I am trying to create a geometric object represented by the intersection of a sphere and the space below a plane using ImplicitRegion. When I use the sphere alone, it works. When I use the plane alone, it also works... But when I use them both together, it does not work! I get the error message "DiscretizeRegion was unable to discretize the region ImplicitRegion".
(* A sphere by itself works *)
reg1 = DiscretizeRegion[
ImplicitRegion[
x^2 + y^2 + z^2 == 1 && -40 <= x <= 40 && -40 <= y <= 40 && -20 <=
z <= 40, {x, y, z}]];
(* The region below a given plane alone works *)
reg2 = DiscretizeRegion[
ImplicitRegion[-(64/(3 Sqrt[3])) + (16 x)/3 - (16 y)/3 + (16 z)/
3 <= 0 && -40 <= x <= 40 && -40 <= y <= 40 && -20 <= z <=
40, {x, y, z}]];
(* The sphere and region below the plane together does not work *)
reg12 = DiscretizeRegion[
ImplicitRegion[
x^2 + y^2 + z^2 ==
1 && -(64/(3 Sqrt[3])) + (16 x)/3 - (16 y)/3 + (16 z)/3 <=
0 && -40 <= x <= 40 && -40 <= y <= 40 && -20 <= z <= 40, {x, y,
z}]];
Show[reg1, reg2, reg12]
Any idea how to make it work for the Implicit Region defined by both the sphere and the plane?
x^2 + y^2 + z^2 == 10
, it works for me. I have to admit, the error message is pretty useless... $\endgroup$Method -> "Semialgebraic"
seems to work. $\endgroup$