MATLAB Three Dimensional Plotting Notes

Three Dimensional Plotting

• Overview: Three-dimensional plotting in MATLAB allows visualization of data points in 3D space, commonly using line plots, surface plots, and contour plots.

1. Three Dimensional Line Plots

• Input Required: Set of ordered triples (x, y, z values).
• Z-Axis: Labeled similar to x and y axes.
• Coordinate System: Uses a right-hand rule consistent with traditional mathematical conventions.

2. Surface Plots

• Surface Representation: Surface plots represent x-y-z data in a three-dimensional surface format.
• Functions to Use:
  • mesh for a mesh plot.
  • surf for a colored surface plot.
• Matrix Indexing: The x and y coordinates can be treated as matrix indices (rows and columns). For instance, Y refers to rows, and X refers to columns.
• Example Code:

  z = [1 10 20; 2 20 40];
  mesh(z);

3. Animation Functionality

• Comet3 function: Generates an animated 3D plot of the input data.
• Usage: comet3(x,y,z).
• Tips: If the animation runs slowly, increase data points.

4. Code Examples

• To create line and animated plots:

  x = linspace(0,10*pi,1000);
  y = cos(x);
  z = sin(x);
  plot3(x,y,z);
  comet3(x,y,z);

5. Surface Plot Implementation

• Syntactical Options:

  surf(z);
  surf(x,y,z);

• When using mesh with known x and y corresponding to values of z:

  mesh(x,y,z);

• Ensure that the number of columns in x matches z and the number of rows in y matches z.

6. Shading Techniques

• Shading Options:
  • shading interp: Interpolated shading for smoother visual transition.
  • shading flat: Sections of the surface are displayed in flat colors.
• Color Maps: Changing the color scheme using colormap can enhance visualization:
  • Examples of colormaps: hot, cool, jet, hsv, etc.
  • Example code:
    matlab colormap('hot');

7. Contour Plots

• Contour Syntax: Contour plots represent data levels in 3D space using lines:
  • Filled contour example: contourf(x,y,z,20,'k').
• Usage:

   [x, y, z] = peaks;
   contourf(x, y, z, 20, 'k');

8. Creating 3D Plots of Spheres

• Sphere Functionality:
• Create a sphere using:

  [x,y,z] = sphere(N);
  surf(x,y,z);

• N represents the resolution.

9. Saving and Editing Plots

• To save plots, use the Save As... option in the MATLAB figure window, selecting a desired format (e.g., JPEG).
• Interactive Edit Options: You can modify plots using the menu bar after the plot is created.
  • Such adjustments include adding legends, labels, and changing aspect ratios.

Summary of Key Functions

• Note: When adjusting a figure interactively, these changes will not be captured in the M-file unless explicitly saved to the script.