Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints

Authors:
João Paulo Gois;Diogo Fernando Trevisan;Harlen Costa Batagelo;Ives Macêdo
Affiliations:
Universidade Federal do ABC, Santo André, Brazil;Universidade Federal do ABC, Santo André, Brazil;Universidade Federal do ABC, Santo André, Brazil;University of British Columbia, Vancouver, Canada
Venue:
The Visual Computer: International Journal of Computer Graphics
Year:
2013

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Abstract

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.