Animations with Spline Curves

Spline curves used as animation pfaths
and the Spline_Trans Makro made by Rune S. Johansen.

Spline Curves as Animation Pfaths: To let an object fly along a spline curve defined by a spline i.e. called "Spline_1(..)" is not the problem:
We just use the simple statement "translate Spline_1(clock)"
Sample:

sphere{ <0,0,0>, 0.25
        texture{
                 pigment{ color Red}
                 finish { diffuse 0.9
                          phong 1}
               } // end of texture
   translate Spline_1(clock) //<--!!
}  // end of sphere -------------

complete scene description for POV-Ray:
"spline_fly1.ini" and
"spline_fly1.pov"

The Spline_Trans Makro
made by Rune S. Johansen
The Orientation of objects along a spline curve

A special problem causes the adaption of the orientation of an object to a spline curve used as animation pfath. The question: How can we bring an airplane on a spline curve in a manner that its turning correctly in the right direction?

The perfect solution of this problem brings the Spline_Trans Makro made by Rune S. Johansen.
This is a feature of POV-Ray!
For using this macro we need to include the include file transforms.inc by:

#include "transforms.inc"

complete scene description for POV-Ray:
"spline_fly1.ini" file and "spline_fly1.pov" file

Syntax of this macro: (See also in the text of "transforms.inc"!)
Spline_Trans(SplineName, TimeValue, Upwards, ForeSight, Banking)
Die Parameter im einzelnen:
SplineName = The name of the used spline function.
TimeValue = The time value to feed to the spline, i.e. "clock"
Upwards = The vector that is upwards in your scene, usually "y " or "<0,1,0>.
ForeSight = A positive value that controls how much in advance the object will turn and bank. Values close to 0 will give precise results, while higher values give smoother results. It will not affect parsing speed, so just find the value that looks best.
Banking = How much the object tilts when turning. The amount of tilting is equally much controlled by the ForeSight value.
Sample:

object {My_Object Spline_Trans( My_Spline, clock, y, 0.05, 0.70)}

Fly Animation:
A Fly with sharp s-curves, screwing and looping!

Air Race!

For another interesting samples on the animation with spline curves take a look at the POV-Ray subdirectory "scenes\animation\splinefollow"