2.7 (optional)

# 2.7 (optional) - 2.7 Applications to Computer Graphics...

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Unformatted text preview: 2.7 Applications to Computer Graphics Computer graphics - Concerned with digitally synthesizing and manipulating visual content subfields: • geometry – study ways to represent and process surfaces • animation – study ways to represent and manipulate motion • rendering – study algorithms to reproduce light transport • imaging – study image acquisition or image editing We’ll look at some basic aspects of first & last of these. A first principle: objects in CG are normally collections of straight line seg- ments – linear transformations map them to other line segments. Ex: Take letter “N” as 8 straight lines with 8 vertices, see how various trans- formations modify it. 1 2 3 4 5 6 7 8 Store 8 vertices in data matrix D = bracketleftbigg . 5 . 5 6 6 5 . 5 5 . 5 6 . 42 0 8 8 1 . 58 8 bracketrightbigg x y vertex 1 2 3 4 5 6 7 8 Apply SHEAR transformation A = bracketleftbigg 1 0 . 25 1 bracketrightbigg AD = bracketleftbigg . 5 2 . 105 6 8 7 . 5 5 . 895 2 6 . 42 0 8 8 1 . 58 8 bracketrightbigg x y vertex 1 2 3 4 5 6 7 8 1 1 2 3 4 5 6 7 8 SHRINK width of this italic N with S = bracketleftbigg . 75 0 1 bracketrightbigg , so composite trans- formation is SA = bracketleftbigg . 75 0 1 bracketrightbiggbracketleftbigg 1 0 . 25 1 bracketrightbigg = bracketleftbigg . 75 0 . 1875 1 bracketrightbigg 1 2 3 4 5 6 7 8 ROTATE counterclockwise with R = bracketleftbigg cos θ- sin θ sin θ cos θ bracketrightbigg for θ = 90 ◦ , so R = bracketleftbigg- 1 1 bracketrightbigg and composite transformation is RSA = bracketleftbigg- 1 1 bracketrightbiggbracketleftbigg . 75 0 . 1875 1 bracketrightbigg = bracketleftbigg- 1 .....
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2.7 (optional) - 2.7 Applications to Computer Graphics...

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