benedict@chaos.utexas.edu (Thomas Benedict) (11/13/90)
I was talking with a colleague who had an interesting problem. He has a four-dimensional data set he needs to view. The data set consists of an X Y grid of around 80 elements on a side. At each gridpoint there are 64 elements, each corresponding to a certain doppler shift toward and away from the viewer. At each (x, y, doppler) is a measurement of flux. So the data looks something like this: |<----- 80 ---->| / ____ / /___/| 32 units of speed toward us - +--+--+-- ... --+--+ |____|/ ^ | | | | | |____|/ | +--+--+-- --+--+ | | | | | | | \ ... 80 . . \ |____|/ 0 speed toward us | . . |____|/ V | | | | | | | - +--+--+-- --+--+ ... |____|/ 32 units of speed away from us |____|/ All of this data was taken from the center of a spiral galaxy. What he needs to get from this data is an idea of the gas flow at the center of this galaxy. I've thought of a couple of ways of looking at the data, but none are quite satisfactory. A perfect way of looking at it would be a three dimensional vector field for the gas, but I don't think that can be done with just this data. If we had another viewer at a position 90 degrees away from our own we might be able to, but alas warp speed space travel is still restricted to the movies. If you can think of a way of looking at this, please mail it to me. I don't often read this newsgroup and might miss a reply. Tom Benedict benedict@chaos.utexas.edu
eugene@eos.arc.nasa.gov (Eugene Miya) (11/15/90)
I had friends with similar but more simplistic problems:
complex functions which map from one complex space to another.
One of the usual suggestions is "Well you can't plot 4-D but
you can take the Euclidean norm of the function (3-D) and..."
That doesn't cut it, too much detail is lost.
I am certainly open to hearing other suggestions and forwarding them.
--e.n. miya, NASA Ames Research Center, eugene@eos.arc.nasa.gov
{uunet,mailrus,most gateways}!ames!eugene
AMERICA: CHANGE IT OR LOSE IT.landheim@bbn.com (Greg Landheim) (11/15/90)
In article <7588@eos.arc.nasa.gov> eugene@eos.UUCP (Eugene Miya) writes: >One of the usual suggestions is "Well you can't plot 4-D but > >I am certainly open to hearing other suggestions and forwarding them. > Of course you can alway plot 4-D by using the color of a 3-D point to represent the fourth dimension. Another alternative was described in: "Plotting Contour Surfaces of a Function of Three Variables," Granville Sewell, University of Texas at El Paso, ACM Transactions on Mathematical Software, Vol. 14, No. 1, March 1988, Pages 33-34. G. Landheim
cyberoid@milton.u.washington.edu (Robert Jacobson) (11/16/90)
ENVISIONING INFORMATION by Edward Tufte (Graphics Press, 1990) describes many methods of capturing fourth and higher dimensions of data -- and he's primarily using static 2-D, on-printed page displays.
wex@dali.pws.bull.com (Buckaroo Banzai) (11/21/90)
[The original question related to how to view 4D-info in 3D.] One thing I'm fond of, which I think frequently get shortchanged, is to map the 4th dimension to time. Paint a series of 3D pictures and show them in a closed loop. It's a little more compute-intensive, and you have to be careful you don't imply something with motion that you didn't intend, but it avoids having to collapse your data too much. -- --Alan Wexelblat phone: (508)294-7485 Bull Worldwide Information Systems internet: wex@pws.bull.com Never worry about theory as long as the machinery does what it's supposed to do.