Seeking to improve the precision of 3D models? This paper introduces the 'permission grid,' a novel spatial occupancy grid designed to guide polygonal surface simplification algorithms. Unlike many current methods, this approach guarantees a geometric error bound, ensuring that all points on the approximation remain within a user-specified distance from the original surface. This is particularly crucial for applications in scientific computing and adaptive level of detail control. The permission grid constrains the simplification algorithm, preventing it from generating approximations outside a defined volume. The method works on arbitrary triangular models, handling mesh degeneracies gracefully. Further, the error tolerance can be easily expanded, allowing the construction of error-bounded level of detail hierarchies with vertex correspondences among all levels of detail. The permission grid's representation complexity is independent of the input model size, making it efficient. This research offers a practical and efficient solution for error-bounded surface simplification, addressing limitations in existing methods. Its application extends to various fields requiring accurate and adaptable 3D models, including scientific visualization, computer graphics, and engineering simulations. The ability to create level of detail hierarchies with guaranteed error bounds is invaluable for optimizing performance and maintaining accuracy in complex simulations.
As a publication in ACM Transactions on Graphics, this paper fits squarely within the journal's scope of computer graphics and geometric modeling. The proposed "permission grid" method addresses a key challenge in 3D graphics: simplifying complex models while maintaining accuracy. This research contributes to the journal's focus on advancing algorithms and techniques for efficient and high-quality rendering and manipulation of graphical data.