X-Git-Url: https://git.lizzy.rs/?a=blobdiff_plain;f=builtin%2Fcommon%2Fvector.lua;h=a08472e322c7b42513f084e9f94560791e778e20;hb=4fbcc33ee08e521015529ba4f494fc9cff771ebb;hp=77944b612111c6019ff057ae869ae65985f4eafb;hpb=1cd512913e4d4ad1fb43d4b6e3d7971bb6c67528;p=minetest.git

diff --git a/builtin/common/vector.lua b/builtin/common/vector.lua
index 77944b612..a08472e32 100644
--- a/builtin/common/vector.lua
+++ b/builtin/common/vector.lua
@@ -1,146 +1,368 @@
+--[[
+Vector helpers
+Note: The vector.*-functions must be able to accept old vectors that had no metatables
+]]
 
-vector = {}
+-- localize functions
+local setmetatable = setmetatable
 
-local function assert_vector(v)
-	assert(type(v) == "table" and v.x and v.y and v.z, "Invalid vector")
+-- vector.metatable is set by C++.
+local metatable = vector.metatable
+
+local xyz = {"x", "y", "z"}
+
+-- only called when rawget(v, key) returns nil
+function metatable.__index(v, key)
+	return rawget(v, xyz[key]) or vector[key]
+end
+
+-- only called when rawget(v, key) returns nil
+function metatable.__newindex(v, key, value)
+	rawset(v, xyz[key] or key, value)
+end
+
+-- constructors
+
+local function fast_new(x, y, z)
+	return setmetatable({x = x, y = y, z = z}, metatable)
 end
 
 function vector.new(a, b, c)
+	if a and b and c then
+		return fast_new(a, b, c)
+	end
+
+	-- deprecated, use vector.copy and vector.zero directly
 	if type(a) == "table" then
-		assert(a.x and a.y and a.z, "Invalid vector passed to vector.new()")
-		return {x=a.x, y=a.y, z=a.z}
-	elseif a then
-		assert(b and c, "Invalid arguments for vector.new()")
-		return {x=a, y=b, z=c}
+		return vector.copy(a)
+	else
+		assert(not a, "Invalid arguments for vector.new()")
+		return vector.zero()
 	end
-	return {x=0, y=0, z=0}
 end
 
+function vector.zero()
+	return fast_new(0, 0, 0)
+end
+
+function vector.copy(v)
+	assert(v.x and v.y and v.z, "Invalid vector passed to vector.copy()")
+	return fast_new(v.x, v.y, v.z)
+end
+
+function vector.from_string(s, init)
+	local x, y, z, np = string.match(s, "^%s*%(%s*([^%s,]+)%s*[,%s]%s*([^%s,]+)%s*[,%s]" ..
+			"%s*([^%s,]+)%s*[,%s]?%s*%)()", init)
+	x = tonumber(x)
+	y = tonumber(y)
+	z = tonumber(z)
+	if not (x and y and z) then
+		return nil
+	end
+	return fast_new(x, y, z), np
+end
+
+function vector.to_string(v)
+	return string.format("(%g, %g, %g)", v.x, v.y, v.z)
+end
+metatable.__tostring = vector.to_string
+
 function vector.equals(a, b)
-	assert_vector(a)
-	assert_vector(b)
 	return a.x == b.x and
 	       a.y == b.y and
 	       a.z == b.z
 end
+metatable.__eq = vector.equals
+
+-- unary operations
 
 function vector.length(v)
-	assert_vector(v)
-	return math.hypot(v.x, math.hypot(v.y, v.z))
+	return math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z)
 end
+-- Note: we can not use __len because it is already used for primitive table length
 
 function vector.normalize(v)
-	assert_vector(v)
 	local len = vector.length(v)
 	if len == 0 then
-		return {x=0, y=0, z=0}
+		return fast_new(0, 0, 0)
 	else
 		return vector.divide(v, len)
 	end
 end
 
+function vector.floor(v)
+	return vector.apply(v, math.floor)
+end
+
 function vector.round(v)
-	assert_vector(v)
-	return {
-		x = math.floor(v.x + 0.5),
-		y = math.floor(v.y + 0.5),
-		z = math.floor(v.z + 0.5)
-	}
+	return fast_new(
+		math.round(v.x),
+		math.round(v.y),
+		math.round(v.z)
+	)
+end
+
+function vector.apply(v, func)
+	return fast_new(
+		func(v.x),
+		func(v.y),
+		func(v.z)
+	)
+end
+
+function vector.combine(a, b, func)
+	return fast_new(
+		func(a.x, b.x),
+		func(a.y, b.y),
+		func(a.z, b.z)
+	)
 end
 
 function vector.distance(a, b)
-	assert_vector(a)
-	assert_vector(b)
 	local x = a.x - b.x
 	local y = a.y - b.y
 	local z = a.z - b.z
-	return math.hypot(x, math.hypot(y, z))
+	return math.sqrt(x * x + y * y + z * z)
 end
 
 function vector.direction(pos1, pos2)
-	assert_vector(pos1)
-	assert_vector(pos2)
-	local x_raw = pos2.x - pos1.x
-	local y_raw = pos2.y - pos1.y
-	local z_raw = pos2.z - pos1.z
-	local x_abs = math.abs(x_raw)
-	local y_abs = math.abs(y_raw)
-	local z_abs = math.abs(z_raw)
-	if x_abs >= y_abs and
-	   x_abs >= z_abs then
-		y_raw = y_raw * (1 / x_abs)
-		z_raw = z_raw * (1 / x_abs)
-		x_raw = x_raw / x_abs
-	end
-	if y_abs >= x_abs and
-	   y_abs >= z_abs then
-		x_raw = x_raw * (1 / y_abs)
-		z_raw = z_raw * (1 / y_abs)
-		y_raw = y_raw / y_abs
-	end
-	if z_abs >= y_abs and
-	   z_abs >= x_abs then
-		x_raw = x_raw * (1 / z_abs)
-		y_raw = y_raw * (1 / z_abs)
-		z_raw = z_raw / z_abs
-	end
-	return {x=x_raw, y=y_raw, z=z_raw}
+	return vector.subtract(pos2, pos1):normalize()
+end
+
+function vector.angle(a, b)
+	local dotp = vector.dot(a, b)
+	local cp = vector.cross(a, b)
+	local crossplen = vector.length(cp)
+	return math.atan2(crossplen, dotp)
+end
+
+function vector.dot(a, b)
+	return a.x * b.x + a.y * b.y + a.z * b.z
+end
+
+function vector.cross(a, b)
+	return fast_new(
+		a.y * b.z - a.z * b.y,
+		a.z * b.x - a.x * b.z,
+		a.x * b.y - a.y * b.x
+	)
+end
+
+function metatable.__unm(v)
+	return fast_new(-v.x, -v.y, -v.z)
 end
 
+-- add, sub, mul, div operations
 
 function vector.add(a, b)
-	assert_vector(a)
 	if type(b) == "table" then
-	    assert_vector(b)
-		return {x = a.x + b.x,
-			y = a.y + b.y,
-			z = a.z + b.z}
+		return fast_new(
+			a.x + b.x,
+			a.y + b.y,
+			a.z + b.z
+		)
 	else
-		return {x = a.x + b,
-			y = a.y + b,
-			z = a.z + b}
+		return fast_new(
+			a.x + b,
+			a.y + b,
+			a.z + b
+		)
 	end
 end
+function metatable.__add(a, b)
+	return fast_new(
+		a.x + b.x,
+		a.y + b.y,
+		a.z + b.z
+	)
+end
 
 function vector.subtract(a, b)
-	assert_vector(a)
 	if type(b) == "table" then
-	    assert_vector(b)
-		return {x = a.x - b.x,
-			y = a.y - b.y,
-			z = a.z - b.z}
+		return fast_new(
+			a.x - b.x,
+			a.y - b.y,
+			a.z - b.z
+		)
 	else
-		return {x = a.x - b,
-			y = a.y - b,
-			z = a.z - b}
+		return fast_new(
+			a.x - b,
+			a.y - b,
+			a.z - b
+		)
 	end
 end
+function metatable.__sub(a, b)
+	return fast_new(
+		a.x - b.x,
+		a.y - b.y,
+		a.z - b.z
+	)
+end
 
 function vector.multiply(a, b)
-	assert_vector(a)
 	if type(b) == "table" then
-	    assert_vector(b)
-		return {x = a.x * b.x,
-			y = a.y * b.y,
-			z = a.z * b.z}
+		return fast_new(
+			a.x * b.x,
+			a.y * b.y,
+			a.z * b.z
+		)
+	else
+		return fast_new(
+			a.x * b,
+			a.y * b,
+			a.z * b
+		)
+	end
+end
+function metatable.__mul(a, b)
+	if type(a) == "table" then
+		return fast_new(
+			a.x * b,
+			a.y * b,
+			a.z * b
+		)
 	else
-		return {x = a.x * b,
-			y = a.y * b,
-			z = a.z * b}
+		return fast_new(
+			a * b.x,
+			a * b.y,
+			a * b.z
+		)
 	end
 end
 
 function vector.divide(a, b)
-	assert_vector(a)
 	if type(b) == "table" then
-        assert_vector(b)
-		return {x = a.x / b.x,
-			y = a.y / b.y,
-			z = a.z / b.z}
+		return fast_new(
+			a.x / b.x,
+			a.y / b.y,
+			a.z / b.z
+		)
 	else
-		return {x = a.x / b,
-			y = a.y / b,
-			z = a.z / b}
+		return fast_new(
+			a.x / b,
+			a.y / b,
+			a.z / b
+		)
 	end
 end
+function metatable.__div(a, b)
+	-- scalar/vector makes no sense
+	return fast_new(
+		a.x / b,
+		a.y / b,
+		a.z / b
+	)
+end
+
+-- misc stuff
 
+function vector.offset(v, x, y, z)
+	return fast_new(
+		v.x + x,
+		v.y + y,
+		v.z + z
+	)
+end
+
+function vector.sort(a, b)
+	return fast_new(math.min(a.x, b.x), math.min(a.y, b.y), math.min(a.z, b.z)),
+		fast_new(math.max(a.x, b.x), math.max(a.y, b.y), math.max(a.z, b.z))
+end
+
+function vector.check(v)
+	return getmetatable(v) == metatable
+end
+
+local function sin(x)
+	if x % math.pi == 0 then
+		return 0
+	else
+		return math.sin(x)
+	end
+end
+
+local function cos(x)
+	if x % math.pi == math.pi / 2 then
+		return 0
+	else
+		return math.cos(x)
+	end
+end
+
+function vector.rotate_around_axis(v, axis, angle)
+	local cosangle = cos(angle)
+	local sinangle = sin(angle)
+	axis = vector.normalize(axis)
+	-- https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
+	local dot_axis = vector.multiply(axis, vector.dot(axis, v))
+	local cross = vector.cross(v, axis)
+	return vector.new(
+		cross.x * sinangle + (v.x - dot_axis.x) * cosangle + dot_axis.x,
+		cross.y * sinangle + (v.y - dot_axis.y) * cosangle + dot_axis.y,
+		cross.z * sinangle + (v.z - dot_axis.z) * cosangle + dot_axis.z
+	)
+end
+
+function vector.rotate(v, rot)
+	local sinpitch = sin(-rot.x)
+	local sinyaw = sin(-rot.y)
+	local sinroll = sin(-rot.z)
+	local cospitch = cos(rot.x)
+	local cosyaw = cos(rot.y)
+	local cosroll = math.cos(rot.z)
+	-- Rotation matrix that applies yaw, pitch and roll
+	local matrix = {
+		{
+			sinyaw * sinpitch * sinroll + cosyaw * cosroll,
+			sinyaw * sinpitch * cosroll - cosyaw * sinroll,
+			sinyaw * cospitch,
+		},
+		{
+			cospitch * sinroll,
+			cospitch * cosroll,
+			-sinpitch,
+		},
+		{
+			cosyaw * sinpitch * sinroll - sinyaw * cosroll,
+			cosyaw * sinpitch * cosroll + sinyaw * sinroll,
+			cosyaw * cospitch,
+		},
+	}
+	-- Compute matrix multiplication: `matrix` * `v`
+	return vector.new(
+		matrix[1][1] * v.x + matrix[1][2] * v.y + matrix[1][3] * v.z,
+		matrix[2][1] * v.x + matrix[2][2] * v.y + matrix[2][3] * v.z,
+		matrix[3][1] * v.x + matrix[3][2] * v.y + matrix[3][3] * v.z
+	)
+end
+
+function vector.dir_to_rotation(forward, up)
+	forward = vector.normalize(forward)
+	local rot = vector.new(math.asin(forward.y), -math.atan2(forward.x, forward.z), 0)
+	if not up then
+		return rot
+	end
+	assert(vector.dot(forward, up) < 0.000001,
+			"Invalid vectors passed to vector.dir_to_rotation().")
+	up = vector.normalize(up)
+	-- Calculate vector pointing up with roll = 0, just based on forward vector.
+	local forwup = vector.rotate(vector.new(0, 1, 0), rot)
+	-- 'forwup' and 'up' are now in a plane with 'forward' as normal.
+	-- The angle between them is the absolute of the roll value we're looking for.
+	rot.z = vector.angle(forwup, up)
+
+	-- Since vector.angle never returns a negative value or a value greater
+	-- than math.pi, rot.z has to be inverted sometimes.
+	-- To determine wether this is the case, we rotate the up vector back around
+	-- the forward vector and check if it worked out.
+	local back = vector.rotate_around_axis(up, forward, -rot.z)
+
+	-- We don't use vector.equals for this because of floating point imprecision.
+	if (back.x - forwup.x) * (back.x - forwup.x) +
+			(back.y - forwup.y) * (back.y - forwup.y) +
+			(back.z - forwup.z) * (back.z - forwup.z) > 0.0000001 then
+		rot.z = -rot.z
+	end
+	return rot
+end