Rotate a Rectangle within boundaries

I am trying to have a red rectangle be inside the green rectangle with a random rotation. I have almost accomplished this, but the only thing that is not working is that the rotation goes out the green rectangle's bounds...

cla reset
hold on

width = 1;
P = rectangle('Position',[ 0.2 -width/2 width width],'FaceColor','green'); % Placement square

a = 0.2;
b = 1.2-0.3;
r = a + (b-a).*rand(1,1); % random for horz

a = -0.5;
b = 0.5-0.2;
r2 = a + (b-a).*rand(1,1); % random for vert

x1 = r;
x2 = r + 0.3;
y1 = r2;
y2 = r2 + 0.2;

X= [x1 x1 x2 x2];
Y= [y1 y2 y2 y1];
hSquare = fill(X,Y,'r');
thetad = 45;
% thetad  = randi([0 360],1);
R = [cosd(thetad) -sind(thetad); sind(thetad) cosd(thetad)];
C = repmat([0 0], 4, 1)';
axis([-1 1 -1 1])

V = get(hSquare,'Vertices')';  % get the current set of vertices
V = R*(V - C) + C;             % do the rotation relative to the centre of the square
set(hSquare,'Vertices',V');    % update the vertices
axis equal

Answer 1

[Benjamin Thompson]

If you want the red shape to sometimes touch the boundaries of the green shape while staying entirely within the green, then you cannot have both the center of the red shape and its rotation angle entirely random. You may need to choose the rotation angle first, and then based on that choose the allowable center position of the red shape.

Answer 2

[DGM]

Here.

% rectangle parameters
szR1 = [1 1]; % size of large rectangle
osR1 = [0.2 -szR1(2)/2]; % offset of large rectangle
szR2 = [0.3 0.2]; % size of small rectangle

% generate random angle
thR2 = randi([0 360],1);

% build point list, rotate
R = [cosd(thR2) -sind(thR2); sind(thR2) cosd(thR2)];
XY = [-1 -1; 1 -1; 1 1; -1 1].*szR2/2;
XY = (R*XY.').';

% apply constrained random translation
randos = rand(1,2);
os0 = range(XY,1); % this is the size of the rotated block
XY = XY + (szR1-os0).*randos + osR1 + os0/2;

% plot stuff
P = rectangle('Position',[osR1 szR1],'FaceColor','green');
hold on; 

hSquare = fill(XY(:,1),XY(:,2),'r');
axis equal

axis([0 2 -1 1])

Or you could draw a bunch of red blocks

figure
% rectangle parameters
szR1 = [1 1];
osR1 = [0.2 -szR1(2)/2];
szR2 = [0.3 0.2];
nblocks = 50;

% plot bg
P = rectangle('Position',[osR1 szR1],'FaceColor','green'); % Placement square
hold on; 

for k = 1:nblocks
    % generate random angle
    thR2 = randi([0 360],1);
    
    % build point list, rotate
    R = [cosd(thR2) -sind(thR2); sind(thR2) cosd(thR2)];
    XY = [-1 -1; 1 -1; 1 1; -1 1].*szR2/2;
    XY = (R*XY.').';
    
    % apply constrained random translation
    randos = rand(1,2);
    os0 = range(XY,1); % this is the size of the rotated block
    XY = XY + (szR1-os0).*randos + osR1 + os0/2;
    
    % plot block
    hSquare = fill(XY(:,1),XY(:,2),'r','facealpha',0.5);
    axis equal
end
axis([0 2 -1 1])