An hp-adaptive discretization algorithm for signed distance field generation

Abstract

In this paper we present an hp-adaptive algorithm to generate discrete higher-order polynomial Signed Distance Fields (SDFs) on axis-aligned hexahedral grids from manifold polygonal input meshes. Using an orthonormal polynomial basis, we efficiently fit the polynomials to the underlying signed distance function on each cell. The proposed error-driven construction algorithm is globally adaptive and iteratively refines the SDFs using either spatial subdivision ( h-refinement) following an octree scheme or by cell-wise adaption of the polynomial approximation's degree ( p-refinement). We further introduce a novel decision criterion based on an error-estimator in order to decide whether to apply p- or h-refinement. We demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption compared to previous approaches. While the cell-wise polynomial approximation will result in highly accurate SDFs, it can not be guaranteed that the piecewise approximation is continuous over cell interfaces. Therefore, we propose an optimization-based post-processing step in order to weakly enforce continuity. Finally, we apply our generated SDFs as collision detector to the physically-based simulation of geometrically highly complex solid objects in order to demonstrate the practical relevance and applicability of our method.

Target‐driven cloud evolution using position‐based fluids

“…Let the sign of the distance to be determined by whether a given point x is in . The signed distance function 41 is then defined as follows: …”

Efficient 2D Simulation on Moving 3D Surfaces

“…For converting polygon meshes to signed distance fields, several methods are available, e.g., [SGGM06], [XB14], or [KDBB17]. A special case arises when we convert particle systems to distance fields.…”

Real-Time Collision Detection for Deformable Characters with Radial Fields

“…Adaptive resolutions [2] can improve memory efficiency, but make dynamic updates even harder. Like BVH techniques that take advantage of an object's topological or skeletal structure, alternative parameterisations can reduce memory usage [35]. Matching the shape of an embedded coordinate system to that of the object being represented uses the parameterisation itself to store geometric information.…”

“…Carr et al [38] represented geometry by fitting signeddistance functions to imperfect 3D scanner data for interpolation and extrapolation, while Koschier et al [35] fit polynomials piecewise to spatially subdivided Signed Distance Fields. These representations are highly efficient and have the nice property of being differentiable anywhere.…”

“…Radial fields trade off generality of techniques such as hpadaptive distance fields [35], in favour of GPU acceleration, but this imposes limitations. Radial fields can only support star-convex geometry.…”