Interpolatory subdivision scheme based on type 2 Coons surface
An interpolatory subdivision method based on type 2 Coons surface is proposed,which is defined on quadrilateral meshes of any topology.Step 1,set the tangent vector of the initial grid point on each edge.Step 2,in each layer of subdivision,the curve boundary is constructed from two points and tangent vectors on the mesh edge by combining with the De Casteljau's algorithm.The center point of curve parameter is set as the new edge point,and the new tangent vector of two endpoints and new edge point is calculated.And then,set the boundary derivative on the boundary of four curves,and give the endpoint torsion vector to construct type 2 Coons surface.The parameter center point of the sampling surface is taken as the new surface point,and the new tangent vector on the connection edge of the surface point and the edge point is calculated.Step 3,set the shape parameters to adjust the tangent vector of the regular points,and finally,the limit surface is iteratively obtained.Numericals examples shows that,compared with Kobbelt subdivision method and 4-point surface subdivision method,the proposed method which can obtain interpolatory surfaces with higher smoothness is controllable easily.Convergence and continuity analysis prove that the interpolation surface is at least G1 continuous.
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