Data structures and network algorithms
Data structures and network algorithms
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
Designing a data structure for polyhedral surfaces
Proceedings of the fourteenth annual symposium on Computational geometry
Progressive forest split compression
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Subdivision-based multilevel methods for large scale engineering simulation of thin shells
Proceedings of the seventh ACM symposium on Solid modeling and applications
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In this paper we introduce a fast and efficient linear time and space algorithm to detect and reconstruct uniform Loop subdivision structure, or triangle quadrisection, in irregular triangular meshes. Instead of a naive sequential traversal algorithm, and motivated by the concept of covering surface in Algebraic Topology, we introduce a new algorithm based on global connectivity properties of the covering mesh. We consider two main applications for this algorithm. The first one is to enable interactive modelling systems that support Loop subdivision surfaces, to use popular interchange file formats which do not preserve the subdivision structure, such as VRML, without loss at information. The second application is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Extensions to other popular uniform subdivision schemes such as Catmull-Clark and Doo-Sabin, are relatively straightforward but will be studied elsewhere.