TileMerging

This algorithm is for 2D tile maps. The algorithm generates a (hopefully) minimum set of rectangles that cover all tiles of a certain type.

This is useful for physics where you can generate rectangles to cover all wall tiles. You use the rectangles to create physics bodies that can cover multiple wall tiles, instead of create a physics body for every single tile.

-- map_width and map_height are the dimensions of the map
-- is_wall_f checks if a tile is a wall
 
local rectangles = {} -- Each rectangle covers a grid of wall tiles
 
for x = 0, map_width - 1 do
    local start_y
    local end_y
 
    for y = 0, map_height - 1 do
        if is_wall_f(x, y) then
            if not start_y then
                start_y = y
            end
            end_y = y
        elseif start_y then
            local overlaps = {}
            for _, r in ipairs(rectangles) do
                if (r.end_x == x - 1)
                  and (start_y <= r.start_y)
                  and (end_y >= r.end_y) then
                    table.insert(overlaps, r)
                end
            end
            table.sort(
                overlaps,
                function (a, b)
                    return a.start_y < b.start_y
                end
            )
 
            for _, r in ipairs(overlaps) do
                if start_y < r.start_y then
                    local new_rect = {
                        start_x = x,
                        start_y = start_y,
                        end_x = x,
                        end_y = r.start_y - 1
                    }
                    table.insert(rectangles, new_rect)
                    start_y = r.start_y
                end
 
                if start_y == r.start_y then
                    r.end_x = r.end_x + 1
 
                    if end_y == r.end_y then
                        start_y = nil
                        end_y = nil
                    elseif end_y > r.end_y then
                        start_y = r.end_y + 1
                    end
                end
            end
 
            if start_y then
                local new_rect = {
                    start_x = x,
                    start_y = start_y,
                    end_x = x,
                    end_y = end_y
                }
                table.insert(rectangles, new_rect)
 
                start_y = nil
                end_y = nil
            end
        end
    end
 
    if start_y then
        local new_rect = {
            start_x = x,
            start_y = start_y,
            end_x = x,
            end_y = end_y
        }
        table.insert(rectangles, new_rect)
 
        start_y = nil
        end_y = nil
    end
end

Here's how the rectangles would be used for physics.

-- Use contents of rectangles to create physics bodies
-- phys_world is the world, wall_rects is the list of...
-- wall rectangles
 
for _, r in ipairs(rectangles) do
    local start_x = r.start_x * TILE_SIZE
    local start_y = r.start_y * TILE_SIZE
    local width = (r.end_x - r.start_x + 1) * TILE_SIZE
    local height = (r.end_y - r.start_y + 1) * TILE_SIZE
 
    local x = start_x + (width / 2)
    local y = start_y + (height / 2)
 
    local body = love.physics.newBody(phys_world, x, y, 0, 0)
    local shape = love.physics.newRectangleShape(body, 0, 0,
      width, height)
 
    shape:setFriction(0)
 
    table.insert(wall_rects, {body = body, shape = shape})
end

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