Selection Booleans

How do you make wierd selections? Sometimes you need to "cut" one selection out of another; this tutorial teaches you how. After you finish this tutorial, you will be able to make complicated selections with a few keyboards shortcuts and the Marquee Tool.

Some Basic Maths

Before we start with Photoshop, let me introduce a few basic Mathematics concepts regarding sets. These concepts will help you understand and work better with selections in Photoshop.

Consider the following sets, Set 1 and Set 2. Set 1 contains the elements "a", "b" and "c" while Set 2 contains the elements "c", "d" and "e" as illustrated in the diagram above.

An intersection is when the same element exists in different sets. If we were to find the intersection between Set 1 and Set 2, the result would be the shaded area, which contains the elements "c".

A union is when both the elements of different sets are added together, disregarding whether the elements are overlapping. Therefore, the result of the union of Set A and Set B would contain elements "a", "b", "c", "d" and "e".

When a set is substracted by another set, the elements which exist in both sets are removed from the former set. This is clearly illustrated in the graphic above, where Set A is subtracted by Set B. Element "c", which exists in both sets, is removed from Set A, leaving behind the shaded area.

Applying It In Photoshop

However, in Photoshop, we are only interested in obtaining the shape of the shaded area since we are only thinking of selections in terms of sets. Therefore, if you don't understand the mathematical rant above, don't fret.

To achieve the effect of sets, I am going to introduce a method where shapes are filled to "define" sets. Then, some simple keyboard shortcuts are going to be used for commands "intersection", "union" and "subtraction".

Union

Consider we want to make a selection with the shape above, a rectangle with one side rounded. This can easily be achieved by taking the union of a perfect circle with a rectangle, as shown in the picture.

To do this in Photoshop, first we shall create a perfect circular marquee selection by using the Marquee Tool and dragging a circle while pressing Shift. Then, we shall fill the selection with a colour for it to act as a "placeholder". (Don't worry if you don't understand yet. ) Make sure you do this on a new layer (i.e. NOT the background layer).

Then, we shall drag a rectangular marquee selection with the Marquee Tool. Line up the rectangular selection with the opaque circle such that the rectangle touches the circle (refer image above). Now, with the rectangular selection still active, hold CTRL + SHIFT on your keyboard and click the layer in which the opaque circle lies in the Layers tab. Your cursor should look like during this time.

If you have done this correctly, your selection should now look like:

Subtraction

Consider this case:

Pretty straight-forward huh?

Let's back-track a few steps and go back to this state to save some time (and my bandwidth, lol). This is when we have an opaque circle and a rectangular marquee coinciding with it.

Now, with the rectangular marquee selection still active, hold CTRL + ALT on the keyboard while you click on the opaque circle layer. Your cursor should look like .

You should get this:

How does this work? When you have a selection, holding CTRL + SHIFT and clicking on a layer with an opaque object adds the shape of the object to the selection, hence union.

When you have a selection, holding CTRL + ALT and clicking on a layer with an opaque object subtracts from the current selection by the shape of the opaque object. Keep in mind that only areas where the selection and the opaque shape coincide will be subtracted.

If you have fully understood the concepts at work on this page, read on to learn about intersections and grab some miscellaneous tips.

Intersection

Once again, let's back-track a few steps and go back to this state. This is when we have an opaque circle and a rectangular marquee coinciding with it.

Observe this straightforward diagram:

This time, hold CTRL + ALT + SHIFT while clicking on the opaque circle layer. You should get this selection:

When you hold CTRL + ALT + SHIFT while clicking on a layer, Photoshop compares the current selection with the opaque shape on which the layer is clicked. The area which coincides is loaded as a selection.

The techniques introduced above can be used to make some very interesting selections, like the one below:

Summary

Here is a list of keyboard shortcuts and what they do when held while clicking on a layer with opaque objects:

• CTRL
  Loads the shape of the opaque object in the layer clicked as selection.
• CTRL + SHIFT
  Adds the shape of the opaque object in the layer clicked to the current selection.
• CTRL + ALT
  Subtracts the shape of the opaque object in the layer clicked from the selection.
• CTRL + ALT + SHIFT
  Loads the area where the shape of the opaque object in the layer clicked and the current selection coincides.
• CTRL + SHIFT + I
  Inverts the current selection.

And with this list I end this tutorial. Hopefully, you can grasp the concepts introduced here despite my unhelpful attempts to sound classy throughout the tutorial. Thank you for reading!