Draw an Isosurface, a Three Dimension Contour Plot
Computes and renders 3D contours or isosurfaces computed by the marching cubes algorithm.
contour3d(f, level, x, y, z, mask = NULL, color = "white", color2 = NA,
alpha = 1, fill = TRUE, col.mesh = if (fill) NA else color,
material = "default", smooth = 0,
add = FALSE, draw = TRUE, engine = "rgl", separate=FALSE, ...)f |
a function of 3 arguments or a three dimensional array. |
level |
The level or levels at which to construct contour surfaces. |
x,y,z |
locations of grid planes at which values in |
mask |
a function of 3 arguments returning a logical array, a
three dimensional logical array, or |
color |
color to use for the contour surface. Recycled to the
length of |
color2 |
opposite face color. Recycled to the length of
|
alpha |
alpha channel level, a number between 0 and 1. Recycled to the
length of |
fill |
logical; if |
col.mesh |
color to use for the wire frame. Recycled to the
length of |
smooth |
integer or logical specifying Phong shading level for
"standard" and "grid" engines or whether or not to use shading for
the "rgl" engine. Recycled to the length of |
material |
material specification; currently only used by
"standard" and "grid" engines. Currently possible values are the
character strings "dull", "shiny", "metal", and "default". Recycled
to the length of |
add |
logical; if |
draw |
logical; if |
engine |
character; currently "rgl", "standard", "grid" or "none"; for "none" the computed triangles are returned. |
separate |
logical and one for each |
... |
additional rendering arguments, e.g. material and texture
properties for the "rgl" engine. See documentation for
|
Uses the marching-cubes algorithm, with adjustments for dealing with face and internal ambiguities, to draw isosurfaces. See references for the details.
For the "rgl" engine the returned value is NULL. For the
"standard" and "grid" engines the returned value is the viewing
transformation as returned by persp. For the engine "none", or
when draw is not true, the returned value is a structure
representing the triangles making up the contour, or a list of such
structures for multiple contours.
The "rgl" engine now uses the standard rgl coordinates instead of
negating y and swapping y and z. If you need to
reproduce the previous behavior you can use
options(old.misc3d.orientation=TRUE).
Transparency only works properly in the "rgl" engine. For standard or grid graphics on pdf or quartz devices using alpha levels less than 1 does work but the triangle borders show as a less transparent mesh.
Chernyaev E. (1995) Marching Cubes 33: Construction of Topologically Correct Isosurfaces Technical Report CN/95-17, CERN
Daniel Adler, Oleg Nenadic and Walter Zucchini (2003) RGL: A R-library for 3D visualization with OpenGL
Lorensen W. and Cline H. (1987) Marching Cubes: A High Resolution 3D Surface Reconstruction Algorithm Computer Graphics vol. 21, no. 4, 163-169
Nielson G. and Hamann B. (1992) The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes Proc. IEEE Visualization 92, 83-91
#Example 1: Draw a ball
f <- function(x, y, z)x^2+y^2+z^2
x <- seq(-2,2,len=20)
contour3d(f,4,x,x,x)
contour3d(f,4,x,x,x, engine = "standard")
# ball with one corner removed.
contour3d(f,4,x,x,x, mask = function(x,y,z) x > 0 | y > 0 | z > 0)
contour3d(f,4,x,x,x, mask = function(x,y,z) x > 0 | y > 0 | z > 0,
engine="standard", screen = list(x = 290, y = -20),
color = "red", color2 = "white")
# ball with computed colors
w <- function(x,y,z) {
v <- sin(x) + cos(2 * y) * sin(5 * z)
r <- range(v)
n <- 100
i <- pmax(pmin(ceiling(n * (v - r[1]) / (r[2] - r[1])), n), 1)
terrain.colors(n)[i]
}
contour3d(f,4,x,x,x, color = w)
#Example 2: Nested contours of mixture of three tri-variate normal densities
nmix3 <- function(x, y, z, m, s) {
0.4 * dnorm(x, m, s) * dnorm(y, m, s) * dnorm(z, m, s) +
0.3 * dnorm(x, -m, s) * dnorm(y, -m, s) * dnorm(z, -m, s) +
0.3 * dnorm(x, m, s) * dnorm(y, -1.5 * m, s) * dnorm(z, m, s)
}
f <- function(x,y,z) nmix3(x,y,z,.5,.5)
g <- function(n = 40, k = 5, alo = 0.1, ahi = 0.5, cmap = heat.colors) {
th <- seq(0.05, 0.2, len = k)
col <- rev(cmap(length(th)))
al <- seq(alo, ahi, len = length(th))
x <- seq(-2, 2, len=n)
contour3d(f,th,x,x,x,color=col,alpha=al)
rgl::bg3d(col="white")
}
g(40,5)
gs <- function(n = 40, k = 5, cmap = heat.colors, ...) {
th <- seq(0.05, 0.2, len = k)
col <- rev(cmap(length(th)))
x <- seq(-2, 2, len=n)
m <- function(x,y,z) x > .25 | y < -.3
contour3d(f,th,x,x,x,color=col, mask = m, engine = "standard",
scale = FALSE, ...)
rgl::bg3d(col="white")
}
gs(40, 5, screen=list(z = 130, x = -80), color2 = "lightgray", cmap=rainbow)
## Not run:
#Example 3: Nested contours for FMRI data.
library(AnalyzeFMRI)
a <- f.read.analyze.volume(system.file("example.img", package="AnalyzeFMRI"))
a <- a[,,,1]
contour3d(a, 1:64, 1:64, 1.5*(1:21), lev=c(3000, 8000, 10000),
alpha = c(0.2, 0.5, 1), color = c("white", "red", "green"))
# alternative masking out a corner
m <- array(TRUE, dim(a))
m[1:30,1:30,1:10] <- FALSE
contour3d(a, 1:64, 1:64, 1.5*(1:21), lev=c(3000, 8000, 10000),
mask = m, color = c("white", "red", "green"))
contour3d(a, 1:64, 1:64, 1.5*(1:21), lev=c(3000, 8000, 10000),
color = c("white", "red", "green"),
color2 = c("gray", "red", "green"),
mask = m, engine="standard",
scale = FALSE, screen=list(z = 60, x = -120))
## End(Not run)
#Example 4: Separate the triangles from the contours of
# mixture of three tri-variate normal densities
nmix3 <- function(x, y, z, m, s) {
0.3*dnorm(x, -m, s) * dnorm(y, -m, s) * dnorm(z, -m, s) +
0.3*dnorm(x, -2*m, s) * dnorm(y, -2*m, s) * dnorm(z, -2*m, s) +
0.4*dnorm(x, -3*m, s) * dnorm(y, -3 * m, s) * dnorm(z, -3*m, s) }
f <- function(x,y,z) nmix3(x,y,z,0.5,.1)
n <- 20
x <- y <- z <- seq(-2, 2, len=n)
contour3dObj <- contour3d(f, 0.35, x, y, z, draw=FALSE, separate=TRUE)
for(i in 1:length(contour3dObj))
contour3dObj[[i]]$color <- rainbow(length(contour3dObj))[i]
drawScene.rgl(contour3dObj)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.