CARTESIO is a very nice freeware package from Instituto Universitario di Architettura in Venice, Italy, which allows you to explore many different projection systems, with a huge gallery of geometric solids.

Dismiss the brief help window (which contains a few tips in broken English). Note that there is a comprehensive Help menu, but in Italian only!

Before you can do anything else, you must establish a projection system. For example, from the Projections menu, select Orthographic projection.

You should see a screen like this:

When you introduce a solid, this window will show a (top) plan view. The origin of the x, y, z coordinate axes is at the middle of this view. The directions of the x-and y-axes are indicated, respectively, by the short blue and red lines. The grid on the x-y surface (i.e., the surface z = 0) is 0.2 units, with major grid lines shown at 1.0 unit intervals.

Now introduce a solid to be looked at. From the Solids menu, select Tetrahedron. You should now see:

The top panel is an isometric view of:

- the coordinate axes,
- the projection plane (the turquoise quadrilateral), and
- the line of sight (green)

Below this, the same features can be seen in three principal orthogonal views. In the case illustrated above, the projection plane is the x-y plane, and the projection is in the positive z-direction (or if you like, the viewer is looking at the object from somewhere out on the positive z axis).

The bottom panel shows the axis directions for the view in the main window.

To change the projection direction, use the arrow keys:

• the down arrow gives a bottom plan view
• the up arrow restores the top plan view
• the left arrow rotates the projection plane counter-clockwise about the z-axis, giving a sequence of side (lateral) views
• the right arrow rotates the projection plane clockwise

The tetrahedron has sides 1 unit long. You can get the coordinates of any point on the projection plane with a CTRL+left mouse click. Dragging with CTRL+right mouse will pan the view.

Many other projections are available. For example, an isometric axonometric view:

Up to six windows can be displayed. To tile the currently open windows, select Cascade (!) from the Windows menu (this is a bug):

Press CTRL+F1 to see a help window relating to the current projection, and how to use the arrow keys and mouse buttons.

Solids may be viewed shaded (as above) or as wireframe models, with or without the axes, grid, etc.:

Note that the tetrahedron has been sectioned in the views above. To manipulate solids (section, translate, rotate ...), you must first Make selection group... from the Transformations menu.