Please can you advise me how to speed up the rendering of the following two planes? When I click and drag to rotate the plot, its movement is quite jerky. Presumably it is working harder than I need it to. The matrix equation A.X = B
represents two flat planes embedded in 3D space. The solution of the system is the line of intersection of the two planes. I believe ContourPlot3D
interprets the matrix equation as a list of the two planes. In fact, A.X == B
evaluates as {{x + y + z}, {x - y + 2 z}} == {{4}, {0}}
.
A = {{1, 1, 1}, {1, -1, 2}};
B = {{4}, {0}};
X = {{x}, {y}, {z}};
ContourPlot3D[A.X == B, {x, -10, 10}, {y, -10, 10}, {z, -10, 10},
ContourStyle -> Directive[Opacity[.6]], MeshStyle -> Gray]
I have tried using Evaluate
on the expression A.X == B
, and on the expression A.X
, but to no avail.
You might think it better to separate the two planes, and use Plot3D
command for each, but I would like my code to work automatically for general linear systems, i.e., for different choices of A
, B
and X
, and I would like it to accomodate vertical planes, to which I guess Plot3D
would not apply.