Measuring the Boundaries of a Shape

In your projects, you’ll often want to have interactive mouse events tied to specific shapes or drawings. It’s important to remember that any shape or object drawn on the canvas can’t simply be referred to by name, since p5.js has no way of knowing the difference between a green triangle or a pink square. In order to determine whether or not a user has clicked on a 2D object, we have to use conditional statements to measure whether or not the mouse click occurred within the boundaries of that object.

The process of tracking and reacting to mouse clicks on objects will becomes easier with the use of a specialty library, particularly ones used to make game development more intuitive. We'll begin working with just such a library,, in the next chapter.

Stationary Shape Measurements

Squares and Rectangles

Let’s imagine that you want to register whenever a user clicks their mouse inside of the square drawn below. The function called to draw the square looks like this:

rect(200, 50, 150, 150);

The coordinates of the upper lefthand corner of the square match the first two arguments of our rect() function. Using basic math and the last two arguments of the function, we can figure out the coordinates of the remaining corners:

Now we can see that the corners of our rectangle have a handful of shared coordinates. Let’s look at our shape again, highlighting the four significant borders we need to measure (pink for our X coordinates, orange for our Y coordinates) and image what we should measure to know when our mouse cursor has landed inside:

Based on our math, we need to code a test that can only pass if our mouse is clicked and if it’s located at a point greater than 200 X and less than 350 X and less than 200 Y and greater than 50 Y. We can do this by making a conditional that measures all four of those conditions simultaneously. As a reminder, the && operator will stand in for the word “and” in our test. The following code demonstrates a border measurement click test, causing the background color to change only when we click inside the bounds of the square:

See the Pen Example Code by LSU DDEM ( @lsuddem) on CodePen.

Try modifying this code by removing the “mouseIsPressed” portion of the test. This allows the background to change when the mouse cursor simply hovers over the square.

You'll notice that the individual greater than/lesser than tests in the example above are incased inside of parenthesis pairs. This is done in order to make out code look cleaner and to make each portion of this multi-portion test easier to identify. Be careful to count your individual symbols and not leave out the essential parenthesis that forms the if ( ) test format!


Measuring the boundaries of a circle is a slightly more challenging task, since there are no sides for us to measure. Instead, we’ll need to know the coordinates of the circle’s center, the diameter of the circle, and its radius:

The first three values can be found as the four arguments passed into the ellipse( ) function called to draw the circle to the canvas. The circle’s radius is half of its diameter. We should declare a variable to hold that result of the circle’s diameter divided by 2 so that we can use that value later.

Since the radius is the distance between the center of the circle and its enter outer perimeter, our next step is find a way to trigger an event whenever our mouseX and mouseY variables cross that perimeter. If we can compare the value in our circle radius variable against the distance between the current mouse location and the circle’s center, we could use that to test if our mouse has hovered over or been been clicked inside of our circle:

To accomplish this, we can use p5.js’ dist() function. This function lets us pass in two pairs of X/Y coordinates and returns the number of pixels between those two points. Using this function, we need to devise a test that compares the distance between our mouse location and the circle’s center with the circle’s radius value. The test should only pass if the distance value is less than the radius value and if the mouse is clicked. Storing the ever-changing result of our dist() function inside of a variable will make this test easier to understand, and the code embedded below shows an example of what this test should look like:

See the Pen Example Code by LSU DDEM ( @lsuddem) on CodePen.

Moving Shape Measurements

The techniques learned above will also work for shapes that are moving across the canvas. The only difference in our boundary measurement tests will is the need to measure our mouse location against variables that stand in for the ever-changing location of the shape’s edges/centers. Take a look at the code below and test it out. The background will change to different colors when you click on the square versus when you click on the circle. Compare this code to the ones we studied above:

See the Pen Example Code by LSU DDEM ( @lsuddem) on CodePen.