Uniform tension algebraic trigonometric spline wavelets of class C2 and order four

In this paper we first describe a multiresolution curve representation based on periodic uniform tension algebraic trigonometric (UTAT) spline wavelets of class C^2 and order four. Then we determine the decomposition and the reconstruction vectors corresponding to UTAT-spline spaces. Finally, we give some applications in order to illustrate the efficiency of the proposed approach.

[1]  Driss Sbibih,et al.  A multiresolution method for fitting scattered data on the sphere , 2009 .

[2]  Tom Lyche,et al.  Interpolation with Exponential B-Splines in Tension , 1993, Geometric Modelling.

[3]  Jiwen Zhang C-curves: an extension of cubic curves , 1996 .

[4]  B. I. Kvasov,et al.  Algorithms for shape preserving local approximation with automatic selection of tension parameters , 2000, Comput. Aided Geom. Des..

[5]  L. Schumaker Spline Functions: Basic Theory , 1981 .

[6]  Carla Manni,et al.  Polynomial cubic splines with tension properties , 2010, Comput. Aided Geom. Des..

[7]  Joe D. Warren,et al.  A subdivision scheme for surfaces of revolution , 2001, Comput. Aided Geom. Des..

[8]  Guozhao Wang,et al.  NUAT B-spline curves , 2004, Comput. Aided Geom. Des..

[9]  P. Sattayatham,et al.  GB-splines of arbitrary order , 1999 .

[10]  Gershon Elber,et al.  Detail preserving deformation of B-spline surfaces with volume constraint , 2008, Comput. Aided Geom. Des..

[11]  Guozhao Wang,et al.  Unified and extended form of three types of splines , 2008 .

[12]  Tom Lyche,et al.  On a class of weak Tchebycheff systems , 2005, Numerische Mathematik.

[13]  Carolina Vittoria Beccari,et al.  A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics , 2007, Comput. Aided Geom. Des..

[14]  David Salesin,et al.  Multiresolution curves , 1994, SIGGRAPH.

[15]  Tom Lyche,et al.  A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere , 2000, SIAM J. Sci. Comput..

[16]  C. Manni,et al.  Geometric Construction of Generalized Cubic Splines , 2006 .

[17]  David H. Eberly,et al.  On gray scale image measurements : I. Arc length and area , 1991, CVGIP Graph. Model. Image Process..

[18]  Peng Zhao,et al.  A novel area measurement scheme based on a multi-resolution dynamic contour , 2008 .

[19]  Weiyin Ma,et al.  A generalized curve subdivision scheme of arbitrary order with a tension parameter , 2010, Comput. Aided Geom. Des..

[20]  Jiwen Zhang,et al.  Two different forms of C-B-splines , 1997, Comput. Aided Geom. Des..

[21]  Tom Lyche,et al.  L-Spline Wavelets , 1994 .

[22]  Guozhao Wang,et al.  Optimal properties of the uniform algebraic trigonometric B-splines , 2006, Comput. Aided Geom. Des..

[23]  Basile Sauvage,et al.  Area preserving deformation of multiresolution curves , 2005, Comput. Aided Geom. Des..

[24]  Zhixun Su,et al.  Arc-length preserving curve deformation based on subdivision , 2006 .