Filling In N-sided Hole Based On Triangular Gregory Patch

The scheme of connecting the triangular patches smoothly in a rapid and efficient way,as well as the reconstruction method of global geometric continuous shape surface, is studiedin this paper. In order to overcome the difficulty and complexity of piecing two adjacenttriangular patches by using traditional parametric surface modeling, Gregory triangular patchis used to interpolate the given shape control meshes, which can effectively eliminate thedistortions of splitting triangular domain into quadrilateral patch. Moreover, the G1and G2smooth conditions of piecing two adjacent triangular Gregory patches and the method ofconstructing global G1and G2smooth surface based on triangular Gregory patches are studied.In filling procedure, the method of filling N-sided holes are also explored. The main work andthe results can be depicted as follows:(1) Gregory method takes the rational combination of two twists along two differentisoperimetric directions respectively as its corresponding corner point’s twist. It is differentfrom the traditional surface interpolation methods which take invariant evaluation as thecorner points’ twist. Therefore, Gregory method deal well with the incompatibility problemfor corner points.(2) In order to generate global G1and G2continuous surface, many traditional methodsare not complex and difficult to manipulate but also hard to control surface quality sometimes.The G1and G2continuity between two adjacent triangular Gregory patches just depends onthose boundary control points which along their common boundary and the correspondinginterior control points. Experiment results show that just through adjusting the correspondingboundary control points and interior control points can achieve G1and G2smooth connectionfor two adjacent patches. Even with two lathy triangular patches, it can also create G1and G2smooth surface. Furthermore, the use of continuous patches to fill holes and reach the globalgeometry continuity, constructing a smooth and continuous surface shape.(3) A constructing method and its detail procedure which uses triangular Gregory patchto generate global G1and G2smooth surface from the shape control mesh is given. Someexamples show that the method of generating global G1and G2smooth surface based on triangular Gregory patches is effective and easy to implement. Even with sparse controlmeshes this method can create overall G1and G2continuous surface. Triangular Gregoryinterpolation method provides an effective and technique for filling N-sided holes to generatesmooth shape surface.