The Vertices of the Cube

This is a continuation from the previous page.

The eight vertices of the cube must be transformed in the same way as the matrix v. The vertices must be rotated, projected, and represented by visual points. Since the same operations must be applied eigth times, it is easiest to use the spreadsheet.

Let the cube have its vertices in at the coordinates (0,0,0), (1,0,0), (0,1,0), (0,0,1), (0,1,1), (1,0,1), (1,1,0) and (1,1,1).

One way to do the operations is to enter the coordinates in the spreadsheet and then:

• Make a matrix of the coordinates of one point, then make relative copies of that matrix.
• Perform the transformations on one matrix, then make relative copies of the result.
• Make a point of one transformed matrix, then make relative copies of the point.

The operations are done in column A in the picture below. The relative copies are made by dragging to the right.

Rotate the points to fill in the sides of the cube by using the Polygon tool.

It is of course possible to use other coordinates for the vertices of the cube.

Using the same spreadsheet, you can now rotate other 3D objects and project them on 2D.