cwhmisc (version 5.0)

rotL: Rotation matrices

Description

Rotation matrices for post(pre)-multiplication of row(column) 3-vectors, e.g. for rotation around an axis.

Usage

rotA( phi, P=c(0,0,1) )
  rotV(v, w=c(0,0,1))
  rotL(phi,k=1,m=2,n=3)
  getAp( M )

Arguments

P

c(x,y,z), coordinates of point or projection direction P-O, with O =c(0,0,0).

phi

Real, angle of counter clockwise rotation in radian.

v, w

3-vectors (x, y, z).

n

Order of the square rotation matrix >= 2.

k,m

Integers (m != k) describing the plane of rotation. m=k gives Unit matrix.

M

3x3 rotation matrix.

Value

• rotation matrices rotA: Ratation matrix to rotate around axis P - O. rotV: Ratation matrix to rotate v into w. rotL: Matrix m for multiplication m%*%vector. getAp: List with rotation axis and rotation angle corresponding to input matrix.

Details

rotL with m == k will stop with an error.

Examples

opar <- par(mfrow=c(2,4))
  x <- seq(0,1,0.05)
  phi <- c(pi/6,pi/4,-pi/6)
  Data <- matrix(c(x^2*10,(x^2-10*x)*4,(x+10)*1.5),ncol=3)
##  Data <- matrix(c(rnorm(99)*10,rnorm(99)*4,rnorm(99)*1.5),ncol=3)
  lim <- range(c(Data,-Data))*1.5
  RD <-  Data %*% rotL(phi[1],1,2)   # !! # rotate around z-axis
  RD2 <- RD %*% rotL(phi[2],2,3) # !! # rotate further around x
  RD3 <- RD2 %*% rotL(phi[3],1,2) # !! # rotate back around z
  plot(Data[,-3],xlim=lim,ylim=lim,xlab="x",ylab="y",pty="s")
  plot(RD[,-3],xlim=lim,ylim=lim,xlab="RD x",ylab="y",pty="s",pch=5,col="red")
  plot(RD2[,-3],xlim=lim,ylim=lim,xlab="RD2 x",ylab="y",pch=6,col="blue")
  plot(RD3[,-3],xlim=lim,ylim=lim,xlab="RD3 x",ylab="RD3 y",col="magenta")
  plot(Data[,1],RD3[,1])
  plot(Data[,2],RD3[,2])
  plot(Data[,3],RD3[,3])
  m <- rotL(phi[1],1,2) %*% rotL(phi[2],2,3) %*% rotL(phi[3],1,2) # !! #
  round(m %*% t(m),2) #!! # composite rotation matrix and orthogonality, should be diag(3)
  eye <- c(0.5,2.5,4)
  re  <- rotV(eye)
  getAp(re) #$A [1] -9.805807e-01  1.961161e-01 -1.193931e-16
# $phi [1] 0.5674505
  round(rotA(pi/1.5, c(1,1,1)),2)  # 60 degrees around octant bisector
# [1,]    0    1    0  is permutation of axes 1 -> 2 -> 3 -> 1
# [2,]    0    0    1
# [3,]    1    0    0