【Matlab Axis Masterclass】: 15 Tips to Master Axes Control with Ease

# **Matlab Coordinate Axes: 15 Tips for Mastering Axes**

## **1. Overview of Matlab Coordinate Axes**

Coordinate axes are one of the fundamental elements for plotting graphs in Matlab. They define the spatial positions of data points and provide a visual reference for the graphics. Matlab offers a wide range of options to customize the appearance and behavior of coordinate axes to meet various plotting requirements.

Coordinate axes consist of a horizontal x-axis and a vertical y-axis that intersect at the origin. The range of the axes defines the area where data points can be plotted, while the tick marks provide intervals to help interpret the data. Axes may also include labels and titles to provide additional information about the graph.

## **2. Setting Coordinate Axes Attributes**

Setting coordinate axes attributes is a key part of customizing the appearance and behavior of axes. Matlab provides various properties that allow you to control the range, ticks, labels, title, grid, and background of the axes.

### **2.1 Coordinate Axes Range and Ticks**

#### **2.1.1 Setting the Coordinate Axes Range**

The coordinate axes range defines the minimum and maximum values for data points on the axes. You can use the `axis` function to set the coordinate axes range. The syntax is as follows:

axis([xmin xmax ymin ymax])

Where `xmin` and `xmax` specify the minimum and maximum values for the x-axis, and `ymin` and `ymax` specify the minimum and maximum values for the y-axis.

**Code Block:**

% Set the x-axis range to [0, 10]
axis([0 10 0 10])

% Set the y-axis range to [-5, 5]
axis([0 10 -5 5])

**Logical Analysis:**

* The first code block sets the x-axis range to [0, 10] and the y-axis range to [0, 10].
* The second code block maintains the x-axis range and sets the y-axis range to [-5, 5].

#### **2.1.2 Setting the Coordinate Axes Ticks**

Coordinate axes ticks define the tick marks and tick labels displayed on the axes. You can use the `set` function to set the coordinate axes ticks. The syntax is as follows:

set(gca, 'XTick', [x1 x2 ...])
set(gca, 'YTick', [y1 y2 ...])

Where `gca` gets the current axis handle, and `XTick` and `YTick` specify the tick values for the x-axis and y-axis, respectively.

**Code Block:**

% Set the x-axis ticks to [0, 2, 4, 6, 8, 10]
set(gca, 'XTick', [0 2 4 6 8 10])

% Set the y-axis ticks to [-5, -2, 0, 2, 5]
set(gca, 'YTick', [-5 -2 0 2 5])

**Logical Analysis:**

* The first code block sets the x-axis ticks to [0, 2, 4, 6, 8, 10].
* The second code block sets the y-axis ticks to [-5, -2, 0, 2, 5].

### **2.2 Coordinate Axes Labels and Titles**

#### **2.2.1 Setting Coordinate Axes Labels**

Coordinate axes labels are the text displayed next to the tick marks on the axes. You can use the `xlabel` and `ylabel` functions to set coordinate axes labels. The syntax is as follows:

xlabel('X-Axis Label')
ylabel('Y-Axis Label')

Where `xlabel` and `ylabel` specify the label text for the x-axis and y-axis, respectively.

**Code Block:**

% Set the x-axis label to "Time (s)"
xlabel('Time (s)')

% Set the y-axis label to "Amplitude (V)"
ylabel('Amplitude (V)')

**Logical Analysis:**

* The first code block sets the x-axis label to "Time (s)".
* The second code block sets the y-axis label to "Amplitude (V)".

#### **2.2.2 Setting Coordinate Axes Titles**

Coordinate axes titles are the text displayed on the axes to describe their content. You can use the `title` function to set coordinate axes titles. The syntax is as follows:

title('Plot Title')

Where the string 'Plot Title' is replaced with the title you want to set for the graph.

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# **3. Axis Transformations**

## **3.1 Linear Transformations**

Linear transformations are among the most basic types of coordinate axes transformations. They can translate or scale the axes along the x-axis or y-axis.

### **3.1.1 Translating Axes**

Translating axes involves moving the axes along the x-axis or y-axis by a certain distance. You can use the `xlim` and `ylim` functions to set the range of the axes, thus achieving translation.

% Create an axes
figure;
plot(1:10, rand(1, 10));

% Translate the axes
xlim([0, 12]);
ylim([0, 1.5]);

**Logical Analysis of the Code:**

* `plot(1:10, rand(1, 10))`: Draws a line graph containing 10 random numbers.
* `xlim([0, 12])`: Sets the x-axis range to [0, 12], translating the axes 2 units to the right along the x-axis.
* `ylim([0, 1.5])`: Sets the y-axis range to [0, 1.5], translating the axes 0.5 units up along the y-axis.

### **3.1.2 Scaling Axes**

Scaling axes involves enlarging or reducing the axes by a certain multiple along the x-axis or y-axis. You can use the `daspect` function to set the aspect ratio of the axes, thus achieving scaling.

% Create an axes
figure;
plot(1:10, rand(1, 10));

% Scale the axes
daspect([2 1 1]);

**Logical Analysis of the Code:**

* `plot(1:10, rand(1, 10))`: Draws a line graph containing 10 random numbers.
* `daspect([2 1 1])`: Sets the aspect ratio of the axes to [2 1 1], enlarging the x-axis by 2 times while keeping the y-axis unchanged.

## **3.2 Logarithmic Transformations**

Logarithmic transformations are nonlinear transformations that can distribute the data on different scales, making the relationship between data points clearer.

### **3.2.1 Creating Logarithmic Axes**

You can use the `loglog` function to create logarithmic axes.

% Create a logarithmic axes
figure;
loglog(1:10, rand(1, 10));

**Logical Analysis of the Code:**

* `loglog(1:10, rand(1, 10))`: Draws a logarithmic axis line graph containing 10 random numbers.

### **3.2.2 Setting Logarithmic Axes Properties**

The properties of logarithmic axes can be set using the `set` function.

% Create a logarithmic axes
figure;
loglog(1:10, rand(1, 10));

% Set logarithmic axes properties
set(gca, 'XScale', 'log', 'YScale', 'log');

**Logical Analysis of the Code:**

* `loglog(1:10, rand(1, 10))`: Draws a logarithmic axis line graph containing 10 random numbers.
* `set(gca, 'XScale', 'log', 'YScale', 'log')`: Sets both the x-axis and y-axis scales to logarithmic scales.

# **4. Axis Annotations**

Axis annotations are elements used to add additional information to axes. These annotations can be text, graphics, or a combination of both.

### **4.1 Text Annotations**

#### **4.1.1 Adding Text Annotations**

To add text annotations, you can use the `text` function. The syntax for this function is as follows:

text(x, y, str, 'PropertyName', PropertyValue, ...)

Where:

* `x` and `y` specify the location of the annotation.
* `str` is the text to be displayed.
* `'PropertyName'` and `PropertyValue` are optional pairs of property names and values used to set the annotation's properties.

For example, the following code adds a text annotation to the axes:

text(10, 20, 'Text Annotation', 'Color', 'red', 'FontSize', 14);

This creates a red text annotation with a font size of 14 located at `x = 10` and `y = 20`.

#### **4.1.2 Setting Text Annotation Properties**

Text annotation properties can be set using the `'PropertyName'` and `PropertyValue` parameters. Some commonly used properties include:

* `'Color'`: Sets the text color.
* `'FontSize'`: Sets the text font size.
* `'FontName'`: Sets the text font.
* `'HorizontalAlignment'`: Sets the horizontal alignment of the text.
* `'VerticalAlignment'`: Sets the vertical alignment of the text.

### **4.2 Graphic Annotations**

#### **4.2.1 Adding Graphic Annotations**

To add graphic annotations, you can use functions like `line`, `rectangle`, or `circle`. The syntax for these functions is as follows:

line(x, y, 'PropertyName', PropertyValue, ...)
rectangle('Position', [x, y, width, height], 'PropertyName', PropertyValue, ...)
circle('Center', [x, y], 'Radius', radius, 'PropertyName', PropertyValue, ...)

Where:

* `x` and `y` specify the location of the graphic.
* `'PropertyName'` and `PropertyValue` are optional pairs of property names and values used to set the graphic's properties.

For example, the following code adds a rectangle annotation to the axes:

rectangle('Position', [10, 20, 50, 30], 'FaceColor', 'blue', 'EdgeColor', 'red');

This creates a rectangle annotation with a blue fill and red border located at `x = 10`, `y = 20`, with a width of 50 and a height of 30.

#### **4.2.2 Setting Graphic Annotation Properties**

Graphic annotation properties can be set using the `'PropertyName'` and `PropertyValue` parameters. Some commonly used properties include:

* `'FaceColor'`: Sets the fill color.
* `'EdgeColor'`: Sets the border color.
* `'LineWidth'`: Sets the border width.
* `'LineStyle'`: Sets the border style.
* `'Marker'`: Sets the marker type.
* `'MarkerSize'`: Sets the marker size.

# **5. Axis Layout**

### **5.1 Multiple Axes**

#### **5.1.1 Creating Multiple Axes**

Creating multiple axes in the same graphic can realize visualizing different datasets or information in different coordinate systems. Matlab provides the `subplot` function to create multiple axes. The syntax for the `subplot` function is as follows:

subplot(m, n, p)

Where:

* `m`: Specifies the number of rows of subplots in the figure.
* `n`: Specifies the number of columns of subplots in the figure.
* `p`: Specifies the position of the current subplot in the figure.

For example, to create a figure with two subplots, where the first subplot is in the first row and first column, and the second subplot is in the first row and second column, you can use the following code:

subplot(1, 2, 1);
subplot(1, 2, 2);

#### **5.1.2 Coordinating Multiple Axes**

When creating multiple axes, it may be necessary to coordinate them to ensure they have the same scale or range. Matlab provides the `linkaxes` function to coordinate axes. The syntax for the `linkaxes` function is as follows:

linkaxes(axes_array, 'property')

Where:

* `axes_array`: An array of axes to be coordinated.
* `property`: The property to be coordinated, such as `'xlims'`, `'ylims'`, or `'view'`.

For example, to link the x-axis range of two axes together, you can use the following code:

linkaxes([ax1, ax2], 'xlims');

### **5.2 Sub-Axes**

#### **5.2.1 Creating Sub-Axes**

Sub-axes are smaller axes nested within the main axes. They are often used to display information related to the main axes but with a different range or scale. Matlab provides the `axes` function to create sub-axes. The syntax for the `axes` function is as follows:

axes('Position', [left, bottom, width, height])

Where:

* `Position`: The position and size of the sub-axes, specified as `[left, bottom, width, height]`, where `left` and `bottom` are the relative positions of the lower-left corner of the sub-axes, and `width` and `height` are the width and height of the sub-axes.

For example, to create a sub-axes in the top right corner of the main axes, you can use the following code:

axes('Position', [0.6, 0.6, 0.3, 0.3]);

#### **5.2.2 Setting Sub-Axes Properties**

Sub-axes have the same properties as the main axes and can be set to customize their appearance and behavior. You can use the same functions and methods for the main axes to set the properties of sub-axes.

For example, to set the title of the sub-axes, you can use the following code:

title('Sub-Axes Title');

# **6.1 Axis Event Handling**

### **6.1.1 Responding to Axis Events**

Matlab provides various events that can be used to respond to user interactions on the axes. These events include:

- `ButtonDownFcn`: Triggered when the mouse is pressed on the axes.
- `ButtonUpFcn`: Triggered when the mouse is released on the axes.
- `WindowButtonDownFcn`: Triggered when the mouse is pressed within the axes window.
- `WindowButtonUpFcn`: Triggered when the mouse is released within the axes window.
- `WindowButtonMotionFcn`: Triggered when the mouse is moved within the axes window.

To respond to these events, you can use the `set` function to assign an event handling function to the corresponding event properties. For example, to respond to the event of the mouse being pressed on the axes, you can use the following code:

set(gca, 'ButtonDownFcn', @myButtonDownFcn);

Where `myButtonDownFcn` is a custom event handling function.

### **6.1.2 Customizing Axis Event Handling Functions**

Custom axis event handling functions must be functions that accept an event object as the input parameter. The event object contains information about the triggering event, such as mouse position and button status.

Below is an example of a custom axis event handling function that prints the mouse position when the mouse is pressed on the axes:

function myButtonDownFcn(hObject, eventdata)
    % Get the mouse position
    mousePosition = get(gca, 'CurrentPoint');
    % Print the mouse position
    disp(['Mouse position: ', num2str(mousePosition(1)), ', ', num2str(mousePosition(2))]);
end

To use a custom event handling function, assign it to the corresponding event property as shown above.