Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
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    3D Animations with POV-Ray
        Some basics and examples on animations.
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  3D Animation Tutorial
   Index of Content
  0. Basic Knowledge
     1. Basic Example
     2. Example 2
     3. Images to Animated Gif
     4. From Images to Video
     5. Basic Terms
     6. Animation Commands  
  I. Cyclic Animations
     1. Rotating Objects
     1.2. Planets in Orbit
     1.3. Clock Animation
     2. Rotating Camera
     2.1. Straight Moving Camera
     3. Western Wheel
         Problem
     3.1. Rolling Wheels
  > 4. Gears
     4.1. Roller Chain
     4.2. Bike Chain
     5. Swinging Pendulum
     5.1. Newton's Cradle
     5.2: Rock the Rocker
     6. Spiral Pendulum
     7. Coupling Rods
     7.1. Connecting Rods
     8. Psychedelic + Op-Art
     9. Counters + Countdowns
    10. Folding of a Cube
  II. Non-linear Movements
     1.0 Speed Up/Slow Down 1
     1.1 Speed Up/Slow Down 2
     2. Fall + Bounce
     3. Acceleration by
          physical Formulas
     4. Speed Controll by
          Spline Functions
  III. Animation Paths
      with Spline Curves
     1. Spline Curves
     2. Closed Splines
     3. Animation Paths
                                                       

Rotating Gears  

About cyclic animated rotating gears.
           


Gears in Motion:
As long as the gears don't have any spokes, a gear with N cogs has a N-fold radial symmetry
For a cyclic animation we have to turn this gear only by the maximal angle depending on the distance of the cogs. The angle between two cogs is 360 degrees / number of cogs!
If we have gears of different sizes we have to rotate with the smallest common multiple of all angles between two cogs of all gears in game.

gear

scene description for POV-Ray:
"gear00.ini" and
"gear00.pov"

This trick described above allows realising animated scenes with a incredibly low number of frames - the animation above consists of 10 frames! (file size: 95.3 kB!!!)
There's a snag to this: The centre of the gear seems to be immobile! This is more eye catching if the cogs are very small and the centre of a gear is in focus of attention!.

Also here the paradox effect of wheels rotating in the opposite direction may occur. This will happen when a cog moves more the a half cog distance during one frame and the next!

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© Friedrich A. Lohmüller, 2008
http://www.f-lohmueller.de