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\name{parametric3d}
\alias{parametric3d}
\title{Draw a 3D Parametric Plot}
\description{
Plot a two-parameter surface in three dimensions.
}
\usage{
parametric3d(fx, fy, fz, u, v, umin, umax, vmin, vmax, n = 100,
color = "white", color2 = NA, alpha = 1,
fill = TRUE, col.mesh = if (fill) NA else color,
smooth = 0, material = "default",
add = FALSE, draw = TRUE, engine = "rgl", ...)
}
\arguments{
\item{fx,fy,fz}{vectorized functions of u and v to compute the
\code{x}, \code{y}, and \code{z} coordinates.}
\item{u}{numeric vector of u values.}
\item{v}{numeric vector of v values.}
\item{umin}{numeric; the minimum value of u. Ignored in \code{u} is
supplied.}
\item{umax}{numeric; the maximum value of u. Ignored in \code{u} is
supplied.}
\item{vmin}{numeric; the minimum value of v. Ignored in \code{v} is
supplied.}
\item{vmax}{numeric; the maximum value of v. Ignored in \code{v} is
supplied.}
\item{n}{the number of equally spaced \code{u} and \code{v} values to
use. Ignored in \code{u} and \code{v} are supplied.}
\item{color}{color to use for the surface. Can also be a function of
three arguments. This is called with three arguments, the
coordinates of the midpoints of the triangles making up the surface.
The function should return a vector of colors to use for the
triangles.}
\item{color2}{opposite face color; only used for "standard" and "grid"
engines.}
\item{alpha}{alpha channel level, a number between 0 and 1..}
\item{fill}{logical; if \code{TRUE}, drawing should use filled
surfaces; otherwise a wire frame should be drawn.}
\item{col.mesh}{color to use for the wire frame.}
\item{smooth}{integer specifying Phong shading level; currently only
used by "standard" and "grid" engines.}
\item{material}{material specification; currently only used by
"standard" and "grid" engines. Currently possible values are the
character strings "dull", "shiny", "metal", and "default".}
\item{add}{logical; if \code{TRUE}, add to current 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 surface.
}
\details{
Analogous to Mathematica's \code{Param3D}. Evaluates the
functions \code{fx}, \code{fy}, and \code{fz} specifying the
coordinates of the surface at an equally spaced grid of values for the
parameters \code{u} and \code{v}.
}
\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{
Daniel Adler, Oleg Nenadic and Walter Zucchini (2003)
RGL: A R-library for 3D visualization with OpenGL
}
\seealso{
\code{\link[rgl]{rgl.surface}},
\code{\link[rgl]{rgl.material}},\code{\link[scatterplot3d]{scatterplot3d}}.
}
\examples{
#Example 1: Ratio-of-Uniform sampling region of bivariate normal
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
umin = -20, umax = 20, vmin = -20, vmax = 20,
n = 100)
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101))
parametric3d(fx = function(u, v) u * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fy = function(u, v) v * exp(-0.5 * (u^2 + v^2 -
2 * 0.75 * u * v)/sqrt(1-.75^2))^(1/3),
fz = function(u, v) exp(-0.5 * (u^2 + v^2 - 2 * 0.75 * u *
v)/sqrt(1-.75^2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
engine = "standard", scale = FALSE, screen = list(x=-90, y=20))
#Example 2: Ratio-of-Uniform sampling region of Bivariate t
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
umin = -20, umax = 20, vmin = -20, vmax = 20,
n = 100, color = "green")
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
color = "green")
parametric3d(fx = function(u,v) u*(dt(u,2) * dt(v,2))^(1/3),
fy = function(u,v) v*(dt(u,2) * dt(v,2))^(1/3),
fz = function(u,v) (dt(u,2) * dt(v,2))^(1/3),
u = qcauchy((1:100)/101), v = qcauchy((1:100)/101),
color = "green", engine = "standard", scale = FALSE)
#Example 3: Surface of revolution
parametric3d(fx = function(u,v) u,
fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi)
parametric3d(fx = function(u,v) u,
fy = function(u,v) sin(v)*(u^3+2*u^2-2*u+2)/5,
fz = function(u,v) cos(v)*(u^3+2*u^2-2*u+2)/5,
umin = -2.3, umax = 1.3, vmin = 0, vmax = 2*pi,
engine = "standard", scale = FALSE,
color = "red", color2 = "blue", material = "shiny")
}
}
\keyword{hplot}
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