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Centroid Triangulations to bivariate BSplines

CREATED: 200702090252 Speaker: Jack Snoeyink Collaborator: Yuanxin Liu ** Motivation

  • representation of surfaces (irregular point set) ** triangulations ** B-splines
  • join between different surfaces, i.e. in model of tea pot ** Splines
  • piecewise polynomials
  • B-spline: linear combination of basic functions
  • B-spline of degree k: defined for any k+2 points ** can represent any polynomial of degree k ** local support ** optimal smoothness ** Multivariate splines
  • Tensor product, sub division, box splines
  • Properties ** no restriction on knot properties ** properties of 1D B splines
  • Simplex splines ** projection from a polyhedron in $R^n$
  • key to multivariate splines is in choosing the right configurations as the basis simplex splines ** Voronoi/Delaunay
  • order k: set of points with the same k closest points
  • Lee’s algorithm ** order k -> order k+1 ** computing centroids and flipping, computing delaunay in holes ** Centroid triangulations
  • generalize Lee’s algorithm, use some other data dependent triangulations instead of Delaunay

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