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- Can derive the matrix for angle-axis rotation by
composing basic transformations.
- Rotation given by
and
.
- Assume that
.
- General idea: Map
onto one of the canonical axes,
rotate by
, map back.
- Pick the closest axis to
using
.
(Assume we chose the x-axis in the following).
- Project
onto
in the xz plane:
- Compute
and
, where
is the angle of
with the x-axis.
- Use
and
to create
:
- Rotate
onto the xy plane using
:
- Compute
and
, where
is the angle of
with the x-axis.
- Use
and
to create
:
- Rotate
onto the x axis using
.
- Rotate about the x-axis by
:
.
- Reverse z-axis rotation:
.
- Reverse y-axis rotation:
.
The overall transformation is
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab
cs488@cgl.uwaterloo.ca