Le 06.10.2007 13:33, honnza nous fit lire :
> 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.
> 
> 
Do you also want continuity in E (intersection of both arcs): same
tangent direction  ?

restricting analysis to 2D, I already have a puzzle with
 A: <0,0>
 B: <1,0>
 a: <0,1>
 b: <-1, 0>

Where are C and D ?

Even stranger, the basic:
A: <0,0>
B: <1,0>
a: <0,1>
b: <0,1>

An obvious single arc (centered at <0.5,0>), but how to do that with
2 (short of degenerated solution like twice the same center) ?


Back in 3D, two points and 1 tangent might define a plane (excepted
when tangent is colinear to delta of the points). Remains the
question: is the second tangent in the same plane or not.
If yes, a 2D solution is enough.
If no, is there a solution ?

-- 
The superior man understands what is right;
the inferior man understands what will sell.
-- Confucius

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