Martin Ambrožič (2011) Implementation of selected subdivision schemes. EngD thesis.
Subdivision is the process of generating smooth curves or surfaces from a finite set of initial control points, defined on a regular mesh. In the case of curves this is simply a subset of integers, while with generating surfaces it depends on the topology of the control points. The subdivision scheme determines the refinement rule by which new points are calculated on a denser mesh - by adding in-between points we get a curve or surface in the limit. Linear subdivision schemes calculate new points as linear combinations of points from the previous level. The subdivision mask contains the linear combination coefficients and so determines the refinement rule for calculating points of the kth level: . By implementing linear subdivision schemes in the MATLAB environment I aimed to present through examples several types of subdivision schemes, including schemes from cardinal B-splines, interpolation schemes and tensor product schemes. Also through examples I checked various conditions for the continuity and smoothness of curves and surfaces, generated by subdivision schemes.
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