Contour Plot Example

Contour Plot Example

Problem Statement

Create a contour and surface plot for the function Z = sin^(x) + cos^(y) where both x and y vary from 0 to 360 degrees. (0 to 2*pi radians).

How to perform analysis

Step 1: Open Sigma Magic
  1. Click on the Sigma Magic button on the Excel toolbar.
  2. Click on the New button to create a new project.
Step 2: Add analysis template
  1. Click on the Tool Wizard to add the analysis template.
  2. Click on Graph and then Contour Plot.

Step 3: Specify the analysis options
A new Contour Plot worksheet will be added to your workbook, and the following dialog box will be opened. Click on the Setup tab on the right. Accept the default values and specify the analysis options.


Next, click on the Data tab and specify the data. 
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If you need to change the charts, specify the optional settings in the Charts tab.

 Labels:

  • Add a title for the chart.
  • Label the X-axis and Y-axis appropriately.

Appearance:

  • Adjust colors, font sizes, or other visual elements as needed.
  • Enable/disable gridlines or background shading.

Finally, click the Verify tab to ensure all the inputs are okay and shown in a green checkmark.


Step5: Generate analysis results
Click on the OK button to generate analysis results. The following figure shows an example output screen.


Interpretation of Results

1. Key Analysis Results

  • N (Number of Data Points): 2601 data points were analyzed.
  • Minimum Z Value: 0.0036, meaning there is a very low point in the dataset.
  • Mean Z Value: 1, which suggests the average of all computed ZZZ values.
  • Maximum Z Value: 2.00, which represents the highest peak in the dataset.

2. Interpretation of Trends

  • Since sin⁡2(x)\sin^2(x)sin2(x) and cos⁡2(y)\cos^2(y)cos2(y) both oscillate between 0 and 1, their sum varies between 0 and 2.
  • The contour and surface plots will show high peaks where both sin⁡(x)2\sin(x)^2sin(x)2 and cos⁡(y)2\cos(y)^2cos(y)2 reach 1.
  • The low valleys appear where both values are close to 0.

3. Conclusion from the Report

  • The contour and surface plots were successfully created.
  • The dataset follows a predictable pattern, confirming periodic variations in ZZZ.

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