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4.2

Joining straight segments with circular segments

Asked by satsumo in Algorithms, 3D Game Programming, Math & Science

Tags: geometry trigonometry 3d math

I have two arbitrary vectors in 3 space, each vector has an arbitrary direction (they are the end and start of two linear segments).  It is possible to smoothly join the two points along the direction vectors with two circular segments of equal radius.

I need to find both the radius and the arcs.  The plane for each arc is straightforward enough.

The circular segments usually have different arcs, sometimes one of the segments has an arc of zero (so that only one segment appears).  Note the problem is in 3 space, the arcs can be at right angles to each other.

I know this is possible, been banging my head at it for a while now.  The correct math has evaded me so far.
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About this solution

Zones: Algorithms, 3D Game Programming, Math & Science
Tags: geometry trigonometry 3d math
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Solution Provided By: satsumo
Participating Experts: 4
Solution Grade: A
 
 
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