网格曲面上自由形状特征设计重用

Design and Reuse of Freeform Features on Mesh Surface

针对目前网格曲面上复杂特征重用困难的问题,提出一种保细节的特征重用方法。借助于拉普拉斯坐标蕴含的曲率、法矢等微分几何信息,提出基于微分坐标的重用特征边界环参数化方法,具有保长度、保曲率和保形状的特性,减小特征边界环从兴趣区域映射至目标区域时所产生的形变。采用离散测地极坐标方法对目标网格进行局部参数化,按照参数坐标一致原则将重用特征的边界环映射至目标网格的指定区域,并以映射后的边界环顶点位置和法矢信息为约束边界条件,基于旋转不变量的改进拉普拉斯变形框架,对重用特征进行变形操作,使重用特征与目标区域实现自然过渡。所提特征设计重用框架无须对重用特征本身参数化,因而可以重用任意复杂的特征,且对特征的亏格数亦无限制。试验结果表明,所介绍方法健壮、有效,可用于复杂特征的迁移式设计重用。

To solve the difficulty of reusing complex freeform features on mesh surface,a detail-preserving method is proposed. By means of differential geometry information contained in Laplacian coordinates,such as curvature,normal and so on,put forward a new method to parameterize the boundary loop of features,which is based on differential coordinates. The method of parameterization based on differential coordinates can preserve the length,curvature and the shape of features＇ boundary curve,which can reduce the deformation of the boundary curve mapped onto the target mesh. The target mesh is parameterized by Geodesic Polar Coordinates method. The boundary curve of features is mapped onto target mesh by the principle of common parameter coordinates. Thus the boundary constraint conditions including position constraint conditions and normal constrain conditions,which are used as the constrain conditions of mesh deformation; can get from the mapped boundary loop. Finally,the feature is deformed to match the target mesh using Laplacian deformation which combines with linear rotation-invariant coordinates. The algorithm avoids parameterizing the reuse features directly,which makes it easy to work with the complex features,and unrelated with the number of feature genus. The results show that the proposed method is robust,effective and can be used to clone the complex features.