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2D Viewing

2D Viewing. 고려대학교 컴퓨터 그래픽스 연구실. Contents. 3 D Rendering Pipeline 2D Rendering Pipeline Clipping Cohen-Sutherland Line Clipping Sutherland-Hodgeman Polygon Clipping Viewport Transformation Scan Conversion Summary of Transformation. 3 D Rendering Pipeline. 3 D Primitives.

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2D Viewing

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  1. 2D Viewing 고려대학교 컴퓨터 그래픽스 연구실 cgvr.korea.ac.kr

  2. Contents • 3D Rendering Pipeline • 2D Rendering Pipeline • Clipping • Cohen-Sutherland Line Clipping • Sutherland-Hodgeman Polygon Clipping • Viewport Transformation • Scan Conversion • Summary of Transformation cgvr.korea.ac.kr

  3. 3D Rendering Pipeline 3D Primitives 3D Modeling Coordinates Model Transformation 3D World Coordinates Lighting 3D World Coordinates Viewing Transformation 3D ViewingCoordinates Projection Transformation 2D Projection Coordinates Clipping 2D Projection Coordinates Viewport Transformation 2D Device Coordinates Scan Conversion 2D Device Coordinates Image cgvr.korea.ac.kr

  4. 3D Rendering Pipeline 3D Primitives 3D Modeling Coordinates Model Transformation 3D World Coordinates Lighting 3D World Coordinates Viewing Transformation 3D Viewing Coordinates Projection Transformation 2D Projection Coordinates Clipping 2D Projection Coordinates Viewport Transformation 2D Device Coordinates Scan Conversion 2D Device Coordinates Image cgvr.korea.ac.kr

  5. 2D Rendering Pipeline 3D Primitives 2D Primitives Clipping Clip portions of geometric primitives residing outside window Viewport Transformation Transform the clipped primitives from screen to image coordinates Scan Conversion Fill pixel representing primitives in screen coordinates Image cgvr.korea.ac.kr

  6. 2D Rendering Pipeline 3D Primitives 2D Primitives Clipping Clip portions of geometric primitives residing outside window Viewport Transformation Transform the clipped primitives from screen to image coordinates Scan Conversion Fill pixel representing primitives in screen coordinates Image cgvr.korea.ac.kr

  7. Clipping • Avoid Drawing Parts of Primitives Outside Window • Window defines part of scene being viewed • Must draw geometric primitives only inside window World Coordinates cgvr.korea.ac.kr

  8. Clipping • Avoid Drawing Parts of Primitives Outside Window • Window defines part of scene being viewed • Must draw geometric primitives only inside window cgvr.korea.ac.kr

  9. Clipping • Avoid Drawing Parts of Primitives Outside Window • Points • Lines • Polygons • Circles • etc. cgvr.korea.ac.kr

  10. Point Clipping • Is Point(x,y) Inside the Clip Window? wy2 Inside = (x>=wx1) && (x<=wx2) && (y>=wy1) && (y<=wy2); (x, y) wy1 wx1 wx2 cgvr.korea.ac.kr

  11. Line Clipping • Find the Part of a Line Inside the Clip Window P7 P1 P4 P8 P3 P2 P6 P10 P5 P9 Before Clipping cgvr.korea.ac.kr

  12. Line Clipping • Find the Part of a Line Inside the Clip Window P’7 P’8 P4 P3 P6 P’5 After Clipping cgvr.korea.ac.kr

  13. Cohen-Sutherland Line Clipping • Use Simple Tests to Classify Easy Cases First P7 P1 P4 P8 P3 P2 P6 P10 P5 P9 cgvr.korea.ac.kr

  14. Cohen-Sutherland Line Clipping • Classify Some Lines Quickly by AND of Bit Codes Representing Regions of Two Endpoints (Must Be 0) P7 1001 0001 0101 Bit 4 P1 P4 P8 1000 0000 0100 P3 P2 P6 P10 Bit 3 1010 0010 0110 P5 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  15. Cohen-Sutherland Line Clipping • Classify Some Lines Quickly by AND of Bit Codes Representing Regions of Two Endpoints (Must Be 0) P7 1001 0001 0101 Bit 4 P1 P4 P8 1000 0000 0100 P3 P2 P6 P10 Bit 3 1010 0010 0110 P5 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  16. Cohen-Sutherland Line Clipping • Classify Some Lines Quickly by AND of Bit Codes Representing Regions of Two Endpoints (Must Be 0) P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 1010 0010 0110 P5 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  17. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 1010 0010 0110 P5 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  18. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 1010 0010 0110 P5 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  19. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  20. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  21. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  22. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly P7 1001 0001 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  23. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  24. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P4 P8 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  25. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  26. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  27. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  28. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 1010 0010 0110 P9 Bit 1 Bit 2 cgvr.korea.ac.kr

  29. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 P’9 1010 0010 0110 Bit 1 Bit 2 cgvr.korea.ac.kr

  30. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 P10 Bit 3 P’5 P’9 1010 0010 0110 Bit 1 Bit 2 cgvr.korea.ac.kr

  31. Cohen-Sutherland Line Clipping • Compute Intersections with Window Boundary for Lines That Can’t be Classified Quickly 1001 0001 P’7 0101 Bit 4 P’8 P4 1000 0000 0100 P3 P6 Bit 3 P’5 1010 0010 0110 Bit 1 Bit 2 cgvr.korea.ac.kr

  32. Polygon Clipping • Find the Part of a Polygon Inside the Clip Window? Before Clipping cgvr.korea.ac.kr

  33. Polygon Clipping • Find the Part of a Polygon Inside the Clip Window? After Clipping cgvr.korea.ac.kr

  34. Sutherland-Hodgeman Polygon Clipping • Clip to Each Window Boundary One at a Time cgvr.korea.ac.kr

  35. Sutherland-Hodgeman Polygon Clipping • Clip to Each Window Boundary One at a Time cgvr.korea.ac.kr

  36. Sutherland-Hodgeman Polygon Clipping • Clip to Each Window Boundary One at a Time cgvr.korea.ac.kr

  37. Sutherland-Hodgeman Polygon Clipping • Clip to Each Window Boundary One at a Time cgvr.korea.ac.kr

  38. Sutherland-Hodgeman Polygon Clipping • Clip to Each Window Boundary One at a Time cgvr.korea.ac.kr

  39. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside Outside P5 P3 P4 cgvr.korea.ac.kr

  40. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside Outside P5 P3 P4 cgvr.korea.ac.kr

  41. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside Outside P5 P3 P4 cgvr.korea.ac.kr

  42. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside Outside P5 P3 P4 cgvr.korea.ac.kr

  43. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside P’ Outside P5 P3 P4 cgvr.korea.ac.kr

  44. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside P’ Outside P5 P3 P4 cgvr.korea.ac.kr

  45. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside P’ Outside P5 P3 P4 cgvr.korea.ac.kr

  46. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside P’ P” Outside P5 P3 P4 cgvr.korea.ac.kr

  47. Clipping to a Boundary • Do Inside Test for Each Point in Sequence, Insert New Points When Cross Window Boundary, Remove Points Outside Window Boundary P2 P1 Window Boundary Inside P’ P” Outside cgvr.korea.ac.kr

  48. 2D Rendering Pipeline 3D Primitives 2D Primitives Clipping Clip portions of geometric primitives residing outside window Viewport Transformation Transform the clipped primitives from screen to image coordinates Scan Conversion Fill pixel representing primitives in screen coordinates Image cgvr.korea.ac.kr

  49. Viewport Transformation • Transform 2D Geometric Primitives from Screen Coordinate System (Projection Coordinates) to Image Coordinate System (Device Coordinates) Image Screen Viewport cgvr.korea.ac.kr

  50. Window vs. Viewport • Window • World-coordinate area selected for display • What is to be viewed • Viewport • Area on the display device to which a window is mapped • Where it is to be displayed cgvr.korea.ac.kr

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