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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

  1. CoSc 450: Programming Paradigms 04 Orders of Growth and Tree Recursion

  2. CoSc 450: Programming Paradigms 04 Graphics primitive operations

  3. CoSc 450: Programming Paradigms 04 Graphics primitive operations y 1 x -1 0 1 -1 Co-ordinate system

  4. CoSc 450: Programming Paradigms 04 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))))))))

  5. CoSc 450: Programming Paradigms 04 C-Curve code (define c-curve (lambda (x0 y0 x1 y1 level) Base case (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))))))))

  6. CoSc 450: Programming Paradigms 04 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

  7. CoSc 450: Programming Paradigms 04 (x1, y1) (xa, ya) (x0, y0) The three key points in a c-curve of level greater than zero. Figure 4.10

  8. CoSc 450: Programming Paradigms 04 (x1, y1) Level = 0 (xa, ya) (x0, y0) The three key points in a c-curve of level greater than zero. Figure 4.10

  9. CoSc 450: Programming Paradigms 04 (x1, y1) Level = 1 (xa, ya) (x0, y0) The three key points in a c-curve of level greater than zero. Figure 4.10

  10. CoSc 450: Programming Paradigms 04 (x1, y1) Level = 2 (xa, ya) (x0, y0) The three key points in a c-curve of level greater than zero. Figure 4.10

  11. CoSc 450: Programming Paradigms 04 Sierpinski’s gasket — Exercise for the student An example of Sierpinski’s gasket. Figure 4.6

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