Curves visualization
This tutorial illustrates how to visualize plane and space curves using Atlas package.
To visualize a curve you can use the
Visualize function with the following syntax:
Visualize[{y1, y2,..., yn}] where
{y1, y2,..., yn} is a list with the curve parametric equations.
If you define the curve parametric 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.
Plane curves
Astroid
Visualization with parameter a as a variable
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Visualization with fixed parameter a
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Epicycloid
Visualization with parameters a and b as variables
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Visualization with fixed parameters a and b
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Epitrochoid
Visualization with parameters a and b as variables
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Visualization with parameter b as a variable
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Visualization with fixed parameters a, b, h
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Space curves
Toroidal Spiral with Manipilate
Visualization of Toroidal Spiral
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Visualization of Toroidal Spiral projections
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Rotating Sine Wave with Manipilate
Visualization of Rotating Sine Wave
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Visualization Rotating Sine Wave Projections
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Hyperboloid Sine Wave with Manipilate
Visualization of Hyperboloid Sine Wave
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Visualization of Hyperboloid Sine Wave projections
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- Lie derivative
- Exterior product
- Tensor product
- Hodge operator
- Covariant derivative
