###### Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller     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
5.2: 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

# Closed Spline CurvesFor the animation of cyclic repeating non-linear motions.

Animation paths with spline curves: As a camera path or as a flight path of animated objects we i.e. can use a closed spline curve.
 ```#declare P1 = <-2.00, 0.20, -2.00>; #declare P2 = < 1.00, 0.20, -2.00>; #declare P3 = < 2.00, 0.70, -1.00>; #declare P4 = < 2.00, 1.20, 2.00>; #declare P5 = < 0.00, 0.20, 2.00>; #declare P6 = <-2.00, 3.20, 1.50>; #declare P7 = <-2.00, 0.70, -1.00>; #declare P8 = <-2.00, 0.00, -2.00>; #declare Spline_1 = spline { natural_spline -0.250, P7, // control point 0.000, P1, // starting point 0.125, P2, 0.250, P3, 0.420, P4, 0.490, P5, 0.780, P6, 0.900, P7, 1.000, P1, // end point 1.125, P2 // control point }// end of spline ---------------```

##### Complete scene description for POV-Ray:"spline00.pov"

Closed Spline Curves:
We'll get a perfectly closed spline curve under the following conditions:
The end point is the same as the starting point.
The control point before the beginning is the point before the end point.
The control point at the end is the point behind the starting point.
The distances of the time values at the control point must also fit to those of their according points.

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