Rotation about the line x=y=z - University of Cincinnati
Rotation about the line x = y = z
David A Herron
David.Herron@UC.edu
3D Rotation
FS 2017 1 / 9
The Problem: rotate 60 about the line x = y = z
Here we find a formula for a 60 rotation about the line x = y = z.
David.Herron@UC.edu
3D Rotation
FS 2017 2 / 9
The Problem: rotate 60 about the line x = y = z
Here we find a formula for a 60 rotation about the line x = y = z. Since this rotation is a linear transformation R3 -T R3, there is a 3 ? 3 matrix A such that for every vector x in R3, T (x) = Ax .
David.Herron@UC.edu
3D Rotation
FS 2017 2 / 9
The Problem: rotate 60 about the line x = y = z
Here we find a formula for a 60 rotation about the line x = y = z. Since this rotation is a linear transformation R3 -T R3, there is a 3 ? 3 matrix A such that for every vector x in R3, T (x) = Ax . Recall that A is the standard matrix for T , and the columns of A are given by the T images of the standard basis vectors, so
A = [T ]E = T (e1)T (e2)T (e3) .
David.Herron@UC.edu
3D Rotation
FS 2017 2 / 9
The Problem: rotate 60 about the line x = y = z
Here we find a formula for a 60 rotation about the line x = y = z. Since this rotation is a linear transformation R3 -T R3, there is a 3 ? 3 matrix A such that for every vector x in R3, T (x) = Ax . Recall that A is the standard matrix for T , and the columns of A are given by the T images of the standard basis vectors, so
A = [T ]E = T (e1)T (e2)T (e3) . Lets look at a picture!
David.Herron@UC.edu
3D Rotation
FS 2017 2 / 9
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