VARKON Version 1.15 1997-10-16

### Selecting solutions when there is more than one

There are many geometrical problems that have more than one solution. A line tangent to a curve (lin_tan1 in MBS) is one example. If the curve oscillates then it is probably easy to find many lines starting in the same position but joining the curve with tangency in different places. Intersect is another example. If a line intersects a curve or if a curve intersects another curve (or arc) then it's clearly possible to end up with more than one solution.
In interactive CAD-systems it is common practice to supply routines like lin_tan1 or intersect with a hint in the form of an approximate position. This gives the underlying mathematical algorithm a good starting value for the numerical solution and makes it unnecessary to calculate more than one solution which saves time.
In VARKON all solutions are always calculated and the user only supplies a relative number to select which one he's interested in. This approach takes more CPU-time of course but also makes it possible to solve problems without having to supply approximate solutions. In parametric design this is important since changes to parameters may change the corresponding geometry significantly and thereby move points of tangency or intersect to completely new positions.
Other routines based on the same principle are lin_tan2, arc_fil, inv_on, inv_on_sur, inv_tang and inv_curv.

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