2D viewing

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

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 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 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 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]

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’ P”

Clipping to a Boundary ,[object Object],[object Object],P 1 P 2 Inside Outside Window Boundary P’ P”

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);

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

2D viewing

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