Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
'Meshsweeper': Dynamic Point-to-Polygonal-Mesh Distance and Applications
IEEE Transactions on Visualization and Computer Graphics
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
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We introduce the concept of couple points as a global feature of surfaces. Couple points are pairs of points $({\mathbf x}_1,{\mathbf x}_2)$ on a surface with the property that the vector ${\mathbf x}_2 - {\mathbf x}_1$ is parallel to the surface normals both at ${\mathbf x}_1$ and ${\mathbf x}_2$. In order to detect and classify them, we use higher order local feature detection methods, namely a Morse theoretic approach on a 4D scalar field. We apply couple points to a number of problems in Computer Graphics: the detection of maximal and minimal distances of surfaces, a fast approximation of the shortest geodesic path between two surface points, and the creation of stabilizing connections of a surface.