Find complementary cones from a cone
Suppose I have a cone constructed from a set of points. In 2d for instance:
cone1 = Cone([[-1, 4], [4, -1]])
The rays of this cone1
are exactly those two vectors I used to define the cone.
Now, I take the cone
cone2 = Cone([[1, 0], [0, 1]])
Again its rays are given by the two vectors used to define it.
Now, cone1
contains cone2
, and its intersection with cone2
is exactly cone2
.
I would like to know if there is a way to extract the complementary cones from cone1
"subtracting" cone2
. Basically I would need:
cone3 = Cone([[-1, 4], [0, 1]])
and
cone4 = Cone([[1, 0], [4, -1]])
Is there a way to extract these cones?
I know that in the 2d example I can plot the cones with .plot() and subtract them visualizing them, of course this is an example. What I would like to know if there is an algorithmic way to extract all the "complementary cones" from a bigger cone that contains (completely) another cone. So I would like to find a way to define cone3
and cone4
in higher dimensions, and "algorithmically".