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Efficient Clipping Algorithms in Computer Graphics

Learn about clipping objects within a defined window to optimize rendering. Explore point and line clipping algorithms like Cohen-Sutherland for accurate visualization.

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Efficient Clipping Algorithms in Computer Graphics

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  1. Clipping Lines Dr. Scott Schaefer

  2. Why Clip? • We do not want to waste time drawing objects that are outside of viewing window (or clipping window)

  3. Clipping Points • Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn (xmax,ymax) (x,y) (xmin,ymin)

  4. Clipping Points • Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn (xmax,ymax) (x,y) xmin<=x<=xmax? (xmin,ymin) ymin<=y<=ymax?

  5. Clipping Points • Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn (xmax,ymax) (x2,y2) (x1,y1) xmin<=x<=xmax? (xmin,ymin) ymin<=y<=ymax?

  6. Clipping Points • Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn (xmax,ymax) (x2,y2) (x1,y1) xmin<=x1<=xmax Yes (xmin,ymin) ymin<=y1<=ymaxYes

  7. Clipping Points • Given a point (x, y) and clipping window (xmin, ymin), (xmax, ymax), determine if the point should be drawn (xmax,ymax) (x2,y2) (x1,y1) xmin<=x2<=xmaxNo (xmin,ymin) ymin<=y2<=ymax Yes

  8. Clipping Lines

  9. Clipping Lines

  10. Clipping Lines • Given a line with end-points (x0, y0), (x1, y1) and clipping window (xmin, ymin), (xmax, ymax), determine if line should be drawn and clipped end-points of line to draw. (xmax,ymax) (x1, y1) (x0, y0) (xmin,ymin)

  11. Clipping Lines

  12. Clipping Lines – Simple Algorithm • If both end-points inside rectangle, draw line • Otherwise, intersect line with all edges of rectangle clip that point and repeat test

  13. Clipping Lines – Simple Algorithm

  14. Clipping Lines – Simple Algorithm

  15. Clipping Lines – Simple Algorithm

  16. Clipping Lines – Simple Algorithm

  17. Clipping Lines – Simple Algorithm

  18. Clipping Lines – Simple Algorithm

  19. Clipping Lines – Simple Algorithm

  20. Clipping Lines – Simple Algorithm

  21. Clipping Lines – Simple Algorithm

  22. Clipping Lines – Simple Algorithm

  23. Clipping Lines – Simple Algorithm

  24. Window Intersection (x1, y1), (x2, y2) intersect with vertical edge at xright • yintersect = y1 + m(xright – x1) where m=(y2-y1)/(x2-x1) (x1, y1), (x2, y2) intersect with horizontal edge at ybottom • xintersect = x1 + (ybottom – y1)/m where m=(y2-y1)/(x2-x1)

  25. Clipping Lines – Simple Algorithm • Lots of intersection tests makes algorithm expensive • Complicated tests to determine if intersecting rectangle • Is there a better way?

  26. Trivial Accepts • Big Optimization: trivial accepts/rejects • How can we quickly decide whether line segment is entirely inside window • Answer: test both endpoints

  27. Trivial Accepts • Big Optimization: trivial accepts/rejects • How can we quickly decide whether line segment is entirely inside window • Answer: test both endpoints

  28. Trivial Rejects • How can we know a line is outside of the window • Answer: both endpoints on wrong side of same edge, can trivially reject the line

  29. Trivial Rejects • How can we know a line is outside of the window • Answer: both endpoints on wrong side of same edge, can trivially reject the line

  30. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments

  31. Cohen-Sutherland Algorithm • Every end point is assigned to a four-digit binary value, i.e. Region code • Each bit position indicates whether the point is inside or outside of a specific window edge bit 4 bit 3 bit 2 bit 1 top bottom right left

  32. Cohen-Sutherland Algorithm

  33. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments

  34. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments

  35. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments Line is outside the window! reject

  36. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments Line is inside the window! draw

  37. Cohen-Sutherland Algorithm • Classify p0, p1 using region codes c0, c1 • If , trivially reject • If , trivially accept • Otherwise reduce to trivial cases by splitting into two segments

  38. Cohen-Sutherland Algorithm

  39. Cohen-Sutherland Algorithm

  40. Cohen-Sutherland Algorithm

  41. Cohen-Sutherland Algorithm

  42. Cohen-Sutherland Algorithm

  43. Cohen-Sutherland Algorithm

  44. Cohen-Sutherland Algorithm

  45. Cohen-Sutherland Algorithm

  46. Cohen-Sutherland Algorithm

  47. Cohen-Sutherland Algorithm

  48. Cohen-Sutherland Algorithm

  49. Cohen-Sutherland Algorithm

  50. Cohen-Sutherland Algorithm

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