1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
|
\name{contour3d}
\alias{contour3d}
\title{Draw an Isosurface, a Three Dimension Contour Plot}
\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", ...)
}
\arguments{
\item{f}{a function of 3 arguments or a three dimensional array.}
\item{level}{The level or levels at which to construct contour surfaces.}
\item{x,y,z}{locations of grid planes at which values in \code{f} are
measured or \code{f} is to be evaluated. Can be omitted if \code{f}
is an array.}
\item{mask}{a function of 3 arguments returning a logical array, a
three dimensional logical array, or \code{NULL}. If not
\code{NULL}, only cells for which \code{mask} is true at all eight
vertices are used in forming the contour. Can also be a list of
functions the same length as \code{level}.}
\item{color}{color to use for the contour surface. Recycled to the
length of \code{'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.}
\item{color2}{opposite face color; only used for "standard" and "grid"
engines. Recycled to the length of \code{'levels'}.}
\item{alpha}{alpha channel level, a number between 0 and 1. Recycled to the
length of \code{'levels'}.}
\item{fill}{logical; if \code{TRUE}, drawing should use filled
surfaces; otherwise a wire frame should be drawn. Recycled to the
length of \code{'levels'}.}
\item{col.mesh}{color to use for the wire frame. Recycled to the
length of \code{'levels'}.}
\item{smooth}{integer specifying Phong shading level; currently only
used by "standard" and "grid" engines. Recycled to the length of
\code{'levels'}.}
\item{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 \code{'levels'}.}
\item{add}{logical; if \code{TRUE}, add to current \code{rgl} graph.}
\item{draw}{logical; if \code{TRUE}, draw the results; otherwise,
return contour triangles.}
\item{engine}{character; currently "rgl", "standard", "grid" or "none";
for "none" the computed triangles are returned.}
\item{...}{additional rendering arguments, e.g. material and texture
properties for the "rgl" engine. See documentation for
\code{\link[misc3d]{drawScene}} and \code{\link[misc3d]{drawScene.rgl}}}
}
\value{
For the "rgl" engine the returned value is \code{NULL}. For the
"standard" and "grid" engines the returned value is the viewing
transformation as returned by \code{persp}. For the engine "none", or
when \code{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.
}
\details{
Uses the marching-cubes algorithm, with adjustments for dealing with
face and internal ambiguities, to draw isosurfaces.
See references for the details.
}
\note{
The "rgl" engine now uses the standard rgl coordinates instead of
negating \code{y} and swapping \code{y} and \code{z}. If you need to
reproduce the previous behavior you can use
\code{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
\emph{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
\emph{Computer Graphics} \bold{vol. 21, no. 4}, 163-169
Nielson G. and Hamann B. (1992)
The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes
\emph{Proc. IEEE Visualization} \bold{92}, 83-91
}
\seealso{
\code{\link[rgl]{rgl.triangles}}, \code{\link[rgl]{rgl.material}},
\code{\link[rgl]{rgl.surface}}.
}
\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.bg(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.bg(col="white")
}
gs(40, 5, screen=list(z = 130, x = -80), color2 = "lightgray", cmap=rainbow)
\dontrun{
#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))
}
}
\keyword{hplot}
|
