[R] distance to eye in persp()

(Ted Harding) Ted.Harding at nessie.mcc.ac.uk
Mon Sep 19 11:48:31 CEST 2005

On 19-Sep-05 Robin Hankin wrote:
> Hi
> the manpage for persp() has a wonderful section where a the
> trans3d()  function is used with points() and lines() to add
> red dots and a green sinusoid to the Mexican hat surface.
> Does anyone have a way to tell what distance  a point is from
> the eye/camera?
> Take the following line:
> lines (trans3d(x, y=10, z= 6 + sin(x), pm = res), col = 3)
> Is there a function like trans3d() that returns a vector of
> distances from the x,y,z point to the camera?  I want this so
> I can plot clouds of points with the further ones in smaller
> plotsizes, and perhaps even fading to white (as though viewed
> through fog).

Wonderfully put! That's what statistics is about!

I think you may have to write your own. This is possible given
the values for the parameters xlim, ylim, zlim, r, theta, phi
(default as defined in ?persp, or explicitly user-defined),
since you can then determine the 3D coordinates of the "Eye"
relative to the (X,Y,Z) axes being plotted, after which the
distance to a particular (x,y,z) point is trivial.


1. Coordinates of Eye relative to the centre of the box

   xE <- r*sin(theta + pi)*cos(phi)
   yE <- r*cos(theta + pi)*cos(phi)
   zE <- r*sin(phi)

2. Centre of box relative to real (0,0,0)

   xC <- mean(xlim); yC <-mean(ylim); xC <- mean(zlim)

3. Coordinates of (x,y,z) relative to Eye

   x1 <- x - xE - xC; y1 <- y - yE - yC; z1 <- z - zE - zC

4. Distance from Eye to (x,y,z)

   d = sqrt(x1^2 + y1^2 + z1^2)

(Hoping I've not got anything the wrong way round there!)

Best wishes,

E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 19-Sep-05                                       Time: 10:17:55
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