\name{clipMesh3d}
\alias{clipMesh3d}
\alias{clipObj3d}
\title{
Clip mesh or RGL object to general region
}
\description{
Modifies a mesh3d object so that values of 
a function are bounded.
}
\usage{
clipMesh3d(mesh, fn, bound = 0, greater = TRUE, 
           minVertices = 0, plot = FALSE, keepValues = FALSE)
clipObj3d(ids = tagged3d(tags), fn, bound = 0, greater = TRUE,
           minVertices = 0,
           replace = TRUE, tags)
}
\arguments{
  \item{mesh}{
A \code{\link{mesh3d}} object.
}
  \item{fn}{
A function used to determine clipping, or a vector of values from such
a function, with one value per vertex.
}
  \item{bound}{
The value(s) of \code{fn} on the clipping boundary.
}
  \item{greater}{
Logical; whether to keep \code{fn >= bound} or not.
}
  \item{minVertices}{
See Details below.
  }
  \item{plot}{Logical; whether or not to plot the mesh.}
  \item{keepValues}{Logical; whether to save the function values at 
  each vertex when \code{plot = FALSE}.}
  \item{ids}{
The RGL id value(s) of objects to clip.
  }
  \item{tags}{
  Alternate way to specify \code{ids}.  Ignored if \code{ids} is
given.
  }
  \item{replace}{
Should the \code{ids} objects be deleted after the clipped
ones are drawn?
  }
}
\details{
These functions transform a mesh3d object or other
RGL objects by removing parts where \code{fn} violates
the bound.

For \code{clipMesh3d} the \code{fn} argument can be any
of the following:
\itemize{
\item{a character vector naming a function (with special
names \code{"x"}, \code{"y"}, and \code{"z"} corresponding
to functions returning those coordinates)}
\item{a function}
\item{a numeric vector with one value per vertex}
\item{\code{NULL}, indicating that the numeric values
are saved in \code{mesh$values}}
}
For \code{clipObj3d} any of the above except \code{NULL}
may be used.

If \code{fn}
is a numeric vector, with one value per vertex, those values will be
used in the test.
If it is a function with formal arguments \code{x},
\code{y} and \code{z}, it will receive the coordinates of 
vertices in those arguments, otherwise it will receive 
the coordinates in a single n x 3 matrix.   The function
should be vectorized and return one value per vertex, 
to check against the bound.

These operations are performed on the mesh:

First, all quads are converted to triangles.

Next, each vertex is checked against the condition.

Modifications to triangles depend
on how many of the vertices satisfy the condition 
(\code{fn >= bound} or \code{fn <= bound}, depending on \code{greater})
for inclusion.
\itemize{
\item If no vertices in a triangle satisfy the condition, the triangle is omitted.
\item If one vertex satisfies the condition, the other two vertices
in that triangle are shrunk towards it by assuming \code{fn}
is locally linear.
\item If two vertices satisfy the condition, the third vertex
is shrunk along each edge towards each other vertex, forming a
quadrilateral made of two new triangles.
\item If all vertices satisfy the condition, they are included
with no modifications.
}
Modifications to line segments are similar:  the segment
will be shortened if it crosses the boundary, or omitted
if it is entirely out of bounds.  Points, spheres, text
and sprites will just be kept or rejected.

The \code{minVertices} argument is used to improve the 
approximation to the boundary when \code{fn} is a non-linear
function.  In that case, the interpolation described above
can be inaccurate.  If \code{minVertices} is set to a
positive
number (e.g. \code{10000}), then each object is modified
by subdivision to have at least that number of vertices, 
so that pieces are smaller and the linear interpolation
is more accurate.  In the \code{clipObj3d} function, 
\code{minVertices} can be a vector, with entries corresponding
to each of the entries in \code{ids}.
}
\value{
If \code{plot = FALSE},
\code{clipMesh3d} returns new mesh3d object in which all vertices (approximately) satisfy the
clipping condition.  Note that the order of vertices will likely
differ from the original order, and new vertices will be added near
the boundary (and if \code{minVertices > 0}, in the 
interior).  If in addition \code{keepValues = TRUE},
a component named \code{"values"} will be added to the 
mesh containing the values for each vertex.

If \code{plot = TRUE}, the result will be 
plotted with \code{\link{shade3d}} and its result returned.

\code{clipObj3d} is called for the side effect of modifying
the scene.  It returns a list of new RGL id values
corresponding to the \code{ids} passed as arguments.
}
\author{
Duncan Murdoch
}
\references{
See \url{https://stackoverflow.com/q/56242470/2554330} and
\url{https://laustep.github.io/stlahblog/posts/MeshClipping.html} for a
motivating example.
}
\seealso{
See \code{\link{contourLines3d}} and
\code{\link{filledContour3d}} for ways to display function 
values without clipping.
}
\examples{

# Show the problem that minVertices solves:

cube <- cube3d(col = "red")

# This function only has one argument, so it will 
# be passed x, y and z in columns of a matrix
vecnorm <- function(vals) apply(vals, 1, function(row) sqrt(sum(row^2)))

open3d()
mfrow3d(2, 2, sharedMouse = TRUE)
id1 <- shade3d(cube)
# All vertices have norm sqrt(3), so this clips nothing:
clipObj3d(id1, fn = vecnorm, bound = sqrt(2))
next3d()
id2 <- wire3d(cube, lit = FALSE)
clipObj3d(id2, fn = vecnorm, bound = sqrt(2))

# This subdivides the cube, and does proper clipping:
next3d()
id3 <- shade3d(cube)
clipObj3d(id3, fn = vecnorm, bound = sqrt(2), minVertices = 200)
next3d()
id4 <- wire3d(cube, lit = FALSE)
clipObj3d(id4, fn = vecnorm, bound = sqrt(2), minVertices = 200)

}
