This document discusses algorithms for clipping circles and curves to a bounding region. It describes a fast circle clipping algorithm that uses an accept/reject test to determine whether points are inside or outside the clipping region. It also discusses a midpoint circle algorithm that uses incremental steps to scan convert circles. Finally, it explains that curved objects can be clipped by first testing if their bounding rectangles overlap the clipping region before solving nonlinear equations to find curve-window intersection points.

1. Circle & Curve Clipping Algorithm Presented By : Mohamed El-Serngawy

2. Outline Fast Circle Clipping Algorithm Clipping Circle By Accept/Reject Test

3. Fast Circle Clipping Algorithm Introduction:

4. Fast Circle Clipping Algorithm Algorithm

5. Fast Circle Clipping Algorithm Algorithm

6. Fast Circle Clipping Algorithm Algorithm

7. Fast Circle Clipping Algorithm Algorithm

8. Fast Circle Clipping Algorithm Algorithm

9. Clipping Circle By Accept/Reject Test 1-Scan Conversion of Circles 2-Write Points(x,y) 3-Clipping Circles

10. Midpoint Circle Algorithm Choose E as the next pixel if M lies inside the circle, and SE otherwise. d = d<0: Select E dnew = d + (2xp+3) d>0: Select SE dnew = d + (2xp–2yp+5) E M SE xp xp+1

11. Midpoint Circle Algorithm Start with P (x = 0, y = r). Compute d for the first midpoint at (1, r - ½): d = F(1, r - ½) = 5/4 - r While (x < y) { If (d <= 0) // E is chosen d = d + 2 * x + 3 Else // SE is chosen y = y – 1 d = d + 2 * x – 2 * y + 5 x = x+1; WritePixel (x, y) }

12. Write Points(x,y) Writes pixels to the seven other octants

13. Clipping Circles Accept/Reject test – Does bounding box of the circle intersect with clipping box? If yes, condition pixel write on clipping box inside/outside test Also we can test Circle points by Point Clipping . -the point P=(x, y) is display in clipping Boundry if xmin< x <xmaxandymin<y<ymax

14. Curve Clipping Areas with curved boundaries can be clipped with methods similar to those discussed in the previous .sections. Curve-clipping procedures will involve nonlinear equations, however, and this requires more processing than for objects with linear boundaries. The bounding rectangle for a circle or other curved object can be used first to test for overlap with a rectangular clip window. If the bounding rectangle for the object is completely inside the window, we save the object. If the rectangle is determined to be completely outside the window, we discard the object. In either case, there is no further computation necessary. But if the bounding rectangle test fails, we can look for other computation-saving approaches. For a circle, we can use the coordinate extents of individual quadrants and then octants for preliminary testing before calculating curve-window intersections. For an ellipse, we can test the coordinate extents of individual quadrants. Figure blew illustrates circle clipping against a rectangular window.

15. Curve Clipping Similar procedures can be applied when clipping a curved object against a general polygon clip region. On the first pass, we can clip the bounding rectangle of the object against the bounding rectangle of the clip region. If the two regions overlap, we will need to solve the simultaneous line-curve equations to obtain the clipping intersection points.