PICO: Procedural Iterative Constrained Optimizer for Geometric Modeling

Procedural modeling has produced amazing results, yet fundamental issues such as controllability and limited user guidance persist. We introduce a novel procedural system called PICO (Procedural Iterative Constrained Optimizer) using PICO-Graph, a procedural model designed with optimization in mind. PICO enables the exploration of generative designs by combining user and environmental constraints into a single framework and using optimization without the need to write procedural rules. The PICO-Graph is a data-flow procedural model consisting of a set of geometry-generating operation nodes. The forward generation is initiated by sending geometric objects from initial nodes. These objects travel through the graph, triggering generation of more objects along the way. We combine the PICO-Graph with evolutionary optimization that allows for exploration of the generated models and the generation of variants. The user defines the geometry-generating operations and the set of constraints; e.g, whether an existing object should be supported by the generated model, whether symmetries exist, etc. PICO then generates geometric models that fulfill the constraints through optimization, allowing interactive user control of constraints. We show PICO on a variety of examples, including generation of procedural chairs, generation of support structures for 3D printing, or generation of procedural terrains matching a given input.