# R/eq_triangle_maze.r In mazealls: Generate Recursive Mazes

#### Documented in eq_triangle_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
# 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 <[email protected]>

#' @title eq_triangle_maze .
#'
#' @description
#'
#' Recursively draw an equilateral triangle maze, with sides consisting
#' of \eqn{2^{depth}} pieces of length \code{unit_len}.
#'
#' @details
#'
#' Draws a maze in an equilateral triangle, starting from the midpoint
#' of the first side (or the corner before the first side via the
#' \code{start_from} option). A number of different recursive methods
#' are supported, dividing the triangle into sub-triangles, or hexagons,
#' parallelogram and triangles, and so on.  Optionally draws boundaries
#' around the triangle, with control over which sides have lines and
#' holes. Side length of triangles consists of \eqn{2^{depth}} segments
#' of length \code{unit_len}, though \code{depth} may be non-integral.
#' A number of different methods are supported.
#'
#' For \code{method='uniform'}:
#'
#' \if{html}{
#' \figure{eq-tri-uniform-1.png}{options: width="100\%" alt="Figure: uniform"}
#' }
#' \if{latex}{
#' \figure{eq-tri-uniform-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='triangles'}:
#'
#' \if{html}{
#' \figure{eq-tri-four-tri-1.png}{options: width="100\%" alt="Figure: triangles"}
#' }
#' \if{latex}{
#' \figure{eq-tri-four-tri-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='two_ears'}:
#'
#' \if{html}{
#' \figure{eq-tri-two-ears-1.png}{options: width="100\%" alt="Figure: two ears"}
#' }
#' \if{latex}{
#' \figure{eq-tri-two-ears-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='hex_and_three'}:
#'
#' \if{html}{
#' \figure{eq-tri-hex-and-three-1.png}{options: width="100\%" alt="Figure: hex and three triangles"}
#' }
#' \if{latex}{
#' \figure{eq-tri-hex-and-three-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='shave'}:
#'
#' \if{html}{
#' \figure{eq-tri-shave-1.png}{options: width="100\%" alt="Figure: shave"}
#' }
#' \if{latex}{
#' \figure{eq-tri-shave-1.png}{options: width=7cm}
#' }
#'
#' For \code{method='shave_all'}:
#'
#' \if{html}{
#' \figure{eq-tri-shave-all-1.png}{options: width="100\%" alt="Figure: shave all"}
#' }
#' \if{latex}{
#' \figure{eq-tri-shave-all-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.
#'
#' @param method there are many ways to recursive draw a triangle. The
#' following values are acceptable:
#' \describe{
#' \item{stack_trapezoids}{Isosceles trapezoids are stacked on top of each
#' other, with the long sides aligned to the first side.}
#' \item{triangles}{The triangle maze is recursively drawn as four
#' equilateral triangle mazes of half size, each connected to their neighbors.}
#' \item{uniform}{The triangle maze is recursively drawn as four
#' equilateral triangle uniform mazes of half size, each connected to their
#' neighbors.}
#' \item{two_ears}{The triangle maze is recursively drawn as a large
#' parallelogram maze connected to two two half size equilateral triangle
#' mazes, which are \sQuote{ears}.}
#' \item{random}{A method is randomly selected from the available methods.}
#' \item{hex_and_three}{When \eqn{2^{depth}} is a power of three, the triangle
#' is drawn as a hexagonal maze of one third size connected to three
#' equilateral triangular mazes, each one third size, at the corners.}
#' \item{shave}{Here \eqn{2^{depth}} can be arbitrary. A single line is
#' \sQuote{shaved} off the triangle, connected to another equilateral triangle of
#' length one less is drawn next to it. This sub triangle will either be
#' drawn using a \sQuote{hex_and_three}, \sQuote{random}, or \sQuote{shave}
#' methods, in decreasing order of preference, depending on the side length.}
#' \item{shave_all}{Here \eqn{2^{depth}} can be arbitrary. A single line is
#' \sQuote{shaved} off the triangle, connected to another equilateral triangle of
#' length one less is drawn next to it. This sub triangle will also be drawn
#' using the \sQuote{shave_all} method. These mazes tend to look boring, and
#' are not recommended.}
#' }
#'
#' @examples
#' library(TurtleGraphics)
#' turtle_init(2500,2500)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#'   turtle_left(90)
#'   turtle_forward(40)
#'   turtle_right(90)
#'   eq_triangle_maze(depth=3,12,clockwise=FALSE,method='two_ears',draw_boundary=TRUE)
#' })
#'
#' turtle_init(2500,2500)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#'   turtle_left(90)
#'   turtle_forward(40)
#'   turtle_right(90)
#'   eq_triangle_maze(depth=3,12,clockwise=FALSE,method='random',draw_boundary=TRUE)
#' })
#'
#' # join two together, with green holes on opposite sides
#' turtle_init(2500,2500)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#'   turtle_left(90)
#'   turtle_forward(40)
#'   turtle_right(90)
#'   eq_triangle_maze(depth=3,12,clockwise=TRUE,method='two_ears',draw_boundary=TRUE,
#'     boundary_holes=c(1,3),boundary_hole_color=c('clear','clear','green'))
#'   eq_triangle_maze(depth=3,12,clockwise=FALSE,method='uniform',draw_boundary=TRUE,
#'     boundary_lines=c(2,3),boundary_holes=c(2),boundary_hole_color='green')
#' })
#'
#' # non integral depths also possible:
#' turtle_init(2500,2500)
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#'   turtle_left(90)
#'   turtle_forward(40)
#'   turtle_right(90)
#'   eq_triangle_maze(depth=log2(27),12,clockwise=TRUE,method='hex_and_three',draw_boundary=TRUE,
#'     boundary_holes=c(1,3),boundary_hole_color=c('clear','clear','green'))
#'   eq_triangle_maze(depth=log2(27),12,clockwise=FALSE,method='shave',draw_boundary=TRUE,
#'     boundary_lines=c(2,3),boundary_holes=c(2),boundary_hole_color='green')
#' })
#' @export
eq_triangle_maze <- function(depth,unit_len,clockwise=TRUE,
method=c('stack_trapezoids','triangles','uniform','two_ears','random','hex_and_three','shave_all','shave'),
start_from=c('midpoint','corner'),
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 hex and three ...
# check for off powers of two
non_two <- ! .near_integer(depth)
num_segs <- round(2^depth)
by_three <- num_segs / 3

acceptable <- c('shave','shave_all')
if (.near_integer(by_three) && (num_segs > 6)) {
acceptable <- c('hex_and_three',acceptable)
}
if (.is_even(num_segs)) {
acceptable <- c('stack_trapezoids','uniform','triangles','two_ears',acceptable)
}
if (method != 'random') {
if (! method %in% acceptable) { method <- 'random' }
}

multiplier <- ifelse(clockwise,1,-1)

if (start_from=='corner') { turtle_forward(distance=unit_len * num_segs/2) }

if (num_segs > 1) {
my_method <- switch(method,
shave_all={ 'shave' },
uniform={ 'triangles' },
random={ sample(acceptable,1) },
method)
my_method <- switch(my_method,
shave_all={ 'shave' },
uniform={ 'triangles' },
my_method)
switch(my_method,
stack_trapezoids={
iso_trapezoid_maze(depth=depth-1,unit_len=unit_len,clockwise=clockwise,draw_boundary=FALSE,boustro=boustro)
# now move over
magic_ratio <- sqrt(3) / 4

turtle_up()
.turn_right(multiplier * 90)
turtle_forward(num_segs * unit_len * magic_ratio)
.turn_left(multiplier * 90)
eq_triangle_maze(depth=depth-1,unit_len=unit_len,clockwise=clockwise,method=method,draw_boundary=TRUE,
boustro=rev(boustro),boundary_lines=c(1),boundary_holes=c(1))
.turn_left(multiplier * 90)
turtle_forward(num_segs * unit_len * magic_ratio)
.turn_right(multiplier * 90)
},
hex_and_three={
hexagon_maze(depth=log2(by_three),unit_len=unit_len,clockwise=clockwise,method='random',
start_from='midpoint',draw_boundary=TRUE,num_boundary_holes=0,
boustro=rev(boustro),
boundary_hole_locations=.rboustro(6,boustro=boustro,nsegs=2^by_three),
boundary_lines=c(2,4,6),boundary_holes=c(2,4,6))
for (iii in c(1:3)) {
turtle_forward(distance=num_segs * unit_len/2)
.turn_right(multiplier*120)
eq_triangle_maze(depth=log2(by_three),unit_len=unit_len,clockwise=clockwise,
boustro=rev(boustro),start_from='corner',method='random',draw_boundary=FALSE)
turtle_forward(distance=num_segs * unit_len/2)
}
},
two_ears={
# parallelogram and two triangles
turtle_backward(unit_len*num_segs/2)
parallelogram_maze(unit_len=unit_len,height=num_segs/2,width=num_segs/2,angle=60,clockwise=clockwise,
method='random',start_from='corner',
height_boustro=boustro,width_boustro=boustro,
draw_boundary=TRUE,boundary_lines=c(2,3),boundary_holes=c(2,3))
# now the other two triangles.
for (iii in c(1,2)) {
turtle_forward(unit_len*num_segs)
.turn_right(multiplier * 120)
eq_triangle_maze(depth=depth-1,unit_len=unit_len,clockwise=clockwise,method=method,
boustro=rev(boustro),start_from='corner',draw_boundary=FALSE)
}
turtle_forward(unit_len*num_segs)
.turn_right(multiplier * 120)
turtle_forward(unit_len*num_segs/2)
},
shave={
sub_num <- num_segs - 1
sub_method <- switch(method,
shave_all={ 'shave_all' },
shave={  ifelse(.is_divisible_by_three(sub_num),'hex_and_three',
ifelse(.is_power_of_two(sub_num),'random','shave')) })

shave_side <- sample.int(n=3,size=1)
turtle_backward(unit_len*num_segs/2)
for (iii in seq_len(shave_side-1)) {
turtle_forward(unit_len*num_segs)
.turn_right(multiplier*120)
}
eq_triangle_maze(depth=log2(sub_num),unit_len=unit_len,clockwise=clockwise,method=sub_method,start_from='corner',
boustro=rev(boustro),draw_boundary=TRUE,boundary_lines=c(2),boundary_holes=c(2))
for (iii in seq_len(shave_side-1)) {
.turn_left(multiplier*120)
turtle_backward(unit_len*num_segs)
}
turtle_forward(unit_len*num_segs/2)
},
triangles={
sub_method <- method
if (! (sub_method %in% c('random','uniform'))) { sub_method <- sample(c('stack_trapezoids','two_ears'),1) }

turtle_up()
turtle_backward(distance=unit_len * num_segs/2)
for (iii in c(1:3)) {
eq_triangle_maze(depth=depth-1,unit_len=unit_len,clockwise=clockwise,start_from='corner',
boustro=rev(boustro),method=sub_method,draw_boundary=FALSE)
turtle_forward(distance=unit_len * num_segs)
.turn_right(multiplier * 120)
}
turtle_forward(distance=unit_len * num_segs/2)
.turn_right(multiplier * 60)
eq_triangle_maze(depth=depth-1,unit_len=unit_len,clockwise=clockwise,start_from='corner',
boustro=rev(boustro),method=sub_method,draw_boundary=TRUE,num_boundary_holes=3)
.turn_left(multiplier * 60)
})
}
if (draw_boundary) {
if (is.null(boundary_hole_locations)) {
boundary_hole_locations <- .rboustro(3,boustro=boustro,nsegs=num_segs)
}
turtle_backward(distance=unit_len * num_segs/2)
.do_boundary(unit_len,lengths=rep(num_segs,3),angles=multiplier*120,
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/2)
}
# move to ending side
if ((end_side != 1) && (!is.null(end_side))) {
for (iii in 1:(end_side-1)) {
turtle_forward(distance=unit_len * num_segs/2)
.turn_right(multiplier * 120)
turtle_forward(distance=unit_len * num_segs/2)
}
}
if (start_from=='corner') { turtle_backward(distance=unit_len * num_segs/2) }
}

#for vim modeline: (do not edit)
# vim:fdm=marker:fmr=FOLDUP,UNFOLD:cms=#%s:syn=r:ft=r


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mazealls documentation built on May 2, 2019, 3:39 a.m.