Filling n-sided regions with G 1 triangular Coons B-spline patches

Shi, Kan-Le; Yong, Jun-Hai; Sun, Jun; Paul, Jean-Claude; Gu, He-Jin

doi:10.1007/s00371-010-0468-4

Cited by 11 publications

(6 citation statements)

References 11 publications

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“…Noncircular blending surfaces can be generated with some other methods such as filling n-sided regions [17], polyhedral vertex blending with setbacks using rational S-patches [18], branching blends between two natural quadrics with Pythagorean normal surfaces [19], and partial differential equation (PDE)-based methods [20]. The earliest work about PDE-based surface blending was described in [20].…”

Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

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Section: Related Workmentioning

confidence: 99%

C2 Continuous Blending of Time-Dependent Parametric Surfaces

You

Tian

Tang

2019

Journal of Computing and Information Science in Engineering

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“…In general situations, the shapes of blending surfaces are noncircular. This problem can be tackled by other blending methods such as N-sided hole filling [17][18][19][20][21][22], vertex blending using S-patches [23,24], branching blends with Pythagorean normal surfaces [25], or generating arbitrary shapes of blending surfaces with the following PDE-based methods.…”

Section: Related Workmentioning

confidence: 99%

A unified approach to blending of constant and varying parametric surfaces with curvature continuity

You

Tian

Tang

2018

Proceedings of Computer Graphics International 2018

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In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuity.

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“…Guiqing Li et al [9] recommended an approach to blend parametric patches with subdivision surfaces. Some of the latest results can also be found in [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 98%

Construction of B-spline Surface via Interpolating to Boundary Information and Approximating Inner Points

Mu¹

2013

TOAUTOCJ

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This paper discusses how to construct a B-spline surface from its boundary information and inner points. First, an algorithm is presented which can construct a B-spline surface that interpolates four given boundary curves and simultaneously approximates given inner points. Then, the approach is extended to interpolate the cross-boundary derivatives as well. The main idea of this method is that an initial surface interpolating four given boundary curves and the crossboundary derivatives is constructed at first. Then, the inner control vertices of the surface are repositioned through energy optimization while the boundary control vertices of the initial surface remain unchanged. Examples are given which prove that the algorithm is practicable and effective.

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Filling n-sided regions with G 1 triangular Coons B-spline patches

Cited by 11 publications

References 11 publications

C2 Continuous Blending of Time-Dependent Parametric Surfaces

C2 Continuous Blending of Time-Dependent Parametric Surfaces

A unified approach to blending of constant and varying parametric surfaces with curvature continuity

Construction of B-spline Surface via Interpolating to Boundary Information and Approximating Inner Points

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