Visualization in Atlas package
Visualization in Atlas package allows visualize n-dimensional differential geometry objects. The following differential geometry objects can be visualized:
- n-dimentional coordinate systems
- curves in n-dimentional manifolds
- m-dimentional submanifolds in n-dimentional manifolds
The visualize function splits visual space and parameters space in 1,2 or 3-dimensional subspaces to visualize an n-dimensional object.
The visualize function has simple uniform sintax which is appropriate for objects of any dimensions:
Visualize[{expr1, expr2, ..., exprn}, {x1, a1, b1}, {x2, a2, b2}, ..., {xm, am, bm}]
The function automatically selects appropriate native Mathematica plot function to visualize an object. Moreover the function can automatically choose bounds for visualization and manipulate parameters. And even more, the function automatically splits the visualized object parameters into 2 or 3 dimensional sections and make appropriate projectors on 1, 2 or 3 dimentional subspaces of the visualization.
One can controll the visualization process completely by using only a few options:
- VisualConstants
- VisualDimensions
- VisualManipulate
- VisualPlot
- VisualProjectors
Nevertheless the function understands all options for any native Mathematica plot function.
Visualize visualize multidimensional differential geometry objects