Boolean Operations

The term Boolean operation comes from its inventor, George Boole (1815-1864), who came up with a way to combine logic elements using operators called And, Or, Not, If, Then, and Except. For example, if you want a shirt that is red and has short sleeves, then you want to buy a red, shirt-sleeved shirt out of all shirts in the store. The AND operator is like Visio's Boolean operation called Intersect, which returns only the common portions of overlapping shapes as a single shape.

If you want a shirt that is red or has short sleeves, then you are interested in any shirt that contains red or has short sleeves in the store. The OR operator is like Visio's Boolean operation called Union, which returns all portions of overlapping shapes as a single shape.

You use Boolean operations to create new shapes. For operations to work, the shapes must be overlapping. Very often, the order in which you select shapes is important to the outcome, as noted below. The stacking order of overlapping shapes is not important. The Operations selection of the Shape menu performs Boolean operations on shapes:

• The Union operation joins all selected shapes into a single shape. The new shape takes on the attributes of the shape selected first.
• The Combine operation is like the Union operation but removes the portions in common. The new shape takes on the attributes of the shape selected first.
• The Fragment operation creates three new shapes from two overlapping shapes; the overlapping portion becomes an independent shape. All three shapes take on the attributes of the first selected shape.
• The Intersect operation removes everything except the overlapping areas of the two shapes. Intersect is the opposite of the Combine operation.
• The Subtract operation removes the overlapping portion of the second shape from the first shape. Another way of looking at it is that the overlapping portion is removed from the first shape.
• The Build Region macro joins shapes that have been enabled for arranging. Specifically, the macro joins map shapes, such as countries and states.

1. Select one shape. This is the shape whose properties the new shape takes on.

2. Hold down the Shift key and select one or more additional shapes.

3. Select Shape > Operations > Union.

4. Notice that Visio creates one new shape with the outline of all selected shapes and the attributes of the first shape.

1. Select one shape. This is the shape whose properties the new shape takes on.

2. Hold down the Shift key and select one or more additional shapes.

3. Select Shape > Operations > Combine.

4. Notice that Visio creates one new shape with the outline of all selected shapes and the attributes of the first shape. Overlapping areas are removed.

1. Select one shape. This is the shape whose properties the new shape takes on.

2. Hold down the Shift key and select one or more additional shapes.

3. Select Shape > Operations > Fragment.

4. Notice that Visio creates a new fragmented shape from the overlapping portions of the original shapes. All shapes take on the attributes of the first shape. The illustration shows the three shapes moved apart.

1. Select one shape. This is the shape whose properties the new shape takes on.

2. Hold down the Shift key and select one or more additional shapes.

3. Select Shape > Operations > Intersect.

4. Notice that Visio creates one new shape from the overlapping portions of the original shapes; the new shape takes on the attributes of the first shape.

1. Select one shape. This is the shape whose properties the new shape takes on.

2. Hold down the Shift key and select one or more additional shapes.

3. Select Shape > Operations > Subtract.

4. Notice that Visio creates one new shape by removing the second shape and the overlapping portions of the second shape from the first shape.

1. Select two or more map shapes.

2. Select Tools > Macro > Maps > Build Region from the menu bar.

3. Notice that Visio moves the map shapes together so that they join up logically along borders. In the illustration, the American states of Alaska and Washington, and the Canadian province of British Columbia, have been brought together by the Build Region command.