An Effective Method for Slicing Triangle Meshes Using a Freeform Curve

Abstract

Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user's viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line-Surface Intersection (LSI) problem is broken down into two subproblems: Plane-Curve Intersection (PCI) followed by Line-Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing.