Representations of Surfaces (part 1):  z=f(x,y)

Surface of the form: (z=f(x,y))

We construction an example function of the form z = U(S,V) for display with different kinds of superimposed information.

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A default view of the surface.

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Plotting the surface with levels of constant height superimposed and colored according to its height.

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This function will be used to paint surface according to an angular variable.

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Drawing circles on the plot and coloring accoding to the angle; this is superposing a visualization of the cylindrical coordinate system.

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Here we write a function to calculate the curvature of f(x,y) as a function of x and y. We will use this to draw lines of constant curvature.

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This is a moderately advanced application---here I define a function symbolically by evaluating the curvature function, this will be passed to Plot3D as the MeshFunction.

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 Created by Wolfram Mathematica 6.0  (28 September 2007)