A branch of the robotics research is motion planning. In this sector one of the problems that we encounter is the representation of the robots and the world where they work.

This representation is necessary, for example, to apply the algorithms of collision detection.

We can use some methods from the 3D geometry used in many 3D graphic program, but all these methods have pros and cons.

Another method of solid oject representation is the CSG (Constructive Solid Geometry).

This system is based on the combination of some primitive objects by some boolean operations.

This semplifies the work of creating a data file to describe the 3D object, but makes more complicated the computation of the real profile of the object.

It’s a more powerful system, faster and simple to configure. It is used in most 3D graphic program to represent the creation of complex objects throught simple operations.

A widley used method is the Triangulation. This method is based on a approximation of the solid object to represent. In fact the objects are represented with many triangles linked on the vertexes.

This type of representation is good for the application of the algorithms of collision detection, but it is very complex for the user that has to create the data file with all the coordinates of the vertexes and the links information. But the most complicated step is the object approximation and decomposition, specially if the object contains curves.