Browsing by Author "Zayer, Rhaleb"

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    Interactive Modeling of Cellular Structures on Surfaces with Application to Additive Manufacturing
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Stadlbauer, Pascal; Mlakar, Daniel; Seidel, Hans-Peter; Steinberger, Markus; Zayer, Rhaleb; Panozzo, Daniele and Assarsson, Ulf
    The rich and evocative patterns of natural tessellations endow them with an unmistakable artistic appeal and structural properties which are echoed across design, production, and manufacturing. Unfortunately, interactive control of such patterns-as modeled by Voronoi diagrams, is limited to the simple two dimensional case and does not extend well to freeform surfaces. We present an approach for direct modeling and editing of such cellular structures on surface meshes. The overall modeling experience is driven by a set of editing primitives which are efficiently implemented on graphics hardware. We feature a novel application for 3D printing on modern support-free additive manufacturing platforms. Our method decomposes the input surface into a cellular skeletal structure which hosts a set of overlay shells. In this way, material saving can be channeled to the shells while structural stability is channeled to the skeleton. To accommodate the available printer build volume, the cellular structure can be further split into moderately sized parts. Together with shells, they can be conveniently packed to save on production time. The assembly of the printed parts is streamlined by a part numbering scheme which respects the geometric layout of the input model.
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    Subdivision-Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPU
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Mlakar, Daniel; Winter, Martin; Stadlbauer, Pascal; Seidel, Hans-Peter; Steinberger, Markus; Zayer, Rhaleb; Panozzo, Daniele and Assarsson, Ulf
    Subdivision surfaces have become an invaluable asset in production environments. While progress over the last years has allowed the use of graphics hardware to meet performance demands during animation and rendering, high-performance is limited to immutable mesh connectivity scenarios. Motivated by recent progress in mesh data structures, we show how the complete Catmull-Clark subdivision scheme can be abstracted in the language of linear algebra. While this high-level formulation allows for a fully parallel implementation with significant performance gains, the underlying algebraic operations require further specialization for modern parallel hardware. Integrating domain knowledge about the mesh matrix data structure, we replace costly general linear algebra operations like matrix-matrix multiplication by specialized kernels. By further considering innate properties of Catmull-Clark subdivision, like the quad-only structure after refinement, we achieve an additional order of magnitude in performance and significantly reduce memory footprints. Our approach can be adapted seamlessly for different use cases, such as regular subdivision of dynamic meshes, fast evaluation for immutable topology and feature-adaptive subdivision for efficient rendering of animated models. In this way, patchwork solutions are avoided in favor of a streamlined solution with consistent performance gains throughout the production pipeline. The versatility of the sparse matrix linear algebra abstraction underlying our work is further demonstrated by extension to other schemes such as √3 and Loop subdivision.
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    A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Weinrauch, Alexander; Mlakar, Daniel; Seidel, Hans-Peter; Steinberger, Markus; Zayer, Rhaleb; Myszkowski, Karol; Niessner, Matthias
    The humble loop shrinking property played a central role in the inception of modern topology but it has been eclipsed by more abstract algebraic formalisms. This is particularly true in the context of detecting relevant non-contractible loops on surfaces where elaborate homological and/or graph theoretical constructs are favored in algorithmic solutions. In this work, we devise a variational analogy to the loop shrinking property and show that it yields a simple, intuitive, yet powerful solution allowing a streamlined treatment of the problem of handle and tunnel loop detection. Our formalization tracks the evolution of a diffusion front randomly initiated on a single location on the surface. Capitalizing on a diffuse interface representation combined with a set of rules for concurrent front interactions, we develop a dynamic data structure for tracking the evolution on the surface encoded as a sparse matrix which serves for performing both diffusion numerics and loop detection and acts as the workhorse of our fully parallel implementation. The substantiated results suggest our approach outperforms state of the art and robustly copes with highly detailed geometric models. As a byproduct, our approach can be used to construct Reeb graphs by diffusion thus avoiding commonly encountered issues when using Morse functions.