Limits of the geometry building module

Introduction

The algorithms of automatic construction of faces and volumes are powerful, but difficulties can however arise, being determined:

• either by a «bad» geometrical description: problems of intersection or superposition of entities…
• or by numerical problems…

Construction problems connected to intersection/ superposition of objects

Construction problems may occur in the presence of:

• overlapping points, or lines of null length;
• intersection or superposition of lines;
• intersection of faces.

These different items are treated in the preceding paragraph.

Numerical problems of recognition of faces or volumes

Numerical problems of recognition of faces or volumes can also occur in the presence of faces characterized by too important numerical waves.

What is the problem ?

The algorithm of automatic construction of faces identifies in the first step all the existing surfaces, then, it determines to which surfaces belong the points and the lines. A surface is defined by four coefficients computed from the coordinates of three points. The test of association of points to surfaces is defined with an error criterion (epsilon tolerance criterion) and it may occur that the points and lines that the user consider in the same surface will not be considered in the same surface by the software. In this case, we speak about significant numerical waves.

This kind of situation may occur when the points are described by a "cascade" of parameters, of local coordinate systems and of transformations. When the point coordinates are evaluated in a global coordinate system, there is an accumulation of numerical errors and the tolerance is then exceeded.

In spite of a very particular care taken for solving these numerical problems, it may occur, in case of complex geometries, that the automatic construction of faces or volumes raises difficulties.