`cylinder3d.Rd`

This function converts a description of a space curve into a `"mesh3d"`

object forming a cylindrical tube around the curve.

```
cylinder3d(center, radius = 1, twist = 0, e1 = NULL, e2 = NULL, e3 = NULL,
sides = 8, section = NULL, closed = 0,
rotationMinimizing = is.null(e2) && is.null(e3),
debug = FALSE, keepVars = FALSE)
```

- center
An n by 3 matrix whose columns are the x, y and z coordinates of the space curve.

- radius
The radius of the cross-section of the tube at each point in the center.

- twist
The amount by which the polygon forming the tube is twisted at each point.

- e1, e2, e3
The local coordinates to use at each point on the space curve. These default to a rotation minimizing frame or Frenet coordinates.

- sides
The number of sides in the polygon cross section.

- section
The polygon cross section as a two-column matrix, or

`NULL`

.- closed
Whether to treat the first and last points of the space curve as identical, and close the curve, or put caps on the ends. See the Details.

- rotationMinimizing
Use a rotation minimizing local frame if

`TRUE`

, or a Frenet or user-specified frame if`FALSE`

.- debug
If

`TRUE`

, plot the local Frenet coordinates at each point.- keepVars
If

`TRUE`

, return the local variables in attribute`"vars"`

.

The number of points in the space curve is determined by the vector lengths in `center`

,
after using `xyz.coords`

to convert it to a list. The other arguments
`radius`

, `twist`

, `e1`

, `e2`

, and `e3`

are extended to the same
length.

The `closed`

argument controls how the ends of the cylinder are
handled. If `closed > 0`

, it represents the number of points of
overlap in the coordinates. `closed == TRUE`

is the same as
`closed = 1`

. If `closed > 0`

but the ends don't actually
match, a warning will be given and results will be somewhat
unpredictable.

Negative values of `closed`

indicate that caps should be put on the
ends of the cylinder. If `closed == -1`

, a cap will be put on the
end corresponding to `center[1, ]`

. If `closed == -2`

, caps
will be put on both ends.

If `section`

is `NULL`

(the default), a regular
`sides`

-sided polygon is used, and `radius`

measures the
distance from the center of the cylinder to each vertex. If not
`NULL`

, `sides`

is ignored (and set internally to
`nrow(section)`

), and `radius`

is used as a multiplier to
the vertex coordinates. `twist`

specifies the rotation of the
polygon. Both `radius`

and `twist`

may be vectors, with
values recycled to the number of rows in `center`

, while
`sides`

and `section`

are the same at every point along the
curve.

The three optional arguments `e1`

, `e2`

, and `e3`

determine the local coordinate system used to create the vertices at
each point in `center`

. If missing, they are computed by simple
numerical approximations. `e1`

should be the tangent coordinate,
giving the direction of the curve at the point. The cross-section of
the polygon will be orthogonal to `e1`

. When `rotationMinimizing`

is `TRUE`

, `e2`

and `e3`

are chosen to give
a rotation minimizing frame (see Wang et al., 2008). When it is
`FALSE`

, `e2`

defaults to an
approximation to the normal or curvature vector; it is used as the
image of the `y`

axis of the polygon cross-section. `e3`

defaults to an approximation to the binormal vector, to which the
`x`

axis of the polygon maps. The vectors are orthogonalized and
normalized at each point.

A `"mesh3d"`

object holding the cylinder, possibly with
attribute `"vars"`

containing the local environment of the function.

Wang, W., Jüttler, B., Zheng, D. and Liu, Y. (2008). Computation of rotation minimizing frames. ACM Transactions on Graphics, Vol. 27, No. 1, Article 2.

```
# A trefoil knot
open3d()
theta <- seq(0, 2*pi, len = 25)
knot <- cylinder3d(
center = cbind(
sin(theta) + 2*sin(2*theta),
2*sin(3*theta),
cos(theta) - 2*cos(2*theta)),
e1 = cbind(
cos(theta) + 4*cos(2*theta),
6*cos(3*theta),
sin(theta) + 4*sin(2*theta)),
radius = 0.8,
closed = TRUE)
shade3d(addNormals(subdivision3d(knot, depth = 2)), col = "green")
```