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We introduce Arenite, a novel physics-based approach for modeling sandstone structures. The key insight of our work is that simulating a combination of stress and multi-factor erosion enables the generation of a wide variety of sandstone structures observed in nature. We isolate the key shape-forming phenomena: multi-physics fabric interlocking, wind and fluvial erosion, and particle-based deposition processes. Complex 3D structures such as arches, alcoves, hoodoos, or buttes can be achieved by creating simple 3D structures with user-painted erodable areas and vegetation and running the simulation. We demonstrate the algorithm on a wide variety of structures, and our GPU-based implementation achieves the simulation in less than 5 minutes on a desktop computer for our most complex example. 

Efficient urban layout generation is an interesting and important problem in many applications dealing with computer graphics and entertainment. We introduce a novel framework for intuitive and controllable small and large-scale urban layout editing. The key inspiration comes from the observation that cities develop in small incremental changes e.g., a building is replaced, or a new road is created. We introduce a set of atomic operations that consistently modify the city. For example, two buildings are merged, a block is split in two, etc. Our second inspiration comes from volumetric editings, such as clay manipulation, where the manipulated material is preserved. The atomic operations are used in interactive brushes that consistently modify the urban layout. The city is populated with agents. Like volume transfer, the brushes attract or repulse the agents, and blocks can be merged and populated with smaller buildings. We also introduce a large-scale brush that repairs a part of the city by learning style as distributions of orientations and intersections. 

We introduce Dendry, a procedural function that generates dendritic patterns and is locally computable. The function is controlled by parameters such as the level of branching, the degree of local smoothing, random seeding and local disturbance parameters, and the range of the branching angles. It is also controlled by a global control function that defines the overall shape and can be used, for example, to initialize local minima. The algorithm returns the distance to a tree structure which is implicitly constructed on the fly, while requiring a small memory footprint. The evaluation can be performed in parallel for multiple points and scales linearly with the number of cores. We demonstrate an application of our model to the generation of terrain heighfields with consistent river networks. A quad core implementation of our algorithm takes about ten seconds for a 512 × 512 resolution grid on the CPU.