diff --git a/res/modules/vector2.lua b/res/modules/vector2.lua new file mode 100644 index 00000000..c0c9ccb8 --- /dev/null +++ b/res/modules/vector2.lua @@ -0,0 +1,310 @@ +local vector2 = +{ + __type = "vec2", + __call = function(vector2, x, y) + return vector2:new(x, y) end +} + +vector2.__index = vector2 + + +-- vec2 cocnrtuct +function vector2:new(x, y) + if type(x) ~= "number" or type(y) ~= "number" then + error("Invalid input argument. Expected two numbers. [ vec2(number, number) ]") + end + + local obj = { + x = x or 0, + y = y or 0 + } + + setmetatable(obj, self) + return obj +end + +-- string vec +function vector2:strvec2() + return "(" .. self.x .. ", " .. self.y .. ")" +end + +-- round vector components +-- @param decimals -> integer +-- @return round(vec2) +-- @usage: +-- @example-1: +-- local v1 = vec2(1, 0.5) +-- print(v1:round()) -- Output: (1, 1) +-- @example-2: +-- local v1 = vec2(0.707, 0.5) +-- print(v1:round(2)) -- Output: (0.71, 0.5) +function vector2:round(decimals) + decimals = decimals or 0 + self.x = math.floor(self.x * 10^decimals + 0.5) / 10^decimals + self.y = math.floor(self.y * 10^decimals + 0.5) / 10^decimals + return self +end + + +-- vec2 magnitude (length) +-- @return {number} - the magnitude of the vector +-- @usage: +-- @example-1: +-- local v1 = vec2(-10, 25) +-- print(v1:len()) -- Output: 26.925824035673 +-- @example-2: +-- local v1 = vec2(0.32, 89) +-- print(v1:len()) -- Output: 89. +function vector2:len() + return math.sqrt(self.x * self.x + self.y * self.y) +end + +-- angle between 2 vec2 +-- @param vector {ve2} +-- @return {number} -> radians - angle between the 2 vec +function vector2:abtw(vector) + local dot_product = self:dot(vector) + local len_product = self:len() * vector:len() + if len_product == 0 then + return 0 + end + local radians = math.acos(dot_product / len_product) + return radians +end + + +-- Normalize vec2 +-- @return {vector2} - The normalized vector2 +-- @usage: +-- @example-1: +-- local v1 = vec2(10, 15) +-- print(v1:norm()) -- Output: (0.55470019622523, 0.83205029433784) +-- @example-2: +-- local v1 = vec2(-1, 1) +-- print(v1:norm()) -- Output: (-0.70710678118655, 0.70710678118655) +function vector2:norm() + local length_vectors = self:len() + return vector2:new(self.x / length_vectors, self.y / length_vectors) +end + + +-- project vec2 +-- @param vector {vec2} +-- @return {vec2} project +function vector2:proj(vector) + if type(vector) == "number" then + print("\n(( TypeError : proj(vec2) ))\nType arg proj(vec2)") + error("Invalid input argument. Expected a vector2 object") + end + local dot_product = self:dot(vector) + return vector:new(dot_product * (vector.x / vector:len()^2), dot_product * (vector.y / vector:len()^2)) +end + + +-- exclude vector2 +-- @param vector {vec2} +-- @return {vec2} +function vector2:vxld(vector) + if type(vector) == "number" then + print("\n(( TypeError : vxld(vec2) ))\nType arg vxld(vec2, vec2)") + error("Invalid input argument. Expected a vector2 object\n") + end + return vector2:new(self.x - vector.x, self.y - vector.y) +end + + +-- vec2 dot product +-- @param vector {vec2} +-- @return {number} +-- @usage: +-- @example-1: +-- local v1 = vec2(10, 15) +-- local v2 = vec2(-1, 1) +-- print(v1:dot(v2)) -- Output: 5 +-- @example-2: +-- local v1 = vec2(-15, 10) +-- print(v1:dot(v1)) -- Output: (-0.83205029433784, 0.55470019622523) +function vector2:dot(vector) + if type(vector) == "number" then + print("\n(( TypeError : dot(vec2) ))\nType arg dot(vec2)") + error("Invalid input argument. Expected a vector2 object") + end + return self.x * vector.x + self.y * vector.y +end + + +-- Linear interpolation for vector2 +-- @param b {vector2} - The target vector2 +-- @param t {number} - (0 <= t <= 1) the interpolation factor +-- @return {vector2} - The interpolated vector2 +function vector2:lerp(b, t) + if type(b) ~= "table" then + print("\n(( TypeError : lerp(vec2) ))\nType arg lerp(vec2, number)") + error("Invalid input argument. Expected a vector2 object\n") + end + if type(t) ~= "number" or t < 0 or t > 1 then + error("Invalid input argument. Expected a number between 0 and 1 .. (0 <= t <= 1)") + end + return vector2:new(self.x + t * (b.x - self.x), self.y + t * (b.y - self.y)); +end + + +-- Dist btw 2 vec2 +-- @param vector {vector2} +-- @return {number} - distance between the 2 vect2 +function vector2:dist(vector) + if type(vector) ~= "table" then + print("\n(( TypeError : dist(vec2) ))\nType arg dist(vec2)") + error("Invalid input argument. Expected a vec2 object or a table with two numbers.") + end + local dx = self.x - vector.x + local dy = self.y - vector.y + local result = vec2(dx, dy) + return result:len() +end + +-- cross product for vec2 (in 3D space) +-- @param {vec2} v - The other vec2 +-- @return {number} -> float || integer +-- @usage +-- local v1 = vec2(10, 15) +-- local v2 = vec2(15, 10) +-- print(v1:cross(v2)) -- Output: -125 +function vector2:cross(v) + if type(v) == "number" then + print("\n(( TypeError : cross ))\nType arg cross(vec2)") + error("Invalid input argument. Expected a vec2 object.\n") + end + return self.x * v.y - self.y * v.x +end + +-- rotate vec2 +-- @param angle {number} +-- @param axis {string} - axis rotate around (x, y, or z) +-- @param convert2deg {bool} .. if true => deg convert to rad +-- @return {vector2} - rotated vector2 +function vector2:rot(angle, axis, convert2deg) + if convert2deg == true then + angle = math.rad(angle) + end + + if type(axis) == "string" then + if axis == "x" then + local x_new = self.x + local y_new = self.y * math.cos(angle) - self.y * math.sin(angle) + self.y = y_new + elseif axis == "y" then + local x_new = self.x * math.cos(angle) + self.x * math.sin(angle) + local y_new = self.y + self.x = x_new + elseif axis == "z" then + local x_new = self.x * math.cos(angle) - self.y * math.sin(angle) + local y_new = self.x * math.sin(angle) + self.y * math.cos(angle) + self.x, self.y = x_new, y_new + end + elseif axis == nil then + local x_new = self.x * math.cos(angle) - self.y * math.sin(angle) + local y_new = self.x * math.sin(angle) + self.y * math.cos(angle) + self.x, self.y = x_new, y_new + end + return self:round(15) +end + +-- add vec +function vector2.__add(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return vector2:new(value_2.x, value_2.y) + else + return vector2:new(value_2.x + value_1, value_2.y + value_1) + end + else + if type(value_2) == "number" then + if value_2 == 0 then + return vector2:new(value_1.x, value_1.y) + else + return vector2:new(value_1.x + value_2, value_1.y + value_2) + end + else + return vector2:new(value_1.x + value_2.x, value_1.y + value_2.y) + end + end +end + + + +-- mul vec +function vector2.__mul(value_1, value_2) + if type(value_1) == "number" then + return vector2:new(value_2.x * value_1, value_2.y * value_1) + else + if type(value_2) == "number" then + return vector2:new(value_1.x * value_2, value_1.y * value_2) + else + return vector2:new(value_1.x * value_2.x, value_1.y * value_2.y) + end + end +end + +-- pow vec +function vector2.__pow(value_1, value_2) + if type(value_1) == "number" then + return vector2:new(value_1.x ^ value_2, value_2.y ^ value_1) + else + if type(value_2) == "number" then + return vector2:new(value_1.x ^ value_2, value_1.y ^ value_2) + else + return vector2:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y) + end + end +end + + + +-- div vec +function vector2.__div(value_1, value_2) + if type(value_1) == "number" then + return vector2:new(value_2.x / value_1, value_2.y / value_1) + else + if type(value_2) == "number" then + return vector2:new(value_1.x / value_2, value_1.y / value_2) + else + return vector2:new(value_1.x / value_2.x, value_1.y / value_2.y) + end + end +end + + +-- eq vec +function vector2.__eq(a, b) + return a.x == b.x and a.y == b.y +end + + +-- eq vec +function vector2.__eq(a, b) + return a.x == b.x and a.y == b.y +end + +function vector2.__tostring(vcrt) + return vcrt:strvec2() +end + +return setmetatable(vector2, vector2) + + + + + + + + + + + + + + + + + diff --git a/res/modules/vector3.lua b/res/modules/vector3.lua new file mode 100644 index 00000000..a5a731b7 --- /dev/null +++ b/res/modules/vector3.lua @@ -0,0 +1,354 @@ +local vector3 = +{ + __type = "vec3", + __call = function(vector3, x, y, z) + return vector3:new(x, y, z) end +} + +vector3.__index = vector3 + + + + + +-- vec3 construct +function vector3:new(x, y, z) + if type(x) ~= "number" or type(y) ~= "number" or type(z) ~= "number" then + print("\n(( TypeError : new vec3))\nType arg vec3(x, y, z) = " .. "(" .. type(x) .. ", " .. type(y) .. ", " .. type(z) .. ")") + error("Invalid input argument. Expected a vector obj. [ vec3(scalar, scalar, scalar) ]\n\n") + end + local obj = { + x = x or 0, + y = y or 0, + z = z or 0 + } + setmetatable(obj, self) + return obj + end + +-- str vec +function vector3:strvec3() + return "(" .. self.x .. ", " .. self.y .. ", " .. self.z .. ")" +end + +-- dot product +-- @param {vec3} +-- @return {number} -> float || integer +-- @usage: +-- local v1 = vec3(10, 15) +-- local v2 = vec3(15, 10, 1) +-- print(v1:dot(v2)) -- Output: 301 +function vector3:dot(v) + if type(v) == "number" then + print("\n(( TypeError : dot ))\nType arg dot(vector3), your arg: " .. "dot(" .. type(v) .. ")") + error("Invalid input argument. Expected a vector3 obj.\n") + end + return self.x * v.x + self.y * v.y + self.z * v.z +end + +-- cross product +function vector3:cross(v) + if type(v) == "number" then + print("\n(( TypeError : cross ))\nType arg cross(vector3), your arg: " .. "cross(" .. type(v) .. ")") + error("Invalid input argument. Expected a vector3 obj.\n") + end + return vector3:new( + self.y * v.z - self.z * v.y, + self.z * v.x - self.x * v.z, + self.x * v.y - self.y * v.x + ) +end + +-- round vector components +function vector3:round(decimals) + decimals = decimals or 0 + self.x = math.floor(self.x * 10^decimals + 0.5) / 10^decimals + self.y = math.floor(self.y * 10^decimals + 0.5) / 10^decimals + self.z = math.floor(self.z * 10^decimals + 0.5) / 10^decimals + return self +end + + +-- check if two vectors are parallel +-- @param {vec3} +-- @return {bool} +-- @usage: +-- local v1 = vec3(10, 15, 1) +-- local v2 = vec3(10, 15, 1) +-- print(v1:isParallel(v2)) -- Output: true +function vector3:isParallel(val) + if type(val) ~= "table" or type(val) == "number" then + print("\n(( TypeError : isParallel ))\nType arg isParallel(vector3)") + error("Invalid input argument. Expected a vector3 object.\n") + end + return self:cross(val):len() < 1e-6 +end + +-- magnitude (length) vec +-- @return {number} +function vector3:len() + return math.sqrt(self.x * self.x + self.y * self.y + self.z * self.z) +end + +-- project vec3 +-- @param vector {vec3} - The direction vector +-- @return {vec3} - The projected vector3 +function vector3:proj(vector) + if type(vector) == "number" then + print("\n(( TypeError : proj(vec3) ))\nType arg proj(vector3)") + error("Invalid input argument. Expected a vector3 object\n") + end + local dot_product = self:dot(vector) + return vector:new(dot_product * (vector.x / vector:len()^2), dot_product * (vector.y / vector:len()^2), dot_product * (vector.z / vector:len()^2)) +end + +-- normalize vector +-- @return {number} +-- @usage: +-- local v1 = vec3(10, 15, 1) +-- print(v1:norm()) -- Output: 18.1 +function vector3:norm() + local length_vectors = self:len() + return vector3:new(self.x / length_vectors, self.y / length_vectors, self.z / length_vectors) +end + + +-- linear interpolation (lerp) for vector3 +-- @param b {vec3} - The target vector3 object +-- @param t {number} - (0 <= t <= 1) the interpolation factor +-- @return {vec3} +function vector3:lerp(b, t) + if type(b) ~= "table" then + print("\n(( TypeError : lerp(vec3) ))\nType arg lerp(vec3, number)") + error("Invalid input argument. Expected a vector3 object\n") + end + if type(t) ~= "number" or t < 0 or t > 1 then + error("Invalid input argument. Expected a number between 0 and 1 .. (0 <= t <= 1)\n") + end + return vector3:new(self.x + t * (b.x - self.x), self.y + t * (b.y - self.y), self.z + t * (b.z - self.z)); +end + +-- distance to line vec3 +-- @param point1 {vec3} - The first point on the line +-- @param point2 {vec3} - The second point on the line +-- @return {number} - The shortest distance from the point to the line +function vector3:dist2line(point1, point2) + if type(point1) ~= "table" or type(point2) ~= "table" then + print("\n(( TypeError : dist2line(vec3) ))\nType arg dist2line(vector3 , vector3)") + error("Invalid input argument. Expected two vector3 objects\n") + end + local line_vector = point2 - point1 + local point_to_line = self - point1 + local projection = point_to_line - line_vector:proj(point_to_line) + return projection:len() +end + + +-- angle between vec3 +-- @param vector {vec3} - The other vector3 +-- @return {number} -> rad .. angle between 2 vectors +function vector3:abtw(vector) + if type(vector) == "number" then + print("\n(( TypeError : abtw(vec3) ))\nType arg abtw(vector3)") + error("Invalid input argument. Expected a vector3 object\n") + end + local dot_prod = self:dot(vector) + local len_prod = self:len() * vector:len() + if len_prod == 0 then + return 0 + end + return math.acos(dot_prod / len_prod) +end + + +-- exclude vector3 +-- @param vector {vec3} +-- @return {vec3} +function vector3:vxld(vector) + if type(vector) == "number" then + print("\n(( TypeError : vxld(vec3) ))\nType arg vxld(vec3, vec3)") + error("Invalid input argument. Expected a vector3 object") + end + return vector3:new(self.x - vector.x, self.y - vector.y, self.z - vector.z) +end + + +-- rot vec3 +-- @param angle {number} -> float || int +-- @param axis {string} .. if nil => rot axis z +-- @param convert2deg {bool} .. if true => deg convert to rad +-- @return {vec3} +function vector3:rot(angle, axis, convert2deg) + if convert2deg == true then + angle = math.rad(angle) + end + + if type(axis) == "string" then + local cx, sx = math.cos(angle), math.sin(angle) + if axis == "x" then + local x, y, z = self.x, self.y, self.z + self.y = cx * y - sx * z + self.z = sx * y + cx * z + elseif axis == "y" then + local x, y, z = self.x, self.y, self.z + self.x = cx * x + sx * z + self.z = -sx * x + cx * z + elseif axis == "z" then + local x, y, z = self.x, self.y, self.z + self.x = cx * x - sx * y + self.y = sx * x + cx * y + end + elseif axis == nil then + local cosx, sx, cy, sy = math.cos(angle), math.sin(angle), math.cos(angle), math.sin(angle) + local x, y, z = self.x, self.y, self.z + self.x = cx * x - sx * y + self.y = sx * x + cx * y + self.z = cy * z - sy * self:len() + local len = self:len() + if len ~= 0 then + self.z = self.z / len + end + end + return self:round(15) +end + + +-- add vec +function vector3.__add(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return value_2 + end + return vector3:new(value_2.x + value_1, value_2.y + value_1, value_2.z + value_1) + else + if type(value_2) == "number" then + if value_2 == 0 then + return value_1 + end + return vector3:new(value_1.x + value_2, value_1.y + value_2, value_1.z + value_2) + else + if value_1.z ~= nil and value_2.z ~= nil then + return vector3:new(value_1.x + value_2.x, value_1.y + value_2.y, value_1.z + value_2.z) + else + return vector3:new(value_1.x + value_2.x, value_1.y + value_2.y) + end + end + end +end + + + + + +function vector3.__sub(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return value_2 + end + return vector3:new(value_2.x - value_1, value_2.y - value_1, value_2.z - value_1) + else + if type(value_2) == "number" then + if value_2 == 0 then + return value_1 + end + return vector3:new(value_1.x - value_2, value_1.y - value_2, value_1.z - value_2) + else + if value_1.z ~= nil and value_2.z ~= nil then + return vector3:new(value_1.x - value_2.x, value_1.y - value_2.y, value_1.z - value_2.z) + else + return vector3:new(value_1.x - value_2.x, value_1.y - value_2.y) + end + end + end +end + + + + + +-- mul vec +function vector3.__mul(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return value_2 + end + return vector3:new(value_2.x * value_1, value_2.y * value_1, value_2.z * value_1) + else + if type(value_2) == "number" then + if value_2 == 0 then + return value_1 + end + return vector3:new(value_1.x * value_2, value_1.y * value_2, value_1.z * value_2) + else + if value_1.z ~= nil and value_2.z ~= nil then + return vector3:new(value_1.x * value_2.x, value_1.y * value_2.y, value_1.z * value_2.z) + else + return vector3:new(value_1.x * value_2.x, value_1.y * value_2.y) + end + end + end +end + +function vector3.__pow(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return value_2 + end + return vector3:new(value_2.x ^ value_1, value_2.y ^ value_1, value_2.z ^ value_1) + else + if type(value_2) == "number" then + if value_2 == 0 then + return value_1 + end + return vector3:new(value_1.x ^ value_2, value_1.y ^ value_2, value_1.z ^ value_2) + else + if value_1.z ~= nil and value_2.z ~= nil then + return vector3:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y, value_1.z ^ value_2.z) + else + return vector3:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y) + end + end + end +end + + + +-- div vec +function vector3.__div(value_1, value_2) + if type(value_1) == "number" then + if value_1 == 0 then + return value_2 + end + return vector3:new(value_2.x / value_1, value_2.y / value_1, value_2.z / value_1) + else + if type(value_2) == "number" then + if value_2 == 0 then + return value_1 + end + return vector3:new(value_1.x / value_2, value_1.y / value_2, value_1.z / value_2) + else + if value_1.z ~= nil and value_2.z ~= nil then + return vector3:new(value_1.x / value_2.x, value_1.y / value_2.y, value_1.z / value_2.z) + else + return vector3:new(value_1.x / value_2.x, value_1.y / value_2.y) + end + end + end +end + + + + +-- eq vec +function vector3.__eq(a, b) + return a.x == b.x and a.y == b.y and a.z == b.z +end + + + +function vector3.__tostring(vcrt3) + return vcrt3:strvec3() +end + +return setmetatable(vector3, vector3) +