Figure 1: Our method procedurally generates structures with graded material elasticities, which can be directly fabricated. Here the user paints elasticity on a 3D model to create a flexible figurine. Model: Moomin (thing:1173447) by Jeroentjj.
Figure 1: Our by-example pattern synthesis algorithm produces structurally sound patterns along the surface of an objects, resembling the input exemplar. The reinforcements are integrated within the pattern, by a joint optimization of appearance and structural properties. Top: The Standford bunny with a variety of synthesized patterns. Bottom: Example patterns. These objects are printed in ABS plastic on low-cost filament printers, using a dense support. The patterns are fully connected and survived the cleaning process thanks to their reinforced structure. Yet, the reinforcements are inconspicuous as they seamlessly blend within the appearance.
Fig. 1. A selection of the automatically generated pure hexahedral and hexahedral-dominant meshes in our test set. The colors denote the type of basis used. In the bottom-right, we show the result of a Poisson problem solved over a hex-dominant, polyhedral mesh.We introduce an integrated meshing and finite element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson's equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.
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