G¹ Scattered Data Interpolation with Minimized Sum of Squares of Principal Curvatures
- 26 July 2005
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 385-390
- https://doi.org/10.1109/cgiv.2005.39
Abstract
One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V = {(x/sub i/, y/sub i/), i=1,...,n} /spl isin/ R/sup 2/ over a polygonal domain and a corresponding set of real numbers {z/sub i/}/sub i=1//sup n/, we wish to construct a surface S which has continuous varying tangent plane everywhere (G/sup 1/) such that S(x/sub i/, y/sub i/) = z/sub i/. Specifically, the polynomial being considered belong to G/sup 1/ quartic Bezier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bezier patches with coefficients satisfying the G/sup 1/ continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.Keywords
This publication has 13 references indexed in Scilit:
- G/sup 1/ surface interpolation for irregularly located dataPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Scattered data interpolation methods for electronic imaging systems: a surveyJournal of Electronic Imaging, 2002
- A variational method to modelG1surfaces over triangular meshes of arbitrary topology inR3ACM Transactions on Graphics, 2000
- Algorithm 792ACM Transactions on Mathematical Software, 1999
- Scattered data interpolation with multilevel B-splinesIEEE Transactions on Visualization and Computer Graphics, 1997
- Geometric continuity between adjacent Bézier patches and their constructionsComputer Aided Geometric Design, 1996
- A triangular G1 patch from boundary curvesComputer-Aided Design, 1996
- A G1 triangular spline surface of arbitrary topological typeComputer Aided Geometric Design, 1994
- Efficient, fair interpolation using Catmull-Clark surfacesPublished by Association for Computing Machinery (ACM) ,1993
- Triangular Bernstein-Bézier patchesComputer Aided Geometric Design, 1986