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)

Course Material