A Multi‐sided Bézier Patch with a Simple Control Structure

Várady, Tamás; Salvi, Péter; Karikó, György

doi:10.1111/cgf.12833

Cited by 28 publications

(36 citation statements)

References 16 publications

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“…To this end, one could employ constructions that rely on generalized barycentric coordinates such as those of [32,33] and construct a single patch satisfying the interpolation conditions. However, we believe it might be preferable to employ constructions that are fully compatible with standard CAD systems, such as the variants [34] of Clough-Tocher splines [35] or other spline constructions [36,37,38], where the parametric n-gon needs to be decomposed into n − 2 macro-triangles.…”

Section: Resultsmentioning

confidence: 99%

Skinning and blending with rational envelope surfaces

Bizzarri

Lvika

Kosinka

2017

Computer-Aided Design

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We continue the study of rational envelope (RE) surfaces. Although these surfaces are parametrized with the help of square roots, when considering an RE patch as the medial surface transform in 4D of a spatial domain it yields a rational parametrization of the domain's boundary, i.e., the envelope of the corresponding 2-parameter family of spheres. We formulate efficient algorithms for G 1 data interpolation using RE surfaces and apply the developed methods to rational skinning and blending of sets of spheres and cones/cylinders, respectively. Our results are demonstrated on several computed examples of skins and blends with rational parametrizations.

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Section: Resultsmentioning

confidence: 99%

Skinning and blending with rational envelope surfaces

Bizzarri

Lvika

Kosinka

2017

Computer-Aided Design

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“…[64,99], and non-4-sided transfinite constructions, e.g. [11,91,92,100,101], yield internally infinitely smooth multi-sided patches (see [27] for efficient hardware rendering). Exactly computing their higher-order derivatives is, however, costly due to an underlying very high rational degree; finite difference approximations of the derivatives are therefore often used instead.…”

Section: (E)mentioning

confidence: 99%

Splines for Meshes with Irregularities

Peters¹

2019

The SMAI Journal of Computational Mathematics

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Splines form an elegant bridge between the continuous real world and the discrete computational world. Their tensor-product form lifts many univariate properties effortlessly to the surfaces, volumes and beyond. Irregularities, where the tensor-structure breaks down, therefore deserve attention-and provide a rich source of mathematical challenges and insights. This paper reviews and categorizes techniques for splines on meshes with irregularities. Of particular interest are quad-dominant meshes that can have n = 4 valent interior points and T-junctions where quad-strips end. "Generalized" splines can use quad-dominant meshes as control nets both for modeling geometry and to support engineering analysis without additional meshing.

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“…We investigated multi-sided surface modeling for interpolating general topology free-form curve networks, and have formulated a new surface type that generalizes the well-known tensor-product Bézier patches [111]. We continued our research in digital shape reconstruction, in particular, how to detect and enforce various geometric constraints for perfecting reconstructed CAD models [112].…”

Section: Geometric Modelingmentioning

confidence: 99%

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

Charaf

Harsányi

Poppe

et al. 2017

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

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Preface Since being established in 1949, the Faculty of Electrical Engineering and Informatics (VIK) BME has played a flagship role in the development of electronics, IT and computer science in Hungary.We László Jakab (dean, BME VIK) János Levendovszky (vice-dean in charge of scientific affairs, BME VIK) are proud of combining engineering applications with sound scientific results, which is the assurance of high-level industrial collaboration leading to novel results and innovation. The various collaborations with our industrial partners has made it clear that the industry expects methods and results which make their industrial processes more effective and increase productivity and quality. Thus, participation in these collaborations give a competitive edge and ensure the continuous development of VIK. These factors have positioned our Department of Automation and Applied InformaticsDepartment of Automation and Applied Informatics (AUT) is one of the largest and dynamically developing departments at BME with diverse scope competences such as control theory, embedded systems, software modelling, applied software development, Internet of Things, power electronics, mechatronics, and many others. The department's main activities are education, research and development. Training versatile electrical and software engineers with solid practical knowledge is our top priority. Our profile also includes developing high quality software and hardware solutions for industry partners. All of our activities are backed by strong research background.In 2016, the department organized and hosted a number of domestic and international events. In cooperation with the industry, AUT has organized the IoT4U conference. It was dedicated to Internet of Things, cloud and data management as well as the integration of IoT into various formats. RobonAUT, the yearly domestic amateur robotics contest was organized by the department in February 2016. The yearly contest is open to teams of students, organized either in student projects within the department or independent research teams.The next sections summarize the key research results of the department in year 2016. Software Development Methods and Mobile PlatformsThe diversity of mobile platforms necessitates the development of the same mobile application for all major mobile platforms, what requires considerable development effort. Mobile application developers are multiplatform developers, but they still prioritize the platforms, therefore, not all platforms are equally important for them. Appropriate methods, processes and tools are required to support the development in order to achieve better productivity.The research on educational mobile applications that adapt to the mental state of the user required a method for estimating the difficulty of tasks found in the serious games. There are generated or random assignments where the effort required from the user is not known or cannot be estimated in advance.61 (2) IoT and Smart CityThe Internet of Things (IoT) is transforming the surroun...

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A Multi‐sided Bézier Patch with a Simple Control Structure

Cited by 28 publications

References 16 publications

Skinning and blending with rational envelope surfaces

Skinning and blending with rational envelope surfaces

Splines for Meshes with Irregularities

BME VIK Annual Research Report on Electrical Engineering and Computer Science 2016

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