MATLAB Curve Overlay: Merging Multiple Curves to Reveal Relationships Between Data

# 1. Overview of MATLAB Curve Overlay

MATLAB curve overlay is a powerful technique for drawing multiple curves on the same graph, facilitating comparison and analysis. It is widely used in data visualization, trend analysis, and model fitting.

By overlaying curves, users can easily identify similarities and differences between different datasets and uncover hidden patterns and trends. MATLAB provides the hold command, which allows users to overlay multiple curves on the same graph using functions like plot, line, or scatter to create these curves.

# 2. Theoretical Foundation of Curve Overlay

### 2.1 Principles and Advantages of Curve Overlay

Curve overlay involves plotting multiple curves on the same coordinate system. The principle is to add the x-coordinates and y-coordinates of each curve to get new coordinates, then plot the new curve.

Curve overlay has the following advantages:

- **Data Visualization:** Overlaying multiple curves allows for a visual comparison of the differences and trends between different datasets.
- **Trend Analysis:** By overlaying curves from different time periods or conditions, data change trends and patterns can be analyzed.
- **Model Fitting:** Overlaying experimental data with model fitting curves can evaluate the goodness of fit and prediction accuracy of the model.

### 2.2 Comparison of Different Curve Overlay Methods

In MATLAB, there are various functions for overlaying curves, with the commonly used ones being:

| Function | Description |
|---|---|
| `hold on` | Maintains the current coordinate system, allowing multiple curves to be drawn on the same coordinate system |
| `plot` | Draws a curve, and if `hold on` is enabled, overlays the curve on the current coordinate system |
| `subplot` | Creates subplots, allowing multiple sets of curves to be drawn within the same figure window |

**Code Block:**

% Create data
x1 = 1:10;
y1 = rand(1, 10);
x2 = 1:10;
y2 = rand(1, 10);

% Overlay curves using hold on
figure;
hold on;
plot(x1, y1, 'b', 'LineWidth', 2); % blue solid line, line width of 2
plot(x2, y2, 'r--', 'LineWidth', 1); % red dashed line, line width of 1

% Add legend
legend('Curve 1', 'Curve 2');

% Logical Analysis:
% The hold on command maintains the current coordinate system, allowing multiple curves to be drawn on the same coordinate system.
% The plot function draws two curves, a blue solid line and a red dashed line.
% The legend function adds a legend to identify each curve by name.

**mermaid Flowchart:**

graph LR
subgraph Overlay Curve Methods
    hold on --> plot(x1, y1)
    hold on --> plot(x2, y2)
end

# 3. Practical Application of MATLAB Curve Overlay

### 3.1 Importing Data and Creating Curves

**Importin