shortest distance between two cones in 3-dim space

Question

How can I find the shortest distance between two cones in 3-dim space?

cone 1:

apex - $(x_{0}, y_{0}, z_{0})$

angle - $\alpha_{0}$

base circle - $(cx_{0}, cy_{0}, cz_{0}, r_{0})$

cone 2:

apex - $(x_{1}, y_{1}, z_{1})$

angle - $\alpha_{1}$

base circle - $(cx_{1}, cy_{1}, cz_{1}, r_{1})$

Are these finite cones (that end at their base circles), or are do they extend infinitely? — bubba, Nov 30 '13 at 04:16

score 0 · Answer 1 · answered Aug 20 '14 at 18:05

Parameterize each cone surface. Find connecting distance vector from a general point of each cone.

Impose condition of orthogonality between minimum distance vector and tangent vectors on each cone.

Alternately, combine equations of cone surfaces through a Lagrange multiplier and use Euler-Bernoulli equation.

1 Answers1