Some algorithms of GEOM module return a list of shapes sorted in accordance with some criterion. The goal of this sorting is a possibility to obtain stable result regardless SALOME version being used.

The algorithm that provides such a possibility consists of the following steps:

For each shape a pair of point and number is associated. The point and number depend on the shape type:

Shape Type	Point	Number
Vertex	Vertex isself	Orientation value converted to double
Edge, Wire	Center of mass	Total length of edges
Face, Shell	Center of mass	Total area of faces
Other	Center of mass	Total volume of solids

Each point is converted to double using the following expression:
point.X() * 999.0 + point.Y() * 99.0 + point.Z() * 0.9
The shapes are sorted in ascending order. The shape comparison criterion is the following. Shape_1 is considered less then Shape_2 if:
- Shape_1's double value obtained on the step 2 is less than the corresponding value of Shape_2.
  Otherwise if they are equal with the confusion tolerance (1.e-7):
- Shape_1's number obtained on the step 1 is less than the corresponding number of Shape_2.
  Otherwise if they are equal with the confusion tolerance (1.e-7) and the shapes have either Face or more complex type:
- Shape_1's squared diagonal of bounding box is less than the one of Shape_2.
  Otherwise if they are equal with the confusion tolerance (1.e-7):
- Get the minimal and maximal values of X, Y and Z coordinates of bounding boxes for Shape_1 and Shape_2. Compute the following values for Shape_1 and Shape_2:
  (aXmin+aXmax) * 999.0 + (aYmin+aYmax) * 99.0 + (aZmin+aZmax) * 0.9
  
  Shape_1 is less than Shape_2 if this value for Shape_1 is less than the value for Shape_2.

This algorithm is used in the following geomBuilder methods:

and as a part of some other algorithms where sorting is required.