2.2.2. Creating simple plots

The basic MATLAB graphing procedure, for example in 2D, is to take a vector of x-coordinates, x = (x₁,...,xₙ), and a vector of y-coordinates, y = (y₁,...,yₙ), locate the points (xᵢ,yᵢ), with i = 1,2,...,n and then join them by straight lines. You need to prepare x and y in an identical array form; namely, x and y are both row arrays or column arrays of the same length.

In MATLAB, when we want to create a simple plot, we first need to prepare two sets of data: one for the x-coordinates and one for the y-coordinates. For instance, if we have x = (1, 2, 3) and y = (3, 2, 1), it means that our first point is (1, 3), our second point is (2, 2), and so on. To create this plot, both the x and y vectors must be the same length. If they are, MATLAB can easily pair each x value with its corresponding y value and draw lines between the points to create the graph.

Think of plotting like connecting dots on a piece of paper. Each dot represents a point on the graph determined by paired values from the x and y coordinates. If you have dots for x = 1, 2, and 3; and their corresponding y values are 3, 2, and 1, you can visualize it as marking these points on the paper and then connecting them with a straight ruler to see the pattern or trend.

The MATLAB command to plot a graph is plot(x,y). The vectors x = (1,2,3,4,5,6) and y = (3,-1,2,4,5,1) produce the picture shown in Figure 2.1.

x = [1 2 3 4 5 6]; y = [3 -1 2 4 5 1]; plot(x,y)

To create a graph in MATLAB, you use the command plot(x,y), where x and y are your vectors containing the x-coordinates and y-coordinates, respectively. In the provided example, when you input the values for x and y and then call plot(x,y), MATLAB generates a graph that visually represents these points and connects them with lines. The result gives you a quick visual insight into how the values relate to one another.

Visualize plotting on a graph as drawing a bridge connecting different islands. Each island stands for a point of data defined by its x and y coordinates. The plot command helps build the bridge, allowing you to see which islands are connected at what heights, just like seeing how one value relates to another in a graph.

For example, to plot the function sin(x) on the interval [0,2π], we first create a vector of x values ranging from 0 to 2π, then compute the sine of these values, and finally plot the result:

x = 0:pi/100:2*pi; y = sin(x); plot(x,y)

When plotting mathematical functions such as sine, you first need to define a range of x values. In this case, x = 0:pi/100:2*pi generates x values starting from 0, increasing in increments of π/100, up to 2π. After defining x, we calculate the corresponding y values using y = sin(x). Finally, using the command plot(x,y), MATLAB draws the sine curve, which visually illustrates how the sine function behaves over the specified range.

Think of plotting a sine function as taking a roller coaster ride along a landscape. As you define your path (the x values), you measure how high or low the ride goes at each point (the y values calculated by the sine function). When you finally draw that path on a graph, you see the ups and downs represented beautifully, just like how the roller coaster rises and falls.

Notes:

0:pi/100:2*pi yields a vector that starts at 0, takes steps (or increments) of π/100, stops when 2π is reached.

If you omit the increment, MATLAB automatically increments by 1.

This note emphasizes how MATLAB generates vectors through specific commands. By using 0:pi/100:2*pi, you create an array that starts at 0 and ends at 2π, with small increments in between. If you instead write just 0:2*pi, MATLAB defaults to a step of 1, creating a very different set of x values. Understanding how to generate these x coordinates properly is vital for accurate plotting.

Imagine baking cookies where the number of cookies you prepare depends on the time you allow for each batch. If you plan to bake every minute, adding more batches of cookies to your tray means spacing them just right—this is like defining increments for your vector. If you forgot to space them correctly, you’d end up with a mismatched pile instead of a neat row of cookies, similar to how incorrect increments result in inaccurate graphing.

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