MATLAB: Problem with rotation matrix

rotation matrix

Hi, I have this U shape which is in this code. I was wondering how I could rotate it using 2-D rotation matrix.
theta = pi/2;
rotation_matrix = [cos(theta), -sin(theta); sin(theta), cos(theta)];
obstacle_matrix = [z1, z2];
obstacle_shape = obstacle_matrix * rotation_matrix;
plot(obstacle_shape)
here is my other file.
% obstacle definition
function [z1 z2] = toric_obstacle(enl_fac)
x0 = -1.2*enl_fac;
y0 = -1*enl_fac;
x1 = -0.6/enl_fac;
y1 = -0.5/enl_fac;
x2 = 0.6/enl_fac;
x3 = 1.2*enl_fac;
y3 = 0.8*enl_fac;
delta = 0.01;
z1 = zeros(1000,1);
z2 = zeros(1000,1);
%line 1
i = 0;
for x = x0:delta:x3
    i = i + 1;
    z1(i) = x;
    z2(i) = y0;
end
%line 2
i = i - 1;
for y = y0:delta:y3
    i = i + 1;
    z1(i) = x3;
    z2(i) = y;
end
%line 3
i = i - 1;
for x = x3:-delta:x2
    i = i + 1;
    z1(i) = x;
    z2(i) = y3;
end
%line 4
i = i - 1;
for y = y3:-delta:y1
    i = i + 1;
    z1(i) = x2;
    z2(i) = y;
end
%line 5
i = i - 1;
for x = x2:-delta:x1
    i = i + 1;
    z1(i) = x;
    z2(i) = y1;
end
%line 6
i = i - 1;
for y = y1:delta:y3
    i = i + 1;
    z1(i) = x1;
    z2(i) = y;
end
%line 7
i = i - 1;
for x = x1:-delta:x0
    i = i + 1;
    z1(i) = x;
    z2(i) = y3;
end
%line 8
i = i - 1;
for y = y3:-delta:y0
    i = i + 1;
    z1(i) = x0;
    z2(i) = y;
end
i = i - 1;
z1 = z1(1:i);
z2 = z2(1:i);

Best Answer

Your code works fine, but you're just not plotting it correctly.
    plot(obstacle_shape(:,1), obstacle_shape(:,2));
You might also want to correct the aspect ratio:
    pos = get(gcf, 'Position');
    aspect = pos(3) / pos(4);
    set(gca, 'XLim', [-2,2]);
    set(gca, 'YLim', [-2,2] / aspect);
By the way, your rotation is backwards. It is rotating clockwise, which is unconventional. You should negate both the sin terms in your rotation matrix.
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