R: 3D to 2D Transformation for Perspective Plots

trans3d {grDevices}

R Documentation

3D to 2D Transformation for Perspective Plots

Description

Projection of 3-dimensional to 2-dimensional points using a 4x4 viewing transformation matrix. Mainly for adding to perspective plots such as persp.

Usage

trans3d(x, y, z, pmat, continuous = FALSE, verbose = TRUE)

Arguments

`x`, `y`, `z`	numeric vectors of equal length, specifying points in 3D space.
`pmat`	a `4 \times 4` viewing transformation matrix, suitable for projecting the 3D coordinates `(x,y,z)` into the 2D plane using homogeneous 4D coordinates `(x,y,z,t)`; such matrices are returned by `persp()`.
`continuous`	logical flag specifying if the transformation should check if the transformed points are continuous in the sense that they do not jump over `a/0` discontinuity. As these assume `(x,y,z)` to describe a continuous curve, the default must be false. In case of projecting such a curve however, setting `continuous=TRUE` may be advisable.
`verbose`	only for `continuous=TRUE`, indicates if a warning should be issued when points are cut off.

Value

a list with two components

x, y

the projected 2d coordinates of the 3d input (x,y,z).

Examples

## See  help(persp) {after attaching the 'graphics' package}
##      -----------

## Example for 'continuous = TRUE' (vs default):
require(graphics)
x <- -10:10/10 # [-1, 1]
y <- -16:16/16 # [-1, 1] ==> z = fxy := outer(x,y) is also in [-1,1]

p <- persp(x, y, fxy <- outer(x,y), phi = 20, theta = 15, r = 3, ltheta = -75,
           shade = 0.8, col = "green3", ticktype = "detailed")
## 5 axis-parallel auxiliary lines in x-y  and y-z planes :
lines(trans3d(-.5 , y=-1:1, z=min(fxy),  pmat=p), lty=2)
lines(trans3d(  0 , y=-1:1, z=min(fxy),  pmat=p), lty=2)
lines(trans3d(-1:1, y= -.7, z=min(fxy),  pmat=p), lty=2)
lines(trans3d( -1,  y= -.7, z=c(-1,1) ,  pmat=p), lty=2)
lines(trans3d( -1,  y=-1:1, z= -.5    ,  pmat=p), lty=2)
## 2 pillars to carry the horizontals below:
lines(trans3d(-.5 , y= -.7, z=c(-1,-.5), pmat=p), lwd=1.5, col="gray10")
lines(trans3d( 0  , y= -.7, z=c(-1,-.5), pmat=p), lwd=1.5, col="gray10")
## now some "horizontal rays" (going from center to very left or very right):
doHor <- function(x1, x2, z, CNT=FALSE, ...)
    lines(trans3d(x=seq(x1, x2, by=0.5), y= -0.7, z = z, pmat = p, continuous = CNT),
          lwd = 3, type="b", xpd=NA, ...)
doHor(-10,  0, z = -0.5, col = 2)  # x in [-10, 0] -- to the very left : fine
doHor(-.5,  2, z = -0.52,col = 4) # x in [-0.5, 2] only {to the right} --> all fine
## but now, x in [-0.5, 20] -- "too far" ==> "wrap around" problem (without 'continuous=TRUE'):
doHor(-.5, 20, z = -0.58, col = "steelblue", lty=2)
## but it is fixed with continuous = CNT = TRUE:
doHor(-.5, 20, z = -0.55, CNT=TRUE, col = "skyblue")