BOUNDARY, REGION and Booleans (UNION/SUBTRACT/INTERSECT)

What it does

Where to find it

• Ribbon: Draw › Modify › Region ▾ (Region, Union, Subtract, Intersect) and Draw › Polyline ▾ › Boundary from a Pick (BOUNDARY)
• Command line: see the table above

Steps

1. Draw overlapping closed shapes, for example a rectangle and a circle.
2. Select both shapes. For SUBTRACT, select the main shape first.
3. Type UNION (or SUBTRACT, INTERSECT) and press Enter.

Note: A Boolean operation needs at least two overlapping closed shapes (rectangle, circle or closed polyline). Open lines are ignored.

Try it: Café floor with a round bay window

A small café with a curved bay window you can sit in, and a storeroom corner cut away. You use UNION and SUBTRACT, then measure the real floor area with AREA.

1. Type REC, Enter, 0,0, Enter, then 8000 Tab 5000 Enter (an 8 x 5 m floor).
2. Type C, Enter, 8000,2500, Enter, then radius 1500 and Enter (the bay window).
3. Select the rectangle and the circle, type UNION and press Enter. You now have one outline.
4. Draw the storeroom in the top-left corner: REC, 0,4000, then 1500 Tab 1000 Enter.
5. Click the café outline first, then the storeroom. Type SUBTRACT and press Enter. The corner is cut away.
6. Select the result, type AREA and press Enter. It reports about 42,029,800 sq units, roughly 42 m². (The half circle is split into short straight segments, so the number is a little below the theoretical value.)

Challenge: Try INTERSECT on a fresh rectangle and circle. Only the overlapping half-round remains, which makes a nice semicircular planter.

See also

• HATCH
• Measure area with AREA