Math Problem Statement
2.) Create contour plot using the following Elevation data sets.
Grid coordinates:
x = linspace(0, 100, 10); // X coordinates, from 0 to 100 meters
y = linspace(0, 100, 10); // Y coordinates, from 0 to 100 meters
Elevation Data set
Z = [50, 55, 60, 65, 68, 70, 72, 74, 76, 80; 48, 52, 57, 63, 67, 69, 71, 73, 75, 78; 46, 50,
55, 60, 64, 68, 70, 72, 74, 76; 45, 49, 53, 58, 63, 66, 68, 70, 72, 75; 43, 47, 51, 56, 61,
64, 67, 69, 71, 73; 42, 46, 50, 54, 59, 62, 65, 68, 70, 72; 40, 44, 48, 52, 57, 61, 64, 66,
69, 71; 39, 43, 47, 51, 55, 59, 62, 64, 67, 69; 37, 41, 45, 50, 54, 58, 60, 63, 66, 68; 35,
40, 44, 49, 53, 56, 59, 62, 65, 67];
Solution
To create a contour plot using the provided elevation dataset, you can use the following Python code with libraries such as NumPy and Matplotlib. Here’s how to do it:
pythonimport numpy as np import matplotlib.pyplot as plt # Grid coordinates x = np.linspace(0, 100, 10) # X coordinates y = np.linspace(0, 100, 10) # Y coordinates # Elevation data set Z = np.array([ [50, 55, 60, 65, 68, 70, 72, 74, 76, 80], [48, 52, 57, 63, 67, 69, 71, 73, 75, 78], [46, 50, 55, 60, 64, 68, 70, 72, 74, 76], [45, 49, 53, 58, 63, 66, 68, 70, 72, 75], [43, 47, 51, 56, 61, 64, 67, 69, 71, 73], [42, 46, 50, 54, 59, 62, 65, 68, 70, 72], [40, 44, 48, 52, 57, 61, 64, 66, 69, 71], [39, 43, 47, 51, 55, 59, 62, 64, 67, 69], [37, 41, 45, 50, 54, 58, 60, 63, 66, 68], [35, 40, 44, 49, 53, 56, 59, 62, 65, 67] ]) # Create contour plot plt.figure(figsize=(8, 6)) plt.contourf(x, y, Z, cmap='viridis') # Filled contours plt.colorbar(label='Elevation (meters)') plt.title('Contour Plot of Elevation Data') plt.xlabel('X Coordinate (meters)') plt.ylabel('Y Coordinate (meters)') plt.grid() plt.show()
Explanation:
- Data Preparation: The grid coordinates and elevation data are set up.
- Contour Plotting:
contourf
is used for filled contour plots, and a color bar is added for reference. - Visualization: The plot includes labels for axes and a title.
Would you like further details on any specific part of this process, or do you have questions? Here are some related topics you might consider:
- How to customize the color map for better visualization?
- Ways to save the plot as an image file.
- Additional plotting techniques for elevation data.
- How to interpolate missing elevation data points.
- The significance of contour lines in topography.
Tip: Explore different colormaps in Matplotlib for better representation of elevation changes!
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Math Problem Analysis
Mathematical Concepts
Contour Plotting
Data Visualization
Grid Coordinates
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12