Abstract Rendering tree‐based analytical Signed Distance Fields (SDFs) through sphere tracing often requires to evaluate many primitives per tracing step, for many steps per pixel of the end image. This cost quickly becomes prohibitive as the number of primitives that constitute the SDF grows. In this paper, we alleviate this cost by computing local pruned trees that are equivalent to the full tree within their region of space while being much faster to evaluate. We introduce an efficient hierarchical tree pruning method based on the Lipschitz property of SDFs, which is compatible with hard and smooth CSG operators. We propose a GPU implementation that enables real‐time sphere tracing of complex SDFs composed of thousands of primitives with dynamic animation. Our pruning technique provides significant speedups for SDF evaluation in general, which we demonstrate on sphere tracing tasks but could also lead to significant improvement for SDF discretization or polygonization.

We introduce Sphere Carving , a novel method for automatically computing bounding volumes that closely bound a procedurally defined implicit surface. Starting from an initial bounding volume located far from the object, we iteratively approach the surface by leveraging the signed distance function information. Field function queries define a set of empty spheres, from which we extract intersection points that are used to compute a bounding volume. Our method is agnostic of the function representation and only requires a conservative signed distance field as input. This encompasses a large set of procedurally defined implicit surface models such as exact or Lipschitz functions, BlobTrees, or even neural representations. Sphere Carving is conceptually simple, independent of the function representation, requires a small number of function queries to create bounding volumes, and accelerates queries in Sphere Tracing and polygonization.

Abstract Hardware tessellation is de facto the preferred mechanism to adaptively control mesh resolution with maximal performances. However, owing to its fixed and uniform pattern, leveraging tessellation for feature‐aware LOD rendering remains a challenging problem. We relax this fundamental constraint by introducing a new spatial and temporal blending mechanism of tessellation levels, which is built on top of a novel hierarchical representation of multi‐resolution meshes. This mechanism allows to finely control topological changes so that vertices can be removed or added at the most appropriate location to preserve geometric features in a continuous and artifact‐free manner. We then show how to extend edge‐collapse based decimation methods to build feature‐aware multi‐resolution meshes that match the tessellation patterns. Our approach is fully compatible with current hardware tessellators and only adds a small overhead on memory consumption and tessellation cost.