| Student: |
Muhsin INCESU |
| Supervisor: |
Prof.Dr. Osman GURSOY |
| Department: |
Mathematics |
| Institution: |
Graduate School of Natural and Applied Sciences |
| University: |
Karadeniz Technical University, Turkey |
|
| Title of the Thesis: |
BEZIER CURVES, BEZIER SURFACES, AND THEIR NUMERICAL ALGORITHMS USING MATLAB |
| Level: |
M.Sc. |
| Acceptance Date: |
22/8/2003 |
| Number of Pages: |
117 |
| Registration Number: |
i1403 |
|
| Summary: The curves that have the most stable numerical solutions among of the curves recently used in computer aided design (CAD) are Bezier and rational Bezier curves. Bezier curves can be defined by points called control points.
In this study some theorems are given on Bernstein polynomials and investigated continuity conditions of piecewise Bezier curves. Then the numerical algorithms such as De Casteljau and subdivision, and their application using MATLAB on Bezier curves, rational Bezier curves, and Bezier surfaces were given in chapter 2.3., 2.4., and 2.5. respectively. In chapter 2.6. the curvatures of Bezier curves and Bezier surfaces are represented by in terms of their control points and given codes of the algorithms on the curvatures of Bezier curves and Bezier surfaces in MATLAB. Consequently the first and second fundamental forms of Bezier surfaces were presented.
Key Words: Bezier Curves, Rational Bezier Curves, Bezier Surfaces, MATLAB and Curvatures of Bezier Surfaces
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