Geometric Hermite curves with minimum strain energy

Yong, Jun-Hai; Cheng, Fuhua

doi:10.1016/j.cagd.2003.08.003

Cited by 76 publications

(50 citation statements)

References 14 publications

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“…When the intention is to realize a ribbed surface by bending physical materials, geometric smoothness is desirable. To this end one can replace Hermite curves with optimized geometric Hermite curves or composite optimized geometric Hermite curves that adjust the magnitudes of the curve end tangents so as to minimize overall strain energy [11]. The initial endpoint tangents could be specified as detailed above, and then sent to an optimization procedure to construct the energetically optimized and geometrically smoothed curves.…”

Section: Rib Optimizationmentioning

confidence: 99%

Ribbed Surfaces for Art, Architecture and Visualization

Hamlin¹,

Séquin²

2009

Computer-Aided Design and Applications

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Section: Rib Optimizationmentioning

confidence: 99%

Ribbed Surfaces for Art, Architecture and Visualization

Hamlin¹,

Séquin²

2009

Computer-Aided Design and Applications

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“…(4), (5), (7), (11), (12). Research work in the second category focuses on producing a G 1 Hermite curve without loops, cusps and folds (8), (9), (13), (15), (16) . In the beginning, a Tcubic curve was introduced by implicitly restricting the directions of the input tangent vectors (8) , which can be joined with circular arcs to form nice spirals if the curve segment is short enough.…”

Section: Introductionmentioning

confidence: 99%

“…In the beginning, a Tcubic curve was introduced by implicitly restricting the directions of the input tangent vectors (8) , which can be joined with circular arcs to form nice spirals if the curve segment is short enough. Then one idea to construct optimized geometric Hermite (OGH) curve was presented by Yong (15) , which was defined by optimizing the magnitudes of the endpoint tangent vec-tors based on the minimal strain energy. This research results advanced the development of this problem, but the results couldn't ensure another faring criterion, thus the minimal curvature variation.…”

Section: Introductionmentioning

confidence: 99%

Discussion on Minimal Curvature Variation in Cubic Hermite Curve Construction

Zhang

et al. 2012

JAMDSM

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In the fields of computer aided geometric design, computer graphics and so on, curvature variation minimization has been widely used for constructing curve and surface. This paper investigates the minimal curvature variation in constructing the cubic Hermite curve that interpolates the given positions and unit tangent vectors at two points, while the magnitudes of the tangent vectors are unknown. The computation of this problem is very hard to handle and a very time-consuming task. To reduce the computing cost, simpler models are used to approximate it, but the existing simpler models can't give a good approximation, and hence make the curves constructed have unsatisfactory shapes. So a new model is presented in this paper. In the new model, the magnitude of each tangent vector is expressed as polynomial function of the tangent vector angles, which is easy to compute, and the shapes of constructed curves are visually similar to the ones constructed by minimizing the accurate curvature variation.

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“…The constructed target highlight lines reveal the shape of the new surface and new highlight lines without actually performing the optimization, and enables the user to decide whether the specification of modification region is appropriate. The target highlight lines are constructed using optimized geometric Hermite(OGH) interpolation [26] , which is able to generate smooth interpolating curves without undesired loops, cusps, or folds. By optimizing a fairness function that considers the quality of the new surface as well as the new highlight line model, we obtain a modified surface with desired shape of highlight line model.…”

Section: Introductionmentioning

confidence: 99%

Removing local irregularities of triangular meshes with highlight line models

Yong

Deng

Cheng

et al. 2009

Sci. China Ser. F-Inf. Sci.

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The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an arbitrary triangular mesh is presented. Based on the highlight line model, a technique to remove local shape irregularities of a triangular mesh is then presented. The shape modification is done by solving a minimization problem and performing an iterative procedure. The new technique improves not only the shape quality of the mesh surface, but also the shape of the highlight line model. It provides an intuitive and yet suitable method for locally optimizing the shape of a triangular mesh.highlight lines, mesh optimization, shape modification, model repair

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Geometric Hermite curves with minimum strain energy

Cited by 76 publications

References 14 publications

Ribbed Surfaces for Art, Architecture and Visualization

Ribbed Surfaces for Art, Architecture and Visualization

Discussion on Minimal Curvature Variation in Cubic Hermite Curve Construction

Removing local irregularities of triangular meshes with highlight line models

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