A free‐form surface flattening algorithm that minimizes geometric deformation energy

Abstract

Based on the analysis of the advantages and disadvantages of existing surface flattening algorithms, this paper proposes a free‐form surface flattening algorithm that minimizes geometric deformation by combining the advantages of the geometric flattening method and the mechanical energy flattening method to address the problems of many iterations, large changes in convergence, and weak visualization of deformation. The point cloud surface is meshed using the triangular slice search method, and the 3D surface mesh is wrapped around the surface using geometric mapping relationships. The initial correction and deformation analysis of the ring flatten graphic are carried out according to the average flattening error, and a global geometric deformation energy model is established to obtain the energy‐minimizing unfolding conditions and optimize the initial flattening graph by iterative optimization. The verification of the algorithm shows that the algorithm is general, has good robustness, high flattening accuracy, and visualizes the flattening deformation. The method is suitable for some design occasions of machining, such as the flattening calculation of automobile outer cladding parts and sheet metal parts. It is especially suitable for the flattening calculation of ring‐like parts, and is a good guide for the design calculation and stamping process of sheet‐metal‐like parts.

Loading method for a 3D geological entity model based on free-form deformation technique

“…Using Equation ( 7) and the local coordinates of each vertex on the object to be deformed, the new global coordinates of the object are calculated. The deformation of the internal 3D model is then completed (Xiong et al 2019;Zheng et al 2022).…”