OpenABF::ABF< T, MeshType, Solver, > Class Template Reference

Compute parameterized interior angles using Angle-based flattening. More...

#include <OpenABF/OpenABF.hpp>

Public Types
using	Mesh = MeshType
	Mesh type alias.

Public Member Functions
void	setMaxIterations (const std::size_t it)
	Set the maximum number of iterations.
void	setGradientThreshold (T t)
	Set the gradient convergence threshold.
auto	gradient () const -> T
	Get the mesh gradient.
auto	iterations () const -> std::size_t
	Get the number of iterations of the last computation.
void	compute (typename Mesh::Pointer &mesh)
	Compute parameterized interior angles.

Static Public Member Functions
static void	Compute (typename Mesh::Pointer &mesh, std::size_t &iters, T &gradient, const std::size_t maxIters=10, T gradThreshold=T(0.001))
	Compute parameterized interior angles.
static void	Compute (typename Mesh::Pointer &mesh)
	Compute parameterized interior angles.

Protected Attributes
T	grad_ {0}
std::size_t	iters_ {0}
std::size_t	maxIters_ {10}
T	gradThreshold_ {0.001}

Detailed Description

template<typename T, class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>
class OpenABF::ABF< T, MeshType, Solver, >

Compute parameterized interior angles using Angle-based flattening.

Iteratively computes a new set of interior angles which minimize the total angular error of the parameterized mesh. This follows the standard angled-based flattening formulation, which directly solves for the objective functions and constraints. ABFPlusPlus is generally preferred as it dramatically simplifies the size of the solved problem without introducing more error.

This class does not compute a parameterized mesh. Rather, it calculates the optimal interior angles for such a mesh. To convert this information into a full parameterization, pass the processed HalfEdgeMesh to AngleBasedLSCM.

Implements "Parameterization of faceted surfaces for meshing using angle-based flattening" by Sheffer and de Sturler (2001) [4].

Template Parameters

T	Floating-point type
MeshType	HalfEdgeMesh type which implements the ABF traits
Solver	A solver implementing the Eigen Sparse solver concept and templated on Eigen::SparseMatrix<T>

Member Function Documentation

compute()

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

void OpenABF::ABF< T, MeshType, Solver, >::compute ( typename Mesh::Pointer &  mesh )

inline

Compute parameterized interior angles.

Exceptions

SolverException	If matrix cannot be decomposed or if solver fails to find a solution.
MeshException	If mesh gradient cannot be calculated.

Compute() [1/2]

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

static void OpenABF::ABF< T, MeshType, Solver, >::Compute ( typename Mesh::Pointer &  mesh )

inlinestatic

Compute parameterized interior angles.

Exceptions

SolverException	If matrix cannot be decomposed or if solver fails to find a solution.
MeshException	If mesh gradient cannot be calculated.

Compute() [2/2]

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

static void OpenABF::ABF< T, MeshType, Solver, >::Compute ( typename Mesh::Pointer &  mesh, std::size_t &  iters, T &  gradient, const std::size_t  maxIters = 10, T  gradThreshold = T(0.001)  )

inlinestatic

Compute parameterized interior angles.

Exceptions

SolverException	If matrix cannot be decomposed or if solver fails to find a solution.
MeshException	If mesh gradient cannot be calculated.

gradient()

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

auto OpenABF::ABF< T, MeshType, Solver, >::gradient ( ) const -> T

inline

Get the mesh gradient.

Note: Result is only valid after running compute().

iterations()

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

auto OpenABF::ABF< T, MeshType, Solver, >::iterations ( ) const -> std::size_t

inline

Get the number of iterations of the last computation.

Note: Result is only valid after running compute().

Member Data Documentation

grad_

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

T OpenABF::ABF< T, MeshType, Solver, >::grad_ {0}

protected

Gradient

gradThreshold_

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

T OpenABF::ABF< T, MeshType, Solver, >::gradThreshold_ {0.001}

protected

Gradient convergence threshold

iters_

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::size_t OpenABF::ABF< T, MeshType, Solver, >::iters_ {0}

protected

Number of executed iterations

maxIters_

template<typename T , class MeshType = detail::ABF::Mesh<T>, class Solver = Eigen::SparseLU<Eigen::SparseMatrix<T>, Eigen::COLAMDOrdering<int>>, std::enable_if_t< std::is_floating_point_v< T >, bool > = true>

std::size_t OpenABF::ABF< T, MeshType, Solver, >::maxIters_ {10}

protected

Max iterations