Fairing cubic B-spline curves

Farin, Gerald; Rein, Gerhard; Sapidis, Nickolas S.; Worsey, A. J.

doi:10.1016/0167-8396(87)90027-6

Cited by 135 publications

(41 citation statements)

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“…• subdivision schemes, where the curve is described as the limit of a refinement process (Micchelli and Prautzsch, 1989;Deslauriers and Dubuc, 1991;Warren and Weimer, 2002); • parametric schemes, where the curve is described continuously by some coefficients using basis functions (Farin et al, 1987;Piegl, 1991;Farin, 1997;Schumaker, 2007).…”

Section: Introductionmentioning

confidence: 99%

Exponential splines and minimal-support bases for curve representation

Delgado-Gonzalo

Thévenaz

Unser

2012

Computer Aided Geometric Design

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Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential Bsplines. These minimal-support basis functions form a natural multiscale hierarchy, which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally, we illustrate our scheme by constructing minimalsupport bases that reproduce ellipses and higher-order harmonic curves.

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Section: Introductionmentioning

confidence: 99%

Exponential splines and minimal-support bases for curve representation

Delgado-Gonzalo

Thévenaz

Unser

2012

Computer Aided Geometric Design

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“…Minimal region knot removal: Solve the linear system (5) This knotremoval-reinsertion step changes the curve only in the interval [t j , t j+4 ] and is therefore the most local knot removal procedure, see [7]. Nevertheless it should be mentioned, that the difference between both curves will generally be higher than in the following case.…”

Section: Knot Removal For Curvesmentioning

confidence: 99%

“…Different approximate solutions of this system are possible. A detailed description of these knot removal algorithms can be found in [7,6]. We want to focus on two of them, because they can also be used for knot removal in the surface case:…”

Section: Knot Removal For Curvesmentioning

confidence: 99%