diff --git a/examples/stereographic_projection_maze.scad b/examples/stereographic_projection_maze.scad new file mode 100644 index 00000000..56f81f46 --- /dev/null +++ b/examples/stereographic_projection_maze.scad @@ -0,0 +1,263 @@ +include ; +include ; + +maze_rows = 5; +block_width = 40; +wall_thickness = 20; +fn = 24; +shadow = "YES"; // [YES, NO] +wall_height = 2; + +// Constants for wall types + +NO_WALL = 0; +UPPER_WALL = 1; +RIGHT_WALL = 2; +UPPER_RIGHT_WALL = 3; + +function block_data(x, y, wall_type, visited) = [x, y, wall_type, visited]; +function get_x(block_data) = block_data[0]; +function get_y(block_data) = block_data[1]; +function get_wall_type(block_data) = block_data[2]; + +// create a starting maze for being visited later. +function starting_maze(rows, columns) = [ + for(y = [1:rows]) + for(x = [1:columns]) + block_data( + x, y, + // all blocks have upper and right walls except the exit + y == rows && x == columns ? UPPER_WALL : UPPER_RIGHT_WALL, + // unvisited + false + ) +]; + +// find out the index of a block with the position (x, y) +function indexOf(x, y, maze, i = 0) = + i > len(maze) ? -1 : ( + [get_x(maze[i]), get_y(maze[i])] == [x, y] ? i : + indexOf(x, y, maze, i + 1) + ); + +// is (x, y) visited? +function visited(x, y, maze) = maze[indexOf(x, y, maze)][3]; + +// is (x, y) visitable? +function visitable(x, y, maze, rows, columns) = + y > 0 && y <= rows && // y bound + x > 0 && x <= columns && // x bound + !visited(x, y, maze); // unvisited + +// setting (x, y) as being visited +function set_visited(x, y, maze) = [ + for(b = maze) + [x, y] == [get_x(b), get_y(b)] ? + [x, y, get_wall_type(b), true] : b +]; + +// 0（right）、1（upper）、2（left）、3（down） +function rand_dirs() = + [ + [0, 1, 2, 3], + [0, 1, 3, 2], + [0, 2, 1, 3], + [0, 2, 3, 1], + [0, 3, 1, 2], + [0, 3, 2, 1], + [1, 0, 2, 3], + [1, 0, 3, 2], + [1, 2, 0, 3], + [1, 2, 3, 0], + [1, 3, 0, 2], + [1, 3, 2, 0], + [2, 0, 1, 3], + [2, 0, 3, 1], + [2, 1, 0, 3], + [2, 1, 3, 0], + [2, 3, 0, 1], + [2, 3, 1, 0], + [3, 0, 1, 2], + [3, 0, 2, 1], + [3, 1, 0, 2], + [3, 1, 2, 0], + [3, 2, 0, 1], + [3, 2, 1, 0] + ][round(rands(0, 24, 1)[0])]; + +// get x value by dir +function next_x(x, dir) = x + [1, 0, -1, 0][dir]; +// get y value by dir +function next_y(y, dir) = y + [0, 1, 0, -1][dir]; + +// go right and carve the right wall +function go_right_from(x, y, maze) = [ + for(b = maze) [get_x(b), get_y(b)] == [x, y] ? ( + get_wall_type(b) == UPPER_RIGHT_WALL ? + [x, y, UPPER_WALL, visited(x, y, maze)] : + [x, y, NO_WALL, visited(x, y, maze)] + + ) : b +]; + +// go up and carve the upper wall +function go_up_from(x, y, maze) = [ + for(b = maze) [get_x(b), get_y(b)] == [x, y] ? ( + get_wall_type(b) == UPPER_RIGHT_WALL ? + [x, y, RIGHT_WALL, visited(x, y, maze)] : + [x, y, NO_WALL, visited(x, y, maze)] + + ) : b +]; + +// go left and carve the right wall of the left block +function go_left_from(x, y, maze) = [ + for(b = maze) [get_x(b), get_y(b)] == [x - 1, y] ? ( + get_wall_type(b) == UPPER_RIGHT_WALL ? + [x - 1, y, UPPER_WALL, visited(x - 1, y, maze)] : + [x - 1, y, NO_WALL, visited(x - 1, y, maze)] + ) : b +]; + +// go down and carve the upper wall of the down block +function go_down_from(x, y, maze) = [ + for(b = maze) [get_x(b), get_y(b)] == [x, y - 1] ? ( + get_wall_type(b) == UPPER_RIGHT_WALL ? + [x, y - 1, RIGHT_WALL, visited(x, y - 1, maze)] : + [x, y - 1, NO_WALL, visited(x, y - 1, maze)] + ) : b +]; + +// 0（right）、1（upper）、2（left）、3（down） +function try_block(dir, x, y, maze, rows, columns) = + dir == 0 ? go_right_from(x, y, maze) : ( + dir == 1 ? go_up_from(x, y, maze) : ( + dir == 2 ? go_left_from(x, y, maze) : + go_down_from(x, y, maze) // 這時 dir 一定是 3 + + ) + ); + + +// find out visitable dirs from (x, y) +function visitable_dirs_from(x, y, maze, rows, columns) = [ + for(dir = [0, 1, 2, 3]) + if(visitable(next_x(x, dir), next_y(y, dir), maze, maze_rows, columns)) + dir +]; + +// go maze from (x, y) +function go_maze(x, y, maze, rows, columns) = + // have visitable dirs? + len(visitable_dirs_from(x, y, maze, rows, columns)) == 0 ? + set_visited(x, y, maze) // road closed + : walk_around_from( + x, y, + rand_dirs(), + set_visited(x, y, maze), + rows, columns + ); + +// try four directions +function walk_around_from(x, y, dirs, maze, rows, columns, i = 4) = + // all done? + i > 0 ? + // not yet + walk_around_from(x, y, dirs, + // try one direction + try_routes_from(x, y, dirs[4 - i], maze, rows, columns), + , rows, columns, + i - 1) + : maze; + +function try_routes_from(x, y, dir, maze, rows, columns) = + // is the dir visitable? + visitable(next_x(x, dir), next_y(y, dir), maze, rows, columns) ? + // try the block + go_maze( + next_x(x, dir), next_y(y, dir), + try_block(dir, x, y, maze, rows, columns), + rows, columns + ) + // road closed so return maze directly + : maze; + +module stereographic_projection_maze2(maze_rows, block_width, wall_thickness, fn, wall_height, shadow) { + maze_blocks = go_maze( + 1, 1, // starting point + starting_maze(maze_rows, maze_rows), + maze_rows, maze_rows + ); + + length = block_width * maze_rows + wall_thickness; + + module draw_block(wall_type, block_width, wall_thickness) { + if(wall_type == UPPER_WALL || wall_type == UPPER_RIGHT_WALL) { + // draw a upper wall + line2d( + [0, block_width], [block_width, block_width], wall_thickness + ); + } + + if(wall_type == RIGHT_WALL || wall_type == UPPER_RIGHT_WALL) { + // draw a right wall + line2d( + [block_width, block_width], [block_width, 0], wall_thickness + ); + } + } + + module draw_maze(rows, columns, blocks, block_width, wall_thickness) { + for(block = blocks) { + // move a block to a right position. + translate([get_x(block) - 1, get_y(block) - 1] * block_width) + draw_block( + get_wall_type(block), + block_width, + wall_thickness + ); + } + + // the lowermost wall + line2d([0, 0], [block_width * columns, 0], + wall_thickness); + // the leftmost wall + line2d([0, block_width], [0, block_width * rows], + wall_thickness); + } + + module maze() { + translate([-block_width * maze_rows / 2, -block_width * maze_rows / 2, 0]) union() { + draw_maze( + maze_rows, + maze_rows, + maze_blocks, + block_width, + wall_thickness + ); + + line2d([0, wall_thickness], [0, wall_thickness], wall_thickness); + + line2d( + [ + block_width * maze_rows, + block_width * (maze_rows - 1) + wall_thickness + ], + [ + block_width * maze_rows, + block_width * (maze_rows - 1) + wall_thickness + ], + wall_thickness + ); + } + } + + stereographic_extrude(shadow_side_leng = length, $fn = fn) + maze(); + + if(shadow == "YES") { + color("black") linear_extrude(wall_height) maze(); + } +} + +stereographic_projection_maze2(maze_rows, block_width, wall_thickness, fn, wall_height, shadow); \ No newline at end of file