Making the Applications Interesting - Essentials of Interactive Computer Graphics - page 341

uv=(0,0) uv=(1,0)

Y

xy=(-1,1)

xy=(cosθ, sinθ)

U

cosθ

u= 0.5x + 0.5

sinθ

θ

X

v= 1 - (0.5y + 0.5)

xy=(-1,-1) xy=(1,-1) uv=(0,1) uv=(1,1)

V

Figure 12.18.

The circle xy position and uv texture placement.

( DrawUnitCirce() ). At label A, we see the declaration of four vertices with the
new vertex format ( DeviceVertexFormat ) from Listing 12.8. At label B, each
vertex is assigned with the corresponding geometric xy values and the appropriate
uv texture-placement values according to Figure 12.14. At label C, we first inform
the API about the vertex format with the SetFVF() function, and then we draw
the vertices as a triangle-fan. At label D, we compute the geometric xy vertex
positions for the unit circle, whereas the uv texture placements are computed at
label F. The left side of Figure 12.18 shows the xy position of a circle with unit
radius centered around the origin. The right side of Figure 12.18 shows that our
uv texture placement strategy is to maximize the image in the circle. In this case,
the xy coordinate space covered by the circle is

⎧
⎨

center =( c x , c y )=( 0 , 0 ) ,

xy geometric range = = = . ,

width W x 2 0

⎩

height = H y = 2 . 0 ,

and our texture-placement strategy is to define the same circle to occupy the max-
imum uv texture coordinate space, or

Coordinate transformation.
See Figure 10.16 (on p. 273)
and Equation (10.14), where
we learned about transforming
positions

⎧
⎨

=( , )=( . , . ) ,

center c u c v 0 5 0 5

uv texture coordinate range = width = W u = 1 . 0 ,

⎩

between bounded

height = H v = 1 . 0 .

coordinate regions.

Notice that we have an almost identical situation to the coordinate transformation
in Chapter 10. The only difference here is the fact that the y -axis and v -axis
directions are opposite. Similar to the hardware-to-device coordinate transform,
we will have to flip the y -axis values. If v is defined with respect to the lower-left