- Referenced in 394 articles
- diagrams), polygons (Boolean operations, offsets, straight skeleton), polyhedra (Boolean operations), arrangements of curves and their...
- Referenced in 316 articles
- polyhedral geometry. It deals with polytopes, polyhedra and fans as well as simplicial complexes, matroids...
- Referenced in 101 articles
- Possibly not closed convex polyhedra and the Parma Polyhedra Library. The domain of convex polyhedra ... Cousot and N. Halbwachs, convex polyhedra have thus played an important role in the formal ... existing libraries for the manipulation of convex polyhedra are still research prototypes and suffer from ... applications. Furthermore, there is inadequate support for polyhedra that are Not Necessarily Closed...
- Referenced in 126 articles
- collection of routines for analyzing polytopes and polyhedra. The polyhedra are either given...
- Referenced in 117 articles
- Parma Polyhedra Library, which supports arbitrarily large numbers. To manage the complexity of the polyhedral ... number of bits and constraints of polyhedra. Experimental results for a navigation benchmark...
- Referenced in 70 articles
- tasks such as the classification of reflexive polyhedra in 4 dimensions and the creation ... very large lists of 5-dimensional polyhedra. While originally intended for low-dimensional applications...
- Referenced in 61 articles
- free library for manipulating special kinds of polyhedra called octagons that correspond to sets ... dimension two, these polyhedra have at most eight faces). This library is targeted at static...
- Referenced in 47 articles
- objects made up of unions of polyhedra of any dimension. It was first developed ... version (1.1) manipulates non parameterized unions of polyhedra through the following operations: intersection, difference, union ... plus some input and output functions. The polyhedra are computed in their dual implicit...
- Referenced in 75 articles
- piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets...
- Referenced in 33 articles
- affine setting, the basic objects are polyhedra, which are intersections of finitely many (affine) halfspaces ... Polyhedra can also be described as the convex hull of finitely many points and rays ... called a polytope. In the Convex package, polyhedra are represented by the type POLYHEDRON...
- Referenced in 28 articles
- construction of all 473,800,776 reflexive polyhedra that exist in four dimensions. These polyhedra...
- Referenced in 37 articles
- method for overapproximating reachable sets by orthogonal polyhedra. The tool also allows to synthesize...
- Referenced in 22 articles
- verter enumeration/conver hull problem for conver polyhedra. We describe an important and difficult class ... polyhedra, called configuration polytopes, that have application to determining the ground states of alloy phase...
- Referenced in 18 articles
- linearly trimmed bicubic B-splines Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary ... routine Pcp2Nurb in turn translates planar-cut polyhedra to a collection of four-sided linearly...
- Referenced in 11 articles
- closest pair of features between convex polyhedra, using an approach reminiscent of the Lin-Canny ... cycling problems. The algorithm also handles penetrating polyhedra, and can therefore be used to detect ... collisions between nonvconvex polyhedra described as hierarchies of convex pieces. The article presents the theoretical...
- Referenced in 9 articles
- Polyhedra: a package for computations with convex polyhedral objects. Convex polyhedral objects play an important ... numerous areas of algebraic geometry. The package Polyhedra enables one to work with such convex ... polyhedral objects in Macaulay 2. In particular, Polyhedra implements objects representing polyhedra, cones, and fans...
- Referenced in 11 articles
- possibility of an overlap between the flux polyhedra and hence significantly increases volume conservation ... which avoids topological changes of the flux polyhedra. Our geometrical VoF algorithm is dimension agnostic...
- Referenced in 8 articles
- Uniform solution for uniform polyhedra. A uniform polyhedron in 3-dimensional space has faces which ... provided a complete enumeration of the uniform polyhedra, together with a limited amount of metrical ... with directly. Similar techniques treat the dual polyhedra, which were not dealt with ... drawings of the edge-graphs of the polyhedra and their duals (with a handful...
- Referenced in 14 articles
- convex polygons in 2D or polyhedra in 3D. Contact mechanics obey particle-interaction laws that...