R/octagon_maze.r

In shabbychef/mazealls: Generate Recursive Mazes

# 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: 2017.11.14
# Copyright: Steven E. Pav, 2017
# Author: Steven E. Pav <shabbychef@gmail.com>
# Comments: Steven E. Pav


#' @title octagon_maze .
#'
#' @description 
#'
#' Draw a regular octagon maze, with each side consisting of
#' of \eqn{2^{depth}} pieces of length \code{unit_len}. 
#'
#' @details
#'
#' Draws a maze in a regular octagon via dissection into rhombuses.
#'
#' \if{html}{
#' \figure{simple-octagon-1.png}{options: width="100\%" alt="Figure: Amman Beenker octagon"}
#' }
#' \if{latex}{
#' \figure{simple-octagon-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-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 a few ways to recursively draw an octagon. 
#' The following values are acceptable:
#' \describe{
#' \item{ammann_beenker}{Decompose into 4 45-degree rhombuses and two squares.}
#' }
#'
#' @examples 
#' \dontrun{
#' turtle_init(2000,2000,mode='clip')
#' turtle_hide()
#' turtle_up()
#' turtle_do({
#'   turtle_setpos(75,1000)
#'   turtle_setangle(0)
#' 	octagon_maze(6,12,draw_boundary=TRUE)
#' })
#' }
#' @export
octagon_maze <- function(depth,unit_len=4L,clockwise=TRUE,start_from=c('midpoint','corner'),
												 method=c('ammann_beenker'),
												 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)
	num_segs <- round(2^depth)

	nsides <- 8
	outang <- (180 * (nsides-2)) / nsides
	inang <- 180 - outang

	multiplier <- ifelse(clockwise,1,-1)
	if (start_from=='midpoint') { turtle_backward(distance=unit_len * num_segs/2) }
	switch(method,
				 ammann_beenker={
		starts <- c(1,1,2,2,2,4,5,3)
		ends   <- c(4,2,3,5,4,6,6,5)
		which_holes <- .span_tree(starts,ends)

		# have it go 1 2 4 6 5 3
		inner_lines <- c(FALSE,FALSE,TRUE,TRUE,
										 FALSE,TRUE,TRUE,TRUE,
										 FALSE,FALSE,FALSE,TRUE,
										 FALSE,TRUE,FALSE,FALSE,
										 FALSE,FALSE,TRUE,FALSE,
										 FALSE,FALSE,FALSE,FALSE)
		inner_holes <- rep(FALSE,length(inner_lines))
		inner_holes[which(inner_lines)[which_holes]] <- TRUE

		turn_angles <- c(45,135,90,45,90,45)
		end_sides   <- c(4,4,4,2,3,3)
		flipflop    <- clockwise
		for (iii in seq_along(turn_angles)) {
			myidx <- (1:4) + (iii-1) * 4 
			parallelogram_maze(unit_len,height=num_segs,width=num_segs,angle=turn_angles[iii],clockwise=flipflop,
												 start_from='corner',
												 draw_boundary=TRUE,num_boundary_holes=NULL,
												 boundary_lines=inner_lines[myidx],
												 boundary_holes=inner_holes[myidx],
												 end_side=end_sides[iii])
			flipflop <- !flipflop
		}
		.turn_left(multiplier * 135)
	})
	if (draw_boundary) {
		.do_boundary(unit_len,lengths=rep(num_segs,nsides),angles=multiplier * inang,
								 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)
	}
	# 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)
			.turn_right(multiplier * inang)
		}
	}
	if (start_from=='midpoint') { turtle_forward(distance=unit_len * num_segs/2) }
}

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