967 research outputs found
Wire mesh design
We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods
Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces
We introduce an algorithm to remesh triangle meshes representing developable
surfaces to planar quad dominant meshes. The output of our algorithm consists
of planar quadrilateral (PQ) strips that are aligned to principal curvature
directions and closely approximate the curved parts of the input developable,
and planar polygons representing the flat parts of the input. Developable
PQ-strip meshes are useful in many areas of shape modeling, thanks to the
simplicity of fabrication from flat sheet material. Unfortunately, they are
difficult to model due to their restrictive combinatorics and locking issues.
Other representations of developable surfaces, such as arbitrary triangle or
quad meshes, are more suitable for interactive freeform modeling, but generally
have non-planar faces or are not aligned to principal curvatures. Our method
leverages the modeling flexibility of non-ruling based representations of
developable surfaces, while still obtaining developable, curvature aligned
PQ-strip meshes. Our algorithm optimizes for a scalar function on the input
mesh, such that its level sets are extrinsically straight and align well to the
locally estimated ruling directions. The condition that guarantees straight
level sets is nonlinear of high order and numerically difficult to enforce in a
straightforward manner. We devise an alternating optimization method that makes
our problem tractable and practical to compute. Our method works automatically
on any developable input, including multiple patches and curved folds, without
explicit domain decomposition. We demonstrate the effectiveness of our approach
on a variety of developable surfaces and show how our remeshing can be used
alongside handle based interactive freeform modeling of developable shapes
A Survey of Developable Surfaces: From Shape Modeling to Manufacturing
Developable surfaces are commonly observed in various applications such as
architecture, product design, manufacturing, and mechanical materials, as well
as in the development of tangible interaction and deformable robots, with the
characteristics of easy-to-product, low-cost, transport-friendly, and
deformable. Transforming shapes into developable surfaces is a complex and
comprehensive task, which forms a variety of methods of segmentation,
unfolding, and manufacturing for shapes with different geometry and topology,
resulting in the complexity of developable surfaces. In this paper, we reviewed
relevant methods and techniques for the study of developable surfaces,
characterize them with our proposed pipeline, and categorize them based on
digital modeling, physical modeling, interaction, and application. Through the
analysis to the relevant literature, we also discussed some of the research
challenges and future research opportunities.Comment: 20 pages, 24 figures, Author submitted manuscrip
Shape selection in non-Euclidean plates
We investigate isometric immersions of disks with constant negative curvature
into , and the minimizers for the bending energy, i.e. the
norm of the principal curvatures over the class of isometric
immersions. We show the existence of smooth immersions of arbitrarily large
geodesic balls in into . In elucidating the
connection between these immersions and the non-existence/singularity results
of Hilbert and Amsler, we obtain a lower bound for the norm of the
principal curvatures for such smooth isometric immersions. We also construct
piecewise smooth isometric immersions that have a periodic profile, are
globally , and have a lower bending energy than their smooth
counterparts. The number of periods in these configurations is set by the
condition that the principal curvatures of the surface remain finite and grows
approximately exponentially with the radius of the disc. We discuss the
implications of our results on recent experiments on the mechanics of
non-Euclidean plates
Uniform convergence of discrete curvatures from nets of curvature lines
We study discrete curvatures computed from nets of curvature lines on a given
smooth surface, and prove their uniform convergence to smooth principal
curvatures. We provide explicit error bounds, with constants depending only on
properties of the smooth limit surface and the shape regularity of the discrete
net.Comment: 21 pages, 8 figure
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