Re: Shortest path in 3d with minimum turning radius

If an object enters this path from the bottom its direction is
reversed in the point where the two arcs (270deg each) touches.

 *** ***
*   *   *
*   *   *
 *******
    *
 
It consists of two arcs and one line. However, path made from three
arcs looks definitely better.

Mirek.

   

Virgil <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> In article <[EMAIL PROTECTED]>,
>  [EMAIL PROTECTED] (Miroslav Novak) wrote:
> 
> > I want to calculate shortest trajectory of a rocket between two points
> > in 3D space. Directions in starting and ending points are given. The
> > rocket has certain minimum turning radius.
> > 
> > The trajectory has to consist of starting arc, straight line, and
> > ending arc. The line is tangent for both arcs. The first arc contains
> > the starting point and its tangent there is equal to the starting
> > direction. The second arc has similar properties for the ending point
> > and ending direction.
> > 
> > When I tried to solve this problem I obtained a system of quadratic
> > equations hard to solve. Therefore, I am looking for some relevant
> > resources. Do you have any suggestions?
> > 
> > Mirek.
> 
> This, assuming that arcs are segments of circles, appears to require 
> certain starting and ending configurations be excluded.
> 
> For example, if the ending point is the same as the starting point 
> but with opposite direction required, it cannot be done with only an 
> arc-line-arc sequence, but needs, at least, arc-arc-arc.