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Graphics Pipeline Rasterization

Graphics Pipeline Rasterization. CMSC 435/634. Drawing Terms. Primitive Basic shape, drawn directly Compare to building from simpler shapes Rasterization or Scan Conversion Find pixels for a primitive Usually for algorithms that generate all pixels for one primitive at a time

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Graphics Pipeline Rasterization

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  1. Graphics PipelineRasterization CMSC 435/634

  2. Drawing Terms • Primitive • Basic shape, drawn directly • Compare to building from simpler shapes • Rasterization or Scan Conversion • Find pixels for a primitive • Usually for algorithms that generate all pixels for one primitive at a time • Compare to ray tracing: all primitives for one pixel

  3. Line Drawing • Given endpoints of line, which pixels to draw?

  4. Line Drawing • Given endpoints of line, which pixels to draw?

  5. Line Drawing • Given endpoints of line, which pixels to draw? • Assume one pixel per column (x index), which row (y index)? • Choose based on relation of line to midpoint between candidate pixels ? ? ? ? ? ? ? ?

  6. Line Drawing • Choose with decision variable • Plug midpoint into implicit line equation • Incremental update

  7. Line Drawing • Implicit line equation • Midpoint algorithm y = y0 d = f(x0+1, y0+0.5) for x = x0 to x1 draw(x,y) if (d < 0) then y = y+1 d = d + (x1 - x0) + (y0 - y1) else d = d + (y0 - y1)

  8. Polygon Rasterization • Problem • How to generate filled polygons (by determining which pixel positions are inside the polygon) • Conversion from continuous to discrete domain • Concepts • Spatial coherence • Span coherence • Edge coherence

  9. Scanning Rectangles for ( y from y0 to y1) for ( x from x0 to x1) Write Pixel (x, y)

  10. Scanning Rectangles (2) for ( y from y0 to y1) for ( x from x0 to x1) Write Pixel (x, y)

  11. Scanning Rectangles (3) for ( y from y0 to y1) for ( x from x0 to x1) Write Pixel (x, y)

  12. Triangle Rasterization • Barycentric coordinates are decision variables

  13. Barycentric Triangle Rasterization For all x in xmin to xmax do For all y in ymin to ymaxdo Compute (a, b, g) for (x,y) If (a≥ 0 and b≥ 0 and g≥ 0) then c = ac0 + bc1 + gc2 Draw pixel(x,y) with color c

  14. “Clipless” Homogeneous Rasterization • Compute barycentrics using homogeneous coordinates • Extra edge equations for clip edges • Compute t for clip plane at each vertex • Only visible (w>near) pixels will be drawn • Adds computation • Divide by w per pixel instead of per vertex • But avoids branching and extra triangles • Good for hardware

  15. Homogeneous Barycentrics • Each barycentric coordinate is a linear function of X and Y • It is 1 at one vertex and 0 at the other two

  16. Homogeneous Barycentrics • Write formula for barycentric coordinate in homogeneous form • This defines a system of three equations

  17. Homogeneous Barycentrics • Know • Simplifies the linear equation to • Which we can solve:

  18. Incremental Computation • a, b, and g are linear in X and Y • What about pixel-to-pixel updates?

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