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Orders of Growth and Tree Recursion CoSc 450: Programming Paradigms - - PowerPoint PPT Presentation
Orders of Growth and Tree Recursion CoSc 450: Programming Paradigms - - PowerPoint PPT Presentation
CoSc 450: Programming Paradigms 04 Orders of Growth and Tree Recursion CoSc 450: Programming Paradigms 04 Graphics primitive operations CoSc 450: Programming Paradigms 04 Graphics primitive operations y 1 x -1 0 1 -1 Co-ordinate
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CoSc 450: Programming Paradigms Graphics primitive operations
1
- 1
1
- 1
Co-ordinate system
x y
04
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CoSc 450: Programming Paradigms C-Curve code
(define c-curve (lambda (x0 y0 x1 y1 level) (if (= level 0) (line x0 y0 x1 y1) (let ((xmid (/ (+ x0 x1) 2)) (ymid (/ (+ y0 y1) 2)) (dx (- x1 x0)) (dy (- y1 y0))) (let ((xa (- xmid (/ dy 2))) (ya (+ ymid (/ dx 2)))) (overlay (c-curve x0 y0 xa ya (- level 1)) (c-curve xa ya x1 y1 (- level 1))))))))
04
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CoSc 450: Programming Paradigms C-Curve code
(define c-curve (lambda (x0 y0 x1 y1 level) (if (= level 0) (line x0 y0 x1 y1) (let ((xmid (/ (+ x0 x1) 2)) (ymid (/ (+ y0 y1) 2)) (dx (- x1 x0)) (dy (- y1 y0))) (let ((xa (- xmid (/ dy 2))) (ya (+ ymid (/ dx 2)))) (overlay (c-curve x0 y0 xa ya (- level 1)) (c-curve xa ya x1 y1 (- level 1))))))))
Base case 04
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CoSc 450: Programming Paradigms C-Curve code
(define c-curve (lambda (x0 y0 x1 y1 level) (if (= level 0) (line x0 y0 x1 y1) (let ((xmid (/ (+ x0 x1) 2)) (ymid (/ (+ y0 y1) 2)) (dx (- x1 x0)) (dy (- y1 y0))) (let ((xa (- xmid (/ dy 2))) (ya (+ ymid (/ dx 2)))) (overlay (c-curve x0 y0 xa ya (- level 1)) (c-curve xa ya x1 y1 (- level 1))))))))
Induction case 04
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CoSc 450: Programming Paradigms 04
(x0, y0) (x1, y1) (xa, ya)
Figure 4.10 The three key points in a c-curve of level greater than zero.
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CoSc 450: Programming Paradigms 04
(x0, y0) (x1, y1) (xa, ya)
Figure 4.10 The three key points in a c-curve of level greater than zero.
Level = 0
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CoSc 450: Programming Paradigms 04
(x0, y0) (x1, y1) (xa, ya)
Figure 4.10 The three key points in a c-curve of level greater than zero.
Level = 1
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CoSc 450: Programming Paradigms 04
(x0, y0) (x1, y1) (xa, ya)
Figure 4.10 The three key points in a c-curve of level greater than zero.
Level = 2
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CoSc 450: Programming Paradigms Sierpinski’s gasket — Exercise for the student 04
Figure 4.6 An example of Sierpinski’s gasket.