An Electrostatic Field-Driven Method for Point Cloud Normal Orientation

Point cloud normal orientation is a fundamental task in digital geometry processing and 3D vision, with applications in surface reconstruction and shape analysis. Existing approaches either propagate local normal orientations, which may lack global consistency, or solve global optimization problems over pre-discretized spatial structures, which can limit geometric flexibility. In this paper, we propose an electrostatic field-based formulation for point cloud normal orientation, which models the orientation problem using a set of discrete Coulomb kernels defined by a collection of particles, yielding a smooth field with a closed-form expression. The global orientation is obtained by optimizing this field to be orthogonal to locally estimated tangent planes, resulting in a globally coherent vector field over the point cloud. Our approach adopts a dynamic, grid-free particle representation with adaptive positions, magnitudes, and particle count. The particles evolve during optimization to adapt the field representation to the underlying geometry. Normal orientations are then recovered from the optimized field. We demonstrate that this formulation produces coherent orientations while preserving fine geometric details across representative 3D models.