Functional optimization for fair surface design

Moreton, Henry; Séquin, Carlo H.

doi:10.1145/133994.134035

Cited by 174 publications

(86 citation statements)

References 23 publications

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“…In the geometric design community, stable configurations of deformable linear objects are often called minimal-energy curves. These curves appear in the broader context of fair curve and surface design [7]- [11]. Here, "fair" means minimizing some functional (or energy function).…”

Section: Related Workmentioning

confidence: 99%

Path planning for deformable linear objects

2006

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Abstract-We present a new approach to path planning for deformable linear (one-dimensional) objects such as flexible wires. We introduce a method for efficiently computing stable configurations of a wire subject to manipulation constraints. These configurations correspond to minimal-energy curves. By restricting the planner to minimal-energy curves, the execution of a path becomes easier. Our curve representation is adaptive in the sense that the number of parameters automatically varies with the complexity of the underlying curve. We introduce a planner that computes paths from one minimal-energy curve to another such that all intermediate curves are also minimal-energy curves. This planner can be used as a powerful local planner in a sampling-based roadmap method. This makes it possible to compute a roadmap of the entire "shape space," which is not possible with previous approaches. Using a simplified model for obstacles, we can find minimal-energy curves of fixed length that pass through specified tangents at given control points. Our work has applications in cable routing, and motion planning for surgical suturing and snake-like robots.

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Section: Related Workmentioning

confidence: 99%

Path planning for deformable linear objects

2006

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“…with j q being the adjacent vertices to i q , and h is a small constant (the determination method of h according to the value of ) ( i P q G is from [46]). …”

Section: We Adopt the Following Equation To Determine It Numericallymentioning

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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“…The construction of curves and surfaces subject t o certain constraints (to minimize length, area, curvature or other geometric properties) has been studied from the point of view of Graphics (see [4], [ 5 ] , [6] or [7]). In the case of the area of the surface, the interest comes from t.he fact that in some real problems, minimal area means minimal cost of the material used to build the surface.…”

Section: Introductionmentioning

confidence: 99%