Design and Tessellation of B-Spline Developable Surfaces

Maekawa, Takashi; Chalfant, Julie

doi:10.1115/1.2829173

Cited by 44 publications

(17 citation statements)

References 11 publications

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“…The remaining parameters must be solved from the constrained system. Previous studies employed different techniques to simplify the solution process [6][7][8][9][10]. However, such an approach may lack practicality in modeling of complex shapes due to the restricted degrees of freedom in the surface design [11].…”

Section: Introductionmentioning

confidence: 99%

Strip Approximation Using Developable Bézier Patches: A Local Optimization Approach

Chu¹,

Wang²,

Tsai³

2007

Computer-Aided Design and Applications

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This paper proposes a geometric design method for approximation of a strip defined by two space curves with freeform developable surfaces. Given a ruling defined by two sample points taken from each curve, it calculates the feasible patches starting with the ruling. A local optimal solution is selected among them in terms of surface assessment criteria based on a heuristic algorithm. An aggregate of Bézier patches in the conical form, either triangular or quadrilateral, is thus created. Each patch is then degree elevated to gain extra degrees of freedom. They produce G 1 across the patch boundaries by modifying the control points while preserving the surface developability. Test examples with different design parameters are illustrated to validate the feasibility of the proposed method. In comparison with previous studies using the BBT (Bridge Boundary Triangulations) method, this work allows surface design with freeform developable patches, generates better results in the surface assessment, and provides more flexible control on the approximation shape. It serves as a simple but effective approach for geometric design of developable surfaces.

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Section: Introductionmentioning

confidence: 99%

Strip Approximation Using Developable Bézier Patches: A Local Optimization Approach

Chu¹,

Wang²,

Tsai³

2007

Computer-Aided Design and Applications

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“…For instance, the surface of a complex product is often constructed by splicing multiple developable patches together in the appearance design of auto bodies, airplane skins, ship hulls, pipelines, clothing, and other manufacturing fields with materials that are not amenable to stretching. Based on the significance of developable surfaces, its properties and characteristics have been widely studied, and some other results have been achieved: the construction and precise representation, fitting, mesh approximation, geometric constraints of developable surface and developable mesh surface as well as quasidevelopable surface …”

Section: Introductionmentioning

confidence: 99%

“…For developable surfaces, their computer‐aided representations greatly expand their application range in engineering, and their constructing methods can be divided into 2 categories: (1) 1 is the point geometric representation, by which a developable surface is considered as a tensor product surface who satisfies certain constraints in Euclidean space, and (2) the other is the line and plane geometric representation, by which a developable surface is considered as a curve in 3D projective space and can be constructed by using the duality between points and planes. Basically, there are 2 ways to implement the point geometric representation: (1) 1 way is to construct a developable surface with a given directrix and original direction and (2) the other way is to construct a developable surface by interpolating 2 boundary curves.…”

Section: Introductionmentioning

confidence: 99%

Construction of generalized developable Bézier surfaces with shape parameters

Cao

Qin

2018

Math Methods in App Sciences

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In this paper, we propose a novel method for constructing generalized developable Bézier surfaces with shape parameters. The generalized developable Bézier surfaces are designed by using control planes with generalized Bernstein basis functions, and their shapes can be adjusted by changing their shape parameters. When the shape parameters take on different values, a family of developable surfaces, which retain the characteristics of developable Bézier surfaces, can be constructed. In addition, we derive the necessary and sufficient conditions for G1 continuity, Farin‐Boehm G2 continuity, and G2 Beta continuity between 2 adjacent generalized developable Bézier surfaces. Finally, some properties of the new developable surfaces are discussed, and the influence rules of shape parameters on the new developable surfaces are studied. The modeling examples show that the proposed method is effective and so can greatly improve problem‐solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces.

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“…Research related to Computer Aided Geometric Design, in particular those concerning the design and approximation of developable surfaces, can be found in [18][19][20][21][22][23][24][25][26][27]. Most of them are in terms of NURBS or its special case -B-spline or Bézier surfaces [18][19][20][21][22][23][24]. Aumann [18] proposed the condition under which a developable Bézier surface can be constructed with two boundary curves.…”

Section: Related Workmentioning

confidence: 99%

“…The boundary curves in his approach are restricted to lie in parallel planes; the projection of the boundary curves on the x-y plane must be a rectangle. Chalfant and Maekawa [19] presented a method to design developable B-spline surfaces where boundary curves do not necessarily lie in parallel planes. In the work of Frey and Bindschadler [20], the results of Aumann are extended by generalizing the degree of the directions.…”

Section: Related Workmentioning

confidence: 99%

Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches

Wang

Tang

2004

Vis Comput

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Surface developability is required in a variety of applications in product design, such as clothing, ship hulls, automobile parts, etc. However, most current geometric modeling systems using polygonal surfaces ignore this important intrinsic geometric property. This paper investigates the problem of how to minimally deform a polygonal surface to attain developability, or the so called developability-by-deformation problem. In our study, this problem is first formulated as a global constrained optimization problem, and a penalty function based numerical solution is proposed for solving this global optimization problem. Next, as an alternative to the global optimization approach which usually requires lengthy computing time, we present an iterative solution based on a local optimization criterion which achieves near real-time computing speed. Both approaches preserve the topology and continuity of the original polygonal surface in the case when more than one individual polygonal patches comprise the surface. Experimental examples are provided to demonstrate the functionality of the proposed two approaches as well as their comparison in terms of computing cost, effectiveness of attaining developability, dimensional difference between the surfaces before and after the optimization, and other important aspects.

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Design and Tessellation of B-Spline Developable Surfaces

Cited by 44 publications

References 11 publications

Strip Approximation Using Developable Bézier Patches: A Local Optimization Approach

Strip Approximation Using Developable Bézier Patches: A Local Optimization Approach

Construction of generalized developable Bézier surfaces with shape parameters

Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches

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