Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments

Weiler, Kevin

doi:10.1109/mcg.1985.276271

Cited by 292 publications

(103 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this paper, we show that the computation of exact geodesic metric is also applicable in edge-based data structures. A direct merit is that some existing CAD systems which use edge-based data structures [19] can simply add a new function for computing exact geodesic without changing the kernel completely to a half-edge data structure. We also show that edge-based implementation of the MMP algorithm can achieve three merits: (1) To find the geodesic path between any two points on T , the MMP algorithm can be run in an on-the-fly fashion; (2) unnecessary wedges can be efficiently pruned during the edge-based wedge propagation process and the MMP algorithm is speeded up; (3) Less wedges need to be stored for establishing the exact geodesic metric on T and thus improving the space efficiency.…”

Section: Discussionmentioning

confidence: 99%

“…This property, however, prevents the algorithms to apply with other widely used data structures in engineering such as doubly-connected edge list [17], winged-edge data structure [18] and its variants for sold modeling [19], in which each edge in T is recorded exactly once and we call these data structures [17,18,19] as edge-based data structures, compared to the half-edge data structures [15,16]. The comparisons of half-edge and edge-based data structures are studied in [20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures

Liu

2013

Computer-Aided Design

View full text Add to dashboard Cite

A natural metric in 2-manifold surfaces is to use geodesic distance. If a 2-manifold surface is represented by a triangle mesh T , the geodesic metric on T can be computed exactly using computational geometry methods. Previous work for establishing the geodesic metric on T only supports using half-edge data structures; i.e., each edge e in T is split into two halves (he 1 , he 2 ) and each half-edge corresponds to one of two faces incident to e. In this paper, we prove that the exact-geodesic structures on two half-edges of e can be merged into one structure associated with e. Four merits are achieved based on the properties which are studied in this paper: (1) Existing CAD systems that use edge-based data structures can directly add the geodesic distance function without changing the kernel to a half-edge data structure; (2) To find the geodesic path from inquiry points to the source, the MMP algorithm can be run in an on-the-fly fashion such that the inquiry points are covered by correct wedges; (3) The MMP algorithm is speeded up by pruning unnecessary wedges during the wedge propagation process; (4) The storage of the MMP algorithm is reduced since less wedges need to be stored in an edge-based data structure. Experimental results show that when compared to the classic half-edge data structure, the edge-based implementation of the MMP algorithm reduces 44% running time and 29% storage on average.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures

Liu

2013

Computer-Aided Design

View full text Add to dashboard Cite

show abstract

“…Since the boundary is used to separate points belonging to the inside and the outside of the set, a first limitation is that the represented set must have a non zero volume. A discussion about adequate methods of representing the boundaries can be found in [Wei85]. A good overview of this structure is given in [Sha02,Hof89].…”

Section: Boundary Representation (B-rep)mentioning

confidence: 99%

Implicit Real Vector Automata

Boigelot

Brusten

Degbomont

2010

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

This thesis introduces a new data structure, the Implicit Real Vector Automaton (IRVA), suited for representing symbolically polyhedra, i.e., regions of n-dimensional space defined by finite Boolean combinations of linear inequalities. IRVA can represent exactly arbitrary convex and non-convex polyhedra, including features such as open and closed boundaries, unconnected parts, and non-manifold components. In addition, they provide efficient procedures for deciding whether a point belongs to a given polyhedron, and determining the polyhedron component (vertex, edge, facet, . . . ) that contains a point.An advantage of IRVA is that they can easily be minimized into a canonical form, which leads to a simple and efficient test for equality between represented polyhedra. Elementary IRVA representing primitive polyhedra, such as linear (in)equations and vector spaces are easily constructed and algorithms have been developed for computing Boolean combinations as well as projections of polyhedra represented by IRVA.These algorithms are illustrated by complete examples of executions as a support for the comprehension of their mechanisms.Another contribution is a first prototype implementation of an IRVA library, containing functions for building and manipulating arbitrary n-dimensional polyhedra. We reinforce the presentation of the implementation by discussing some design choices. Such choices include the use of exact arithmetic.Finally, experimental results are presented and discussed. These experiments pave the way to future adaptations and improvements.

show abstract

“…Among others, the Radial-Edge (Weiler, 1985) and the Non-manifold Indexed Data Structure with Adjacencies (NMIA) (de Floriani and Hui, 2003) are two examples of data structures that can represent non-manifold objects, as well. In this paper we adopt an edge-based mesh representation.…”

Section: Combinatorial Data Structuresmentioning

confidence: 99%

Topological mesh operators

Lewiner

Lopes

Medeiros

et al. 2010

Computer Aided Geometric Design

View full text Add to dashboard Cite

In this paper we introduce an unified framework for topological manipulation on triangulated 2-manifolds with or without boundary. We show that there are two kinds of primitive operators on the underlying meshes: operators that change the topological characteristic of the mesh and operators that just modify its combinatorial structure. We present such operators and demonstrate that they provide a complete and coherent set of elementary operations for mesh construction and editing.

show abstract

Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments

Cited by 292 publications

References 9 publications

Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures

Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures

Implicit Real Vector Automata

Topological mesh operators

Contact Info

Product

Resources

About