On shortest paths in polyhedral spaces
SIAM Journal on Computing
SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
A Fast and Simple Stretch-Minimizing Mesh Parameterization
SMI '04 Proceedings of the Shape Modeling International 2004
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Computerized girth determination for custom footwear manufacture
Computers and Industrial Engineering
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
A Level Set Formulation of Geodesic Curvature Flow on Simplicial Surfaces
IEEE Transactions on Visualization and Computer Graphics
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational mesh decomposition
ACM Transactions on Graphics (TOG)
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Efficiently Computing Exact Geodesic Loops within Finite Steps
IEEE Transactions on Visualization and Computer Graphics
Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures
Computer-Aided Design
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
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Length and girth are central to measure the size of tube shaped objects. This paper extends circular helical curves to general tubular shapes and proposes a novel method for measuring their length and girth. We call the extended circular helixes quasi-helical curves. A formal definition, as well as a set of practical algorithms for quasi-helixes, is presented in this paper. Experimental results demonstrate that our method is fast, intrinsic, insensitive to noises, invariant to triangulation and resolution. Furthermore, quasi-helical curves can also be used in classifying 3D shapes and designing vector fields on surfaces of revolution.