On 11/16/13 1:34 AM, Chris Seberino wrote:
I've been searching the Internet and can't find examples of plots of
functions of THREE
variables like f(x, y, z).
I'd like to use a different color at each point in space to denote the
function value.
Is that possible in Sage? Are there examples somewhere?
(All the examples I saw were for 2 variable functions like g(x, y). )
We don't have volumetric visualization built in, but you can sort of do
it yourself: http://sagecell.sagemath.org/?q=pduwfm
f(x,y,z)=x^2+y^2+z^2
opacity=0.5
pointsize=30
domain=srange(-2,2,.3)
jitter=0.1 # set to 0 to have a truly uniform grid
min=0
max=f(2,2,2)
frange = float(max-min)
from itertools import product
ff=fast_callable(f, domain=RDF)
# this could be much faster if we were evaluating it using vector
arithmetic on a numpy grid, for example.
g=[]
for i,j,k in product(domain,repeat=3):
g.append(point3d((i+random()*jitter,j+random()*jitter,k+random()*jitter), size=pointsize,
opacity=opacity, color=hue((ff(i,j,k)-min)/frange)))
G = sum(g)
show(G)
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