Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints

In this work we investigate a generalized interpolation approach using radial basis functions to reconstruct implicit surfaces from polygonal meshes. With this method, the user can define with great flexibility three sets of constraint interpolants: points, normals, and tangents; allowing to balance...

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Bibliographic Details
Published in:The Visual computer 2013-06, Vol.29 (6-8), p.651-661
Main Authors: Gois, João Paulo, Trevisan, Diogo Fernando, Batagelo, Harlen Costa, Macêdo, Ives
Format: Article
Language:English
Subjects:
Artificial Intelligence
Aspect ratio
Computer Graphics
Computer Science
Finite element method
Flexibility
Image Processing and Computer Vision
Interpolation
Methods
Original Article
Partial differential equations
Polygons
Radial basis function
Tangents
Triangles
Two dimensional models
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Summary:In this work we investigate a generalized interpolation approach using radial basis functions to reconstruct implicit surfaces from polygonal meshes. With this method, the user can define with great flexibility three sets of constraint interpolants: points, normals, and tangents; allowing to balance computational complexity, precision, and feature modeling. Furthermore, this flexibility makes possible to avoid untrustworthy information, such as normals estimated on triangles with bad aspect ratio. We present results of the method for applications related to the problem of modeling 2D curves from polygons and 3D surfaces from polygonal meshes. We also apply the method to problems involving subdivision surfaces and front-tracking of moving boundaries. Finally, as our technique generalizes the recently proposed HRBF Implicits technique, comparisons with this approach are also conducted.
ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-013-0802-8