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Rationalization of TriangleBased PointFolding Structures
, 2012
"... In mechanical engineering and architecture, structural elements with low material consumption and high loadbearing capabilities are essential for lightweight and even selfsupporting constructions. This paper deals with so called pointfolding elements – nonplanar, pyramidal panels, usually form ..."
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Cited by 6 (1 self)
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In mechanical engineering and architecture, structural elements with low material consumption and high loadbearing capabilities are essential for lightweight and even selfsupporting constructions. This paper deals with so called pointfolding elements – nonplanar, pyramidal panels, usually formed from thin metal sheets, which exploit the increased structural capabilities emerging from folds or creases. Given a triangulated freeform surface, a corresponding pointfolding structure is a collection of pyramidal elements basing on the triangles. Userspecified or materialinduced geometric constraints often imply that each individual folding element has a different shape, leading to immense fabrication costs. We present a rationalization method for such structures which respects the prescribed aesthetic and production constraints and finds a minimal set of molds for the production process, leading to drastically reduced costs. For each base triangle we compute and parametrize the range of feasible folding elements that satisfy the given constraints within the allowed tolerances. Then we pose the rationalization task as a geometric intersection problem, which we solve so as to maximize the reuse of mold dies. Major challenges arise from the high precision requirements and the nontrivial parametrization of the search space. We evaluate our method on a number of practical examples where we achieve rationalization gains of more than 90%.
Planar Hexagonal Meshing for Architecture
"... Mesh surfaces with planar hexagonal faces, what we refer to as PH meshes, offer an elegant way of paneling freeform architectural surfaces due to their node simplicity (i.e. valence3 nodes) and naturally appealing layout. We investigate PH meshes to understand how the shape, size, and pattern of P ..."
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Cited by 3 (1 self)
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Mesh surfaces with planar hexagonal faces, what we refer to as PH meshes, offer an elegant way of paneling freeform architectural surfaces due to their node simplicity (i.e. valence3 nodes) and naturally appealing layout. We investigate PH meshes to understand how the shape, size, and pattern of PH faces are constrained by surface geometry. This understanding enables us to develop an effective method for paneling freeform architectural surfaces with PH meshes. Our method first constructs an ideal triangulation of a given smooth surface, guided by surface geometry. We show that such an ideal triangulation leads to a Dupinregular PH mesh via tangent duality on the surface. We have developed several novel and effective techniques for improving undesirable mesh layouts caused by singular behaviors of surface curvature. We compute support structures associated with PH meshes, including exact vertex offsets and approximate edge offsets, as demanded in panel manufacturing. The efficacy of our method is validated by a number of architectural examples.
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold
"... Abstract—Threedimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such ..."
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Abstract—Threedimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics.
Cyclic TwillWoven Objects
"... Classical (or biaxial) twill is a textile weave in which the weft threads pass over and under two or more warp threads, with an offset between adjacent weft threads to give an appearance of diagonal lines. This paper introduces a theoretical framework for constructing twillwoven objects, i.e., cycl ..."
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Classical (or biaxial) twill is a textile weave in which the weft threads pass over and under two or more warp threads, with an offset between adjacent weft threads to give an appearance of diagonal lines. This paper introduces a theoretical framework for constructing twillwoven objects, i.e., cyclic twillweavings on arbitrary surfaces, and it provides methods to convert polygonal meshes into twillwoven objects. It also develops a general technique to obtain exact triaxialwoven objects from an arbitrary polygonal mesh surface. 1.