How to plot an orientated rectangle having coordinates and angle?

Hello everybody,

I have a simple problem that I cannot manage to solve in Matlab.

I am representing the behavior of a vehicle traveling on a given car track and I would like to plot orientated rectangles instead of the standard markers present in the plot environment. I am able to reproduce the orientation through the quiver function, but I am not able to use rectangles instead of the arrows.

Note that I would like to have a rectangle for every instant k (i.e.: if I have 10 instants, ten different rectangles for every position).

This is the code I use for the moment with quiver:

scale_factor = 10;
r = 1; % magnitude (length) of arrow to plot
x = x_c; y = y_c;
angle = alpha+beta;
u = r * cos(angle); % convert polar (theta,r) to cartesian
v = r * sin(angle);
h = quiver(x,y,u*scale_factor,v*scale_factor,'--','LineWidth',3,'AutoScale','off');   

I have also tried this one translating manually each point but it does not work:

function[]= draw_rectangle1(x_c,y_c,theta)
L = 20;
H = 10;

x_low_left = x_c - L/2;
x_low_right = x_c + L/2;
x_up_right = x_c + L/2;
x_up_left = x_c - L/2;

y_low_left = y_c - H/2;
y_low_right = y_c - H/2;
y_up_right = y_c + H/2;
y_up_left = y_c + H/2;

x_low_left_new = cos(theta)*(x_low_left-x_c)-sin(theta)*(y_low_left-x_c)+x_c;
y_low_left_new = sin(theta)*(x_low_left-x_c)+cos(theta)*(y_low_left-x_c)+y_c;
x_low_right_new = cos(theta)*(x_low_right-x_c)-sin(theta)*(y_low_right-x_c)+x_c;
y_low_right_new = sin(theta)*(x_low_right-x_c)+cos(theta)*(y_low_right-x_c)+y_c;
x_up_right_new = cos(theta)*(x_up_right-x_c)-sin(theta)*(y_up_right-x_c)+x_c;
y_up_right_new = sin(theta)*(x_up_right-x_c)+cos(theta)*(y_up_right-x_c)+y_c;
x_up_left_new = cos(theta)*(x_up_left-x_c)-sin(theta)*(y_up_left-x_c)+x_c;
y_up_left_new = sin(theta)*(x_up_left-x_c)+cos(theta)*(y_up_left-x_c)+y_c;

x_coor=[x_low_left_new x_low_right_new x_up_right_new x_up_left_new];
y_coor=[y_low_left_new y_low_right_new y_up_right_new y_up_left_new];
fill(x_coor, y_coor,'r');

end

I have also given a chance to patch but no way.

If anyone can help me with this simple but tricky code it would be awesome.

Thank you!

Answer 1

[Jim Riggs]

You have to perform the rotation in an object-centered coordinate frame.

Define the rectangle:

X = [-L/2  L/2  L/2  -L/2];
Y = [-H/2  -H/2  H/2  H/2];

Now perform the rotation in the object-centered frame:

theta =   % The rotation angle
cth = cos(theta) ; 
sth = sin(theta);
Xrot =  X*cth + Y*sth;
Yrot = -X*sth + Y*cth;

Now when you generate the graphic, add the true position:

fill(Xrot + Xc,  Yrot + Yc,'r')

[mavanz]

Thank you very much Jim!

Your solution is almost perfect, I just noticed a little bug: to make it work perfectly I must pass to the script the angle -theta instead of theta. Should be the sin and cos signs?

[Jim Riggs]

I thought about that detail after I posted my answer. I defined theta to be positive for a clockwise rotation. If you define theta to be positive for as counter-clockwise rotation, then you can either use the minus sign (as you suggest) or you can use the inverse rotation:

Xrot =  X*cth - Y*sth;
Yrot =  X*sth + Y*cth;

This will perform the rotation in the oposite direction.