"honnza" <jan### [at] centrumcz> wrote:
> Is there an easy way to join two points by two circular arcs given their
> tangents?
> Input:
> A,B - endpoints
> a,b - their tangents (oriented parallel to the arcs)
> where A+at and B+bs are skew lines (it's easy to handle the planar case)
> Output:
> C,D - arc centers
> arc normals and radii can be calculated easily from these
> E - intersection point of both points
> together with the arcs' common tangent vector it will be used to cut the
> tori.
>
> I think (after some analysing) it has an infinite number of solutions,
> parametrised by a real number.

Let me make sure I'm understanding this correctly.

Basically, what you want is, given the two lines and two points, to define
what turns out to be a "twisted" plane (an infinite helical surface - if
you take a line perpendicular to both tangents, and use that as the axis of
a cylinder, you get a helical curve where the resultant surface produced by
the lines intersects the cylinder), and then...

....yeah, that's not gonna be easy at all.  I'm not entirely sure even what
the formula for the surface in question is, though I could probably figure
it out given a couple of hours and access to a copy of, say, Mathematica.

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