wmtk::utils::WindingNumberHierarchy Class Reference

The hierarchy libigl's winding_number(V, F, O, W) evaluates a triangle mesh with – igl::WindingNumberAABB, exact method – made deterministic and self-contained. More...

#include <WindingNumberHierarchy.hpp>

Classes
struct	Node

Public Member Functions
	WindingNumberHierarchy (const Eigen::MatrixXd &V, const Eigen::MatrixXi &F)
double	winding_number (const Eigen::RowVector3d &p) const
	Winding number of p with respect to the mesh.

Private Member Functions
int	add_node (Eigen::MatrixXi F)
void	grow (const int node)
	WindingNumberAABB::grow with the median split.
bool	inside (const Node &n, const Eigen::RowVector3d &p) const
double	node_winding_number (const int node, const Eigen::RowVector3d &p) const
	WindingNumberTree::winding_number, exact method.

Static Private Member Functions
static Eigen::MatrixXi	cap_of (const Eigen::MatrixXi &F)
	igl::triangle_fan(igl::exterior_edges(F)), with a fixed apex instead of a random one.

Private Attributes
Eigen::MatrixXd	m_V
std::vector< Node >	m_nodes

Static Private Attributes
static constexpr Eigen::Index	kMinFaces = 100
	Fewest faces a node is split at, as igl's WindingNumberAABB_MIN_F.

Detailed Description

The hierarchy libigl's winding_number(V, F, O, W) evaluates a triangle mesh with – igl::WindingNumberAABB, exact method – made deterministic and self-contained.

The algorithm is igl's, step for step: exact duplicate vertices merged, nodes split at the median face barycenter along the box's longest axis down to 100 faces, and a query outside a node's box answered from the node's boundary, closed by a fan, when that is cheaper than its faces. Two things differ:

• The fan's apex. igl picks it with rand(), so every build of the same mesh closes its nodes differently. The values agree mathematically – the cap lies in the node's box and is only used for points outside it – but not to the last bit: two builds of one mesh disagreed by an ulp on a quarter of the points of a test sphere. The winding number then depended on the process's rand() state, and a point on the surface, at 1/2, could fall either side of the inside test from run to run. Here the apex is the first boundary edge's first vertex.
• The vertices. igl's tree keeps them in a static shared by every tree of its type, so building one tree while another is queried corrupts the other's results. Here each hierarchy owns them.

winding_number(p) is const and touches no shared state, so a hierarchy can be queried from any number of threads at once.

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The documentation for this class was generated from the following file:

• src/wmtk/utils/WindingNumberHierarchy.hpp