8.5.10 Texturing
The texture unit can cover any primitive with a picture. The picture can be
stretched, shared, rotated and translated with the texture unit in one step. To
avoid aliasing the result can be filtered bilinear in u and v directions.
8.5.10.1
Mathematical background
The arbitrary mapping problem is completely determined by a mapping from 3
points in object space (x,y) to 3 points in texture space (u,v).
Let there be the following mapping:
=
=
⇒
=
=
=
⇒
=
=
=
⇒
=
h
v
u
p
y
x
p
w
v
u
p
y
x
p
v
u
p
y
x
p
0
~
0
~
0
0
~
2
2
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
0
While w is the width of the texture and h is the height of the texture.
Examine the following picture in object space. To simplify calculations the
difference vectors are taken for calculations:
0
2
2
0
1
1
p
p
d
p
p
d
−
=
−
=
This is equivalent to transforming from coordinate system O to coordinate system
O’.
Drawing Engine
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