Surfaces visualization
This tutorial illustrates how to visualize surfaces using Atlas package.
To visualize a surface you can use the
Visualize function with the following syntax:
Visualize[{y1, y2,..., yn}] where
{y1, y2,..., yn} is a list with the surface equations.
If you define the surface 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.
2-dimensional surfaces
Torus
Visualization of Torus surface
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Visualization with VisualDimensions→{2,2} - projections
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Moebius strip
Moebius strip visualization
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Visualization with VisualDimensions→{2,2} - projections
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Make Manipulate control
Visualization of Catenoid-Helicoid with Manipulate
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Visualization of projections of Catenoid-Helicoid with Manipulate
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- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
