Parameterizing and extending trimmed regions for tensor-product surface fitting

Vaitkus, Márton; Várady, Tamás

doi:10.1016/j.cad.2017.11.008

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…By Lemma 5,(11) guarantees that ρ( Ĥω,γ,υ ) < 1 for the weights ω, γ, υ chosen and Ĥω,γ,υ defined by (15), so lim k→∞ Ĥk ω,γ,υ = 0. By (14), it holds that lim k→∞…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Since it is linear, the construction of the method may be simpler. One can look for more details about these two kinds of fittings, for examples, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…To improve the smoothness of fitting curves or surfaces, fairness terms with user-defined parameters may be considered sometimes [2,4,5,11,14]. As you know, choices of these user-defined parameters may affect the smoothness and accuracy, but there is no optimal choice of these user-defined parameters.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On a progressive and iterative approximation method with memory for least square fitting

Huang

Wang

2019

Preprint

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In this paper, we present a progressive and iterative approximation method with memory for least square fitting (MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. For any normalized totally positive basis even when the collocation matrix is of deficient column rank, we obtain a condition to guarantee that these curves (surfaces) converge to the least square fitting curve (surface) to the given data points. It is proved that the theoretical convergence rate of the method is faster than the one of the progressive and iterative approximation method for least square fitting (LSPIA) in [Deng C-Y, Lin H-W. Progressive and iterative approximation for least squares B-spline curve and surface fitting. Computer-Aided Design 2014;47:32-44] under the same assumption. Examples verify this phenomenon.

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“…By Lemma 5,(11) guarantees that ρ( Ĥω,γ,υ ) < 1 for the weights ω, γ, υ chosen and Ĥω,γ,υ defined by (15), so lim k→∞ Ĥk ω,γ,υ = 0. By (14), it holds that lim k→∞…”

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On a progressive and iterative approximation method with memory for least square fitting

Huang

Wang

2019

Preprint

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“…Newton-Raphson methods attacking inverse problems use the Hessian i.e. the second derivative of the target function, and particular applications include reverse engineering [2,3], regression methods [4], deep learning [5,6] or medical imaging [7], etc. Second derivatives of parametric surfaces play an important role in non-photorealistic rendering as well to identify the principal curvature directions [8].…”

Section: Introductionmentioning

confidence: 99%

Higher Order Automatic Differentiation with Dual Numbers

Szirmay‐Kalos

2020

Period. Polytech. Elec. Eng. Comp. Sci.

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In engineering applications, we often need the derivatives of functions defined by a program. The approach chosen for derivative computation must be algebraic to allow computer implementation. A particular solution to obtain first derivatives is the application of dual numbers. This paper proposes simple and compact generalizations of this idea to obtain derivatives of arbitrary order for single or multi-variate functions and the automatic handling of 0/0 ambiguities in the calculations. We also provide the C++ code that takes advantage of operator overloading and recursion. The method is demonstrated by path animation, Gaussian curvature computation, and curve fairing.

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“…Usually some fitting method is used, which either creates n quadrilaterals sharing a central vertex [5], or a larger four-sided region with approximated trimming curves. The former does not ensure C ∞ continuity inside the patch, while the latter has an inherent asymmetry, as well as parameterization issues [9].…”

Section: Introductionmentioning

confidence: 99%

On the CAD-compatible conversion of S-patches

Salvi

2020

Preprint

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S-patches have many nice mathematical properties. It is known since their first appearance, that any regular S-patch can be exactly converted into a trimmed rational Bézier surface. This is a big advantage compared to other multi-sided surface representations that have to be approximated for exporting them into CAD/CAM systems. The actual conversion process, however, remained at a theoretical level, with bits and pieces scattered in multiple publications. In this paper we review the entirety of the algorithm, and investigate it from a practical aspect.

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Parameterizing and extending trimmed regions for tensor-product surface fitting

Cited by 9 publications

References 26 publications

On a progressive and iterative approximation method with memory for least square fitting

On a progressive and iterative approximation method with memory for least square fitting

Higher Order Automatic Differentiation with Dual Numbers

On the CAD-compatible conversion of S-patches

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