cwhmisc (version 2.1)

rotm: Rotation matrices and compute rotation angles from orthogonal matrix

Description

Generate a (square) rotation matrix. Decompose the orthogonal matrix Q into the product R3 * R2 * R1 where the Ri are the elementary rotations around the i-th axis.

Usage

rotm(n,x,y,phi)
  rotangle(Q)

Arguments

n

Order of the square matrix.

x,y

Integers describing the plane of rotation.

phi

Angle (counted counter clockwise) of rotation of coordinate system.

Q

Orthogonal matrix.

Value

• rotm: Matrix to use for pre-multiplying. rotangle: The vector containing the rotation angles [radian]

References

"Least squares fit of point clouds" in: W. Gander and J. Hrebicek, ed., Solving Problems in Scientific Computing using Maple and Matlab, Springer Berlin Heidelberg New York, 1993, third edition 1997.

See Also

pointfit, rotm for synthesizing such a matrix.

Examples

par (mfrow=c(2,2))
  Data <- rbind(rnorm(100)*100,rnorm(100)*40,rnorm(100)*5,rnorm(100)*1,rnorm(100)*0.01)
  Rotdata <- rotm(dim(Data)[1],1,2,pi/3)  Rotdata2 <- rotm(dim(Data)[1],2,4,pi/5)  plot(Data[1,],Data[2,])
  plot(Rotdata[1,],Rotdata[2,],col="red")
  points(Rotdata2[1,],Rotdata2[2,],col="blue")
  plot(Rotdata2[2,],Rotdata2[3,],col="red")
  plot(Rotdata2[4,],Rotdata2[3,],col="red")
  rot <- matrix(c(0.847101, -0.480873, -0.226234, 0.489074,  0.538865,
0.685880, -0.207912, -0.691655,  0.691655),3,3,byrow=TRUE)
  rotangle(rot) #> 0.785398  0.209440 -0.523599
  rotangle(rot)/pi*180 #> degrees:  45  12 -30