基于全局无翻转参数化的网格曲面几何纹理激光打印路径生成

Generating Laser Printing Paths for Geometric Textures on Grid Surfaces Based on Inversion-Free Parameterization

摘要: 针对传统曲面网格上几何纹理在激光打印轨迹规划中需要求解复杂的空间求交问题，提出了一种基于全局无翻转参数化的网格曲面几何纹理激光打印路径规划算法。首先采用EBP低扭曲全局无翻转参数化算法将基础曲面展开平面；然后利用平面几何纹理求得分层的切片然后放置在参数域内求得平面分层往复式参数轨迹；最后利用映射分段线性以及双射的特点和高度场映射方法构建空间轨迹。实验结果表明，本算法高效、鲁棒性且扩展性强。

Abstract: We present a novel laser printing path planning algorithm for geometric textures on mesh surfaces that overcomes the complex spatial intersection problems associated with traditional geometric texture laser printing trajectory planning on surface meshes. Our approach is based on an inver-sion-free parameterization of the mesh surface. Specifically, we employ the EBP low-distortion in-version-free parameterization algorithm to flatten the base surface onto a plane. From there, we generate layered slices of the planar geometric texture and place them within the parameter do-main to obtain a planar layered reciprocating parameter trajectory. Finally, we utilize mapping segmentation linear and Bijective properties, as well as height field mapping methods, to construct a spatial trajectory. Experimental results show that our algorithm is efficient, robust, and highly scalable.