Hello,
I am making a very basic test animation of a cannon shell being fired from a
gun.
After a bit of fiddling around, I have sorted out the path of the shell, and can
do pretty much anything I want with it.

However I have not figured out how to rotate it so that it is always tangent to
it's path.

I have written another "still" scene where the path is defined by a spline, but
the
closest I could get to a tangent was this:

#declare S=1;
#declare N=80;
#declare C=0;
#declare A=45;   //firing angle; in animated scene it is defined otherwise.
#declare AR=radians(A);
#declare V=100;  //muzzle velocity m/sec
#declare G=10;   //gravity m/sec, rounded up for simplicity


#declare Path1 = spline {
  linear_spline
  #while(S<=N)
    #declare XV = (sin(radians(90.0)-AR)*V*C);
    #declare YV = (sin(AR)*V*C-G*pow(C,2));
    S/N, <XV, YV, 0>
    #declare S=S+1;
    #declare C=C+0.1;
  #end
}

#declare Cnt=1;
#declare Max=20;

sphere_sweep {
  linear_spline Max
  #while(Cnt<=Max)
    #declare Point = Parabola1((Cnt-1)/(Max-1));
    Point, 0.5
    #declare Cnt=Cnt+1;
  #end
  pigment { Blue }
  translate x*-250
  scale 1/25
}

#declare P = 0.0;

cylinder {
  x*50, x*-50, 1
  pigment { Green }
  rotate x*(A-(2*P*A)      //this rotates the cylinder depending on its position
  translate Path1(P)
  translate x*-250
  scale 1/25
}

While this doesn't look too bad for 45 degrees, any higher or lower and the fact
that it is not tangent becomes apparent.

I have looked at math.inc, and I think that VAngle() and VRotation(), or some of
the Vector Analysis macros might be what I'm looking for, but how to get a
usable value from them is currently beyond my mathematical capabilities.

If I've made anything unnecessarily complex, which is often the case, :-(
could someone point me in the right direction?

Otherwise it looks like I'm in for some fairly complicated math.

D103

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