Analytical Geometry with POVRay
Righthanded and Lefthanded Systems of Coordinates
and the Cross Product
Basics on the handyness of coordinate systems

The lefthanded coordinate system:
This is the default of POVRay.

The lefthanded coordinate system
 the default of POVRay


pros: The students can start easily:
the x axis and the y axis are pointing in the same directions
as they used to do in their exercise books.
Many commercial 3d graphic programs (i.e. Cinema 4D) use it too.
cons: The cross productin physics is defined for righthanded coordinate systems!


The righthanded coordinate system:
This can be made in POVRay by changing the camera as follows:

The righthanded coordinate system
by changing the camera values of POVRay

camera { // for diagonal view
angle 18
right x*image_width/image_height
sky <0,0,1>// right handed !
location <20.0, 20.0, 20.0>
look_at <0.0, 0.0, 0.5>
} // end of camera 

cons: 1. The students have to learn by new:
the x axis and the y axis are not pointing in the same directions
as they used to do in their exercise books.
2. Scenes, designed for a lefthanded coordinate system,
cannot be changed easily for righthanded scenes, because all objects
must be tranformed accordingly!
3. The templates scenes from the "Insert Menu"
and from my "Insert Menu Addon" must be changed accordingly.
pros: In physics is often(but not exclusively) used a righthanded cross product defined for righthanded coordinate systems!


The cross product in a lefthanded coordinate system:

The cross product in a righthanded coordinate system:

The cross product in the standard
lefthanded coordinate system in POVRay
Scene for POVRay:
".txt" file or
".pov" file

The cross product in a
righthanded coordinate system
after changing the camera values of POVRay
Scene for POVRay:
".txt" file or
".pov" file
