基于加权渐进插值的Loop细分曲面等距逼近

Offset Approximation of Loop Subdivision Surface Based on Weighted Progressive Interpolation

等距曲面在CAD/CAM领域有着重要的作用,由于细分曲面没有整体解析表达式,使得计算细分曲面等距比参数曲面更加困难。针对目前已有的两种等距面逼近算法进行了改进,利用加权渐进插值技术避免了传统细分等距逼近算法产生网格偏移的问题。此外,提出了针对边界等距处理方案,使得等距后的细分曲面在内部和边界都均匀等距。该方法无需求解线性方程组,具有全局和局部特性,能够处理闭网格和开网格,为Loop细分曲面数控加工奠定了良好的基础算法。最后给出的实例验证了算法的有效性。

Offset plays an important role in the field of CAD/CAM.The offset approximation computation is more diffficult for subdivision surfaces than parametric surfaces because subdivision surfaces have no analytical expression.The proposed approach is an improvement of two existed subdivision surface offset algorithms.Using the weighted progressive interpolation （WPI） method avoids the mesh deviation caused by the traditional methods.The boundary offset treatment is presented to obtain the uniform offset mesh.The proposed method avoids solving a linear equation system and has the advantages of both local and global methods.The method can be used to deal with either closed or open meshes.Offset approximation is an important operator to the applications of Loop subdivision surfaces in NC machining.Some typical examples are illustrated to demonstrate the efficiency of the proposed approach in the end.