关键词: 参数化, 测地极坐标, 拉普拉斯变形, 旋转不变量, 重用

Abstract: 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.

Key words: geodesic polar coordinates, Laplacian deformation, parameterization, reuse, rotation-invariant coordinates