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

2. 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.
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However, he is conflicting with himself.
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3. Chaikin’s Algorithm : corner cutting

4. 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.

5. 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.

6. 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

7. Basic Limit Function : B-splines
Linear spline Cubic spline

8. Basic Issues Schemes - masks Convergence
Smoothness - Approximation Order

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

10. Construction of Scheme

12. Problem :

13. Masks :

15. Smoothness & Comparison
Dyn approximating scheme
Proposed scheme
Support
Maximal regularity

16. Advantages Design Flexibility
Higher Smoothness than well-known schemes

17. Thank You !
and
Have a Good Time
in Czech Republic!