Fix handling of multiple texmod transforms

minetest/texmod/dsl.lua

@@ -123,35 +123,106 @@ function texmod:invert(channels --[[set with keys "r", "g", "b", "a"]])
 end
 
 function texmod:flip(flip_axis --[["x" or "y"]])
-	assert(flip_axis == "x" or flip_axis == "y")
+	return self:transform(assert(
-	return new{
+		(flip_axis == "x" and "fx")
-		type = "transform",
+		or (flip_axis == "y" and "fy")
-		base = self,
+		or (not flip_axis and "i")))
-		flip_axis = flip_axis
-	}
 end
 
 function texmod:rotate(deg)
+	assert(deg % 90 == 0)
 	deg = deg % 360
-	assert(deg % 90 == 0, "only multiples of 90° supported")
+	return self:transform(("r%d"):format(deg))
-	return new{
-		type = "transform",
-		base = self,
-		rotation_deg = deg
-	}
 end
 
--- First flip, then rotate counterclockwise
+-- D4 group transformations (see https://proofwiki.org/wiki/Definition:Dihedral_Group_D4),
-function texmod:transform(flip_axis, rotation_deg)
+-- represented using indices into a table of matrices
-	assert(flip_axis == nil or flip_axis == "x" or flip_axis == "y")
+-- TODO (...) try to come up with a more elegant solution
-	rotation_deg = (rotation_deg or 0) % 360
+do
-	assert(rotation_deg % 90 == 0, "only multiples of 90° supported")
+	-- Matrix multiplication for composition: First applies a, then b <=> b * a
-	return new{
+	local function mat_2x2_compose(a, b)
-		type = "transform",
+		local a_1_1, a_1_2, a_2_1, a_2_2 = unpack(a)
-		base = self,
+		local b_1_1, b_1_2, b_2_1, b_2_2 = unpack(b)
-		rotation_deg = rotation_deg ~= 0 and rotation_deg or nil,
+		return {
-		flip_axis = flip_axis
+			a_1_1 * b_1_1 + a_2_1 * b_1_2, a_1_2 * b_1_1 + a_2_2 * b_1_2;
+			a_1_1 * b_2_1 + a_2_1 * b_2_2, a_1_2 * b_2_1 + a_2_2 * b_2_2
+		}
+	end
+	local r90 ={
+		0, -1;
+		1, 0
 	}
+	local fx = {
+		-1, 0;
+		0, 1
+	}
+	local fy = {
+		1, 0;
+		0, -1
+	}
+	local r180 = mat_2x2_compose(r90, r90)
+	local r270 = mat_2x2_compose(r180, r90)
+	local fxr90 = mat_2x2_compose(fx, r90)
+	local fyr90 = mat_2x2_compose(fy, r90)
+	local transform_mats = {[0] = {1, 0; 0, 1}, r90, r180, r270, fx, fxr90, fy, fyr90}
+	local transform_idx_by_name = {i = 0, r90 = 1, r180 = 2, r270 = 3, fx = 4, fxr90 = 5, fy = 6, fyr90 = 7}
+	-- Lookup tables for getting the flipped axis / rotation angle
+	local flip_by_idx = {
+		[4] = "x",
+		[5] = "x",
+		[6] = "y",
+		[7] = "y",
+	}
+	local rot_by_idx = {
+		[1] = 90,
+		[2] = 180,
+		[3] = 270,
+		[5] = 90,
+		[7] = 90,
+	}
+	local idx_by_mat_2x2 = {}
+	local function transform_idx(mat)
+		-- note: assumes mat[i] in {-1, 0, 1}
+		return mat[1] + 3*(mat[2] + 3*(mat[3] + 3*mat[4]))
+	end
+	for i = 0, 7 do
+		idx_by_mat_2x2[transform_idx(transform_mats[i])] = i
+	end
+	-- Compute a multiplication table
+	local composition_idx = {}
+	local function ij_idx(i, j)
+		return i*8 + j
+	end
+	for i = 0, 7 do
+		for j = 0, 7 do
+			composition_idx[ij_idx(i, j)] = assert(idx_by_mat_2x2[
+				transform_idx(mat_2x2_compose(transform_mats[i], transform_mats[j]))])
+		end
+	end
+	function texmod:transform(...)
+		if select("#", ...) == 0 then return self end
+		local idx = ...
+		if type(idx) == "string" then
+			idx = assert(transform_idx_by_name[idx:lower()])
+		end
+		local base = self
+		if self.type == "transform" then
+			-- Merge with a `^[transform` base image
+			assert(transform_mats[idx])
+			base = self.base
+			idx = composition_idx[ij_idx(self.idx, idx)]
+		end
+		assert(transform_mats[idx])
+		if idx == 0 then return base end -- identity
+		return new{
+			type = "transform",
+			base = base,
+			idx = idx,
+			-- Redundantly store this information for convenience. Do not modify!
+			flip_axis = flip_by_idx[idx],
+			rotation_deg = rot_by_idx[idx] or 0,
+		}:transform(select(2, ...))
+	end
 end
 
 function texmod:verticalframe(framecount, frame)

minetest/texmod/read.lua

@@ -79,34 +79,25 @@ function pr.invert(r)
 end
 
 do
-	local transforms = {
-		[0] = {},
-		{rotation_deg = 90},
-		{rotation_deg = 180},
-		{rotation_deg = 270},
-		{flip_axis = "x"},
-		{flip_axis = "x", rotation_deg = 90},
-		{flip_axis = "y"},
-		{flip_axis = "y", rotation_deg = 90},
-	}
 	function pr.transform(r)
-		-- Note: While it isn't documented, `[transform` is indeed case-insensitive.
 		if r:match_charset"[iI]" then
-			return
+			return pr.transform(r)
+		end
+		local idx = r:match_charset"[0-7]"
+		if idx then
+			return tonumber(idx), pr.transform(r)
 		end
-		local flip_axis
 		if r:match_charset"[fF]" then
-			flip_axis = assert(r:match_charset"[xXyY]", "axis expected"):lower()
+			local flip_axis = assert(r:match_charset"[xXyY]", "axis expected")
+			return "f" .. flip_axis, pr.transform(r)
 		end
-		local rot_deg
 		if r:match_charset"[rR]" then
-			rot_deg = r:int()
+			local deg = r:match_str"%d"
+			-- Be strict here: Minetest won't recognize other ways to write these numbers (or other numbers)
+			assert(deg == "90" or deg == "180" or deg == "270")
+			return ("r%d"):format(deg), pr.transform(r)
 		end
-		if flip_axis or rot_deg then
+		-- return nothing, we're done
-			return flip_axis, rot_deg
-		end
-		local transform = assert(transforms[r:int()], "out of range")
-		return transform.flip_axis, transform.rotation_deg
 	end
 end
 

minetest/texmod/write.lua

@@ -51,28 +51,7 @@ function pw:invert(w)
 end
 
 function pw:transform(w)
-	local rot_deg, flip_axis = self.rotation_deg or 0, self.flip_axis
+	w.int(self.idx)
-	if rot_deg == 0 and flip_axis == nil then
-		w.str"I"
-	elseif rot_deg == 0 then
-		w.str(assert(({x = "FX", y = "FY"})[flip_axis]))
-	elseif flip_axis == nil then
-		w.str"R"; w.int(self.rotation_deg)
-	elseif rot_deg == 90 then
-		w.str(assert(({x = "FX", y = "FY"})[flip_axis]))
-		w.str"R90"
-	elseif rot_deg == 180 then
-		-- Rotating by 180° is equivalent to flipping both axes;
-		-- if one axis was already flipped, that is undone -
-		-- thus it is equivalent to flipping the other axis
-		w.str(assert(({x = "FY", y = "FX"})[flip_axis]))
-	elseif rot_deg == 270 then
-		-- Rotating by 270° is equivalent to first rotating by 180°, then rotating by 90°;
-		-- first flipping an axis and then rotating by 180°
-		-- is equivalent to flipping the other axis as shown above
-		w.str(assert(({x = "FY", y = "FX"})[flip_axis]))
-		w.str"R90"
-	end
 end
 
 function pw:verticalframe(w)