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\name{subdivision3d}
\alias{subdivision3d}
\alias{subdivision3d.mesh3d}
\alias{divide.mesh3d}
\alias{normalize.mesh3d}
\alias{deform.mesh3d}
\title{Subdivide a mesh}
\description{
The subdivision surface algorithm divides and refines (deforms) a
given mesh recursively to certain degree (depth).
The mesh3d algorithm consists of two stages: divide and deform.
The divide step generates for each triangle or quad four new triangles or quads, the deform
step drags the points (refinement step).
}
\usage{
subdivision3d( x, ...)
\method{subdivision3d}{mesh3d}( x, depth = 1, normalize = FALSE,
deform = TRUE, keepTags = FALSE, ... )
divide.mesh3d(mesh, vb = mesh$vb,
ib = mesh$ib, it = mesh$it, is = mesh$is,
keepTags = FALSE)
normalize.mesh3d(mesh)
deform.mesh3d(mesh, vb = mesh$vb, ib = mesh$ib, it = mesh$it,
is = mesh$is)
}
\arguments{
\item{x}{3d geometry mesh}
\item{mesh}{3d geometry mesh}
\item{depth}{recursion depth}
\item{normalize}{normalize mesh3d coordinates after division if \code{deform} is \code{TRUE}}
\item{deform}{deform mesh}
\item{keepTags}{if \code{TRUE}, add a \code{"tags"}
component to the output.}
\item{is}{indices for segments}
\item{it}{indices for triangular faces}
\item{ib}{indices for quad faces}
\item{vb}{matrix of vertices: 4 x n matrix (rows x, y, z, h) or equivalent
vector, where h indicates scaling of each plotted quad}
\item{...}{other arguments (unused)}
}
\details{
\code{subdivision3d} takes
a mesh object and replaces each segment with two new ones, and
each triangle or quad with 4 new ones
by adding vertices half-way along the edges (and one in the
centre of a quad). The positions of the vertices are
deformed so that the resulting surface is smoother than the original. These operations are repeated \code{depth} times.
The other functions do the individual steps of the subdivision.
\code{divide.mesh3d} adds the extra vertices. \code{deform.mesh3d}
does the smoothing by replacing each vertex with the average of each of its neighbours. \code{normalize.mesh3d}
normalizes the homogeneous coordinates, by setting the
4th coordinate to 1. (The 4th coordinate is used as a
weight in the deform step.)
}
\value{
A modified \code{\link{mesh3d}} object. If \code{keepTags} is
\code{TRUE}, it will contain a \code{tags} component. For
details, see the \code{\link{clipMesh3d}} help topic.
}
\examples{
open3d()
shade3d( subdivision3d( cube3d(), depth = 3 ), color = "red", alpha = 0.5 )
}
\seealso{
\code{\link{r3d}}
\code{\link{mesh3d}}
}
\keyword{dynamic}
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