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$Assignment 2: Math Review$

Bad Idea Simplest (and fastest) approach is to compute texture coordinates for polygon vertices and interpolate in screen space. This gives the image on the right. 7 7 Undoing Homogenization Let P i = (x i ,y i ,z i ,h i ) be the i th point of some polygon, after projection, but before homogenization The homogenized point S i = P i /h is the location of on the screen. P i Let X be a point we wish to shade, we have its barycentric coordinates in screen space: X = ! b i S i i 8 8
Undoing Homogenization We know We also know that there exist weights , such that X = (! a i P i )/(! a j h j ) i j Combining the above we have a j h j ) ! i ! i S i = P i /h b i S i = X = (! i b i (P i /h i ) = (! i a i P i )/(! j a i P i )/(! j a j h j ) a i 9 9 Undoing Homogenization b i /h i = a i /(! a j h j ) j a j h j )/h i = a i b i (! j b i (! a j h j )/h i − a i = 0 j ∀i ∀i This is a linear system in ∀i Unfortunately is is non-invertible, so... a i 10 10
Page 1 and 2: CS-184: Computer Graphics Lecture #
Page 3: Barycentric Coordinates X can be ex
Page 7 and 8: Bump Mapping The idea is to perturb
Page 9 and 10: Shadow Maps For each polygon Render
Page 11 and 12: Alpha Channels Alpha channel stores

CS-184: Computer Graphics Today - Inst.eecs.berkeley.edu ...

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