The NURBS book
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing shortest cycles using universal covering space
The Visual Computer: International Journal of Computer Graphics
Reconstruction of convergent G1 smooth B-spline surfaces
Computer Aided Geometric Design
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In this paper, for a closed oriented triangulated surface with genus g, a method with O(g^3nlogn) running time of constructing tight orthogonal homotopic bases is presented, where a tight orthogonal homotopic basis is a homotopic basis with the properties: 1. the elements of this basis are cycles, 2. any two adjacent cycles of this basis have exactly one common point, 3. any two nonadjacent cycles of this basis have no common point, and 4. any cycle of this basis is one of the shortest cycles of its homotopic group. The major difference between orthogonal homotopic bases and the well-known canonical homotopic bases is that all the cycles of a canonical homotopic basis have a common point and there is no other common point between any two cycles of the canonical homotopic basis while any two adjacent cycles of an orthogonal homotopic basis have exactly one common point and there is no common point among any three cycles of this basis.