Game Development Reference
In-Depth Information
14.1.2 Properties of models
According to Michael Mortenson (1985), “a geometric model is an unambiguous
and complete mathematical representation of the shape of a physical object used to
process it on a computer''. Since there exist a variety of models, it will be useful to
compare the different representations of the same object with each other. The criteria
used are:
Domain: It is the set of objects that a representation can model;
Completeness: It is the theoretical capacity of a representation to answer certain
simple geometrical questions like the area of a surface, position of a point with
respect to a volume, etc.;
Uniqueness of the representation of an object: This criterion is important
when we are trying to determine the equality of two objects, having a similar
rotation/translation couple;
Ease of manipulation : This is the basis of creation and modification of the model;
Technical performances: Accuracy, conciseness of the structure and the quickness
of the associated algorithms (collision detection, visual rendering, etc.).
There are two fundamental techniques to represent objects in three dimensions:
Solid model: it consists of determining a computer representation of their volume;
Surface representation: This representation comes from the observation that we
are in a three-dimensional Euclidian space where every standard finished object
has a non-degenerate boundary. We can thus determine the volume of the object as
the interior of its boundary. In short, here we are trying to model a sphere rather
than a ball. Though this may seem more complex in theory, this representation is
more useful in reality because in case of non-transparent solids, the rendering is
only for the single surface of the object.
For solid as well as surface representations, there are a number of mathematical models,
each verifying different properties. In the following parts, we will see the main types of
solid and surface models and then the algorithmics associated to model conversions.
Finally, we will discuss the improvements that we can make in a model to use it in a
virtual environment, with the real time constraints applicable to it.
14.2 SOLID MODELS
The solid models are the models that represent the volume of an object. Two groups
of techniques are used:
Spatial enumeration : It consists of dividing the space into a significant number
of small cells which will belong completely, partly, or not at all to the volume of
the object. The modelling then consists of finding a division of the space and a
function that determines how to fill a cell when only a part of this cell is covered
by the object to be modelled;