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- Create three matrices of the same size. Then plot them as a surface. The surface plot uses Z for both height and color. [X,Y] = meshgrid(1:0.5:10,1:20); Z = sin(X) + cos(Y); surf(X,Y,Z)
www.mathworks.com/help/matlab/ref/surf.html
It is difficult to draw many interesting level surfaces by hand, but CalcPlot3D helps us explore them easily. There are actually two ways to enter and graph the level surface equations for a particular function of three variables in CalcPlot3D:
- Partial Derivatives
Print Plot option; 3D Options menu; View Settings menu;...
- Regions
Just as we could plot the Riemann prisms above for regions...
- Gradients
CalcPlot3D Help. Paul Seeburger, with support from the NSF...
- Partial Derivatives
Nov 21, 2021 · Using CalcPlot3D to Visualize a Level Surface. Often the level surfaces are too complex to graph enough of them, so using a computer program such as CalcPlot3D is the way to go. If you just set the function equal to \(a\), a slider will automatically be created so you can just dynamically observe the level surfaces.
Free online 3D grapher from GeoGebra: graph 3D functions, plot surfaces, construct solids and much more!
Example 1: The graph of $z=f(x,\,y)$ as a surface in $3$-space can be regarded as the level surface $w = 0$ of the function $w(x,\,y,\,z) = z - f(x,\, y)$. Example 2: Spheres $x^2+y^2+z^2 = r^2$ can be interpreted as level surfaces $w = r^2$ of the function $w = x^2+y^2+z^2$.
surf(X,Y,Z) creates a three-dimensional surface plot, which is a three-dimensional surface that has solid edge colors and solid face colors. The function plots the values in matrix Z as heights above a grid in the x-y plane defined by X and Y.
Therefore, the set \(f(x,y,z) = k\) describes a surface in 3D-space rather than a curve in 2D-space. The following diagram shows the level surfaces \[f(x,y,z) = x^2 + y^2 - x^2 = k\] for various \(k\) values. The level surfaces are hyperbolas of one or two sheets, depending on the values of \(k\).
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Both level curves and cross sections are helpful for visualizing and plotting multivariate functions. Select a function from the drop-down menu or type your own function in the text box below and click "Enter" to plot it. Click the radio buttons to view either a level curve or a cross section.
