We introduce Loki, a new framework for robust simulation of fluid, rigid, and deformable objects with non-compromising fidelity on any single element, and capabilities for coupling and representation transitions across multiple elements. Loki adapts multiple best-in-class solvers into a unified framework driven by a declarative state machine where users declare 'what' is simulated but not 'when,' so an automatic scheduling system takes care of mixing any combination of objects. This leads to intuitive setups for coupled simulations such as hair in the wind or objects transitioning from one representation to another, for example bulk water FLIP particles to SPH spray particles to volumetric mist. We also provide a consistent treatment for components used in several domains, such as unified collision and attachment constraints across 1D, 2D, 3D deforming and rigid objects. Distribution over MPI, custom linear equation solvers, and aggressive application of sparse techniques keep performance within production requirements. We demonstrate a variety of solvers within the framework and their interactions, including FLIPstyle liquids, spatially adaptive volumetric fluids, SPH, MPM, and mesh-based solids, including but not limited to discrete elastic rods, elastons, and FEM with state-of-the-art constitutive models. Our framework has proven powerful and intuitive enough for voluntary artist adoption and has delivered creature and FX simulations for multiple major movie productions in the preceding four years.

Procedural representations provide powerful means for generating complex geometric structures. They are also notoriously difficult to control. In this article, we present an algorithm for controlling grammar-based procedural models. Given a grammar and a high-level specification of the desired production, the algorithm computes a production from the grammar that conforms to the specification. This production is generated by optimizing over the space of possible productions from the grammar. The algorithm supports specifications of many forms, including geometric shapes and analytical objectives. We demonstrate the algorithm on procedural models of trees, cities, buildings, and Mondrian paintings.