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A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface

Subdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In this technique, first, a result for computing bounds between 
 
 
 
 P
 
 
 k
 
 
 
 (a polygon at 
 
 k
 
 th level) and 
 
 
 
 P
 
 
 ∞
 
 
 
 (limit surface) of the Doo-Sabin scheme is obtained. After this, subdivision depth (the number of iterations) is computed by using the user-defined error tolerance. In addition, the results of the proposed technique are verified by taking distinct valence numbers of the Doo-Sabin surface scheme.