2.7 (optional)

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 .....
View Full Document

{[ snackBarMessage ]}

Page1 / 11

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online