De Casteljau Algorithm and Degree Elevation of Toric Surface Patches

Li, Jinggai; Ji, Yindong; Zhu, Chuanjie

doi:10.1007/s11424-020-9370-y

Cited by 10 publications

(6 citation statements)

References 16 publications

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“…Li et al [35] investigated the behavior of functionally graded porous plates reinforced by graphene platelets, and incorporated within the IGA framework. Furthermore, different spline basis functions such as T-spline and PHT are utilized to construct the volume parametric model [36,37]. These methods simplify the parameterization process and extend the application of IGA.…”

Section: Related Workmentioning

confidence: 99%

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Chen¹,

Liang²,

Ye³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Lattice structures with excellent physical properties have attracted great research interest. In this paper, a novel volume parametric modeling method based on the skeleton model is proposed for the construction of threedimensional lattice structures. The skeleton model is divided into three types of nodes. And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes. The unit-cell is assembled with distinct nodes according to the geometric features. The final lattice structure is created by the periodic arrangement of unit-cells. Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method. The quality is assessed in terms of the value of the Jacobian matrix. Moreover, the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

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Section: Related Workmentioning

confidence: 99%

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Chen¹,

Liang²,

Ye³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…Secondly, it is also difficult to get exact points on the curve. This issue however, has been resolved using a number of algorithms, for instance de Casteljau [31,32].…”

Section: Source Codementioning

confidence: 99%

Graphics Evolutionary Computations in Higher Order Parametric Bezier Curves

Eze¹,

Okunbor²,

Aleburu³

et al. 2022

Computer Systems Science and Engineering

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This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves. Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above. Bezier curves find real life applications in diverse areas of Engineering and Computer Science, such as computer graphics, robotics, animations, virtual reality, among others. Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations, proof of related theorems, first and second order calculus related computations, among others. A Practical case is demonstrated using a graphical design, physical hand sketching, and programmatic implementation of two opposite-faced handless cups, all evolved using quadratic Bezier curves. The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript. This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others.

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“…To overcome this problem, multi-sided surfaces, e.g. S-surfaces [21] and toric surfaces [16], are widely investigated [10,18,41,42].…”

Section: Introductionmentioning

confidence: 99%

“…However, triangular or quadrilateral representation is not suitable for multi-sided computational domains. As pointed out in [3,18], using quadrilateral surfaces (e.g. Bézier and B-spline surfaces) to parametrize multi-sided domains may cause mesh degeneration or decreased continuity.…”

Section: Introductionmentioning

confidence: 99%

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Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis

Mengyun Wang,

Ye Ji,

Chungang Zhu

2024

JCM

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Generalized Bézier surfaces are a multi-sided generalization of classical tensor product Bézier surfaces with a simple control structure and inherit most of the appealing properties from Bézier surfaces. However, the original degree elevation changes the geometry of generalized Bézier surfaces such that it is undesirable in many applications, e.g. isogeometric analysis. In this paper, we propose an improved degree elevation algorithm for generalized Bézier surfaces preserving not only geometric consistency but also parametric consistency. Based on the knot insertion of B-splines, a novel knot insertion algorithm for generalized Bézier surfaces is also proposed. Then the proposed algorithms are employed to increase degrees of freedom for multi-sided computational domains parameterized by generalized Bézier surfaces in isogeometric analysis, corresponding to the traditional p-, h-, and k-refinements. Numerical examples demonstrate the effectiveness and superiority of our method.

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De Casteljau Algorithm and Degree Elevation of Toric Surface Patches

Cited by 10 publications

References 16 publications

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Graphics Evolutionary Computations in Higher Order Parametric Bezier Curves

Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis

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