constant inner o set empty: unstable lled: unstable optimized inner o set empty: stable lled: unstable optimized inner & outer o set empty: stable lled: stable original model © http://www.modelplusmodel.com Figure 1: We introduce a method for reduced-order shape optimization of 2-manifolds that uses offset surfaces to deform the shape. Left: a bottle model is generated using offset surfaces with constant offsets. The resulting object is unable to stand. Center: the offsets are optimized such that the bottle can stand if empty, however, if filled it is unstable. Right: the model is optimized to stand both empty and filled. In order to account for that, offset surfaces are added inside and outside of the original shape. AbstractGiven the 2-manifold surface of a 3d object, we propose a novel method for the computation of an offset surface with varying thickness such that the solid volume between the surface and its offset satisfies a set of prescribed constraints and at the same time minimizes a given objective functional. Since the constraints as well as the objective functional can easily be adjusted to specific application requirements, our method provides a flexible and powerful tool for shape optimization. We use manifold harmonics to derive a reduced-order formulation of the optimization problem, which guarantees a smooth offset surface and speeds up the computation independently from the input mesh resolution without affecting the quality of the result. The constrained optimization problem can be solved in a numerically robust manner with commodity solvers. Furthermore, the method allows simultaneously optimizing an inner and an outer offset in order to increase the degrees of freedom. We demonstrate our method in a number of examples where we control the physical mass properties of rigid objects for the purpose of 3d printing.

Figure 1: Real-time results of our method for simulating translucent materials (skin on the left, ketchup on the right). Our separable subsurface-scattering method enables the generation of these images using only two convolutions (versus 12 in the sum-of-Gaussians approach [dLE07, JSG09]) and seven samples per pixel, while featuring quality comparable with the current state of the art, at a fraction of its cost. It can be implemented as a post-processing step and takes only 0.489 ms per frame on an AMD Radeon HD 7970 at 1080p, which makes it highly suitable for challenging real-time scenarios. AbstractIn this paper we propose two real-time models for simulating subsurface scattering for a large variety of translucent materials, which need under 0.5 milliseconds per frame to execute. This makes them a practical option for realtime production scenarios. Current state-of-the-art, real-time approaches simulate subsurface light transport by approximating the radially symmetric non-separable diffusion kernel with a sum of separable Gaussians, which requires multiple (up to twelve) 1D convolutions. In this work we relax the requirement of radial symmetry to approximate a 2D diffuse reflectance profile by a single separable kernel. We first show that low-rank approximations based on matrix factorization outperform previous approaches, but they still need several passes to get good results. To solve this, we present two different separable models: the first one yields a high-quality diffusion simulation, while the second one offers an attractive trade-off between physical accuracy and artistic control. Both allow rendering subsurface scattering using only two 1D convolutions, reducing both execution time and memory consumption, while delivering results comparable to techniques with higher cost. Using our importance-sampling and jittering strategies, only seven samples per pixel are required. Our methods can be implemented as simple post-processing steps without intrusive changes to existing rendering pipelines.

Additive manufacturing has recently seen drastic improvements in resolution, making it now possible to fabricate features at scales of hundreds or even dozens of nanometers, which previously required very expensive lithographic methods. As a result, additive manufacturing now seems poised for optical applications, including those relevant to computer graphics, such as material design, as well as display and imaging applications. In this work, we explore the use of additive manufacturing for generating structural colors, where the structures are designed using a fabrication-aware optimization process. This requires a combination of full-wave simulation, a feasible parameterization of the design space, and a tailored optimization procedure. Many of these components should be re-usable for the design of other optical structures at this scale. We show initial results of material samples fabricated based on our designs. While these suffer from the prototype character of state-of-the-art fabrication hardware, we believe they clearly demonstrate the potential of additive nanofabrication for structural colors and other graphics applications.

This paper presents an analytic formulation for anti-aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell-Netravali filter family. This enables high-quality rasterization of triangles and tetrahedra with linearly interpolated vertex values to regular and non-regular grids. A closed form solution of the convolution is presented and an efficient implementation on the GPU using DirectX and CUDA C is described.

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