This article introduces an effective approach to performing matching pursuit calculations with continuous (quasi-infinite) dictionaries. Simulating continuous parameter space is accomplished by combining optimal dictionary construction as introduced ...

We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it ...

For control nets outlining a large class of topological polyhedra, not just tensor-product grids, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Akin to tensor-...

MQSI is a Fortran 2003 subroutine for constructing monotone quintic spline interpolants to univariate monotone data. Using sharp theoretical monotonicity constraints, first and second derivative estimates at data provided by a quadratic facet model are ...

Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new triangle intersection algorithm ensures ...

The traditional workflow in continuum mechanics simulations is that a geometry description —for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) tools—forms the input for a mesh generator. The mesh is then used as ...

We provide a number of corrections to the software component that accompanied this Algorithm submission [3]. An updated version of the code is available from the ACM Collected Algorithms site [1].

We introduce the Colored Abstract Simplicial Complex library (CASC): a new, modern, and header-only C++ library that provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly ...

We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate, and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that comprises ...

Implicitly described domains are a well-established tool in the simulation of time-dependent problems, for example, using level-set methods. To solve partial differential equations on such domains, a range of numerical methods was developed, for example, ...

Voronoi diagrams are useful for spatial reasoning, and the robust and efficient construction of the ordinary Voronoi diagram of points is well known. However, its counterpart for circular disks in R² and spherical balls in R³ remains a challenge. In ...

A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a structured-...

The implementation of a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph (PH) curves is presented using the complex representation. The special algebraic structure of PH curves permits exact algorithms ...

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes—surface triangular meshes or volume tetrahedral meshes—from input surfaces, 3D domains, and 3D multidomains,...

For a common class of two-dimensional (2D) mechanisms called 1-dof tree-decomposable linkages, we present a software package, CayMos, which uses new theoretical results from Sitharam and Wang [2014] and Sitharam et al. [2011a, 2011b] to implement ...

TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses ...

A novel algorithm is presented to compute the convex hull of a point set in ℝ³ using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the approximation of the ...

This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely ...

Balls and spheres are amongst the simplest 3D modeling primitives, and computing the volume of a union of balls is an elementary problem. Although a number of strategies addressing this problem have been investigated in several communities, we are not ...

Bundle adjustment constitutes a large, nonlinear least-squares problem that is often solved as the last step of feature-based structure and motion estimation computer vision algorithms to obtain optimal estimates. Due to the very large number of ...