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CSCE 441 Computer Graphics: Clipping Lines Jinxiang Chai

CSCE 441 Computer Graphics: Clipping Lines Jinxiang Chai. GL_LINES. GL_POLYGON. GL_LINE_STRIP. GL_LINE_LOOP. GL_POINTS. GL_TRIANGLES. GL_QUADS. GL_TRIANGLE_FAN. GL_TRIANGLE_STRIP. GL_QUAD_STRIP. OpenGL Geometric Primitives. All geometric primitives are specified by vertices. Why Clip?.

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CSCE 441 Computer Graphics: Clipping Lines Jinxiang Chai

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  1. CSCE 441 Computer Graphics:Clipping LinesJinxiang Chai

  2. GL_LINES GL_POLYGON GL_LINE_STRIP GL_LINE_LOOP GL_POINTS GL_TRIANGLES GL_QUADS GL_TRIANGLE_FAN GL_TRIANGLE_STRIP GL_QUAD_STRIP OpenGL Geometric Primitives • All geometric primitives are specified by vertices

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

  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,ymin)

  5. 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?

  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=<x<=xmax? (xmin,ymin) ymin=<y<=ymax?

  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=<x1<=xmax Yes (xmin,ymin) ymin=<y1<=ymaxYes

  8. 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

  9. Clipping Lines

  10. Clipping Lines

  11. 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)

  12. Clipping Lines

  13. Outline • Simple line clipping algorithm • Cohen-Sutherland • Liang-Barsky • Required readings: HB 8-5, 8-6, 8-7 and 8-9

  14. Clipping Lines

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

  16. Clipping Lines – Simple Algorithm

  17. Clipping Lines – Simple Algorithm

  18. Intersecting Two Lines

  19. Intersecting Two Lines

  20. Intersecting Two Lines

  21. Intersecting Two Lines

  22. Intersecting Two Lines

  23. Intersecting Two Lines Substitute t or s back into equation to find intersection

  24. Clipping Lines – Simple Algorithm

  25. Clipping Lines – Simple Algorithm

  26. Clipping Lines – Simple Algorithm

  27. Clipping Lines – Simple Algorithm

  28. Clipping Lines – Simple Algorithm

  29. Clipping Lines – Simple Algorithm

  30. Clipping Lines – Simple Algorithm

  31. Clipping Lines – Simple Algorithm

  32. Clipping Lines – Simple Algorithm

  33. Clipping Lines – Simple Algorithm

  34. Clipping Lines – Simple Algorithm

  35. Clipping Lines – Simple Algorithm

  36. Clipping Lines – Simple Algorithm

  37. Clipping Lines – Simple Algorithm

  38. Clipping Lines – Simple Algorithm

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

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

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

  42. Trivial Rejects • How can we know a line is outside of the window • Answer:

  43. Trivial Rejects • How can we know a line is outside of the window • Answer: Wrong side

  44. 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

  45. 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

  46. 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 edges bit 4 bit 3 bit 2 bit 1 top bottom right left If inside, set the corresponding bit to 0; otherwise set it to 1.

  47. Cohen-Sutherland Algorithm bit 4 bit 3 bit 2 bit 1 top bottom right left top right left Region code? bottom

  48. Cohen-Sutherland Algorithm bit 4 bit 3 bit 2 bit 1 top bottom right left top right left 0010 bottom ?

  49. Cohen-Sutherland Algorithm bit 4 bit 3 bit 2 bit 1 top bottom right left top right left 0010 bottom 0100

  50. Cohen-Sutherland Algorithm

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