We study the design and optimization of polyhedral patterns, which are patterns of planar polygonal faces on freeform surfaces. Working with polyhedral patterns is desirable in architectural geometry and industrial design. However, the classical tiling patterns on the plane must take on various shapes in order to faithfully and feasibly approximate curved surfaces. We define and analyze the deformations these tiles must undertake to account for curvature, and discover the symmetries that remain invariant under such deformations. We propose a novel method to regularize polyhedral patterns while maintaining these symmetries into a plethora of aesthetic and feasible patterns.
We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±κ/4(κ e Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user's directional and angular constraints, then apply mixed-integer quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.
Spatial interactions between herbivores and vegetation resources drive plant and animal dynamics and ecosystem functioning. Energy maximization is often proposed as an important factor determining diet selection, however, few studies have made the link between different energy-maximizing strategies and emergent properties, such as the spatial pattern of defoliation. Using an individual-based model, we investigate the role of several hypothetical perceptual traits in the formation of defoliation patterns and the consequences for the foraging performance of the animals. Results suggest that in complex mosaics of poor quality vegetation, highly perceptual strategies are not necessarily an advantage, however, perceptual traits can have a strong impact on the spatial pattern of defoliation.