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Human and animal presence in natural landscapes is initially revealed by the immediate impact of their locomotion, from footprints to crushed grass. In this work, we present an approach to model the effects of virtual characters on natural terrains, focusing on the impact of human locomotion. We introduce a lightweight solution to compute accurate foot placement on uneven ground and infer dynamic foot pressure from kinematic animation data and the mass of the character. A ground and vegetation model enables us to effectively simulate the local impact of locomotion on soft soils and plants over time, resulting in the formation of visible paths. As our results show, we can parameterize various soil materials and vegetation types validated with real-world data. Our method can be used to significantly increase the realism of populated natural landscapes and the sense of presence in virtual applications and games. [ABSTRACT FROM AUTHOR]

Lattice structures can present advantageous mechanical properties while remaining remarkably lightweight. Precise lattice design can however be tricky to set up with classical 3D modeling methods as it involves very fine details. Interestingly, natural porous structures can present such lattice-like or membrane-like features which motivates to seek for more bio-inspired approaches to microstructure design. In this paper, we present a novel method to grow lattice-like and membrane-like structures within an arbitrary shape and aligned along an oriented field. Our method relies on the use of a dedicated anisotropic reaction–diffusion system guided by an orthotropic diffusion tensor field. Assuming for instance the diffusion tensor to be related to the stress analysis of a given shape allows to generate emerging stripes patterns aligned along each one of the principal stress directions independently. A globally coherent mechanical model conforming to the initial shape boundary and infilled with oriented microstructures can therefore be synthesized. Further, we demonstrate the capability of this approach to handle other types of oriented fields such as obtained through optimization of material directions in scenarios with multiple load cases. Our approach relies on spatially and temporally local operations allowing for efficient parallelization. This permits user-interaction and automated adaptation of the design, even for fine meshes over large volumes. For instance, a designer can locally erase or “draw” over the structure and let it regrow and adapt as well as enforce regions to be deliberately full or empty. The proposed approach yields smooth and conformal oriented anisotropic geometrical patterns. This is related to recent effort in the structural optimization community on the topic of optimized oriented infills and microstructure de-homogenization. One of the resulting designs is validated by means of a full scale general non-linear analysis showcasing the advantageous properties of oriented microstructures for stability and robustness to buckling. [ABSTRACT FROM AUTHOR]

Spheres are known to be rigid geometric objects: they cannot be deformed isometrically, i.e., while preserving the length of curves, in a twice differentiable way. An unexpected result by Nash (Ann Math 60:383-396, 1954) and Kuiper (Indag Math 17:545-555, 1955) shows that this is no longer the case if one requires the deformations to be only continuously differentiable. A remarkable consequence of their result makes possible the isometric reduction of a unit sphere inside an arbitrarily small ball. In particular, if one views the Earth as a round sphere, the theory allows to reduce its diameter to that of a terrestrial globe while preserving geodesic distances. Here, we describe the first explicit construction and visualization of such a reduced sphere. The construction amounts to solve a nonlinear PDE with boundary conditions. The resulting surface consists of two unit spherical caps joined by a C1 fractal equatorial belt. An intriguing question then arises about the transition between the smooth and the C1 fractal geometries. We show that this transition is similar to the one observed when connecting a Koch curve to a line segment. [ABSTRACT FROM AUTHOR]