A novel approach to triangulate 3D point clouds for 3-axis sculptured surfaces machining

Reverse Engineering (RE) is employed to replicate sculptured surfaces from 3D point clouds. However, reconstructing continuous surfaces remains challenging. To address this, triangulated models are used as an alternative. In this paper, we present a novel and simple approach based on geometric considerations for generating a 3D triangulation from 3D point clouds with fewer triangles while satisfying a predefined accuracy. In this approach, we combine regular and adaptive triangulations and explicitly integrate approximation accuracy, adaptive subdivision, point distributions within triangles, and triangle quality. The approach involves four steps: (1) generating an initial regular 3D triangulation; (2) adaptively subdividing triangles; (3) verifying triangle qualities; and (4) generating the STL model for use in 3-axis machining. The lower number of generated triangles significantly reduces the processing times for optimizing the machining and the costs. We validated the approach across numerous 3D point clouds of complex sculptured surfaces, proving its performance for triangulation accuracy and processing time.