Game Development Reference
Figure 14.10 Example of a part modelled using a triangular mesh
14.3.1 Using plane surfaces
This model is used most commonly for real time rendering. The boundary surface
of an object is represented using a set of polygonal faces connected to each other. A
boundary is thus represented with three sets: a set of vertices V , a set of edges E and
a set of faces F . The model has to respect certain integrity constraints:
The faces intersect each other only at their common vertices or edges;
An edge belongs to two faces;
All vertices adjacent to a given vertex form a simple polygon (no intersection
between edges, convex if possible) in the space.
We generally use triangles as polygons to simplify the calculations to the maximum,
as a triangle is the simplest closed convex polygonal surface. Besides, it is also planar.
Since every polygon can be divided into a set of triangles, the problems are similar.
Figure 14.10 shows an example of a part modelled using a triangular mesh. The preci-
sion of the mesh is restricted only by the number of triangles we can use. Today, the 3D
graphics cards can display a very large number of triangles per second (several dozen
millions), but on the other hand, most of them can display only triangles at this speed.
Games being the main domain of application and thus the preferred direction of devel-
opment, manufacturers focus on the effects (transparency, cast shadows, shaders , etc.).
14.3.2 Using non-planar surfaces
The model proposed in the previous section can be applied to non-planar surfaces
without any problem. The integrity constraints are more difficult to follow. Non-
planar surfaces generally have the advantage of compactness of representation. They
are easier to manipulate for CAD operators as they require less parameterisation. Their
visual appearance is better with the same quantity of data and they make it possible to
represent smooth surfaces in a more precise and easier manner. Generally, the model