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;

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