viewing transformation
TRANSCRIPT
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Good for mapping objects from one coordinate system
to another
This is what we do with windows and viewports
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Model of objectsworld coordinates: km, mm, etc.
hierarchical models:
human = torso + arm + arm + head + leg + leg
arm = upperarm + lowerarm + hand …
Viewingzoom in, move drawing, etc.
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Viewport:
Area on screen to be used for drawing.
Unit: pixels (screen coordinates)
Note: y-axis often points down
Window:
Virtual area to be used by application
Unit: km, mm,… (world coordinates)
(0,0)
(800,600)
(200,200)
(600,400)
(-2,-1)
(2,1)
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Determine a matrix M, such that the window (wx1, wx2, wy1, wy2) is mapped on the viewport (vx1, vx2, vy1, vy2):
A = T(-wx1, -wy1)
B = S(1/(wx2-wx1), 1/(wy2-wy1)) A
C = S(vx2-vx1 ,vy2-vy1)B
M = T(vx1, vy1) C
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),(minmin yx
),(maxmax vu
),(minmin vu
),(maxmax yx
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yyvv
xxuu
yx
vu
xx
y
x
y
x
minmax
minmax
minmax
minmax
min
min
min
min
,where
1100
10
01
100
00
00
100
10
01
,
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