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    Feature-Preserving Offset Mesh Generation from Topology-Adapted Octrees
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Zint, Daniel; Maruani, Nissim; Rouxel-Labbé, Mael; Alliez, Pierre; Memari, Pooran; Solomon, Justin
    We introduce a reliable method to generate offset meshes from input triangle meshes or triangle soups. Our method proceeds in two steps. The first step performs a Dual Contouring method on the offset surface, operating on an adaptive octree that is refined in areas where the offset topology is complex. Our approach substantially reduces memory consumption and runtime compared to isosurfacing methods operating on uniform grids. The second step improves the output Dual Contouring mesh with an offset-aware remeshing algorithm to reduce the normal deviation between the mesh facets and the exact offset. This remeshing process reconstructs concave sharp features and approximates smooth shapes in convex areas up to a user-defined precision. We show the effectiveness and versatility of our method by applying it to a wide range of input meshes. We also benchmark our method on the Thingi10k dataset: watertight and topologically 2-manifold offset meshes are obtained for 100% of the cases.
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    Poisson Manifold Reconstruction - Beyond Co-dimension One
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Kohlbrenner, Maximilian; Lee, Singchun; Alexa, Marc; Kazhdan, Misha; Memari, Pooran; Solomon, Justin
    Screened Poisson Surface Reconstruction creates 2D surfaces from sets of oriented points in 3D (and can be extended to codimension one surfaces in arbitrary dimensions). In this work we generalize the technique to manifolds of co-dimension larger than one. The reconstruction problem consists of finding a vector-valued function whose zero set approximates the input points. We argue that the right extension of screened Poisson Surface Reconstruction is based on exterior products: the orientation of the point samples is encoded as the exterior product of the local normal frame. The goal is to find a set of scalar functions such that the exterior product of their gradients matches the exterior products prescribed by the input points. We show that this setup reduces to the standard formulation for co-dimension 1, and leads to more challenging multi-quadratic optimization problems in higher co-dimension. We explicitly treat the case of co-dimension 2, i.e., curves in 3D and 2D surfaces in 4D. We show that the resulting bi-quadratic problem can be relaxed to a set of quadratic problems in two variables and that the solution can be made effective and efficient by leveraging a hierarchical approach.
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    A Shape Modulus for Fractal Geometry Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Schor, Alexa L.; Kim, Theodore; Memari, Pooran; Solomon, Justin
    We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be ''painted'' onto meshes.