Decomposition method for extracting face topologies from wireframe models

A new algorithm is presented for the automatic derivation of the surface topologies of a 3D volume from its wireframe representation. This fundamentally new approach overcomes the limitations of the currently known methods, and it relaxes the restriction to manifold solids without holes. A fundamental concept from topology, i.e. that a tetrahedron is the simplest building block for all 3D objects, forms the basis of this development. A general wireframe model is decomposed into a set of simple wireframes (tetrahedra) with the use of a topology-based subdivision strategy. The face data extracted from these simple wireframes are then recombined so that the proper face topology can be established for the original wireframe model. The new algorithm works for objects with holes. It detects and eliminates internal faces, and it is capable of providing all the solutions for ambiguous wireframe models.

[1]  J. Rotman.  An Introduction to Algebraic Topology , 1957 .

[2]  Martti Mäntylä.  An inversion algorithm for geometric models , 1982, SIGGRAPH.

[3]  George Markowsky,et al.  Fleshing Out Wire Frames , 1980, IBM J. Res. Dev..

[4]  Keith Paton,et al.  An algorithm for finding a fundamental set of cycles of a graph , 1969, CACM.

[5]  George Markowsky,et al.  Generation of Solid Models from Two-Dimensional and Three-Dimensional Data , 1984 .

[6]  Uday G. Gujar,et al.  3-D objects from 2-D orthographic views--A survey , 1988, Comput. Graph..

[7]  Kevin Weiler.  Topological Structures for Geometric Modeling , 1986 .

[8]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[9]  Ronald D. Dutton,et al.  Efficiently identifying the faces of a solid , 1983, Comput. Graph..

[10]  David C. Gossard,et al.  Solid model input through orthographic views , 1983, SIGGRAPH.

[11]  Scott Michael Staley.  Knowledge representation and database management for cad (cad/cam) , 1985 .

[12]  John A. Brewer,et al.  Automated conversion of curvilinear wire-frame models to surface boundary models; a topological approach , 1986, SIGGRAPH.

[13]  Masanori Idesawa.  A System to Generate a Solid Figure from Three View , 1972 .

[14]  Réi Lequette,et al.  Automatic construction of curvilinear solids from wireframe views , 1988 .

[15]  J. Heisserman.  Generative geometric design and boundary solid grammars , 1992 .

[16]  Robert E. Tarjan,et al.  An efficient planarity algorithm , 1971 .

[17]  Pat Hanrahan,et al.  Creating volume models from edge-vertex graphs , 1982, SIGGRAPH.

[18]  Frank Harary,et al.  Graph Theory , 2016 .

[19]  Gilles Lafue,et al.  Recognition of three-dimensional objects from orthographic views , 1976, SIGGRAPH.

[20]  P. Giblin.  Graphs, surfaces, and homology , 1977 .

[21]  ARISTIDES A. G. REQUICHA,et al.  Representations for Rigid Solids: Theory, Methods, and Systems , 1980, CSUR.

[22]  Martti Mäntylä,et al.  Introduction to Solid Modeling , 1988 .