Parallelopiped Images

> with(linalg):

Warning, the protected names norm and trace have been redefined and unprotected

Load functions to visualize the effects of linear transformations.
You may need to customize the following path to your environment.

> read `C:/othermaple/pargrm_image.txt`;

Warning, the name changecoords has been redefined

Basic Usage is:

gr := plot_pargrm_2d([ v1, v2 ], A)


where v1 and v2 are vectors in R^2 and A is a 2 by 2 matrix.

The parallelogram with vertices 0, v1, v1+v2, and v2 is drawn in blue.

The parallelogram with vertices 0, Av1, A(v1+v2), and Av2 is drawn in red.

There is also a function


describing the 3 dimensional case.

Standard Basis Vectors.

> e1 :=vector(3,[1,0,0]); e2 :=vector(3,[0,1,0]); e3 :=vector(3,[0,0,1]);

e1 := vector([1, 0, 0])

e2 := vector([0, 1, 0])

e3 := vector([0, 0, 1])

> A := matrix(3,3,[[2,1,0],[1,2,0],[0,0,1/2]]);

A := matrix([[2, 1, 0], [1, 2, 0], [0, 0, 1/2]])

This computes a graphic structure for both the original and image parallelopiped.

> gr1 := pargrm_image_3d([e1,e2,e3],A):

The default display is hidden line and not satisfactory - this could be corrected with the
options panel.

> display(gr1);

[Maple Plot]

Or just immediately specify some good options.

> display(gr1,style=wireframe,scaling=constrained, axes=boxed);

[Maple Plot]