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Unformatted text preview: · w = P · w Or, in matrix notation:
• Or, in matrix notation: !
0 t1 0
Or, in matrix notation:
!
Px
ux uy
0 t1 0
BPytC B vx vy
B PxC = B ux uy
@PztA @wx wy
BPty C B vx vy
B C=B
0
0
1t
@Pz A @wx wy
0
0
1
Graphics Lecture 2: Slide 38 ! uz
vzz
u
wz
vz
0
wz
0 Cv
C ·· w
C·w 10 1
C·u
Px
10 1
C ·· v C BPy C
C uC B PxC
C ··wA @PzyA
C v C BP C
CB C
1 · w A @ Pz A
1
C
1
1
37 / 45 Verticals revisited …!
Verticals revisited . . .
Unlike the previous analysis we now can control the
vertical !
Unlike the previous analysis we now can control the vertical
!
i.e. we can assumethe vdirection is the is the vertical and
I.e. we can assume the vdirection vertical and constrain it
constrain software to software to be upwards !
in the it in the be upwards Graphics Lecture 2: Slide 39 !
38 / 45 Back to ﬂying sequences
Back to ﬂying sequences
We now return to the original problem
Back to viewpoint point C and !
We I Given a ﬂyingoriginal problema view direction d, we need to
now return to the sequences
I Given the transformationC and athat gives us the , we need to
ﬁnd a viewpoint point matrix view direction d canonical
• view.now return to the original gives us !
We
ﬁnd the transformation matrix thatproblem the canonical
–
view. Given a viewpoint point the vectors direction w.
I We do this by ﬁrst ﬁnding C and a viewu, v and d, we need to ﬁnd
the transformation matrix that gives us the canonical view. !
I We do this by ﬁrst ﬁnding the vectors u, v and w .
– We do this by ﬁrst ﬁnding the vectors u, v and w. ! We knowknow that dthethe direction of thenew
We that d is is direction of the new
z that is can write immediately
z knowso we dwe the direction of the !
Weaxis,axis, socan write immediately new
z axis, ! we can write immediately
so
d
w=
d d

w=
d 39 / 45 Graphics Lecture 2: Slide 40 !
39 / 45 Now the horizontal direction
the horizontal direction
Now Now the horizontal direction !
We We write u in terms of some some vector horizontal
• can can u in u in of s...
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This document was uploaded on 03/26/2014.
 Spring '14

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