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
                                                       

The Western Wheel Problem  

About spoke wheels rotating in the opposite direction.
           

The paradox effect:
Nearly everyone who ever had looked an old western movie has discovered this paradox effect: The wheels of a stagecoach some times seem to stop or seem to rotate in the opposite direction. Everyone knows this cannot be real, but we saw this really!

western wheel

The drawing above shows how this effect in movies, videos and computer animations appears.
The deeper reason of the realised rotation in the opposite direction is based on the fact that a movie is a fast sequence of single images - our brain is interpolating this to a continuous motion - most times this works very realistic, but sometimes we also see miracles.
The effect of seeing a rotation in the opposite direction occurs always if a spoke of a wheel rotates by more than the half distance of the spokes during one frame and the next.


westernwheel paradox

Calculated rotation: to the right!
The wheel turns more than a half spoke distance! It seems to turn to the left! Wrong direction!

westernwheel paradox

Calculated rotation: to the right!
The wheel turns less than a half spoke distance! It seems to turn to the right! Correct direction!


This effect may also occur with gears, with propellers with many blades, with the paddle wheels of a Mississippi steamboat, with moving grid patterns and many similar things.

westernwheel paradox

Scene description for POV-Ray:
"westernwheel.ini" and
"westernwheel.pov"
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© Friedrich A. Lohmüller, 2010
http://www.f-lohmueller.de