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Mazes for Programmers

Displaying a 3D Maze

Explore how to display 3D mazes by extending 2D grid concepts into higher dimensions. Learn to represent multiple levels visually with directional arrows indicating passages. Understand updating grid classes to manage spacing and drawing, and adapt maze generation algorithms like Recursive Backtracker to 3D grids for effective maze creation.

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Introduction

We’ll draw these mazes as sets of floor plans, with lower floors to the left and higher floors to the right. The up and down passages, represented by the red arrows in the corresponding cells, indicate which of the adjacent floors each passage leads to. For example, a 3x3x3 maze might look something like this:

A 3×3×3 maze
A 3×3×3 maze

Arrows pointing to the right are like stairs leading to the level above them, and arrows pointing to the left are stairs leading down. If we enter the maze in the northwest corner of the bottom level (the one on the far left), we might take two steps east to the northeast corner, take the stairs up to the same corner of the middle level, go one step to the west and then up another flight of stairs, winding up on the third level. It works, and it’s not too difficult to implement. To implement this, we have to update the Grid3D class.

The updated Grid3D class

C++
require 'grid'
class Cell3D < Cell
  attr_reader :level
  attr_accessor :up, :down
  def initialize(level, row, column)
    @level = level
    super(row, column)
  end
  def neighbors
    list = super
    list << up if up
    list << down if down
    list
  end
end
class Grid3D < Grid
  attr_reader :levels
  def initialize(levels, rows, columns)
    @levels = levels
    super(rows, columns)
  end
  def prepare_grid
    Array.new(levels) do |level|
      Array.new(rows) do |row|
        Array.new(columns) do |column|
          Cell3D.new(level, row, column)
        end
      end
    end
  end
  def configure_cells
    each_cell do |cell|
      level, row, col = cell.level, cell.row, cell.column
      cell.north = self[level, row - 1, col]
      cell.south = self[level, row + 1, col]
      cell.west  = self[level, row, col - 1]
      cell.east  = self[level, row, col + 1]
      cell.down  = self[level - 1, row, col]
      cell.up    = self[level + 1, row, col]
    end
  end
  def [](level, row, column)
    return nil unless level.between?(0, @levels - 1)
    return nil unless row.between?(0, @grid[level].count - 1)
    return nil unless column.between?(0, @grid[level][row].count - 1)
    @grid[level][row][column]
  end
  def random_cell
    level  = rand(@levels)
    row    = rand(@grid[level].count)
    column = rand(@grid[level][row].count)
    @grid[level][row][column]
  end
  def size
    @levels * @rows * @columns
  end
  def each_level
    @grid.each do |level|
      yield level
    end
  end
  def each_row
    each_level do |rows|
      rows.each do |row|
        yield row
      end
    end
  end
  def to_png(cell_size: 10, inset: 0, margin: cell_size/2)
    inset = (cell_size * inset).to_i
    grid_width = cell_size * columns 
    grid_height = cell_size * rows 
    img_width = grid_width * levels + (levels - 1) * margin 
    img_height = grid_height
    background = ChunkyPNG::Color::WHITE
    wall = ChunkyPNG::Color::BLACK
    arrow = ChunkyPNG::Color.rgb(255, 0, 0) 
    img = ChunkyPNG::Image.new(img_width + 1, img_height + 1, background)
    [:backgrounds, :walls].each do |mode|
      each_cell do |cell|
        x = cell.level * (grid_width + margin) + cell.column * cell_size 
        y = cell.row * cell_size
        if inset > 0
          to_png_with_inset(img, cell, mode, cell_size, wall, x, y, inset)
        else
          to_png_without_inset(img, cell, mode, cell_size, wall, x, y)
        end
        if mode == :walls 
          mid_x = x + cell_size / 2
          mid_y = y + cell_size / 2
          if cell.linked?(cell.down)
            img.line(mid_x-3, mid_y, mid_x-1, mid_y+2, arrow)
            img.line(mid_x-3, mid_y, mid_x-1, mid_y-2, arrow)
          end
          if cell.linked?(cell.up)
            img.line(mid_x+3, mid_y, mid_x+1, mid_y+2, arrow)
            img.line(mid_x+3, mid_y, mid_x+1, mid_y-2, arrow)
          end
        end 
      end
    end
    img
  end
end

Code explanation

Line 84: This implementation introduces a new parameter, ...