Polygonal Discrete Differential Geometry (PolyDDG) algorithms and data structures. More...

Classes
struct	PrincipalCurvaturesOptions
	Options for compute_principal_curvatures(). More...

struct	PrincipalCurvaturesResult
	Result of compute_principal_curvatures(). More...

class	DifferentialOperators< Scalar, Index >
	Polygonal mesh discrete differential operators. More...

Functions
template<typename Scalar, typename Index>
LA_POLYDDG_API PrincipalCurvaturesResult	compute_principal_curvatures (SurfaceMesh< Scalar, Index > &mesh, const DifferentialOperators< Scalar, Index > &ops, PrincipalCurvaturesOptions options={})
	Compute per-vertex principal curvatures and principal curvature directions.

template<typename Scalar, typename Index>
LA_POLYDDG_API PrincipalCurvaturesResult	compute_principal_curvatures (SurfaceMesh< Scalar, Index > &mesh, PrincipalCurvaturesOptions options={})
	Compute per-vertex principal curvatures and principal curvature directions.

Detailed Description

Polygonal Discrete Differential Geometry (PolyDDG) algorithms and data structures.

This module is based on the paper "Discrete Differential Operators on Polygonal Meshes" by de Goes et al. [1]. It provides common discrete differential operators to manipulate differential forms and vector fields on polygonal meshes.

[1] De Goes, Fernando, Andrew Butts, and Mathieu Desbrun. "Discrete differential operators on polygonal meshes." ACM Transactions on Graphics (TOG) 39.4 (2020): 110-1.

Function Documentation

◆ compute_principal_curvatures() [1/2]

template<typename Scalar, typename Index>

LA_POLYDDG_API PrincipalCurvaturesResult compute_principal_curvatures	(	SurfaceMesh< Scalar, Index > &	mesh,
		const DifferentialOperators< Scalar, Index > &	ops,
		PrincipalCurvaturesOptions	options = {} )

#include <lagrange/polyddg/compute_principal_curvatures.h>

Compute per-vertex principal curvatures and principal curvature directions.

Performs an eigendecomposition of the adjoint shape operator at each vertex. The two eigenvalues are the principal curvatures (kappa_min <= kappa_max) and the corresponding eigenvectors, mapped back to 3-D through the vertex tangent basis, are the principal directions. Results are stored as vertex attributes in the mesh.

Parameters

[in,out]	mesh	Input surface mesh. Output attributes are added or overwritten.
[in]	ops	Precomputed differential operators for the mesh.
[in]	options	Attribute name options. Defaults produce attributes named @kappa_min, @kappa_max, @principal_direction_min, @principal_direction_max.

Returns: Attribute IDs of the four output attributes.

◆ compute_principal_curvatures() [2/2]