Coordinate systems visualization

This tutorial illustrates how to visualize multidimensional coordinate systems using Atlas package.
To visualize a coordinate system you can use the Visualize function with the following syntax: Visualize[{y1, y2,..., yn}] where {y1, y2,..., yn} is a list with the coordinate system equations.
If you define the coordinate system equations as a variable like that eqs = {y1, y2,..., yn} then you have to use the following syntax: Visualize[Evaluate[eqs]] because the Visualize function has attribute HoldAll.
You can use any option for native Mathematica plot functions with the Visualize function. For instance: PlotLabel, ViewPoint etc.

Examples:

Visualize[{expr1, expr2,..., exprn}]generates visual presentations of m-dimentional mapping, where m is number of indeterminates in {expr1, expr2,..., exprn}

Necessary functions.

Loading Atlas package
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2-dimensional coordinate systems

Polar coordinate system

Visualization
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Bipolar coordinate system

Visualization with parameter a as a variable
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Visualization with fixed parameter a
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Maxwell coordinate system

Visualization with parameter a as a variable
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Visualization with fixed parameter a
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3-dimensional coordinate systems

Spherical coordinate system

Visualization as a set of coordinate surfaces
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Visualization in one plot
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SixSphere coordinate system

Visualization as a set of coordinate surfaces
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Visualization in one plot
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Toroidal coordinate system

Visualization as a set of coordinate surfaces
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Visualization in one plot
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N-dimensional coordinate systems

Cartesian coordinate system

The coordinate system equations for n-dimensions. You can change Dim variable here. Remember that visualization of high dimensional objects may take a lot of time and memory.
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Visualization
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Sherical coordinate system

The coordinate system equations for n-dimensions. You can change Dim variable here. Remember that visualization of high dimensional objects may take a lot of time and memory.
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Visualization
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