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    Light Distribution Models for Tree Growth Simulation
    (Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2024) Nauber, Tristan; Mäder, Patrick
    The simulation and modelling of tree growth is a complex subject with a long history and an important area of research in both computer graphics and botany. For more than 50 years, new approaches to this topic have been presented frequently, including several aspects to increase realism. To further improve these achievements, we present a compact and robust functional‐structural plant model (FSPM) that is consistent with botanical rules. While we show several extensions to typical approaches, we focus mainly on the distribution of light as a resource in three‐dimensional space. We therefore present four different light distribution models based on ray tracing, space colonization, voxel‐based approaches and bounding volumes. By simulating individual light sources, we were able to create a more specified scene setup for plant simulation than it has been presented in the past. By taking into account such a more accurate distribution of light in the environment, this technique is capable of modelling realistic and diverse tree models.
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    Stress‐Aligned Hexahedral Lattice Structures
    (Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2024) Bukenberger, D. R.; Wang, J.; Wu, J.; Westermann, R.
    Maintaining the maximum stiffness of components with as little material as possible is an overarching objective in computational design and engineering. It is well‐established that in stiffness‐optimal designs, material is aligned with orthogonal principal stress directions. In the limit of material volume, this alignment forms micro‐structures resembling quads or hexahedra. Achieving a globally consistent layout of such orthogonal micro‐structures presents a significant challenge, particularly in three‐dimensional settings. In this paper, we propose a novel geometric algorithm for compiling stress‐aligned hexahedral lattice structures. Our method involves deforming an input mesh under load to align the resulting stress field along an orthogonal basis. The deformed object is filled with a hexahedral grid, and the deformation is reverted to recover the original shape. The resulting stress‐aligned mesh is used as basis for a final hollowing procedure, generating a volume‐reduced stiff infill composed of hexahedral micro‐structures. We perform quantitative comparisons with structural optimization and hexahedral meshing approaches and demonstrate the superior mechanical performance of our designs with finite element simulation experiments.
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    Generalized Lipschitz Tracing of Implicit Surfaces
    (Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd., 2024) Bán, Róbert; Valasek, Gábor
    We present a versatile and robust framework to render implicit surfaces defined by black‐box functions that only provide function value queries. We assume that the input function is locally Lipschitz continuous; however, we presume no prior knowledge of its Lipschitz constants. Our pre‐processing step generates a discrete acceleration structure, a Lipschitz field, that provides data to infer local and directional Lipschitz upper bounds. These bounds are used to compute safe step sizes along rays during rendering. The Lipschitz field is constructed by generating local polynomial approximations to the input function, then bounding the derivatives of the approximating polynomials. The accuracy of the approximation is controlled by the polynomial degree and the granularity of the spatial resolution used during fitting, which is independent from the resolution of the Lipschitz field. We demonstrate that our process can be implemented in a massively parallel way, enabling straightforward integration into interactive and real‐time modelling workflows. Since the construction only requires function value evaluations, the input surface may be represented either procedurally or as an arbitrarily filtered grid of function samples. We query the original implicit representation upon ray trace, as such, we preserve the geometric and topological details of the input as long as the Lipschitz field supplies conservative estimates. We demonstrate our method on both procedural and discrete implicit surfaces and compare its exact and approximate variants.