Rotate graph by angle

Question

I have multiple matrices filled with the x and y coordinates of multiple points in 2D space that make up a graph. The matrices look something like this

x1 x2 x3 x4 ...
y1 y2 y3 y4 ...

A possible graph looks something like this

What I want to do is rotate the graph around point A so that the line between the points A and B are parallel to the X-Axis.

My idea was to treat the line AB as the hypothenuse of a right-triangle, calculate α (the angle at point A) and rotate the matrix for this graph by it using a rotation matrix.

What I did so far is the following

#df is the subset of my data that describes the graph we're handling right now,
#df has 2 or more rows

beginx=df[1,]$xcord          #get the x coordinate of point A
beginy=df[1,]$ycord          #get the y coordinate of point A
endx=df[nrow(df)-1,]$xcord   #get the x coordinate of point B
endy=df[nrow(df)-1,]$ycord   #get the y coordinate of point B
xnow=df$xcord
ynow=df$ycord
xdif=abs(beginx-endx)
ydif=abs(beginy-endy)




 if((xdif != 0) & (ydif!=0)){
     direct=sqrt(abs((xdif^2)-(ydif^2))) #calculate the length of the hypothenuse
     sinang=abs(beginy-endy)/direct      
     angle=1/sin(sinang)
     if(beginy>endy){
     angle=angle
 }else{
     angle=360-angle
 }
rotmat=rot(angle)    # use the function rot(angle) to get the rotation matrix for
                         # the calculated angle
A = matrix(c(xnow,ynow),nrow=2,byrow = TRUE)  # matrix containing the graph coords
admat=rotmat%*%A                          #multiply the matrix with the rotation matrix
}

This approach fails because it isn't flexible enough to always calculate the needed angle with the result being that the graph is rotated by the wrong angle and / or in the wrong direction.

Thanks in advance for reading and hopefully some of you can bring some fresh ideas to this

Edit: Data to reproduce this can be found here

X-Coordinates

Y-Coordinates

Not sure how to provide the data you've asked for, I'll gladly provide it in another way if you specify how you'd like it

Answer 1

Like this?

#read in X and Y as vectors
M <- cbind(X,Y)
#plot data
plot(M[,1],M[,2],xlim=c(0,1200),ylim=c(0,1200))
#calculate rotation angle
alpha <- -atan((M[1,2]-tail(M,1)[,2])/(M[1,1]-tail(M,1)[,1]))
#rotation matrix
rotm <- matrix(c(cos(alpha),sin(alpha),-sin(alpha),cos(alpha)),ncol=2)
#shift, rotate, shift back
M2 <- t(rotm %*% (
  t(M)-c(M[1,1],M[1,2])
  )+c(M[1,1],M[1,2]))
#plot
plot(M2[,1],M2[,2],xlim=c(0,1200),ylim=c(0,1200))

Edit:

I'll break down the transformation to make it easier to understand. However, it's just basic linear algebra.

plot(M,xlim=c(-300,1200),ylim=c(-300,1200))
#shift points, so that turning point is (0,0)
M2.1 <- t(t(M)-c(M[1,1],M[1,2]))
points(M2.1,col="blue")
#rotate
M2.2 <- t(rotm %*% (t(M2.1)))
points(M2.2,col="green")
#shift back
M2.3 <- t(t(M2.2)+c(M[1,1],M[1,2]))
points(M2.3,col="red")

Answer 2

Instead of a data frame, it looks like your data is better served as a matrix (via as.matrix).

This answer very similar to Roland's, but breaks things down into more steps and has some special-case handling when the angle is a multiple of pi/2.

#sample data
set.seed(1) #for consistency of random-generated data
d <- matrix(c(sort(runif(50)),sort(runif(50))),ncol=2)

#rotation about point A
rotA <- function(d) {
d.offset <- apply(d,2,function(z) z - z[1]) #offset data
  endpoint <- d.offset[nrow(d.offset),] #gets difference
  rot <- function(angle) matrix(
    c(cos(angle),-sin(angle),sin(angle),cos(angle)),nrow=2) #CCW rotation matrix
  if(endpoint[2] == 0) {
    return(d) #if y-diff is 0, then no action required
  } else if (endpoint[1] == 0) { 
    rad <- pi/2 #if x-diff is 0, then rotate by a right angle
  } else {rad <- atan(endpoint[2]/endpoint[1])}
  d.offset.rotate <- d.offset %*% rot(-rad) #rotation
  d.rotate <- sapply(1:2,function(z) d.offset.rotate[,z] + d[1,z]) #undo offset
  d.rotate
}

#results and plotting to check visually
d.rotate <- rotA(d)
plot(d.rotate)
abline(h=d[1,2])