MATH-7123               Introduction to Subdivision Scheme                                               3 (3+0)

DESCRIPTION AND OBJECTIVES

In recent years, subdivision schemes have become an integral part of computer graphics in view of their extensive variety of applications in the field of visualizations, animation and image processing.

LEARNING OUTCOMES

Promote subdivision that is functional and enhances the knowledge regarding the construction of freeform curves and surfaces.

Contents

1. Bilinear interpolation, The direct de Casteljau Algorithm
2. The tensor product approach & its properties
3. Bernstein polynomial, degree elevation, constructing polynomial patches: Ruled surfaces
4. Coons patches, translational surfaces, tensor product interpolation, bicubic Hermite patches
5. Composite Surfaces
6. Tensor product B-spline surfaces, Matrix representation
7. Cubic spline interpolation
8. Rational Bezier & B-spline surfaces, surface of revolution
9. COONS & trimmed surface
10. Lofted Surfaces
11. Bezier Triangles: The de Casteljau algorithm, triangular blossoms
12. Bernstein polynomial, derivatives, subdivision, differentiability
13. Nonparametric patches
14. S-Patches. Surfaces with Arbitrary Topology
15. Recursive subdivision curve
16. Properties of Subdivision scheme
17. Types of Subdivision scheme
18. Analysis of Subdivision
19. Smoothness analysis of Binary, Ternary , Quaternary Subdivision scheme
20. Tensor product of Subdivision scheme
21. Smoothness analysis of Subdivision scheme

Recommended Texts

1. Gerald, F. (2002). Curves & surfaces for CAGD. A practical guide. (5th Ed.), Burlington: Morgan Kaufmann Publishers.
2. Josef, H., & Dieter, L. (1993). Fundamentals of computer aided geometric design. Natick: A. K Peter Ltd.

Suggested Readings

1. Gerald, F., Josef, H., & Myung, S. (2002). Handbook of computer aided geometric design. Netherlands: Elsevier Science.
2. Armin, I., Ewald, Q., & Michael, S. F. (2002). Tutorials on multiresolution in geometric modeling. Summer School Lecture Notes. New York: Springer-Berlin.
3. Recent research papers.

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

KEY DATES AND TIME OF CLASS MEETING

Monday                                                                                 02:00pm - 03:30pm

Tuesday                                                                                02:00pm - 03:30pm

Mid-Term Examination:

December 28, 2020 to January 01, 2021 (Monday to Friday)

Final-Term Examination:

March 01 to 05, 2021 (Monday to Friday)

Declaration of Result: March 12, 2021 (Friday)