## 3-D VIEW OF THE LS GEOMETRY:
LS.geom <- function(
                    rot = 4,   # number of 360 degree rotations around the z axes
                    spd = .05, # rotation speed, i.e., angular increment between animation frames
                    rg  = c(-.07,1.07), # range of x, y, z
                    cex = 1.5, # point fatness
                    lwd = 1.5, # line fatness
                    ra  = .08, # right angle size
                    ad  = .06, # text moves up and down
                    sq  = sqrt(2),
                    phi = 20,  # view latitude
                    y = c(x=.7, y=.7, z=.7),  # response vector
                    x = c(.1, .5))            # coordinates of x0 and x1: this and switched
{
  for(theta in seq(0,360*rot,by=spd)) {
    persp(x=0:1, y=0:1, z=matrix(c(0,0,0,1),nrow=2,ncol=2),
          xlim=rg, ylim=rg, zlim=rg, mar=rep(0,4),
          xlab="", ylab="", zlab="", border=NA, box=F, axes=F,
          theta=theta, phi=phi, r=10) -> tr
    # Hor square = space of fits
    lines(trans3d(x=c(0,1,1,0,0), y=c(0,0,1,1,0), z=c(0,0,0,0,0), pmat=tr), lwd=2)
    # Vert line = residual space
    lines(trans3d(x=c(0,0), y=c(0,0), z=c(0,1), pmat=tr), lwd=2)
    # Indicators of right angles:
    lines(trans3d(x=c( 0, ra, ra,NA,  0,  0,  0,NA, y[1], y[1]-ra/sq, y[1]-ra/sq),
                  y=c( 0,  0,  0,NA,  0, ra, ra,NA, y[2], y[2]-ra/sq, y[2]-ra/sq),
                  z=c(ra, ra,  0,NA, ra, ra,  0,NA,   ra,         ra,          0), pmat=tr), lwd=1)
    # Predictor vectors:
    lines(trans3d(x=c(0,.5,NA,0,.1), y=c(0,.1,NA,0,.5), z=c(0,0,NA,0,0), pmat=tr),
          pch=16, cex=cex, col="blue", lwd=lwd, type="o")
    # origin, y, yhat, r:
    lines(trans3d(x=c(0, y[1],    0, 0, y[1], y[1]),
                  y=c(0, y[2],    0, 0, y[2], y[2]),
                  z=c(0, y[3], y[3], 0,    0, y[3]), pmat=tr),
          pch=16, cex=cex, col="red", lwd=lwd, type="o")
    text(trans3d(x=c(  0, x[1], x[2], y[1], y[1]+ad, -ad/2),
                 y=c(  0, x[2], x[1], y[2], y[2]+ad, -ad/2),
                 z=c(-ad,  -ad, -ad,  -ad,  y[3]+ad,  y[3]), pmat=tr),
         lab=c(expression(bold(O)), expression(bold(x)[0]), expression(bold(x)[1]),
           expression(hat(bold(y))), expression(bold(y)), expression(bold(r))) )
    text(trans3d(x=1, y=1, z=-.1, pmat=tr), adj=0, cex=.8,
         lab=" Space of Fits\n = Range(P)\n = Null(I-P)" )
    text(trans3d(x=0, y=0, z=.9, pmat=tr), adj=0, cex=.8,
         lab=" Resid. Space\n = Range(I-P)\n = Null(P)" )
  }
}
LS.geom()