For computational simplicity, we have been assuming that the pivot points of our characters ocur at the origin.
a. if we apply a rotation matrix like we have been when the pivot point is at the origin, what happens to
characters that are not located around the origin?
b. let x =
xyz
be the pivot point of any three-dimensional object and a =
abc
a point on the surface of the
object. moving the pivot point to the origin has what effect on a? find a′, the image of a after moving the
object so that its pivot point is the origin.
c. apply a rotation of theta about the x-axis to a′. does this transformation cause a pivot or what you described in
part (a)?
d. after applying the rotation, translate the object so that its pivot point returns to x =
xyz
was the
x-coordinate affected by the rotation? was the pivot point?
e. summarize what you found in parts (a)–(d).