This helps with moving objects but NOT creating projectiles local CframeMovement = CFrame -- dependancies
local Vector3 = require("vector3");
-- CFrame class
local cframe = {__type = "cframe"}; local mt = {__index = cframe};
local prettyPrint = false; -- mainly for debug (not a feature in real CFrames)
-- built-in functions
local pi = math.pi; local max = math.max; local cos = math.cos; local sin = math.sin; local acos = math.acos; local asin = math.asin; local sqrt = math.sqrt; local atan2 = math.atan2; local unpack = unpack; local concat = table.concat;
-- some variables
local identityMatrix = { m11 = 1, m12 = 0, m13 = 0, m21 = 0, m22 = 1, m23 = 0, m31 = 0, m32 = 0, m33 = 1 }; local m41, m42, m43, m44 = 0, 0, 0, 1; local identityCFrame = {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1};
local right = Vector3.new(1, 0, 0); local top = Vector3.new(0, 1, 0); local back = Vector3.new(0, 0, 1);
-- private functions
local function fromAxisAngle(axis, vector, theta) -- http://wiki.roblox.com/index.php?title=User:EgoMoose/Articles/Quaternions_and_slerping#Rodriguez_Rotation_formula:_Axis-angle_rotations local axis = axis.unit; return vector * cos(theta) + vector:Dot(axis) * axis * (1 - cos(theta)) + axis:Cross(vector) * sin(theta); end;
local function cfTimesv3(cf, v3) local _, _, _, m11, m12, m13, m21, m22, m23, m31, m32, m33 = cf:components(); local right = Vector3.new(m11, m21, m31); local top = Vector3.new(m12, m22, m32); local back = Vector3.new(m13, m23, m33); return cf.p + v3.x * right + v3.y * top + v3.z * back; end;
local function fourByfour(a, b) local a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, a41, a42, a43, a44 = unpack(a); local b11, b12, b13, b14, b21, b22, b23, b24, b31, b32, b33, b34, b41, b42, b43, b44 = unpack(b); -- 4x4 matrix multiplication local m11 = a11b11 + a12b21 + a13b31 + a14b41; local m12 = a11b12 + a12b22 + a13b32 + a14b42; local m13 = a11b13 + a12b23 + a13b33 + a14b43; local m14 = a11b14 + a12b24 + a13b34 + a14b44; local m21 = a21b11 + a22b21 + a23b31 + a24b41; local m22 = a21b12 + a22b22 + a23b32 + a24b42; local m23 = a21b13 + a22b23 + a23b33 + a24b43; local m24 = a21b14 + a22b24 + a23b34 + a24b44; local m31 = a31b11 + a32b21 + a33b31 + a34b41; local m32 = a31b12 + a32b22 + a33b32 + a34b42; local m33 = a31b13 + a32b23 + a33b33 + a34b43; local m34 = a31b14 + a32b24 + a33b34 + a34b44; local m41 = a41b11 + a42b21 + a43b31 + a44b41; local m42 = a41b12 + a42b22 + a43b32 + a44b42; local m43 = a41b13 + a42b23 + a43b33 + a44b43; local m44 = a41b14 + a42b24 + a43b34 + a44b44; -- return the components return m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44; end;
local function cfTimescf(cf1, cf2) local a14, a24, a34, a11, a12, a13, a21, a22, a23, a31, a32, a33 = cf1:components(); local b14, b24, b34, b11, b12, b13, b21, b22, b23, b31, b32, b33 = cf2:components(); local m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, m41, m42, m43, m44 = fourByfour({ a11, a12, a13, a14, a21, a22, a23, a24, a31, a32, a33, a34, m41, m42, m43, m44 }, { b11, b12, b13, b14, b21, b22, b23, b24, b31, b32, b33, b34, m41, m42, m43, m44 }); -- return the final CFrame return cframe.new(m14, m24, m34, m11, m12, m13, m21, m22, m23, m31, m32, m33); end;
local function getDeterminant(cf) local a14, a24, a34, a11, a12, a13, a21, a22, a23, a31, a32, a33 = cf:components(); local m41, m42, m43, m44 = 0, 0, 0, 1; local det = a11a22a33m44 + a11a23a34m42 + a11a24a32m43 + a12a21a34m43 + a12a23a31m44 + a12a24a33m41 + a13a21a32m44 + a13a22a34m41 + a13a24a31m42 + a14a21a33m42 + a14a22a31m43 + a14a23a32m41 - a11a22a34m43 - a11a23a32m44 - a11a24a33m42 - a12a21a33m44 - a12a23a34m41 - a12a24a31m43 - a13a21a34m42 - a13a22a31m44 - a13a24a32m41 - a14a21a32m43 - a14a22a33m41 - a14a23a31m42; return det; end;
local function invert4x4(cf) -- this is linear algebra. We're inverting a 4x4 matrix -- see: http://www.cg.info.hiroshima-cu.ac.jp/~miyazaki/knowledge/teche23.html -- it is very possible that the built-in CFrame class does not use this method as computers tend to use elimination methods -- regardless, both functions should return the same answer local a14, a24, a34, a11, a12, a13, a21, a22, a23, a31, a32, a33 = cf:components(); local det = getDeterminant(cf); if (det == 0) then return cf; end; local b11 = (a22a33m44 + a23a34m42 + a24a32m43 - a22a34m43 - a23a32m44 - a24a33m42) / det; local b12 = (a12a34m43 + a13a32m44 + a14a33m42 - a12a33m44 - a13a34m42 - a14a32m43) / det; local b13 = (a12a23m44 + a13a24m42 + a14a22m43 - a12a24m43 - a13a22m44 - a14a23m42) / det; local b14 = (a12a24a33 + a13a22a34 + a14a23a32 - a12a23a34 - a13a24a32 - a14a22a33) / det; local b21 = (a21a34m43 + a23a31m44 + a24a33m41 - a21a33m44 - a23a34m41 - a24a31m43) / det; local b22 = (a11a33m44 + a13a34m41 + a14a31m43 - a11a34m43 - a13a31m44 - a14a33m41) / det; local b23 = (a11a24m43 + a13a21m44 + a14a23m41 - a11a23m44 - a13a24m41 - a14a21m43) / det; local b24 = (a11a23a34 + a13a24a31 + a14a21a33 - a11a24a33 - a13a21a34 - a14a23a31) / det; local b31 = (a21a32m44 + a22a34m41 + a24a31m42 - a21a34m42 - a22a31m44 - a24a32m41) / det; local b32 = (a11a34m42 + a12a31m44 + a14a32m41 - a11a32m44 - a12a34m41 - a14a31m42) / det; local b33 = (a11a22m44 + a12a24m41 + a14a21m42 - a11a24m42 - a12a21m44 - a14a22m41) / det; local b34 = (a11a24a32 + a12a21a34 + a14a22a31 - a11a22a34 - a12a24a31 - a14a21a32) / det; local b41 = (a21a33m42 + a22a31m43 + a23a32m41 - a21a32m43 - a22a33m41 - a23a31m42) / det; local b42 = (a11a32m43 + a12a33m41 + a13a31m42 - a11a33m42 - a12a31m43 - a13a32m41) / det; local b43 = (a11a23m42 + a12a21m43 + a13a22m41 - a11a22m43 - a12a23m41 - a13a21m42) / det; local b44 = (a11a22a33 + a12a23a31 + a13a21a32 - a11a23a32 - a12a21a33 - a13a22a31) / det; return cframe.new(b14, b24, b34, b11, b12, b13, b21, b22, b23, b31, b32, b33); end;
local function quaternionToMatrix(i, j, k, w) local m11 = 1 - 2j^2 - 2k^2; local m12 = 2*(ij - kw); local m13 = 2*(ik + jw); local m21 = 2*(ij + kw); local m22 = 1 - 2i^2 - 2k^2; local m23 = 2*(jk - iw); local m31 = 2*(ik - jw); local m32 = 2*(jk + iw); local m33 = 1 - 2i^2 - 2j^2; return {0, 0, 0, m11, m12, m13, m21, m22, m23, m31, m32, m33}; end;
local function quaternionFromCFrame(cf) -- taken from: http://wiki.roblox.com/index.php?title=Quaternions_for_rotation#Quaternion_from_a_Rotation_Matrix local mx, my, mz, m11, m12, m13, m21, m22, m23, m31, m32, m33 = cf:components(); local trace = m11 + m22 + m33; if (trace > 0) then local s = sqrt(1 + trace); local r = 0.5 / s; return s * 0.5, Vector3.new((m32 - m23) * r, (m13 - m31) * r, (m21 - m12) * r); else -- find the largest diagonal element local big = max(m11, m22, m33); if big == m11 then local s = sqrt(1 + m11 - m22 - m33); local r = 0.5 / s; return (m32 - m23) * r, Vector3.new(0.5 * s, (m21 + m12) * r, (m13 + m31) * r); elseif big == m22 then local s = sqrt(1 - m11 + m22 - m33); local r = 0.5 / s; return (m13 - m31) * r, Vector3.new((m21 + m12) * r, 0.5 * s, (m32 + m23) * r); elseif big == m33 then local s = sqrt(1 - m11 - m22 + m33); local r = 0.5 / s; return (m21 - m12) * r, Vector3.new((m13 + m31) * r, (m32 + m23) * r, 0.5 * s); end; end; end;
local function lerp(a, b, t) -- I have no idea what the internal implemenation is -- get the difference in CFrames, convert to quaternion, convert to axis angle, slerp local cf = a:inverse() * b; local w, v = quaternionFromCFrame(cf); local theta = acos(w) * 2; local p = a.p:Lerp(b.p, t); if theta ~= 0 then local rot = a * cframe.fromAxisAngle(v, theta * t); local _, _, _, m11, m12, m13, m21, m22, m23, m31, m32, m33 = rot:components(); return cframe.new(p.x, p.y, p.z, m11, m12, m13, m21, m22, m23, m31, m32, m33); else local _, _, _, m11, m12, m13, m21, m22, m23, m31, m32, m33 = a:components(); return cframe.new(p.x, p.y, p.z, m11, m12, m13, m21, m22, m23, m31, m32, m33); end; end;
-- meta-methods
function mt.__index(cf, index) if (index == "x" or index == "y" or index == "z") then return rawget(cf, "proxy").p[index]; elseif (index == "p" or index == "lookVector") then return rawget(cf, "proxy")[index]; elseif cframe[index] then return cframe[index]; else error(index .. " is not a valid member of CFrame"); end; end;
function mt.__newindex(v, index, value) error(index .. " cannot be assigned to"); end;
function mt.__add(a, b) local aIsCFrame = type(a) == "table" and a.__type and a.__type == "cframe"; local bIsCFrame = type(b) == "table" and b.__type and b.__type == "cframe"; local bIsVector = type(b) == "table" and b.__type and b.__type == "vector3"; if (aIsCFrame and bIsVector) then local x, y, z, m11, m12, m13, m21, m22, m23, m31, m32, m33 = a:components(); return cframe.new(x + b.x, y + b.y, z + b.z, m11, m12, m13, m21, m22, m23, m31, m32, m33); elseif (bIsCFrame) then local t = type(a); local cust = t == "table" and a.__type or t; -- fun fact, you can't add two CFrames so I assume the error code is wrong on this internally ;) error("bad argument #2 to '?' (CFrame expected, got " .. cust .. ")"); elseif (aIsCFrame) then local t = type(b); local cust = t == "table" and b.__type or t; error("bad argument #2 to '?' (Vector3 expected, got " .. cust .. ")"); end; end;
function mt.__sub(a, b) local aIsCFrame = type(a) == "table" and a.__type and a.__type == "cframe"; local bIsCFrame = type(b) == "table" and b.__type and b.__type == "cframe"; local bIsVector = type(b) == "table" and b.__type and b.__type == "vector3"; if (aIsCFrame and bIsVector) then local x, y, z, m11, m12, m13, m21, m22, m23, m31, m32, m33 = a:components(); return cframe.new(x - b.x, y - b.y, z - b.z, m11, m12, m13, m21, m22, m23, m31, m32, m33); elseif (bIsCFrame) then local t = type(a); local cust = t == "table" and a.__type or t; -- fun fact, you can't add two CFrames so I assume the error code is wrong on this internally ;) error("bad argument #2 to '?' (CFrame expected, got " .. cust .. ")"); elseif (aIsCFrame) then local t = type(b); local cust = t == "table" and b.__type or t; error("bad argument #2 to '?' (Vector3 expected, got " .. cust .. ")"); end; end;
function mt.__mul(a, b) local aIsCFrame = type(a) == "table" and a.__type and a.__type == "cframe"; local bIsCFrame = type(b) == "table" and b.__type and b.__type == "cframe"; local aIsVector = type(a) == "table" and a.__type and a.__type == "vector3"; local bIsVector = type(b) == "table" and b.__type and b.__type == "vector3"; if (aIsCFrame and bIsVector) then return cfTimesv3(a, b); elseif (aIsCFrame and bIsCFrame) then return cfTimescf(a, b); elseif (aIsCFrame) then local t = type(a); local cust = t == "table" and a.__type or t; error("bad argument #2 to '?' (Vector3 expected, got " .. cust .. " )"); elseif (bIsCFrame) then local t = type(a); local cust = t == "table" and a.__type or t; error("bad argument #1 to '?' (CFrame expected, got " .. cust .. " )"); end; end;
function mt.__tostring(t) local components = {t:components()}; if prettyPrint then local s = ""; for i = 1, 12 do s = s .. ((i > 1 and i % 3 == 1 and "\n") or "") .. components[i] .. (i < 12 and ", " or ""); end; return s; else return concat(components, ", "); end; end;
mt.__metatable = false;
-- public class
function cframe.new(...) local self = {}; self.proxy = {};
self.proxy.p = Vector3.new(0, 0, 0);
for k, v in next, identityMatrix do
self.proxy[k] = v;
end;
-- most of this function is error handling from bad userinput
local t = {...};
local length = #t;
if length > 12 then
error("Invalid number of arguments: " .. length);
elseif (length == 1) then -- single vector3 case
local v = t[1];
local isVector = type(v) == "table" and v.__type and v.__type == "vector3";
if (not isVector) then
local t = type(v);
local cust = t == "table" and v.__type or t;
error("bad argument #1 to 'new' (Vector3 expected, got" .. cust .. ")");
end;
-- make a copy to avoid user changing the original vector
self.proxy.p = Vector3.new(v.x, v.y, v.z);
elseif (length == 2) then -- two vector3 case, we much build a lookAt matrix
local eye, look = t[1], t[2];
local eyeIsVector = type(eye) == "table" and eye.__type and eye.__type == "vector3";
local lookIsVector = type(look) == "table" and look.__type and look.__type == "vector3";
if (not eyeIsVector and not lookIsVector) then
local t = type(eye);
local cust = t == "table" and eye.__type or t;
error("bad argument #1 to 'new' (Vector3 expected, got" .. cust .. ")");
end;
local zaxis = (eye - look).unit;
local xaxis = top:Cross(zaxis).unit;
local yaxis = zaxis:Cross(xaxis).unit;
if (xaxis.magnitude == 0) then -- edge cases
if zaxis.y < 0 then
xaxis = Vector3.new(0, 0, -1);
yaxis = Vector3.new(1, 0, 0);
zaxis = Vector3.new(0, -1, 0);
else
xaxis = Vector3.new(0, 0, 1);
yaxis = Vector3.new(1, 0, 0);
zaxis = Vector3.new(0, 1, 0);
end;
end;
self.proxy.p = Vector3.new(eye.x, eye.y, eye.z);
self.proxy.m11, self.proxy.m12, self.proxy.m13 = xaxis.x, yaxis.x, zaxis.x;
self.proxy.m21, self.proxy.m22, self.proxy.m23 = xaxis.y, yaxis.y, zaxis.y;
self.proxy.m31, self.proxy.m32, self.proxy.m33 = xaxis.z, yaxis.z, zaxis.z;
elseif (length == 3) then -- x, y, z
for i = 1, length do
local t = type(t[i]);
local cust = t == "table" and n.__type or t;
if cust ~= "number" then error("bad argument #" .. i .. " to 'new' (Number expected, got " .. cust .. ")"); end;
end;
self.proxy.p = Vector3.new(t[1], t[2], t[3]);
elseif (length == 7) then -- x, y, z, quaternion
for i = 1, length do
local t = type(t[i]);
local cust = t == "table" and n.__type or t;
if cust ~= "number" then error("bad argument #" .. i .. " to 'new' (Number expected, got " .. cust .. ")"); end;
end;
local m = quaternionToMatrix(t[4], t[5], t[6], t[7]);
self.proxy.p = Vector3.new(t[1], t[2], t[3]);
self.proxy.m11, self.proxy.m12, self.proxy.m13 = m[4], m[5], m[6];
self.proxy.m21, self.proxy.m22, self.proxy.m23 = m[7], m[8], m[9];
self.proxy.m31, self.proxy.m32, self.proxy.m33 = m[10], m[11], m[12];
elseif (length == 12) then -- all components provided
for i = 1, length do
local t = type(t[i]);
local cust = t == "table" and n.__type or t;
if cust ~= "number" then error("bad argument #" .. i .. " to 'new' (Number expected, got " .. cust .. ")"); end;
end;
self.proxy.p = Vector3.new(t[1], t[2], t[3]);
self.proxy.m11, self.proxy.m12, self.proxy.m13 = t[4], t[5], t[6];
self.proxy.m21, self.proxy.m22, self.proxy.m23 = t[7], t[8], t[9];
self.proxy.m31, self.proxy.m32, self.proxy.m33 = t[10], t[11], t[12];
elseif length > 0 then -- more than zero components
for i = 1, length do
local t = type(t[i]);
local cust = t == "table" and n.__type or t;
if cust ~= "number" then error("bad argument #" .. i .. " to 'new' (Number expected, got " .. cust .. ")"); end;
end;
error("bad argument #" .. (length + 1) .. " to 'new' (Number expected, got nil)");
end;
self.proxy.lookVector = Vector3.new(-self.proxy.m13, -self.proxy.m23, -self.proxy.m33);
return setmetatable(self, mt);
end;
function cframe.fromAxisAngle(axis, theta) local axis = axis.unit; local r = fromAxisAngle(axis, right, theta); local t = fromAxisAngle(axis, top, theta); local b = fromAxisAngle(axis, back, theta); return cframe.new( 0, 0, 0, r.x, t.x, b.x, r.y, t.y, b.y, r.z, t.z, b.z ); end;
function cframe.Angles(x, y, z) -- two implemenations possible. The commented one is what is what is used in the real CFrame constructor (to my knowledge) -- the uncommented implemenation is easier for me to keep track of and I think makes more sense, but you can use either
-- the method (presumably) used in the real constructor
-- How to find this matrix: http://i.imgur.com/IWDMw0m.png
-- https://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions
--[[
local m11 = cos(y) * cos(z);
local m12 = -cos(y) * sin(z);
local m13 = sin(y);
local m21 = cos(z) * sin(x) * sin(y) + cos(x) * sin(z);
local m22 = cos(x) * cos(z) - sin(x) * sin(y) * sin(z);
local m23 = -cos(y) * sin(x);
local m31 = sin(x) * sin(z) - cos(x) * cos(z) * sin(y);
local m32 = cos(z) * sin(x) + cos(x) * sin(y) * sin(z);
local m33 = cos(x) * cos(y);
return cframe.new(0, 0, 0, m11, m12, m13, m21, m22, m23, m31, m32, m33);
--]]
-- the method I prefer
local cfx = cframe.fromAxisAngle(right, x);
local cfy = cframe.fromAxisAngle(top, y);
local cfz = cframe.fromAxisAngle(back, z);
return cfx * cfy * cfz;
end;
function cframe.fromEulerAnglesXYZ(x, y, z) return cframe.Angles(x, y, z); end;
function cframe:inverse() return invert4x4(self); end;
function cframe:lerp(self2, t) return lerp(self, self2, t); end;
function cframe:toWorldSpace(self2) return self * self2; end;
function cframe:toWorldSpace(self2) return self * self2; end;
function cframe:toObjectSpace(self2) return self:inverse() * self2; end;
function cframe:pointToWorldSpace(v3) return self * v3; end;
function cframe:pointToObjectSpace(v3) return self:inverse() * v3; end;
function cframe:vectorToWorldSpace(v3) return (self - self.p) * v3; end;
function cframe:vectorToObjectSpace(v3) return (self - self.p):inverse() * v3; end;
function cframe:components() local m = rawget(self, "proxy"); return m.p.x, m.p.y, m.p.z, m.m11, m.m12, m.m13, m.m21, m.m22, m.m23, m.m31, m.m32, m.m33; end;
function cframe:toEulerAnglesXYZ() -- based off the method (presumably) used in the real constructor for cframe.Angles local _, _, _, m11, m12, m13, m21, m22, m23, m31, m32, m33 = self:components(); local x = atan2(-m23, m33); local y = asin(m13); local z = atan2(-m12, m11); return x, y, z; end;
return cframe;