R/iso_trapezoid_maze.r
In shabbychef/mazealls: Generate Recursive Mazes
Defines functions
iso_trapezoid_maze
Documented in
iso_trapezoid_maze
# Copyright 2017-2017 Steven E. Pav. All Rights Reserved.
# Author: Steven E. Pav
#
# This file is part of mazealls.
#
# mazealls is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# mazealls is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with mazealls. If not, see <http://www.gnu.org/licenses/>.
# Created: 2017.11.01
# Copyright: Steven E. Pav, 2017
# Author: Steven E. Pav <shabbychef@gmail.com>
# Comments: Steven E. Pav
#' @title iso_trapezoid_maze .
#'
#' @description
#'
#' Recursively draw a isosceles trapezoid maze, with three sides consisting
#' of \eqn{2^{depth}} pieces of length \code{unit_len}, and one long
#' side of length \eqn{2^{depth+1}} pieces, starting from the
#' long side.
#'
#' @details
#'
#' Draws a maze in an isoscelese trapezoid with three sides of equal length
#' and one long side of twice that length, starting from the midpoint
#' of the long side (or the corner before the first side via the
#' \code{start_from} option). A number of different recursive methods
#' are supported.
#' Optionally draws boundaries around the trapezoid,
#' with control over which sides have lines and
#' holes. Three sides of the trapezoid consist of \eqn{2^{depth}} segments
#' of length \code{unit_len}, while the longer has \eqn{2^{depth}}.
#' A number of different methods are supported.
#' For \code{method='four_trapezoids'}:
#'
#' \if{html}{
#' \figure{trap-four-1.png}{options: width="100\%" alt="Figure: four trapezoids"}
#' }
#' \if{latex}{
#' \figure{trap-four-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='one_ear'}:
#'
#' \if{html}{
#' \figure{trap-ear-1.png}{options: width="100\%" alt="Figure: one ear"}
#' }
#' \if{latex}{
#' \figure{trap-ear-1.png}{options: width=7cm}
#' }
#'
#'
#'
#' @keywords plotting
#' @template etc
#' @template param-unitlen
#' @template param-clockwise
#' @template param-start-from
#' @template param-end-side
#' @template param-boustro
#' @template param-boundary-stuff
#' @template param-boundary-hole-controls
#' @template return-none
#' @param depth the depth of recursion. This controls the
#' side length: three sides have \code{round(2^depth)} segments
#' of length \code{unit_len}, while the long side is twice as long.
#' \code{depth} need not be integral.
#' @param method there are many ways to recursive draw an isosceles
#' trapezoid. The following values are acceptable:
#' \describe{
#' \item{four_trapezoids}{Four isosceles trapezoids are packed around each
#' other with a \sQuote{bone} between them.}
#' \item{one_ear}{A parallelogram is placed next to an equilateral triangle
#' (an \sQuote{ear}). Note this method is acceptable when depth is
#' not an integer.}
#' \item{random}{A method is chosen uniformly at random.}
#' }
#'
#' @examples
#'
#' library(TurtleGraphics)
#' turtle_init(1000,1000)
#' turtle_hide()
#' iso_trapezoid_maze(depth=4,20,clockwise=FALSE,draw_boundary=TRUE)
#'
#' turtle_init(1000,1000)
#' turtle_hide()
#' turtle_do({
#' iso_trapezoid_maze(depth=3,20,clockwise=TRUE,draw_boundary=TRUE,boundary_holes=3)
#' })
#'
#' turtle_init(2000,2000)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#' len <- 22
#' iso_trapezoid_maze(depth=log2(len),15,clockwise=TRUE,draw_boundary=TRUE,
#' boundary_holes=c(1,3),method='one_ear',
#' boundary_hole_color=c('clear','clear','green','clear'))
#' iso_trapezoid_maze(depth=log2(len),15,clockwise=FALSE,draw_boundary=TRUE,
#' boundary_lines=c(2,3,4),boundary_holes=c(2),method='one_ear',
#' boundary_hole_color=c('red'))
#' })
#' @export
iso_trapezoid_maze <- function(depth,unit_len=4L,clockwise=TRUE,start_from=c('midpoint','corner'),
method=c('four_trapezoids','one_ear','random'),
boustro=c(1,1),
draw_boundary=FALSE,num_boundary_holes=2,boundary_lines=TRUE,
boundary_holes=NULL,boundary_hole_color=NULL,boundary_hole_locations=NULL,
boundary_hole_arrows=FALSE,
end_side=1) {
method <- match.arg(method)
start_from <- match.arg(start_from)
# check for off powers of two
non_two <- ! .near_integer(depth)
num_segs <- round(2^depth)
if (non_two) {
method <- 'one_ear'
} else if (method=='random') {
method <- sample(c('four_trapezoids','one_ear'),1)
}
multiplier <- ifelse(clockwise,1,-1)
if (start_from=='corner') { turtle_forward(distance=unit_len * num_segs) }
if (depth > 0) {
my_method <- method
switch(my_method,
four_trapezoids={
# recurse.
iso_trapezoid_maze(unit_len=unit_len,depth=depth-1,clockwise=clockwise,start_from='midpoint',
draw_boundary=FALSE,num_boundary_holes=NULL,
boustro=rev(boustro),end_side=1)
# determine inner holes
starts <- c(2,2,3,4,4)
ends <- c(3,1,1,1,3)
which_holes <- .span_tree(starts,ends)
inner_lines <- c(FALSE,TRUE,TRUE,FALSE,
FALSE,FALSE,TRUE,FALSE,
FALSE,FALSE,TRUE,TRUE)
inner_holes <- rep(FALSE,length(inner_lines))
inner_holes[which(inner_lines)[which_holes]] <- TRUE
inner_hole_locs <- .rboustro(12,boustro=boustro,nsegs=num_segs)
# have at it
turn_ang <- c(120,60,60)
for (iii in 1:3) {
turtle_forward(num_segs * unit_len)
.turn_right(multiplier * turn_ang[iii])
myidx <- 1:4 + (iii-1)*4
blines <- inner_lines[myidx]
bholes <- inner_holes[myidx]
iso_trapezoid_maze(unit_len=unit_len,depth=depth-1,clockwise=clockwise,start_from='corner',
boustro=rev(boustro),
draw_boundary=TRUE,
num_boundary_holes=NULL,
boundary_lines=blines,
boundary_holes=bholes,
boundary_hole_locations=inner_hole_locs[myidx],
end_side=1)
}
turtle_forward(num_segs * unit_len)
.turn_right(multiplier * 120)
turtle_forward(num_segs * unit_len)
},
one_ear={
coinflip <- sample.int(n=2,size=1)
if (coinflip==1) {
parallelogram_maze(unit_len=unit_len,height=num_segs,width=num_segs,angle=120,clockwise=clockwise,
method='random',start_from='corner',
height_boustro=boustro,width_boustro=boustro,
draw_boundary=TRUE,num_boundary_holes=NULL,boundary_lines=c(4),boundary_holes=4,
end_side=4)
eq_triangle_maze(depth=log2(num_segs),unit_len=unit_len,clockwise=!clockwise,
method='random',start_from='corner',
boustro=rev(boustro),
draw_boundary=FALSE,end_side=2)
turtle_right(180)
} else {
eq_triangle_maze(depth=log2(num_segs),unit_len=unit_len,clockwise=clockwise,
method='random',start_from='corner',
boustro=rev(boustro),
draw_boundary=FALSE,end_side=3)
parallelogram_maze(unit_len=unit_len,height=num_segs,width=num_segs,angle=60,clockwise=!clockwise,
method='random',start_from='corner',
height_boustro=boustro,width_boustro=boustro,
draw_boundary=TRUE,num_boundary_holes=NULL,boundary_lines=c(1),boundary_holes=1,
end_side=2)
turtle_right(180)
}
})
}
if (draw_boundary) {
turtle_backward(distance=unit_len * num_segs)
if (is.null(boundary_hole_locations)) {
boundary_hole_locations <- .rboustro(4,boustro=boustro,nsegs=num_segs)
boundary_hole_locations[1] <- .rboustro(1,boustro=boustro,nsegs=2*num_segs)
}
.do_boundary(unit_len,lengths=num_segs * c(2,1,1,1),angles=multiplier * 60 * c(2,1,1,2),
num_boundary_holes=num_boundary_holes,boundary_lines=boundary_lines,
boundary_holes=boundary_holes,boundary_hole_color=boundary_hole_color,
boundary_hole_locations=boundary_hole_locations,boundary_hole_arrows=boundary_hole_arrows)
turtle_forward(distance=unit_len * num_segs)
}
# move to ending side
if ((end_side != 1) && (!is.null(end_side))) {
turtle_backward(distance=unit_len * num_segs)
molens <- num_segs * c(2,1,1,1)
angls <- multiplier * 60 * c(2,1,1,2)
holey_path(unit_len=unit_len,
lengths=molens[1:(end_side-1)],
angles=angls[1:(end_side-1)],
draw_line=FALSE,
has_hole=FALSE,
hole_color=NULL)
turtle_forward(distance=unit_len * num_segs/2)
}
if (start_from=='corner') {
turtle_backward(distance=unit_len * num_segs / ifelse(end_side==1,1,2))
}
}
#for vim modeline: (do not edit)
# vim:fdm=marker:fmr=FOLDUP,UNFOLD:cms=#%s:syn=r:ft=r
shabbychef/mazealls documentation built on Oct. 18, 2023, 8:27 p.m.
R Package Documentation
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Defines functions iso_trapezoid_maze
Documented in iso_trapezoid_maze
# Copyright 2017-2017 Steven E. Pav. All Rights Reserved.
# Author: Steven E. Pav
#
# This file is part of mazealls.
#
# mazealls is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# mazealls is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with mazealls. If not, see <http://www.gnu.org/licenses/>.
# Created: 2017.11.01
# Copyright: Steven E. Pav, 2017
# Author: Steven E. Pav <shabbychef@gmail.com>
# Comments: Steven E. Pav
#' @title iso_trapezoid_maze .
#'
#' @description
#'
#' Recursively draw a isosceles trapezoid maze, with three sides consisting
#' of \eqn{2^{depth}} pieces of length \code{unit_len}, and one long
#' side of length \eqn{2^{depth+1}} pieces, starting from the
#' long side.
#'
#' @details
#'
#' Draws a maze in an isoscelese trapezoid with three sides of equal length
#' and one long side of twice that length, starting from the midpoint
#' of the long side (or the corner before the first side via the
#' \code{start_from} option). A number of different recursive methods
#' are supported.
#' Optionally draws boundaries around the trapezoid,
#' with control over which sides have lines and
#' holes. Three sides of the trapezoid consist of \eqn{2^{depth}} segments
#' of length \code{unit_len}, while the longer has \eqn{2^{depth}}.
#' A number of different methods are supported.
#' For \code{method='four_trapezoids'}:
#'
#' \if{html}{
#' \figure{trap-four-1.png}{options: width="100\%" alt="Figure: four trapezoids"}
#' }
#' \if{latex}{
#' \figure{trap-four-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='one_ear'}:
#'
#' \if{html}{
#' \figure{trap-ear-1.png}{options: width="100\%" alt="Figure: one ear"}
#' }
#' \if{latex}{
#' \figure{trap-ear-1.png}{options: width=7cm}
#' }
#'
#'
#'
#' @keywords plotting
#' @template etc
#' @template param-unitlen
#' @template param-clockwise
#' @template param-start-from
#' @template param-end-side
#' @template param-boustro
#' @template param-boundary-stuff
#' @template param-boundary-hole-controls
#' @template return-none
#' @param depth the depth of recursion. This controls the
#' side length: three sides have \code{round(2^depth)} segments
#' of length \code{unit_len}, while the long side is twice as long.
#' \code{depth} need not be integral.
#' @param method there are many ways to recursive draw an isosceles
#' trapezoid. The following values are acceptable:
#' \describe{
#' \item{four_trapezoids}{Four isosceles trapezoids are packed around each
#' other with a \sQuote{bone} between them.}
#' \item{one_ear}{A parallelogram is placed next to an equilateral triangle
#' (an \sQuote{ear}). Note this method is acceptable when depth is
#' not an integer.}
#' \item{random}{A method is chosen uniformly at random.}
#' }
#'
#' @examples
#'
#' library(TurtleGraphics)
#' turtle_init(1000,1000)
#' turtle_hide()
#' iso_trapezoid_maze(depth=4,20,clockwise=FALSE,draw_boundary=TRUE)
#'
#' turtle_init(1000,1000)
#' turtle_hide()
#' turtle_do({
#' iso_trapezoid_maze(depth=3,20,clockwise=TRUE,draw_boundary=TRUE,boundary_holes=3)
#' })
#'
#' turtle_init(2000,2000)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#' len <- 22
#' iso_trapezoid_maze(depth=log2(len),15,clockwise=TRUE,draw_boundary=TRUE,
#' boundary_holes=c(1,3),method='one_ear',
#' boundary_hole_color=c('clear','clear','green','clear'))
#' iso_trapezoid_maze(depth=log2(len),15,clockwise=FALSE,draw_boundary=TRUE,
#' boundary_lines=c(2,3,4),boundary_holes=c(2),method='one_ear',
#' boundary_hole_color=c('red'))
#' })
#' @export
iso_trapezoid_maze <- function(depth,unit_len=4L,clockwise=TRUE,start_from=c('midpoint','corner'),
method=c('four_trapezoids','one_ear','random'),
boustro=c(1,1),
draw_boundary=FALSE,num_boundary_holes=2,boundary_lines=TRUE,
boundary_holes=NULL,boundary_hole_color=NULL,boundary_hole_locations=NULL,
boundary_hole_arrows=FALSE,
end_side=1) {
method <- match.arg(method)
start_from <- match.arg(start_from)
# check for off powers of two
non_two <- ! .near_integer(depth)
num_segs <- round(2^depth)
if (non_two) {
method <- 'one_ear'
} else if (method=='random') {
method <- sample(c('four_trapezoids','one_ear'),1)
}
multiplier <- ifelse(clockwise,1,-1)
if (start_from=='corner') { turtle_forward(distance=unit_len * num_segs) }
if (depth > 0) {
my_method <- method
switch(my_method,
four_trapezoids={
# recurse.
iso_trapezoid_maze(unit_len=unit_len,depth=depth-1,clockwise=clockwise,start_from='midpoint',
draw_boundary=FALSE,num_boundary_holes=NULL,
boustro=rev(boustro),end_side=1)
# determine inner holes
starts <- c(2,2,3,4,4)
ends <- c(3,1,1,1,3)
which_holes <- .span_tree(starts,ends)
inner_lines <- c(FALSE,TRUE,TRUE,FALSE,
FALSE,FALSE,TRUE,FALSE,
FALSE,FALSE,TRUE,TRUE)
inner_holes <- rep(FALSE,length(inner_lines))
inner_holes[which(inner_lines)[which_holes]] <- TRUE
inner_hole_locs <- .rboustro(12,boustro=boustro,nsegs=num_segs)
# have at it
turn_ang <- c(120,60,60)
for (iii in 1:3) {
turtle_forward(num_segs * unit_len)
.turn_right(multiplier * turn_ang[iii])
myidx <- 1:4 + (iii-1)*4
blines <- inner_lines[myidx]
bholes <- inner_holes[myidx]
iso_trapezoid_maze(unit_len=unit_len,depth=depth-1,clockwise=clockwise,start_from='corner',
boustro=rev(boustro),
draw_boundary=TRUE,
num_boundary_holes=NULL,
boundary_lines=blines,
boundary_holes=bholes,
boundary_hole_locations=inner_hole_locs[myidx],
end_side=1)
}
turtle_forward(num_segs * unit_len)
.turn_right(multiplier * 120)
turtle_forward(num_segs * unit_len)
},
one_ear={
coinflip <- sample.int(n=2,size=1)
if (coinflip==1) {
parallelogram_maze(unit_len=unit_len,height=num_segs,width=num_segs,angle=120,clockwise=clockwise,
method='random',start_from='corner',
height_boustro=boustro,width_boustro=boustro,
draw_boundary=TRUE,num_boundary_holes=NULL,boundary_lines=c(4),boundary_holes=4,
end_side=4)
eq_triangle_maze(depth=log2(num_segs),unit_len=unit_len,clockwise=!clockwise,
method='random',start_from='corner',
boustro=rev(boustro),
draw_boundary=FALSE,end_side=2)
turtle_right(180)
} else {
eq_triangle_maze(depth=log2(num_segs),unit_len=unit_len,clockwise=clockwise,
method='random',start_from='corner',
boustro=rev(boustro),
draw_boundary=FALSE,end_side=3)
parallelogram_maze(unit_len=unit_len,height=num_segs,width=num_segs,angle=60,clockwise=!clockwise,
method='random',start_from='corner',
height_boustro=boustro,width_boustro=boustro,
draw_boundary=TRUE,num_boundary_holes=NULL,boundary_lines=c(1),boundary_holes=1,
end_side=2)
turtle_right(180)
}
})
}
if (draw_boundary) {
turtle_backward(distance=unit_len * num_segs)
if (is.null(boundary_hole_locations)) {
boundary_hole_locations <- .rboustro(4,boustro=boustro,nsegs=num_segs)
boundary_hole_locations[1] <- .rboustro(1,boustro=boustro,nsegs=2*num_segs)
}
.do_boundary(unit_len,lengths=num_segs * c(2,1,1,1),angles=multiplier * 60 * c(2,1,1,2),
num_boundary_holes=num_boundary_holes,boundary_lines=boundary_lines,
boundary_holes=boundary_holes,boundary_hole_color=boundary_hole_color,
boundary_hole_locations=boundary_hole_locations,boundary_hole_arrows=boundary_hole_arrows)
turtle_forward(distance=unit_len * num_segs)
}
# move to ending side
if ((end_side != 1) && (!is.null(end_side))) {
turtle_backward(distance=unit_len * num_segs)
molens <- num_segs * c(2,1,1,1)
angls <- multiplier * 60 * c(2,1,1,2)
holey_path(unit_len=unit_len,
lengths=molens[1:(end_side-1)],
angles=angls[1:(end_side-1)],
draw_line=FALSE,
has_hole=FALSE,
hole_color=NULL)
turtle_forward(distance=unit_len * num_segs/2)
}
if (start_from=='corner') {
turtle_backward(distance=unit_len * num_segs / ifelse(end_side==1,1,2))
}
}
#for vim modeline: (do not edit)
# vim:fdm=marker:fmr=FOLDUP,UNFOLD:cms=#%s:syn=r:ft=r
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