Create Basic Shapes

First, create a rectangle and two adjoining circles.

rect1 = [3
    4
    -1
    1
    1
    -1
    0
    0
    -0.5
    -0.5];
C1 = [1
    1
    -0.25
    0.25];
C2 = [1
    -1
    -0.25
    0.25];

Append extra zeros to the circles so they have the same number of rows as the rectangle.

C1 = [C1;zeros(length(rect1) - length(C1),1)];
C2 = [C2;zeros(length(rect1) - length(C2),1)];

Combine the shapes into one matrix.

gd = [rect1,C1,C2];

Create Names for the Basic Shapes

In order to create a formula describing the unions and intersections of basic shapes, you need a name for each basic shape. Give the names as a matrix whose columns contain the names of the corresponding columns in the basic shape matrix. Pad the columns with 0 or 32 if necessary so that each has the same length.

One easy way to create the names is by specifying a character array whose rows contain the names, and then taking the transpose. Use the char function to create the array. This function pads the rows as needed so all have the same length. Continuing the example, give names for the three shapes.

ns = char('rect1','C1','C2');
ns = ns';

Set Formula

Obtain the final geometry by writing a set of characters that describes the unions and intersections of basic shapes. Use + for union, * for intersection, - for set difference, and parentheses for grouping. The precedence order, from the highest to the lowest, is as follows: -, *, +. You can control the precedence by using parentheses.

Continuing the example, specify the union of the rectangle and C1, and subtract C2.

sf = '(rect1+C1)-C2';

Create Geometry and Remove Face Boundaries

After you have created the basic shapes, given them names, and specified a set formula, create the geometry using decsg. Often, you also remove some or all of the resulting face boundaries. Completing the example, combine the basic shapes using the set formula.

[dl,bt] = decsg(gd,sf,ns);

View the geometry with and without boundary removal.

pdegplot(dl,"EdgeLabels","on","FaceLabels","on")
xlim([-1.5,1.5])
axis equal

Remove the face boundaries.

[dl2,bt2] = csgdel(dl,bt);
figure
pdegplot(dl2,"EdgeLabels","on","FaceLabels","on")
xlim([-1.5,1.5])
axis equal