Accelerating Signed Distance Functions

Abstract

Processing and particularly visualizing implicit surfaces remains computationally intensive when dealing with complex objects built from construction trees. We introduce optimization nodes to reduce the computational cost of the field function evaluation for hierarchical construction trees, while preserving the Lipschitz or conservative properties of the function. Our goal is to propose acceleration nodes directly embedded in the construction tree, and avoid external, accompanying data-structures such as octrees. We present proxy and continuous level of detail nodes to reduce the overall evaluation cost, along with a normal warping technique that enhances surface details with negligible computational overhead. Our approach is compatible with existing algorithms that aim at reducing the number of function calls. We validate our methods by computing timings as well as the average cost for traversing the tree and evaluating the signed distance field at a given point in space. Our method speeds-up signed distance field evaluation by up to three orders or magnitude, and applies both to ray-surface intersection computation in Sphere Tracing applications, and to polygonization algorithms.