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2D Viewing 고려대학교 컴퓨터 그래픽스 연구실
Contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
3D Rendering Pipeline Model Transformation Lighting Viewing Transformation Projection Transformation Clipping Viewport Transformation Scan Conversion 3D Primitives Image 3D Modeling Coordinates 3D World Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Projection Coordinates 2D Device Coordinates 2D Device Coordinates
3D Rendering Pipeline Model Transformation Lighting Viewing Transformation Projection Transformation Clipping Viewport Transformation Scan Conversion 3D Primitives Image 3D Modeling Coordinates 3D World Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Projection Coordinates 2D Device Coordinates 2D Device Coordinates
2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives  residing outside window Transform the clipped primitives  from screen to image coordinates Fill pixel representing primitives  in screen coordinates 2D Primitives
2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives  residing outside window Transform the clipped primitives  from screen to image coordinates Fill pixel representing primitives  in screen coordinates 2D Primitives
Clipping ,[object Object],[object Object],[object Object],World Coordinates
Clipping ,[object Object],[object Object],[object Object]
Clipping ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Point Clipping  ,[object Object],(x, y) wx2 wx1 wy1 wy2 Inside = (x>=wx1) && (x<=wx2) && (y>=wy1) && (y<=wy2);
Line Clipping ,[object Object],P 7 P 8 P 10 P 9 P 1 P 2 P 5 P 4 P 3 P 6 Before Clipping
Line Clipping ,[object Object],After Clipping P 4 P 3 P 6 P’ 8 P’ 7 P’ 5
Cohen-Sutherland Line Clipping ,[object Object],P 7 P 8 P 10 P 9 P 1 P 2 P 5 P 4 P 3 P 6
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 5 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 P 1 P 2 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 5 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 P 1 P 2 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 5 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 5 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 5 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 7 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 P 8 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 P 9 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8
Cohen-Sutherland Line Clipping ,[object Object],P 10 P 6 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8 P’ 9
Cohen-Sutherland Line Clipping ,[object Object],P 6 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8 P 10 P’ 9
Cohen-Sutherland Line Clipping ,[object Object],P 6 0001 0101 0100 0110 0010 0000 1010 1000 1001 P 4 P 3 Bit 4 Bit 3 Bit 2 Bit 1 P’ 5 P’ 7 P’ 8
Polygon Clipping ,[object Object],Before Clipping
Polygon Clipping ,[object Object],After Clipping
Sutherland-Hodgeman Polygon Clipping ,[object Object]
Sutherland-Hodgeman Polygon Clipping ,[object Object]
Sutherland-Hodgeman Polygon Clipping ,[object Object]
Sutherland-Hodgeman Polygon Clipping ,[object Object]
Sutherland-Hodgeman Polygon Clipping ,[object Object]
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary P’
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary P’
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary P’
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 P 3 P 4 P 5 Inside Outside Window  Boundary P’ P”
Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 Inside Outside Window  Boundary P’ P”
2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives  residing outside window Transform the clipped primitives  from screen to image coordinates Fill pixel representing primitives  in screen coordinates 2D Primitives
Viewport Transformation ,[object Object],Screen Image Viewport
Window vs. Viewport ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Viewport Transformation ,[object Object],(wx, wy) wx2 wx1 wy1 wy2 (vx, vy) vx2 vx1 vy1 vy2 Window Viewport Screen Coordinates Image Coordinates vx = vx1 + (wx – wx1) * (vx2 – vx1) / (wx2 – wx1); vy = vy1 + (wy – wy1) * (vy2 – vy1) / (wy2 – wy1);
2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives  residing outside window Transform the clipped primitives  from screen to image coordinates Fill pixel representing primitives  in screen coordinates 2D Primitives
Scan Conversion ,[object Object],[object Object],[object Object],[object Object],P 1 P 2 P 3
Triangle Scan Conversion ,[object Object],[object Object],[object Object],[object Object],L 1 L 2 L 3 P
Triangle Scan Conversion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],dx dy
Polygon Scan Conversion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Inside Polygon Rule ,[object Object],[object Object],Convex Polygon Concave Polygon L 1 L 2 L 3 L 4 L 5 L 1 L 2 L 3 L 4 L 5A L 5B
Inside Polygon Rule ,[object Object],[object Object],Concave Self-Intersecting With Holes
Polygon Scan Conversion ,[object Object],[object Object],Triangle Polygon
Polygon Scan Conversion ,[object Object],[object Object]
Summary of Transformation P(x, y, z) Viewing  Transformation Projection  Transformation Window-to-Viewport  Transformation P(x, y) Modeling  Transformation 3D Object Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Device Coordinates

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2D viewing

  • 1. 2D Viewing 고려대학교 컴퓨터 그래픽스 연구실
  • 2.
  • 3. 3D Rendering Pipeline Model Transformation Lighting Viewing Transformation Projection Transformation Clipping Viewport Transformation Scan Conversion 3D Primitives Image 3D Modeling Coordinates 3D World Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Projection Coordinates 2D Device Coordinates 2D Device Coordinates
  • 4. 3D Rendering Pipeline Model Transformation Lighting Viewing Transformation Projection Transformation Clipping Viewport Transformation Scan Conversion 3D Primitives Image 3D Modeling Coordinates 3D World Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Projection Coordinates 2D Device Coordinates 2D Device Coordinates
  • 5. 2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives residing outside window Transform the clipped primitives from screen to image coordinates Fill pixel representing primitives in screen coordinates 2D Primitives
  • 6. 2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives residing outside window Transform the clipped primitives from screen to image coordinates Fill pixel representing primitives in screen coordinates 2D Primitives
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  • 48. 2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives residing outside window Transform the clipped primitives from screen to image coordinates Fill pixel representing primitives in screen coordinates 2D Primitives
  • 49.
  • 50.
  • 51.
  • 52. 2D Rendering Pipeline 3D Primitives Clipping Viewport Transformation Scan Conversion Image Clip portions of geometric primitives residing outside window Transform the clipped primitives from screen to image coordinates Fill pixel representing primitives in screen coordinates 2D Primitives
  • 53.
  • 54.
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  • 61. Summary of Transformation P(x, y, z) Viewing Transformation Projection Transformation Window-to-Viewport Transformation P(x, y) Modeling Transformation 3D Object Coordinates 3D World Coordinates 3D Viewing Coordinates 2D Projection Coordinates 2D Device Coordinates