# R/arrows3d.R In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

#### Documented in arrows3dcone3d

```# code taken from pca3d:  objects3d.R

# return the basic cone mesh
# scale is necessary because of the dependence on the aspect ratio
.getcone <- function( r, h, scale= NULL ) {

## for drawing circles in 3D, precalculate some values
.sin.t <- sin(seq(0, 2 * pi, len= 10))
.cos.t <- cos(seq(0, 2 * pi, len= 10))

n  <- length( .sin.t )
xv <- r * .sin.t
yv <- rep( 0, n )
zv <- r * .cos.t

if( missing( scale ) ) scale <- rep( 1, 3 )

scale <- 1 / scale
sx <- scale[1]
sy <- scale[2]
sz <- scale[3]

tmp <- NULL
for( i in 1:(n-1) ) {
tmp <- rbind( tmp,
c( 0, 0, 0 ),
scale3d( c( xv[i],   yv[i],   zv[i]   ), sx, sy, sz ),
scale3d( c( xv[i+1], yv[i+1], zv[i+1] ), sx, sy, sz ) )
}
for( i in 1:(n-1) ) {
tmp <- rbind( tmp,
c( 0, h, 0 ),
scale3d( c( xv[i],   yv[i],   zv[i]   ), sx, sy, sz ),
scale3d( c( xv[i+1], yv[i+1], zv[i+1] ), sx, sy, sz ) )
}
tmp
}

# vector cross product
.cross3 <- function(a,b) {
c(a[2]*b[3]-a[3]*b[2], -a[1]*b[3]+a[3]*b[1], a[1]*b[2]-a[2]*b[1])
}

#' Draw a 3D cone
#'
#' Draws a cone in 3D from a \code{base} point to a \code{tip} point, with a given \code{radius} at the base.
#'
#' @param base   coordinates of base of the cone
#' @param tip    coordinates of tip of the cone
#' @param col    color
#' @param scale  scale factor for base and tip
#' @param ...    rgl arguments passed down; see \code{\link[rgl]{rgl.material}}
#'
#' @return       returns the integer object ID of the shape that was added to the scene
#' @author       January Weiner, borrowed from from the \pkg{pca3d} package
#' @export
#' @import rgl
#'
#' @examples
#' # none yet

cone3d <- function( base, tip, radius= 10, col= "grey", scale= NULL, ... ) {
#  start <- rep( 0, 3 )

if( missing( scale ) ) scale <- 1 # was: rep( 1, 0 )
else scale <- max( scale ) / scale

tip  <- as.vector( tip ) * scale
base <- as.vector( base ) * scale

v1 <- tip
v2 <- c( 0, 100, 0 )
o <- .cross3( v1, v2 )
theta <- acos( sum( v1 * v2 ) / ( sqrt(sum( v1  *  v1 )) * sqrt(sum( v2  *  v2 )) ) )
vl <- sqrt( sum( tip^2 ) )

tmp <- .getcone( radius, vl )
tmp <- translate3d( rotate3d( tmp, theta, o[1], o[2], o[3] ), base[1], base[2], base[3] )
scale <- 1 / scale
tmp <- t( apply( tmp, 1, function( x ) x * scale ) )
triangles3d( tmp, col= col, ... )
}

#' Draw 3D arrows
#'
#' Draws nice 3D arrows with \code{cone3d}s at their tips.
#'
#' This function is meant to be analogous to \code{\link[graphics]{arrows}}, but for 3D plots using \code{\link[rgl]{rgl}}.
#' 3D cone. The units of these are all in terms of the ranges of the current rgl 3D scene.
#'
#' @param coords     A 2n x 3 matrix giving the start and end (x,y,z) coordinates of n arrows, in pairs.  The first vector
#'                   in each pair is taken as the starting coordinates of the arrow, the second as the end coordinates.
#' @param scale      Scale factor for base and tip of arrow head, a vector of length 3, giving relative scale factors for X, Y, Z
#' @param ref.length length of vector to be used to scale all of the arrow heads (permits drawing arrow heads of the same size as in a previous call);
#'                   if \code{NULL}, arrows are scaled relative to the longest vector
#' @param draw       if \code{TRUE} (the default) draw the arrow(s)
#' @param ...        rgl arguments passed down to \code{\link[rgl]{segments3d}} and \code{cone3d}, for example, \code{col} and \code{lwd}
#'
#' @return           invisibly returns the length of the vector used to scale the arrow heads
#' @author           January Weiner, borrowed from the \pkg{pca3d} package, slightly modified by John Fox
#' @family vector diagrams
#' @export
#'
#' @examples
#'  #none yet
ref.length=NULL, draw=TRUE, ... ) {

# FIXME:  check whether coords is a matrix of 3 cols, and an even # of rows
narr <- nrow( coords ) / 2
n    <- nrow( coords )

starts <- coords[ seq( 1, n, by= 2 ), , drop=FALSE]
ends   <- coords[ seq( 2, n, by= 2 ), , drop=FALSE]
if( missing( radius ) ) radius <- ( max( coords ) - min( coords ) ) / 50

lengths <- sqrt(rowSums(ends - starts)^2)

if (is.null(ref.length)){
ref.length <- max(lengths)
}

if (draw){
segments3d( coords, ... )
for( i in 1:narr ) {
s <- starts[i,]
e <- ends[i,]
base <- e - ( e - s ) * headlength * ref.length/lengths[i]
tip  <- ( e - s ) * headlength * ref.length/lengths[i]
}
}
}
invisible(c(ref.length=ref.length))
}

.show.axes <- function(axes.color, ranges) {
axes <- rbind(
c(ranges[1,1], 0, 0),
c(ranges[2,1], 0, 0),
c(0, ranges[1,2], 0),
c(0, ranges[2,2], 0),
c(0, 0, ranges[1,3]),
c(0, 0, ranges[2,3])
)
segments3d(axes, col= axes.color)

scale <- c(1, 1, 1)
if(! missing(ranges)) {
scale <- ranges[2,]
}

}

# TESTME <- FALSE
# if (TESTME) {
#   ranges <- rbind(min=c(0,0,0), max=c(1,1,1))
#   open3d()
#   .show.axes(c("red", "green", "blue"), ranges)
# }
```

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matlib documentation built on April 4, 2018, 5:03 p.m.