Mass Properties of Polyhedra from their Vertices' Local Topology

Research archive · original page Research.LocalTopology · last recorded update 2009-11-14

These representations use little or no global topology. This contrasts with the complete topologies used in many CAD systems. My local data structure simplifies many operations, such as determination of the mass properties of boolean combinations of objects. That simplifies many operations, such as determination of the mass properties of boolean combinations of objects. There are fewer special cases, and parallel processing is facilitated.

These local representations have various applications, such as computing mass properties of boolean operations on large sets of polyhedra, typically in linear time. More details are in +.

Papers include:

1. WR Franklin. Local topological properties of polyhedra. (unpublished talk), Sept 1992. URL: https://wrfranklin.org/wiki/Research/unpub/localtopo.pdf.

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   BibTeX

   @Unpublished{wrf-localtopo-92,
       author = "Franklin, WR",
       title = "Local topological properties of polyhedra",
       month = "Sept",
       year = "1992",
       note = "(unpublished talk)",
       mykey = "topology",
       abstract = "What various data structures are possible to represent polygons and polyhedra? Having only local information about the location and neighborhood of each vertex is sufficient, and surprisingly useful.",
       url = "https://wrfranklin.org/wiki/Research/unpub/localtopo.pdf"
   }
   

2. WR Franklin, N. Chandrasekhar, M. Kankanhalli, and V. Akman. Fast intersection detection on serial and parallel machines using the uniform grid technique. 1988.

   Paper / file · Download BibTeX

   BibTeX

   @Unpublished{fcka-fidspm-88,
       author = "Franklin, WR and Chandrasekhar, N. and Kankanhalli, M. and Akman, V.",
       title = "Fast intersection detection on serial and parallel machines using the uniform grid technique",
       year = "1988",
       note = "",
       fulltext = "https://wrfranklin.org/p/53-unpub88-fast.pdf",
       href = "\bibhref{53-unpub88-fast}",
       mykey = "akman kankanhalli chandra"
   }
   

   Talk.
3. Wm Randolph Franklin. Polygon properties calculated from the vertex neighborhoods. In Proc. 3rd Annu. ACM Sympos. Comput. Geom., 110–118. 1987.

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   BibTeX

   @inproceedings{f-ppcvn-87,
       author = "Franklin, Wm Randolph",
       title = "Polygon properties calculated from the vertex neighborhoods",
       booktitle = "Proc. 3rd Annu. ACM Sympos. Comput. Geom.",
       year = "1987",
       pages = "110--118",
       oldlabel = "geom-1214",
       fulltext = "https://wrfranklin.org/p/46-scg87-vertex.pdf",
       href = "\bibhref{46-scg87-vertex}",
       mykey = "topology",
       keywords = "rays, measure, polygons"
   }
   

   Paper.
4. Wm Randolph Franklin. Rays — new representation for polygons and polyhedra. Computer Graphics and Image Processing, 22:327–338, 1983.

   Paper / file · Download BibTeX

   BibTeX

   @article{f-rnrpp-83,
       author = "Franklin, Wm Randolph",
       title = "RAYS --- New Representation for Polygons and Polyhedra",
       journal = "Computer Graphics and Image Processing",
       volume = "22",
       year = "1983",
       pages = "327--338",
       fulltext = "https://wrfranklin.org/p/13-cvgip83-rays.pdf",
       href = "\bibhref{13-cvgip83-rays}",
       keywords = "measure, polygons, rays"
   }