45 research outputs found

    Triangular Bézier Developable Patches

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    Developable surfaces are defined as zero gaussian curvature surfaces (intrinsically flat). That is, plane patches that are curved by just folding, rolling or cutting, but without stretching or combing. Useful for depicting steel plates in naval industry, cloth in textile industry. . . But they are difficult to include in the NURBS formulation for the zero curvature requirement

    Möbius Geometry and Cyclidic Nets: A Framework for Complex Shape Generation

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    International audienceFree-form architecture challenges architects, engineers and builders. The geometrical rationalization of complex structures requires sophisticated tools. To this day, two frameworks are commonly used: NURBS modeling and mesh-based approaches. The authors propose an alternative modeling framework called generalized cyclidic nets that automatically yields optimal geometrical properties for the façade and the structure. This framework uses a base circular mesh and Dupin cyclides, which are natural objects of the geometry of circles in space, also known as Möbius geometry. This paper illustrates how new shapes can be generated from generalized cyclidic nets. Finally, it is demonstrated that this framework gives a simple method to generate curved-creases on free-forms. These findings open new perspectives for structural design of complex shells

    Multi-Panel Unfolding with Physical Mesh Data Structures

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    In this thesis, I demonstrate that existing mesh data structures in computer graphics can be used to categorize and construct physical polygonal models. In this work, I present several methods based on mesh data structures for transforming 3D polygonal meshes into developable multi-panels that can be used in physical construction. Using mesh data structures, I developed a system which provides a variety of construction methods. In order to demonstrate that mesh data structures can be used to categorize and construct physical polygonal models, this system visualizes the mathematical theory and generates developable multi-panels that can be printed and assembled to shapes similar to original virtual shapes. The mesh data structures include ones that are orientable: Quad-Edge, Half-Edge, Winged-Edge; and also one that is non-orientable: Extended GRS. The advantages of using mesh data structures as guides for physical construction include: There is no restriction on input design model as long as it is manifold, it can be of any genus with n-sided polygon faces; Different mesh data structures provide more options to better fit the input design while taking the physical constraints and material properties in consideration; Developable panels are easy to obtain from thin planar materials using a laser-cutter; When we use mesh data structures, it is also intuitive to assemble such planar panels using mesh information. Laser-cut developable panels based on mesh data structures provide, therefore, a cost-efficient alternative to 3D printing when dealing with large structures

    Rationalization with ruled surfaces in architecture

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    08221 Abstracts Collection -- Geometric Modeling

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    From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
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