contour3d: Draw an Isosurface, a Three Dimension Contour Plot

In misc3d: Miscellaneous 3D Plots

Description

Computes and renders 3D contours or isosurfaces computed by the marching cubes algorithm.

Usage

   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, ...)

Arguments

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 f are measured or f is to be evaluated. Can be omitted if f is an array.
mask	a function of 3 arguments returning a logical array, a three dimensional logical array, or NULL. If not NULL, only cells for which mask is true at all eight vertices are used in forming the contour. Can also be a list of functions the same length as level.
color	color to use for the contour surface. Recycled to the length of 'levels'. Can also be a function, or list of functions, of three arguments. These are called for each level with three arguments, the coordinates of the midpoints of the triangles making up the surface. They should return a vector of colors to use for the triangles.
color2	opposite face color. Recycled to the length of 'levels'.
alpha	alpha channel level, a number between 0 and 1. Recycled to the length of 'levels'.
fill	logical; if TRUE, drawing should use filled surfaces; otherwise a wire frame should be drawn. Recycled to the length of 'levels'.
col.mesh	color to use for the wire frame. Recycled to the length of 'levels'.
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 'levels'.
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 'levels'.
add	logical; if TRUE, add to current rgl graph.
draw	logical; if TRUE, draw the results; otherwise, return contour triangles.
engine	character; currently "rgl", "standard", "grid" or "none"; for "none" the computed triangles are returned.
separate	logical and one for each level; if it is TRUE, and either the engine is "none" or draw is not true, the triangles from the corresponding level are separated into disconnected chunks, namely that triangles from different chunks have no vertex in common. The default is FALSE for each level.
...	additional rendering arguments, e.g. material and texture properties for the "rgl" engine. See documentation for drawScene and drawScene.rgl

Details

Uses the marching-cubes algorithm, with adjustments for dealing with face and internal ambiguities, to draw isosurfaces. See references for the details.

Value

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.

Note

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.

References

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

See Also

triangles3d, material3d, surface3d.

Examples

  #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)

Example output

Warning message:
no DISPLAY variable so Tk is not available 
Loading required package: R.matlab
R.matlab v3.6.2 (2018-09-26) successfully loaded. See ?R.matlab for help.

Attaching package: ‘R.matlab’

The following objects are masked from ‘package:base’:

    getOption, isOpen

Loading required package: fastICA
Loading required package: tcltk
Loading required package: tkrplot
Warning message:
loading Rplot failed 
Triangles are separated into 3 chunks.

misc3d documentation built on Oct. 8, 2021, 1:06 a.m.