vector<Orientation> results( queries.rows(), DGtal::OUTSIDE );
 
      rawWindingNumberBatch(queries, W);
     
      //Reformating the output
      for(auto i=0u; i < queries.rows(); ++i)
      {
        if (std::abs(W(i)) < threshold )
          results[i] = DGtal::OUTSIDE;
        else
          if (std::abs(W(i)) > threshold)
            results[i] = DGtal::INSIDE;
          else
            results[i] = DGtal::ON;
      }
      return results;
    }

References DGtal::INSIDE, DGtal::ON, DGtal::OUTSIDE, and rawWindingNumberBatch().

Referenced by orientation().

◆ rawWindingNumberBatch()

template<typename TSpace>

void DGtal::WindingNumbersShape< TSpace >::rawWindingNumberBatch	(	const Eigen::MatrixXd &	queries,
		Eigen::VectorXd &	W ) const

inline

Returns the raw value of the Winding Number funciton at a set of points (queries).

Parameters

queries	[in] a "nx3" matrix with the query points in space.
W	[out] a vector with all windung number values.

Definition at line 197 of file WindingNumbersShape.h.

    {
      Eigen::MatrixXd O_CM;
      Eigen::VectorXd O_R;
      Eigen::MatrixXd O_EC;
      
      //Computing the WN values
      igl::fast_winding_number(*myPoints,*myNormals,myPointAreas,myO_PI,myO_CH,2,O_CM,O_R,O_EC);
      igl::fast_winding_number(*myPoints,*myNormals,myPointAreas,myO_PI,myO_CH,O_CM,O_R,O_EC,queries,2,W);
    }