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Edge Equations: Interpolating Color Given redness at the 3 vertices, set up the linear system of equations: The solution works out to: Edge Equations:Interpolating Color Notice that the columns in the matrix are exactly the coefficients of the edge equations! So the setup cost per parameter is basically a matrix multiply Per-pixel cost (the inner loop) cost equates to tracking another edge equation value (which is?) A: 1 add Pros and Cons of Edge Equations Pros If you have the right hardware (PixelPlanes) then it is very fast Fast tests Easy to interpolate colors Cons Can be expensive if you don’t have hardware 50% efficient Recap P0 P1 P2 P1 P2 P0 Content Line Rasterization Circle Rasterization Triangle Rasterization Polygon Rasterization General Polygon Rasterization Now that we can rasterize triangles, what about general polygons? We’ll take an edge-walking approach Triangle Rasterization Issues Sliver Moving Slivers Triangle Rasterization Issues Triangle Rasterization Issues Shared Edge Ordering Polygon Rasterization We want to fill every pixel covered by the polygon those pixel inside the triangle edges should be exactly lit what about the pixels exactly on the edge we need a consistent (if arbitrary) rule And we need to be really careful! suppose we have two adjacent polygons we don’t want any overlap or any cracks visit every covered pixel exactly once General Polygon Rasterization Consider the following polygon: How do we know whether a given pixel on the scanline is inside or outside the polygon? A B C D E F Polygon Rasterization Inside-Outside Points Polygon Rasterization Inside-Outside Points General Polygon Rasterization Basic idea: use a parity test for each scanline edgeCnt = 0; for each pixel on scanline (l to r) if (oldpixel-newpixel crosses edge) edgeCnt ++; // draw the pixel if edgeCnt odd if (edgeCnt % 2) setPixel(pixel); What’s the Inside of a Polygon? This is not obvious when
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