Research On The Method Of Surface Mesh Interpolation Based On Triangular Gregory Patches

The fast and effective techniques of generating smooth surface have received more favor in the application of surface modeling. Appropriate methods of surface representation can reduce the complexities, which will be encountered in many application fields, such as surface generation, surface connection, surface reconstruction and surface deformation etc. In order to overcome the difficulty and complexity of piecing two adjacent triangular patches by using traditional parametric surface modeling, Gregory triangular patch is used to interpolate the given shape control meshes in this paper. Moreover, the G1 smooth conditions of piecing two adjacent triangular Gregory patches and the method of constructing global G1 smooth surface based on triangular Gregory patches are studied. In the field of dynamic shape modeling, the techniques of points-cloud-based shape skeletonization and the method of skeleton drived shape deformation are also explored. The main work and the results can be depicted as follows:(1)Gregory method takes the rational combination of two twist along two different isoparametric directions respectively as its corresponding corner point's twist. It is different from the traditional surface interpolation methods which take invariant evaluation as the corner points'twist. Therefore, Gregory method deal well with the imcompatibility problem for corner points.(2)In order to generate global G1 continuous surface, many traditional methods are not only complex and difficult to manipulate but also hard to control surface quality sometimes. However, due to flexibility of its interior control points'positions, Gregory method provides more freedom for piecing two adjacent patches smoothly. The G1 continuity between two adajcent triangular Gregory patches just depends on those boundary control points which along their common boundary and the corresponding interior control points. Experiment results show that just through adjusting the corresponding boundary control points and interior control points can achieve G1 smooth connection for two adjacent patches. Even with two lathy triangular patches, it can also create G1 smooth surface.(3)A constructing method and its detail procedure which uses triangular Gregory patch to generate global G1 smooth surface from the shape control mesh is given. Some examples show that the method of generating global G1 smooth surface based on triangular Gregory patches is effective and easy to implement. Even with sparse control meshes this method can create overall G1 continous surface. Triangular Gregory interpolation method provides an effective and reliable technique for generating smooth shape surface.(4)In order to extract skeleton from points-cloud of a shape, a skeletonization method which gets the skeleton points of a shape by searching the optimal cutting plane for each point is used. And we devise a straightforward method to search the optimal cutting plane for each surface point. Examples illustrate our method can effectively extract skeleton points from cylindrical shape. Based on skeletonization of a shape we designed a set results of shape deformation and created a brief animation. The deformation technique drived by skeleton can reduce the cost of shape modeling and improve the design efficiency.