G1 rational blend interpolatory schemes: A comparative study

Boschiroli, Maria; Fünfzig, Christoph; Romani, Lucia; Albrecht, Gudrun

doi:10.1016/j.gmod.2011.11.002

Cited by 10 publications

(3 citation statements)

References 9 publications

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“…Several comparable schemes that use rational blending also exist [1]. Shirman and Sequin [26,27] construct a polynomial patch type that is highly similar to triangular Gregory patches in that G 1 continuity is ensured on the boundary by the method of Chiyokura and Kimura.…”

Section: Related Workmentioning

confidence: 99%

Multisided generalisations of Gregory patches

Hettinga

Kosinka

2018

Computer Aided Geometric Design

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We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided Bézier patches. Our rst construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G 1 continuity between adjoining Bézier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised Bézier patch structure to allow for cross-boundary derivatives to be dened independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G 1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation.

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Section: Related Workmentioning

confidence: 99%

Multisided generalisations of Gregory patches

Hettinga

Kosinka

2018

Computer Aided Geometric Design

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“…Motivated by this problem, Fünfzig et al [FMHF08] proposed the PNG1 patch, which is constructed as a blend of three cubic Bézier patches for each triangle, each providing continuity over one edge of the triangle. Curvature properties of such patches have been investigated in [BFRA12], and such approach can be used to obtain per vertex curvature estimates in the same manner as in [ZGYL11].…”

Section: Related Workmentioning

confidence: 99%

Mesh Statistics for Robust Curvature Estimation

Váša

Vaněček

Prantl

et al. 2016

Computer Graphics Forum

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While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing. We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta‐estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta‐estimator, despite its simplicity, provides considerably more robust results than any existing approach.

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“…We estimate the vertex normal by using the weighted-average Figure 4.3). By using rational blending [FMHF08,BFRA12], adjacent Bźier patches can be glued so that they have G 1 continuity along the common edge (See Figure 4.5). Note that other methods for locally construct piecewise smooth surfaces (e.g., [LWZ11]) can also be adopted.…”

Section: Overviewmentioning

confidence: 99%

Initial value problem of discrete geodesics and its application

Cheng¹

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G1 rational blend interpolatory schemes: A comparative study

Cited by 10 publications

References 9 publications

Multisided generalisations of Gregory patches

Multisided generalisations of Gregory patches

Mesh Statistics for Robust Curvature Estimation

Initial value problem of discrete geodesics and its application

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