An Accelerated Slicing Algorithm for Frep Models

Abstract

Complex 3D objects with microstructures can be modelled using the function representation (FRep) approach and then manufactured. The task of modelling a geometric object with a sophisticated microstructure based on unit cell repetition is often too computationally expensive for CAD systems. FRep provides efficient tools to solve this problem. However, even for FRep the slicing step required for manufacturing can take a significant amount of time. An accelerated slicing algorithm for FRep 3D objects is proposed in this paper. This algorithm allows the preparation of FRep models for 3D printing without surface generation stage. The spatial index is employed to accelerate the slicing process. A novel compound adaptive criterion and a novel acceleration criterion are proposed to speed up the evaluation of the defining function of an FRep object. The use of these criteria is significantly reducing the computational time for contour construction during the slicing process. The K-d tree and R-tree data structures are used as spatial indexes. The performance of the accelerated slicing algorithm was tested. The contouring time was reduced 100-fold due to using the novel compound adaptive criterion with the novel acceleration criterion.

Keywords

• function representation
• implicit surface
• additive manufacturing
• 3D printing
• K-d tree
• R-tree