The following applet allows the construction of an entity out of two entities, given in homogenous coordinates.
You need to select the type of entity, then you can specify the coordinates and a whole cof-matrix.
After specifying two entities, you can select an operation (join or intersect) and see the resulting entity (if it exists).
The relation takes your cof-matrix fully into account.
Constructors which need estimation are not working in this applet, for example intersection of two 3D Lines.
More information on how that is done can be found on Documentation page.