Game Development Reference
InDepth Information
Figure 1.1.
Rendered terrain, with the underlying wireframe mesh partially superim
posed.
Our algorithm was heavily inspired by two existing algorithms. The first in
spiration came from the great desire to walk through the procedural mountains
created by F. Kenton Musgrave [Ebert et al. 98], in real time. The second in
spiration came from the visual beauty of the realtime water created by Claes
Johanson, in his introduction of the projected grid concept [Johanson 04]. The
concept helped form one of the ideas for the basis of our subdivision algorithm,
by showcasing effective and ecient vertex placement to display a vast area of
seascape.
1.2
The Algorithm
A few terms are used throughout this paper and are integral to understanding the
general algorithm and the related descriptions. Section 1.2.1 will describe these
terms and provide related calculations. An algorithm overview is provided in
Section 1.2.2
,
and
Sections 1.2.3
to
1.2.5
d
escribe the main separate components
of our algorithm.
1.2.1 Terms and Definitions
Viewable region.
A
viewable region
, denoted by
R
, is defined as an axis aligned
quadrilateral representing a region that is to be subdivided and/or rendered. This
region is defined from a
center position
and an
applied offset
in both the positive
and negative directions along each aligning axis (see
Figure 1.2
).
The center
position is denoted by
R
C
. The applied offset is denoted by
R
λ
. The bounding
points of the region are denoted by
P
1
,
P
2
,
P
3
,and
P
4
.
Viewable region span.
To quantify a
viewable region span
, denoted by
θ
, we defined
the following calculation at point
P
and applied offset
λ
:
θ
(
P, λ
)=

P
ScreenR
−
P
ScreenL

,
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