Variational implicit point set surfaces

Abstract

We propose a new method for reconstructing an implicit surface from an un-oriented point set. While existing methods often involve non-trivial heuristics and require additional constraints, such as normals or labelled points, we introduce a direct definition of the function from the points as the solution to a constrained quadratic optimization problem. The definition has a number of appealing features: it uses a single parameter (parameter-free for exact interpolation), applies to any dimensions, commutes with similarity transformations, and can be easily implemented without discretizing the space. More importantly, the use of a global smoothness energy allows our definition to be much more resilient to sampling imperfections than existing methods, making it particularly suited for sparse and non-uniform inputs. CCS Concepts: • Computing methodologies → Point-based models; Volumetric models.

Boundary-sampled halfspaces

“…We will demonstrate the use of BSH representation in shape design and reverse engineering. Our current implementation considers halfspaces represented either as basic primitives (e.g., planes, spheres, cylinders, cones, tori) or an VIPSS implicit function [Huang et al 2019]. Our choice of VIPSS is motivated by its ability to interpolate sparse spatial locations (e.g., control points), which makes it ideal for shape control.…”

“…If the fitting error of one or multiple primitives is lower than a given tolerance 𝜖, we select the least complex primitive according to this order of ascending complexity: plane, cylinder, cone, sphere, and torus. If the fitting errors of all primitives are greater than 𝜖, we fit a VIPSS implicit surface [Huang et al 2019] in a coarse-to-fine fashion as in [Carr et al 2001]. Starting with three well-spaced points on the segment (i.e., the control points), we iteratively add the point with the greatest distance to the VIPSS surface interpolating the current set of control points as a new control point, until such distance is lower than 𝜖.…”

Delaunay Meshing and Repairing of NURBS Models

“…We adopt its 3D Hermite interpolation variant which interpolates the values and gradients at points. This interpolating spline was used by Huang et al [HCJ19] for surface reconstruction from a set of sampling points, in which it is demonstrated that the interpolating scheme generates reasonable implicit surface with sparse and non-uniform sampling points, and is resilient to sampling imperfections. In our setting, Duchon's interpolating spline is a relevant choice as reliable sampling points and their surface normals can be obtained readily around blending balls.…”

An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

“…The implicit method, on the other hand, only utilizes a set of distinct scatter points to reconstruct the continuous surface. It has drawn increasing attention following the development of reverse engineering, which includes the global methods, such as the level sets and the RBF methods, as well as the local methods like the moving least square (MLS) and multi-level partition of unity (MPU) [7,8]. Compared with the explicit modeling methods, the implicit models can automatically and directly reconstruct the isosurface through scatter sample points and avoid using the extra data structure.…”