Hello,
in a three dimensional coordinate system, I'd like to find all my
experimental data points that fall within an ellipsoid around a fixed
coordinate. The fixed point is defined by (x.coord.point,
y.coord.point, z.coord.point). The coordinates of the ellipsoid are
given by the three vectors x,y,z.
In a previous version of my code, I simply used a box instead of an
ellipsoid to sort my data, which was really easy as I only had to
compare each data point to three coordinates. I used something like this...
XYZ.within <- which( x.data < x.coord.point + multipl &
x.data > x.coord.point - multipl &
y.data < y.coord.point + multipl &
y.data > y.coord.point - multipl &
z.data < z.coord.point + multipl &
z.data > z.coord.point - multipl
)
But now I have many more coordinate sets to compare my data to. How
can I find out in an efficient way which of the data points lie
within the ellipsoid?
Thanks!
Kim
#mock-data for the display with rgl
data.1 <- xyz.coords(5,-2,17)
data.2 <- xyz.coords(15, -10,18)
data.3 <- xyz.coords(-19, 13,9)
#code I use to construct the ellipsoid
x.coord.point <- 4
y.coord.point <- -7
z.coord.point <- -3
radius <- 8
x.radius.multiplier <- 1
y.radius.multiplier <- 2
z.radius.multiplier <- 3
endpoint <- 350
interval <- 2
alpha <- rep(seq(0,endpoint, by
=interval),rep((endpoint+interval)/interval,(endpoint+interval)/interval))
beta <- c(rep(seq(0,endpoint, by =interval),(endpoint+interval)/interval))
x <-
x.coord.point+(x.radius.multiplier*radius)*cos(alpha*pi/180)*sin(beta*pi/180)
y <- y.coord.point+(y.radius.multiplier*radius)*sin(alpha*pi/180)
z <-
z.coord.point+(z.radius.multiplier*radius)*cos(alpha*pi/180)*cos(beta*pi/180)
# using rlg to visualize the mock-data and the ellipsoid
plot.lim <- c(-20,20)
plot3d(x, y, z,
xlim = plot.lim,
ylim = plot.lim,
zlim = plot.lim
)
points3d(data.1, col ="green", size = 6)
points3d(data.2, col ="red", size = 6)
points3d(data.3, col ="blue", size = 6)
__________________________________________
Kim Milferstedt
University of Illinois at Urbana-Champaign
Department of Civil and Environmental Engineering
4125 Newmark Civil Engineering Laboratory
205 North Mathews Avenue MC-250
Urbana, IL 61801
USA
phone: (001) 217 333-9663
fax: (001) 217 333-6968
email: [EMAIL PROTECTED]
http://cee.uiuc.edu/research/morgenroth
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