Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmueller
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  - Overview by Table
      on "analytical_g.inc"
  - Vector Analysis
      with POV-Ray
  > Righthanded & Lefthanded
    Systems of Coordinates
    and the Cross Product

  - Samples from
    Analytical Geometry
    - Parallelogram of the

        Middles of the Edges
    - Trace Points of a Straight Line
    - Calculations about a Triangle
    - Area of a Parallelogram
        and Cross Product
    - Shadow of a Pyramid
    - Hit a plane || yz-plane
    - Angle of triangle & yz-plane
                                       

Analytical Geometry with POV-Ray

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 POV-Ray.
The lefthanded coordinate system
- the default of POV-Ray
              left hand axis
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 POV-Ray by changing the camera as follows:
The righthanded coordinate system
by changing the camera values of POV-Ray
             

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 Add-on" 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 POV-Ray
 
Scene for POV-Ray: ".txt" file or ".pov" file
The cross product in a
righthanded coordinate system
after changing the camera values of POV-Ray
Scene for POV-Ray: ".txt" file or ".pov" file
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© Friedrich A. Lohmüller, 2007
http://www.f-lohmueller.de