How to obtain union of three shapes given the coordinates

I am trying to obtain the union of shapes comprising of 2 rectangles and a circle. Please does anyone know how to get the union coordinates? .Below is the matlab code, and the corresponding figure.

cy_l=0.3; length of rectangle outside the circle

r=0.5; % radius of circle

a=0.3; % width of rectangle

b=2*r+2*cy_l; % length of rectangle

centre=[0.5 0.3]; %circle centre

theta=0:2*pi/360:2*pi;

circ=[r*cos(theta')+centre(1) r*sin(theta')+centre(2)]; % circle coordinates

%% rectangle

xy=[centre(1)-(r+cy_l), centre(2)+a/2]; % top left coordinates of rectangle1

xy1=[centre(1)-a/2, centre(2)+(r+cy_l)]; %top left coordinate of rectangle2

R1=[xy(1), xy(1), xy(1)+b, xy(1)+b, xy(1);

xy(2)-a, xy(2), xy(2), xy(2)-a, xy(2)-a]; % coordinates of rectangle 1

R2= [ xy1(1), xy1(1), xy1(1)+a, xy1(1)+a, xy1(1);

xy1(2)-b, xy1(2), xy1(2), xy1(2)-b, xy1(2)-b]; %coordinates of rectangle 2

plot(circ(:,1), circ(:,2), 'k', R1(1,:), R1(2,:),'k', R2(1,:), R2(2,:), 'k', 'LineWidth', 2)

grid on

axis equal

Answer 1

[Steven Lord]

I'd use polyshape.

cy_l=0.3; % length of rectangle outside the circle
r=0.5; % radius of circle
a=0.3; % width of rectangle
b=2*r+2*cy_l; % length of rectangle
centre=[0.5 0.3]; %circle centre
theta=0:2*pi/360:2*pi;
circ=polyshape(r*cos(theta')+centre(1), r*sin(theta')+centre(2)); % Circle

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

%% rectangle
xy=[centre(1)-(r+cy_l),  centre(2)+a/2]; % top left coordinates of rectangle1
xy1=[centre(1)-a/2,   centre(2)+(r+cy_l)]; %top left coordinate of rectangle2
R1=polyshape([xy(1), xy(1), xy(1)+b, xy(1)+b, xy(1)], ...      
   [xy(2)-a, xy(2), xy(2),   xy(2)-a, xy(2)-a]);  % rectangle 1
R2= polyshape([xy1(1), xy1(1), xy1(1)+a, xy1(1)+a, xy1(1)], ...
    [xy1(2)-b, xy1(2), xy1(2),   xy1(2)-b, xy1(2)-b]); % rectangle 2
plot([circ, R1, R2])
axis equal

% Show the union in a separate figure for comparison
figure
plot(union([circ, R1, R2]), 'FaceColor', 'g')
axis equal

[Oluwaseyi Ogun]

yes, thanks. This is fine

Answer 2

[Alex Alex]

may be command "polyxpoly" help you

[xi1,yi1] = polyxpoly(circ(:,1), circ(:,2), R1(1,:), R1(2,:))

[xi2,yi2] = polyxpoly(circ(:,1), circ(:,2), R2(1,:), R2(2,:))

[xi3,yi3] = polyxpoly(R1(1,:), R1(2,:), R2(1,:), R2(2,:))

plot(xi1,yi1, 'o')

plot(xi2,yi2, 'o')

plot(xi3,yi3, 'o')

[Oluwaseyi Ogun]

ok. i tried that but what i got is not the union of the figure. I got an 'N' shape

Answer 3

[John D'Errico]

Tivial.

1. generate the three objects as polyshapes.
2. Compute the union.

For example...

cy_l=0.3; % length of rectangle outside the circle
r=0.5; % radius of circle
a=0.3; % width of rectangle
b=2*r+2*cy_l; % length of rectangle
centre=[0.5 0.3]; %circle centre
theta=0:2*pi/360:2*pi;
circ=[r*cos(theta')+centre(1) r*sin(theta')+centre(2)]; % circle coordinates
%% rectangle
xy=[centre(1)-(r+cy_l),  centre(2)+a/2]; % top left coordinates of rectangle1
xy1=[centre(1)-a/2,   centre(2)+(r+cy_l)]; %top left coordinate of rectangle2
R1=[xy(1), xy(1), xy(1)+b, xy(1)+b, xy(1);      
   xy(2)-a, xy(2), xy(2),   xy(2)-a, xy(2)-a];  % coordinates of rectangle 1
R2= [ xy1(1), xy1(1), xy1(1)+a, xy1(1)+a, xy1(1);
    xy1(2)-b, xy1(2), xy1(2),   xy1(2)-b, xy1(2)-b]; %coordinates of rectangle 2
PSc = polyshape(circ(:,1),circ(:,2));

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

PSr1 = polyshape(R1(1,:),R1(2,:));
PSr2 = polyshape(R2(1,:),R2(2,:));

PSu = union(union(PSc,PSr1),PSr2);
plot(PSu)