Game Development Reference
In-Depth Information
y
P 1
P 2
R C = Center Position ( R Cx ,R Cy )
R λ = Applied Offset
P 1 =( R Cx R λ ,R Cy + R λ )
P 2 =( R Cx + R λ ,R Cy + R λ )
P 3 =( R Cx + R λ ,R Cy R λ )
P 4 =( R Cx R λ ,R Cy R λ )
R λ
R C
R λ
R λ
R λ
x
P 4
P 3
Figure 1.2. Example of a viewable region and its associated properties.
P ScreenL =( P VProjL xy ) /P ProjLw ,
P ScreenR =( P ProjR xy ) /P ProjRw ,
P ProjL = P WL ×
matProjection ,
P ProjR = P WR ×
matProjection ,
P WL =( P Wx
λ, P Wy ) ,
P WR =( P Wx + λ, P Wy ) ,
P W = P
× matWorldView .
The above calculation for the viewable region span can be used at any position P
and applied offset λ , and is used extensively within the LOD Transition Algorithm
(explained in Section 1.2.4 ) . We use this calculation instead of calculating the
actual viewing surface area to avoid inconsistencies when viewable regions are
viewed from different angles.
Maximum viewable region span. The maximum viewable region span , denoted by
θ max , is the maximum allowable viewable region span. This value, which is set
by the user, is one of the main determining factors of the attainable LOD, and it
plays a key part in both the Subdivision Algorithm (explained in Section 1.2.3 )
and the LOD Transition Algorithm (explained in Section 1.2.4 ) .
Relative quadrant code. This code identifies the relative position of a split view-
able region in relation to its parent viewable region. This code is utilized by the
LOD Transition Algorithm (explained in Section 1.2.4 ) , and calculated in the
Subdivision Algorithm (explained in Section 1.2.3 ) . Usually encoded as a 2-bit
mask, this code becomes part of the definition of a viewable region.