R/koch_maze.r

Defines functions koch_maze .koch_side

Documented in koch_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: 2017.11.05
# Copyright: Steven E. Pav, 2017
# Author: Steven E. Pav <[email protected]>
# Comments: Steven E. Pav

.koch_side <- function(unit_len,depth,draw_boundary=TRUE,clockwise=TRUE,has_hole=FALSE,hole_color=NULL,
											 hole_location=0,hole_arrow=FALSE) {

	multiplier <- ifelse(clockwise,1,-1)
	num_segs <- round(3^depth)
	if (has_hole) { 
		if (hole_location==0) {
			hole_location <- sample.int(round(4^depth),1)
		}
		subd <- round(4^(depth-1))
		bholes <- 1 + floor((hole_location-1) / subd)
		sub_location <- 1 + (hole_location - 1) %% subd
	} else { 
		bholes <- 0
		sub_location <- 0
	}
	stopifnot(depth > 0)
	if (depth > 1) {
		.koch_side(unit_len,depth-1,draw_boundary=draw_boundary,clockwise=clockwise,has_hole=bholes==1,
							 hole_location=sub_location,hole_color=hole_color,hole_arrow=hole_arrow)

		eq_triangle_maze(unit_len,depth=log2(num_segs/3),clockwise=!clockwise,start_from='corner',
										 draw_boundary=TRUE,num_boundary_holes=NULL,boundary_lines=c(1),
										 boundary_holes=1)

		.turn_left(multiplier * 60)
		.koch_side(unit_len,depth-1,draw_boundary=draw_boundary,clockwise=clockwise,has_hole=bholes==2,
							 hole_location=sub_location,hole_color=hole_color,hole_arrow=hole_arrow)
		.turn_right(multiplier * 120)
		.koch_side(unit_len,depth-1,draw_boundary=draw_boundary,clockwise=clockwise,has_hole=bholes==3,
							 hole_location=sub_location,hole_color=hole_color,hole_arrow=hole_arrow)
		.turn_left(multiplier * 60)
		.koch_side(unit_len,depth-1,draw_boundary=draw_boundary,clockwise=clockwise,has_hole=bholes==4,
							 hole_location=sub_location,hole_color=hole_color,hole_arrow=hole_arrow)
	} else if (depth==1) {
		holey_path(unit_len=unit_len,
							 lengths=rep(1,4),
							 angles=multiplier * c(-60,120,-60,0),
							 draw_line=draw_boundary,
							 has_hole=c(1:4) %in% bholes,
							 hole_color=hole_color,
							 hole_arrows=hole_arrow)
	}
}


#' @title koch_maze .
#'
#' @description 
#'
#' Recursively draw an Koch snowflake maze. The inner part of the snowflake
#' maze consists of an equilateral triangle of side length \eqn{3^{depth}}
#' pieces of length \code{unit_len}.
#'
#' @details
#'
#' Draws a maze in an Koch snowflake, starting from the corner of the
#' first side. Relies on generation of triangular mazes for the internals.
#' The triangular part has sides consisting of \code{3^depth} segments
#' of length \code{unit_len}.
#'
#' \if{html}{
#' \figure{koch-flake-1.png}{options: width="100\%" alt="Figure: Koch snowflake"}
#' }
#' \if{latex}{
#' \figure{koch-flake-1.png}{options: width=7cm}
#' }
#'
#' @keywords plotting
#' @template etc
#' @template param-unitlen
#' @template param-clockwise
#' @template param-boundary-hole-controls
#' @template param-boundary-stuff
#' @template param-end-side
#' @template return-none
#' @param depth the depth of recursion. This controls the side length.
#' Should be an integer.
#'
#'
#' @examples 
#'
#' library(TurtleGraphics)
#' turtle_init(2000,2000)
#' turtle_hide() 
#' turtle_up()
#' set.seed(1234)
#' turtle_do({
#' 	turtle_backward(distance=400)
#' 	turtle_left(90)
#' 	turtle_forward(650)
#' 	turtle_right(90)
#' 	turtle_right(30)
#' 	koch_maze(depth=3,unit_len=14)
#' })
#' @export
koch_maze <- function(depth,unit_len,clockwise=TRUE,
											draw_boundary=TRUE,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) {

	# 2FIX: add end_side?

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

	holes <- .interpret_boundary_holes(boundary_holes,num_boundary_holes,nsides=3)
	boundary_lines <- .interpret_boundary_lines(boundary_lines,nsides=3)
	boundary_hole_arrows <- .interpret_boundary_hole_arrows(boundary_hole_arrows,nsides=3)
	if (length(boundary_lines) < 3) {
		boundary_lines <- rep(boundary_lines,3)
		boundary_lines <- boundary_lines[1:3]
	}

	if (is.null(boundary_hole_color)) {
		boundary_hole_color <- rep(c('clear'),3)
	} else if (length(boundary_hole_color) < 3) {
		boundary_hole_color <- rep(boundary_hole_color,3)
		boundary_hole_color <- boundary_hole_color[1:3]
	}
	if (is.null(boundary_hole_locations)) {
		boundary_hole_locations <- rep(0,3)
	} else if (length(boundary_hole_locations) < 3) {
		boundary_hole_locations <- rep(boundary_hole_locations,3)
		boundary_hole_locations <- boundary_hole_locations[1:3]
	}


	for (iii in c(1:3)) {
		.koch_side(unit_len=unit_len,depth=depth,
							 draw_boundary=draw_boundary & (boundary_lines[iii]),
							 clockwise=clockwise,has_hole=holes[iii],
							 hole_color=boundary_hole_color[iii],
							 hole_location=boundary_hole_locations[iii],
							 hole_arrow=boundary_hole_arrows[iii])
		.turn_right(120 * multiplier)
	}
	eq_triangle_maze(unit_len=unit_len,depth=log2(3^depth),start_from='corner',clockwise=clockwise,draw_boundary=FALSE,end_side=end_side)
}

#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.