Distortion Compensation for Mesh-Parameterization Mapping and Its Application in Freeform Surface Machining

To address the problem that the mesh parameterization results usually come with mapping distortions that affect the accuracy in trajectory planning,a new algorithm introducing mapping distortion compensation is proposed based on the analysis of the mapping distortion field over mesh surface.The algorithm includes direction mapping to compensate the angular distortion,length mapping to compensate the stretch distortion,and large span mapping distortion handling strategy which considers that different triangle facets have varied mapping distortions.In the case studies,the mapping distortions results are quantitatively evaluated,and the equidistant circular trajectory and actual trochoidal polishing trajectory are generated on complex mesh surfaces,which verified that the proposed algorithm can effectively compensate the mapping distortions and ensure the accuracy of the trajectory planning,so that it can take good advantage of the dimensionality reduction by the mesh-parameterization mapping.