vector = {} function vector.new(a, b, c) 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} end return {x=0, y=0, z=0} 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 {x = x, y = y, z = z}, np end function vector.to_string(v) return string.format("(%g, %g, %g)", v.x, v.y, v.z) end function vector.equals(a, b) return a.x == b.x and a.y == b.y and a.z == b.z end function vector.length(v) return math.hypot(v.x, math.hypot(v.y, v.z)) end function vector.normalize(v) local len = vector.length(v) if len == 0 then return {x=0, y=0, z=0} else return vector.divide(v, len) end end function vector.floor(v) return { x = math.floor(v.x), y = math.floor(v.y), z = math.floor(v.z) } end function vector.round(v) return { x = math.round(v.x), y = math.round(v.y), z = math.round(v.z) } end function vector.apply(v, func) return { x = func(v.x), y = func(v.y), z = func(v.z) } end function vector.distance(a, 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)) end function vector.direction(pos1, pos2) return vector.normalize({ x = pos2.x - pos1.x, y = pos2.y - pos1.y, z = pos2.z - pos1.z }) 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 { x = a.y * b.z - a.z * b.y, y = a.z * b.x - a.x * b.z, z = a.x * b.y - a.y * b.x } end function vector.add(a, b) if type(b) == "table" then return {x = a.x + b.x, y = a.y + b.y, z = a.z + b.z} else return {x = a.x + b, y = a.y + b, z = a.z + b} end end function vector.subtract(a, b) if type(b) == "table" then return {x = a.x - b.x, y = a.y - b.y, z = a.z - b.z} else return {x = a.x - b, y = a.y - b, z = a.z - b} end end function vector.multiply(a, b) if type(b) == "table" then return {x = a.x * b.x, y = a.y * b.y, z = a.z * b.z} else return {x = a.x * b, y = a.y * b, z = a.z * b} end end function vector.divide(a, b) if type(b) == "table" then return {x = a.x / b.x, y = a.y / b.y, z = a.z / b.z} else return {x = a.x / b, y = a.y / b, z = a.z / b} end end function vector.offset(v, x, y, z) return {x = v.x + x, y = v.y + y, z = v.z + z} end function vector.sort(a, b) return {x = math.min(a.x, b.x), y = math.min(a.y, b.y), z = math.min(a.z, b.z)}, {x = math.max(a.x, b.x), y = math.max(a.y, b.y), z = math.max(a.z, b.z)} 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 = {x = math.asin(forward.y), y = -math.atan2(forward.x, forward.z), 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({x = 0, y = 1, z = 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