Projective splitting of quadric faces

Abstract A method for splitting quadric faces into non-intersecting sets is presented. We simplify the topological processing involved by presegmenting the input faces. A one-to-one correspondence is established between the resultant subfaces and their projection on a properly chosen plane. Splitting is formulated in terms of boundary classification and linking. These computational elements, described here in detail, are implemented by 2D operations on the projected faces.

[1]  John E. Hopcroft,et al.  Geometric ambiguities in boundary representations , 1986 .

[2]  Ramon F. Sarraga,et al.  Algebraic methods for intersections of quadric surfaces in GMSOLID , 1983, Comput. Vis. Graph. Image Process..

[3]  A.A.G. Requicha,et al.  Boolean operations in solid modeling: Boundary evaluation and merging algorithms , 1985, Proceedings of the IEEE.

[4]  Kevin Weiler,et al.  Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments , 1985, IEEE Computer Graphics and Applications.

[5]  T. Pavlidis.  Algorithms for Graphics and Image Processing , 1981, Springer Berlin Heidelberg.

[6]  J. Kripac.  Algorithm for splitting planar faces , 1987 .

[7]  Brown,et al.  PADL-2: A Technical Summary , 1982, IEEE Computer Graphics and Applications.

[8]  Robert B. Tilove,et al.  Set Membership Classification: A Unified Approach to Geometric Intersection Problems , 1980, IEEE Transactions on Computers.

[9]  Vishvjit S. Nalwa,et al.  Line-Drawing Interpretation: Straight Lines and Conic Sections , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Joshua Z. Levin.  Mathematical models for determining the intersections of quadric surfaces , 1979 .

[11]  Fujio Yamaguchi,et al.  A Unified Algorithm for Boolean Shape Operations , 1984, IEEE Computer Graphics and Applications.

[12]  Kevin Weiler.  Polygon comparison using a graph representation , 1980, SIGGRAPH '80.

[13]  C. H. Sisam,et al.  Analytic Geometry Of Space , .

[14]  Peter R. Atherton,et al.  Hidden surface removal using polygon area sorting , 1977, SIGGRAPH.

[15]  P. A. Subrahmanyam,et al.  Boolean Operations on n-Dimensional Objects , 1986, IEEE Computer Graphics and Applications.

[16]  Ivor Faux,et al.  Interfaces for Data Transfer Between Solid Modeling Systems , 1985, IEEE Computer Graphics and Applications.

[17]  Itzhak Wilf,et al.  Tracking parameterized algebraic curves on raster displays , 1989, Comput. Graph..

[18]  James R. Miller,et al.  Geometric approaches to nonplanar quadric surface intersection curves , 1987, TOGS.