BSNS102 Study Guide - Final Guide: Unit Cube, Linear Map, Coordinate Space

• School: University of Otago
• Department: Business Studies
• Course: BSNS102
• Professor: Drew Stelljes

Document Summary

This parallelogram is also known as a skew box. drawing an object inside the box can also help: Figure 7. 3: drawing an object inside the box helps visualize the transformation. It is clear that our example matrix m not only rotates the coordinate space, it also scales it. We can extend the techniques we used to visualize 2d transformations into 3d. In 2d, we had two basis vectors that formed an l. in 3d, we have three basis vectors, and they form a tripod. Figure 7. 4 shows a teapot, a unit cube, and the basis vectors in the identity position: Figure 7. 4: teapot, unit cube, and basis vectors before transformation. 97 (in order to avoid cluttering up the diagram, we have not labeled the +z basis vector [0,0,1], which is partially obscured by the teapot and cube. ) Extracting the basis vectors from the rows of the matrix, we can visualize the transformation rep- resented by this matrix.