Massively parallel rendering of complex closed-form implicit surfaces

We present a new method for directly rendering complex closed-form implicit surfaces on modern GPUs, taking advantage of their massive parallelism. Our model representation is unambiguously solid, can be sampled at arbitrary resolution, and supports both constructive solid geometry (CSG) and more unusual modeling operations (e.g. smooth blending of shapes). The rendering strategy scales to large-scale models with thousands of arithmetic operations in their underlying mathematical expressions. Our method only requires C 0 continuity, allowing for warping and blending operations which break Lipshitz continuity. To render a model, its underlying expression is evaluated in a shallow hierarchy of spatial regions, using a high branching factor for efficient parallelization. Interval arithmetic is used to both skip empty regions and construct reduced versions of the expression. The latter is the optimization that makes our algorithm practical: in one benchmark, expression complexity decreases by two orders of magnitude between the original and reduced expressions. Similar algorithms exist in the literature, but tend to be deeply recursive with heterogeneous workloads in each branch, which makes them GPU-unfriendly; our evaluation and expression reduction both run efficiently as massively parallel algorithms, entirely on the GPU. The resulting system renders complex implicit surfaces in high resolution and at interactive speeds. We examine how performance scales with computing power, presenting performance results on hardware ranging from older laptops to modern data-center GPUs, and showing significant improvements at each stage.