Generalization of (2n+4)-point approximating subdivision scheme Kwan Pyo Ko Dongseo University, South Korea Jan. 30, 2007

What is Subdivision Scheme? Subdivision produces a smooth curve or surface as the limit of a sequence of successive refinements We can classify computer graphics by three parts He is Geri, character of Geri’s game and Toy Story II. Geri's Game received the Academy Award for Best Animated Short Film in 1998 You must see Toy Story II If did not see yet. Please check whether this short is include in video. This is a scene that a person plays chess game alone. However, he is conflicting with himself. This is all of computer graphics.

Chaikin’s Algorithm : corner cutting

Subdivision Schemes Binary or ternary Stationary or non-stationary Type of mesh (triangular or quadrilateral) Approximating or interpolating Arbitrary topology Multi resolution Simple & efficient code We can classify computer graphics by three parts He is Geri, character of Geri’s game and Toy Story II. Geri's Game received the Academy Award for Best Animated Short Film in 1998 You must see Toy Story II If did not see yet. Please check whether this short is include in video. This is a scene that a person plays chess game alone. However, he is conflicting with himself. This is all of computer graphics.

Formulation We can classify computer graphics by three parts He is Geri, character of Geri’s game and Toy Story II. Geri's Game received the Academy Award for Best Animated Short Film in 1998 You must see Toy Story II If did not see yet. Please check whether this short is include in video. This is a scene that a person plays chess game alone. However, he is conflicting with himself. This is all of computer graphics.

Subdivision : The Limit Function : the limit function of the subdivision Let Then is called the basic limit function. In particular, satisfies the two scale relation

Basic Limit Function : B-splines Linear spline Cubic spline

Basic Issues Schemes - masks Convergence Smoothness - Approximation Order

Goal Construct a new approximating scheme with two parameters which reproduces all polynomials Analysis of the proposed scheme Comparison

Construction of Scheme

Problem :

Masks :

Smoothness & Comparison Dyn approximating scheme Proposed scheme Support Maximal regularity

Advantages Design Flexibility Higher Smoothness than well-known schemes

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