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Proceedings of the 18th annual conference on Computer graphics and interactive techniques
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Filling gaps in the boundary of a polyhedron
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Multiresolution analysis of arbitrary meshes
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Surface simplification using quadric error metrics
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Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
SIAM Journal on Scientific Computing
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Using Geometric Hashing To Repair CAD Objects
IEEE Computational Science & Engineering
Generating Topological Structures for Surface Models
IEEE Computer Graphics and Applications
Simplification and Repair of Polygonal Models Using Volumetric Techniques
IEEE Transactions on Visualization and Computer Graphics
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Foundations and Trends® in Computer Graphics and Vision
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
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A Stable Algorithm for Flat Radial Basis Functions on a Sphere
SIAM Journal on Scientific Computing
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Stable computation of multiquadric interpolants for all values of the shape parameter
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SIAM Journal on Scientific Computing
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In this paper we present a process that includes both model/mesh repair and mesh generation. The repair algorithm is based on an initial mesh that may be either an initial mesh of a dirty CAD model or STL triangulation with many errors such as gaps, overlaps and T-junctions. This initial mesh is then remeshed by computing a discrete parametrization with Radial Basis Functions (RBF's). We showed in [1] that a discrete parametrization can be computed by solving Partial Differential Equations (PDE's) on an initial correct mesh using finite elements. Paradoxically, the meshless character of the RBF's makes it an attractive numerical method for solving the PDE's for the parametrization in the case where the initial mesh contains errors or holes. In this work, we implement the Orthogonal Gradients method to be described in [2], as a RBF solution method for solving PDE's on arbitrary surfaces. Different examples show that the presented method is able to deal with errors such as gaps, overlaps, T-junctions and that the resulting meshes are of high quality. Moreover, the presented algorithm can be used as a hole-filling algorithm to repair meshes with undesirable holes. The overall procedure is implemented in the open-source mesh generator Gmsh [3].