0

Suppose I have two sets of linearly independent 3-d vectors denoted by $W=\{\vec{w_1},\vec{w_2},\vec{w_3}\}$ and $V=\{\vec{v_1},\vec{v_2},\vec{v_3}\}$ and then construct two unbounded conic hull,

$C_w=c_1\vec{w_1}+c_2\vec{w_2}+c_2\vec{w_2}$

$C_v=d_1\vec{v_1}+d_2\vec{v_2}+d_2\vec{v_2}$

for $c_i,d_i \in \mathbb{R}_{+}$. Then how can one algebraically find if the two conic hulls intersect or not? simply from the knowledge of the basis vectors $w_i$ and $v_i$. Any matrix equation or any other quick method?

miracle173
  • 11,049
Epsilon
  • 143
  • a conic hull is bounded by three half-lines and three side-faces. If they intersect I think the half-line of one conic line must intersect a side-face of the other conic hull. so you have to check 18 possible intersections to find out, if the conical hulls intersect. – miracle173 Jul 24 '20 at 15:54
  • on the last page of this pdf you see two intersecting bodies and you can see how a side lines of one body intersects a side facet of the other body. – miracle173 Jul 24 '20 at 16:04
  • this is for arbitrary bodies. For conic hulls it is simpler. At least one side line of one body is contained completely in the closure of other body – miracle173 Jul 24 '20 at 16:18

0 Answers0