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Tight cocone: a water-tight surface reconstructor
A simple algorithm called Tight Cocone is described that works on an initial mesh generated by a popular surface reconstruction algorithm and fills up all holes to output a water-tight surface and produces a triangulated surface interpolating the input sample points.
Improved Bounds for Planar k -Sets and Related Problems
- T. Dey
- MathematicsDiscret. Comput. Geom.
- 1 March 1998
This is the first considerable improvement on this bound after its early solution approximately 27 years ago and applies to improve the current bounds on the combinatorial complexities of k -levels in the arrangement of line segments, convex polygons in the union of n lines, parametric minimum spanning trees, and parametric matroids in general.
Defining and computing curve-skeletons with medial geodesic function
This work defines a function called medial geodesic on the medial axis which leads to a methematical definition and an approximation algorithm for curve-skeletons and shows that the algorithm is robust against noise, operates well with a single user parameter, and produces curves with the desirable properties.
A simple algorithm for homeomorphic surface reconstruction
The crust algorithm of  reconstructs a surface with topological and geometric guarantees using the Voronoi diagram of the input point set, and for the first time a proof that the crust is homeomorphic to the input surface.
Delaunay Mesh Generation
- Siu-Wing Cheng, T. Dey, J. Shewchuk
- Computer ScienceChapman and Hall / CRC computer and information…
- 4 December 2012
The authors present algorithms for generating high-quality meshes in polygonal and polyhedral domains and illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces.
A simple provable algorithm for curve reconstruction
An algorithm is presented that provably reconstructs a curve in the framework introduced by Amenta, Bern and Eppstein and requires a sampling density better than previously known and can be adapted for curve reconstruction in higher dimensions straightforwardly.
Computing Topological Persistence for Simplicial Maps
This paper proposes a practical algorithm for computing persistence under Z2 coefficients for a (monotone) sequence of general simplicial maps and shows how these maps arise naturally in some applications of topological data analysis.
Delaunay Refinement for Piecewise Smooth Complexes
A Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions is presented including a new definition of local feature size and a proof for a generalized topological ball property.
Shape Segmentation and Matching with Flow Discretization
A topological approach, namely dynamical systems, is used to define features of shapes to exploit this definition algorithmically, and a shape matching algorithm is developed that takes advantage of the robust feature segmentation step.
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
A nondiscrete approximation straight from the Voronoi diagram with a guarantee of convergence of the medial axis of a surface in 3D is presented and its convergence analysis is presented.