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CINPACT-splines: A Class of \({C^{{\infty }}}\) Curves with Compact Support

  • Adam Runions
  • Faramarz SamavatiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)

Abstract

Recently, Runions and Samavati [7] proposed Partion of Unity Parametrics (PUPs), a generalization of NURBS which replaces B-spline basis functions with arbitrary Weight-Functions (WFs) while preserving affine invariance. A key problem identified by Runions and Samavati was the identification of classes of weight-functions which are well-suited to geometric modeling. In this paper, we propose a class of WF based on bump-functions, which arise in the study of smooth, non-analytic manifolds. These give rise to a class of \(C^{\infty }\) curves with compact-support, which we call CINPACT splines. The WFs are similar in form to B-spline basis functions, and are parameterized by a degree-like shape parameter. We examine the approximating and interpolating curves created using the proposed class of WF. Furthermore, we propose and demonstrate a method to specify the tangents and higher order derivatives of the curve at control points for CINPACT and PUPs curves.

Keywords

Parametric curves Interpolating curves Approximating curves PUPs B-spline NURBS Bump functions 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CalgaryAlbertaCanada

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