Dynamic Sampling and Rendering of Algebraic Point Set Surfaces

TLDR

APSS define smooth surfaces from point sets via local MLS fitting of algebraic spheres. The paper revisits spherical fitting to provide a generic solution with curvature control and introduces a real‑time rendering system that uses dynamic up‑sampling and splatting. The authors develop a generic MLS‑based fitting with curvature parameters, a dynamic up‑sampling rendering pipeline, a view‑dependent geometric error metric, efficient spatial search structures, and a parallel GPU implementation. The system achieves high performance on dynamic or complex models by exploiting temporal coherence at the primitive level, demonstrating flexible and efficient rendering.

Abstract

Abstract Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving least‐squares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature control of the fitted spheres. As a second contribution we present a novel real‐time rendering system of such surfaces using a dynamic up‐sampling strategy combined with a conventional splatting algorithm for high quality rendering. Our approach also includes a new view dependent geometric error tailored to efficient and adaptive up‐sampling of the surface. One of the key features of our system is its high degree of flexibility that enables us to achieve high performance even for highly dynamic data or complex models by exploiting temporal coherence at the primitive level. We also address the issue of efficient spatial search data structures with respect to construction, access and GPU friendliness. Finally, we present an efficient parallel GPU implementation of the algorithms and search structures.