Visual smoothness of polyhedral surfaces

Pellis, Davide; Kilian, Martin; Dellinger, Felix; Wallner, Johannes; Pottmann, Helmut

doi:10.1145/3306346.3322975

Cited by 9 publications

(2 citation statements)

References 22 publications

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“…Doubly curved surface panelized using a planar quad mesh following the principal curvature network (left). This is the smoothest possible panelization of this surface achievable with flat panels [Pellis et al 2019]. The solution using cold bent glass panels designed with our method (right) shows much smoother results.…”

Section: Related Workmentioning

confidence: 76%

Computational design of cold bent glass façades

Gavriil

Гусейнов

Pérez³

et al. 2020

ACM Trans. Graph.

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Cold bent glass is a promising and cost-efficient method for realizing doubly curved glass façades. They are produced by attaching planar glass sheets to curved frames and must keep the occurring stress within safe limits. However, it is very challenging to navigate the design space of cold bent glass panels because of the fragility of the material, which impedes the form finding for practically feasible and aesthetically pleasing cold bent glass façades. We propose an interactive, data-driven approach for designing cold bent glass façades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. The designs are automatically refined to minimize several fairness criteria, while maximal stresses are kept within glass limits. We achieve interactive frame rates by using a differentiable Mixture Density Network trained from more than a million simulations. Given a curved boundary, our regression model is capable of handling multistable configurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show that the predictions are highly accurate and validate our results with a physical realization of a cold bent glass surface.

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Section: Related Workmentioning

confidence: 76%

Computational design of cold bent glass façades

Gavriil

Гусейнов

Pérez³

et al. 2020

ACM Trans. Graph.

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“…Moreover, (2.1) appears as a regularizer in Wu et al, 2015 within a variational model for mesh denoising but the geodesic distances are approximated for the purpose of numerical solution. We also mention the recent Pellis et al, 2019 where (2.1) appears as a measure of visual smoothness of discrete surfaces. Particular emphasis is given to the impact of the mesh connectivity.…”

Section: Comparison With Priormentioning

confidence: 99%

Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems

et al. 2020

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An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element computations. The analysis of the functional is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is found to agree with the discrete total mean curvature known in discrete differential geometry. A split Bregman iteration is proposed for the solution of discretized shape optimization problems, in which the total variation of the normal appears as a regularizer. Unlike most other priors, such as surface area, the new functional allows for piecewise flat shapes. As two applications, a mesh denoising and a geometric inverse problem of inclusion detection type involving a partial differential equation are considered. Numerical experiments confirm that polyhedral shapes can be identified quite accurately.

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Smooth polyhedral surfaces

Günther

Jiang

Pottmann

2020

Advances in Mathematics

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Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the aim of our work is to find and to discuss suitable assessments of smoothness of polyhedral surfaces that only take the geometry of the polyhedral surface itself into account. Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asymptotic directions, and parabolic curves that are invariant under projective transformations. It is remarkable that seemingly mild conditions significantly limit the shapes of faces of a smooth polyhedral surface. Besides being of theoretical interest, we believe that smoothness of polyhedral surfaces is of interest in the architectural context, where vertices and edges of polyhedral surfaces are highly visible.

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Visual smoothness of polyhedral surfaces

Cited by 9 publications

References 22 publications

Computational design of cold bent glass façades

Computational design of cold bent glass façades

Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems

Smooth polyhedral surfaces

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