1. Type to enter a caption.
Computer Graphics
Week 2 Lecture 1

2. Circle Drawing ALGORITHM

3. Basics Cartesian Equation: x2+y2=r2 or f(x,y)= x2+y2-r2 = 0
In terms of trigonometric functions:
x=r sin θ
y=r cos θ
for 00<=θ<3600

4. Basics F(x1,y1) = x12+y12-r2 = 0 → Point lies on the circle
F(x2,y2) = x22+y22-r2 > 0 → Point lies outside the circle
F(x3,y3) = x32+y32-r2 < 0 → Point lies inside the circle

5. 8 Way Symmetry
In circle if we just draw points in one octant we can get points in rest of the octants by suitable reflections

6. 8 Way Symmetry

7. Bresenham Algorithm We will calculate in just 2nd octant
Assume starting pixel P is on y-axis
To find next pixel , see if M is inside or outside of circle
if d <=0 choose E , else choose SE
deltaE = 2xp + 3
deltaSE =2(xp-yp)+5

8. dstart In start xp=0 and yp=R (radius)
f(M) = f(xp+1, yp - 1/2) = f(0+1,R-1/2) = dstart
dstart = 1-R

9. Pseudo Code

10. Filling Rectangles for (ymin to ymax) for (xmin to xmas)
WritePixel(x,y,value)
ymax
ymin
xmin
xmax

11. Pattern Filling

12. Line Styles Define the line style as a 16-bit , bit string
if(bitstring[i%16])
WritePixel(x,y,value);

13. Thickening Primitives
3 techniques are used:
Replicating Pixels
Moving Pen
Filling area between 2 boundaries

14. Replicating Pixels

15. Moving Pen

16. Filling Area b/w Boundaries

17. The End

19. Slide 1

20. Text

21. TEXT
[TEXT]

22. Text

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–Johnny Appleseed