GPGPU Programming for Games and Science

Linear and Affine Algebra 337

(-sin μ, cos μ, 0)

(0,0,0)

(cos μ, sin μ, 0)

(-sin μ, 0, cos μ)

(0,0,0)

(cos μ, 0, sin μ)

X

2

X

1

X

0

FIGURE 6.10: Conversion from (x

0

,x

1

,x

2

) in a right-handed coordinate

system to (x



0

,x



1

,x



2

)inaleft-handedcoordinatesystem.

It so happens that C

−1

= C

T

= C. For orthonormal coordinate axes, generally

C

−1

= C

T

.

Equations (6.148) and (6.149) are easy enough to set up based on a visual

inspection of the coordinate axes. Now suppose that we have a rotation in the

first coordinate system, and that rotation is represented by a rotation matrix

R. We want to determine the rotation matrix R



in the second coordinate

system that produces the same ...