Functional optimization for fair surface design

Moreton, Henry; Séquin, Carlo H.

doi:10.1145/142920.134035

Cited by 179 publications

(101 citation statements)

References 24 publications

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“…Further, (dash) represents the derivative with respect to s. The functional is traditionally defined as L M EC = κ 2 (minimum energy curve) and L M V C = (κ ) 2 (minimum variation curve) [18]. Minimizing the integral of MEC leads to the differential equation [2] κ (s) + 1 2 κ 3 (s) = 0, and minimizing the integral of MVC gives κ (s) = 0 from the Euler-Lagrange equation [7].…”

Section: Related Workmentioning

confidence: 99%

High-quality quadratic curve fitting for scanned data of styling design

Tsuchie

Okamoto²

2016

Computer-Aided Design

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Section: Related Workmentioning

confidence: 99%

High-quality quadratic curve fitting for scanned data of styling design

Tsuchie

Okamoto²

2016

Computer-Aided Design

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“…However, the automatic manipulation process may terminate prematurely occasionally [8]. The second type of algorithms are based on the principle of local or global energy minimization [9][10][11][12]. According to such algorithms, the new control points of the faired curves or surfaces are determined by solving constrained optimization problems of local or global energy.…”

Section: Fairing Algorithmsmentioning

confidence: 99%

Fairness degree based fairness criterion and fairing algorithm

Wang

Zhao

2015

Applied Mathematics and Computation

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“…The literature in the field is vast, and covers almost every surface representation, e.g., subdivision, implicit surfaces, B-Spline and triangle meshes [2,13,20]. In this paper, we limit our discussions to the variational technique for B-Spline, in which we claim our contributions.…”

Section: Variational B-spline Techniquementioning

confidence: 99%

Designing B-Spline Surfaces with Haptics Based on Variational Technique

Liu¹

2014

Computer-Aided Design and Applications

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Due to their 3D nature, many CAD B-Spline surfaces are difficult to design and edit with traditional 2D interfaces, e.g., a 2D mouse. Based on an energy minimization method or variational B-Spline technique, the paper presents the technique of using a haptic device to design B-Spline surfaces. Under complex constraints and without any pre-calculation, the variational B-Spline technique used in the system can solve virtually all practical B-Spline surfaces in a matter of milliseconds. Such results are much more efficient and powerful than previous work in the variational B-Spline field. By using a haptic interface, the system allows a user in a natural 3D environment to directly manipulate/design constraints, e.g., points and curves, and in real time, the system generates energy-minimization B-Spline surfaces in response to haptic operations. The discussed technique delivers all the performance and capacity required for using haptics to design high-quality B-Spline surfaces, and haptic-based surface operations provide a powerful method for designing B-Spline surfaces.

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Functional optimization for fair surface design

Cited by 179 publications

References 24 publications

High-quality quadratic curve fitting for scanned data of styling design

High-quality quadratic curve fitting for scanned data of styling design

Fairness degree based fairness criterion and fairing algorithm

Designing B-Spline Surfaces with Haptics Based on Variational Technique

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