How would one go plotting a plane in matlab or matplotlib from a normal vector and a point?
For Matlab:
point = [1,2,3];
normal = [1,1,2];
%# a plane is a*x+b*y+c*z+d=0
%# [a,b,c] is the normal. Thus, we have to calculate
%# d and we're set
d = -point*normal'; %'# dot product for less typing
%# create x,y
[xx,yy]=ndgrid(1:10,1:10);
%# calculate corresponding z
z = (-normal(1)*xx - normal(2)*yy - d)/normal(3);
%# plot the surface
figure
surf(xx,yy,z)
Note: this solution only works as long as normal(3) is not 0. If the plane is parallel to the z-axis, you can rotate the dimensions to keep the same approach:
z = (-normal(3)*xx - normal(1)*yy - d)/normal(2); %% assuming normal(3)==0 and normal(2)~=0
%% plot the surface
figure
surf(xx,yy,z)
%% label the axis to avoid confusion
xlabel('z')
ylabel('x')
zlabel('y')