1. Speaker: Shuen-Huei Guan (Drake) Date: 2004/03/11
Subdivision Surface
Speaker: Shuen-Huei Guan (Drake)
Date: 2004/03/11

2. Shuen-Huei Guan, CML, NTU
Paper
Edwin E. Catmull and James H. Clark. Recursively generated b-spline surfaces on arbitrary topological meshes. Computer-Aided Design, Vol.10, No.6, p p.355, 1978.
Donald Doo and Malcolm Sabin. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design, Vol.10, No.6, p p.360, 1978.
2004/03/11
Shuen-Huei Guan, CML, NTU

3. Shuen-Huei Guan, CML, NTU
Agenda
Introduction
Curve
Surface
Chaikin’s Curves
Catmull and Clark
Doo and Sabin
2004/03/11
Shuen-Huei Guan, CML, NTU

4. Curves

5. Curve: Parametric Representation
y = f(x), z = g(x)
Circle!
f(x, y, z) = 0
One-half of a circle!
x(t) = axt3 + bxt2 + cxt + dx, y(t) = ayt3 + byt2 + cyt + dy, z(t) = azt3 + bzt2 + czt + dz, 0≦t ≦ 1
2004/03/11
Shuen-Huei Guan, CML, NTU

6. Parametric Representation Cont’d
x(t) = axt3 + bxt2 + cxt + dx, y(t) = ayt3 + byt2 + cyt + dy, z(t) = azt3 + bzt2 + czt + dz , 0≦t ≦ 1
2004/03/11
Shuen-Huei Guan, CML, NTU

7. Parametric Representation Cont’d
Relation to constraints?
2004/03/11
Shuen-Huei Guan, CML, NTU

8. Parametric Representation Cont’d
2004/03/11
Shuen-Huei Guan, CML, NTU

9. Parametric Representation Cont’d
Conclusion
G := 1x4, geometry matrix
M := 4x4, basis matrix
GM := blending functions
2004/03/11
Shuen-Huei Guan, CML, NTU

10. Hermite Curves

11. Shuen-Huei Guan, CML, NTU
Definition
Named for the mathematician.
Determined by endpoints P1 and P2 and tangent vectors at the endpoints T1 and T2.
2004/03/11
Shuen-Huei Guan, CML, NTU

12. Shuen-Huei Guan, CML, NTU
Hermite Form
2004/03/11
Shuen-Huei Guan, CML, NTU

13. Surfaces

14. Shuen-Huei Guan, CML, NTU
B-Spline Curves
2004/03/11
Shuen-Huei Guan, CML, NTU

15. Parametric Bi-Cubic Surfaces
2004/03/11
Shuen-Huei Guan, CML, NTU

16. Parametric Bi-Cubic Cont’d
2004/03/11
Shuen-Huei Guan, CML, NTU

17. Parametric B-Spline Surface
2004/03/11
Shuen-Huei Guan, CML, NTU

18. Subdivision

19. Chaikin’s Curves: At First Glance
2004/03/11
Shuen-Huei Guan, CML, NTU

20. Chaikin’s Curves: At First Glance
2004/03/11
Shuen-Huei Guan, CML, NTU

21. Chaikin’s Curves: At First Glance
2004/03/11
Shuen-Huei Guan, CML, NTU

22. Chaikin’s Curves: At First Glance
2004/03/11
Shuen-Huei Guan, CML, NTU

23. Shuen-Huei Guan, CML, NTU
Chaikin’s Curves
It’s B-Spline Curve!
2004/03/11
Shuen-Huei Guan, CML, NTU

24. Shuen-Huei Guan, CML, NTU
Catmull and Clark
2004/03/11
Shuen-Huei Guan, CML, NTU

25. Shuen-Huei Guan, CML, NTU
Catmull and Clark
2004/03/11
Shuen-Huei Guan, CML, NTU

26. Let’s browse to UCDavis
Catmull and Clark
Let’s browse to UCDavis

27. Let’s browse to UCDavis
Doo and Sabin
Let’s browse to UCDavis

28. Shuen-Huei Guan, CML, NTU
References
Foley, Van Dam, Feiner, Huges, Phillips, Introduction to Computer Graphics, Addison Wesley.
Hermite Curve Interpolation,
On-line Geometric Modeling Notes,
2004/03/11
Shuen-Huei Guan, CML, NTU

29. Thanks for your attendance