Jet subdivision schemes on the k-regular complex

We introduce a new family of subdivision schemes called jet subdivision schemes. Jet subdivision schemes are a natural generalization of the commonly used subdivision schemes for free-form surface modeling. In an order r jet subdivision scheme, rth order Taylor expansions, or r-jets, of functions are the essential objects being generated in a coarse-to-fine fashion. Standard subdivision surface methods correspond to the case r = 0. Just as the standard free-form subdivision surface schemes, jet subdivision schemes are based on combining (i) a symmetric subdivision scheme in the shift-invariant setting with (ii) an extraordinary vertex rule. We formulate the notions of stationarity, symmetry, and smoothness for jet subdivision schemes. We then extend some well-known results in the theory of subdivision surfaces to the setting of jet subdivision schemes. By incorporating high order data into the subdivision rules, jet subdivision schemes offer more degrees of freedom for the design of e...

• Type: Journal
• Year: 2006
• Where: CAGD
• Authors: Yonggang Xue, Thomas P.-Y. Yu, Tom Duchamp
• Keywords: CAGD 2006, Jet Subdivision Scheme, Subdivision Scheme, Subdivision Surface