445 lines
13 KiB
Lua
445 lines
13 KiB
Lua
local vector2 = {__type = "vec2"}
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local vector3 = {__type = "vec3"}
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vector2.__index = vector2
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vector3.__index = vector3
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vec2 = function(x, y) return vector2:new(x, y) end
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vec3 = function(x, y, z) return vector3:new(x, y, z) end
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-- vec2 cocnrtuct
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function vector2:new(x, y)
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if type(x) ~= "number" or type(y) ~= "number" then
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error("Invalid input argument. Expected two numbers. [ vec2(number, number) ]")
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end
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local obj = {
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x = x or 0,
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y = y or 0
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}
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setmetatable(obj, self)
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return obj
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end
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-- string vec
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function vector2:strvec2()
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return "(" .. self.x .. ", " .. self.y .. ")"
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end
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-- round vector components
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function vector2:round(decimals)
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decimals = decimals or 0
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self.x = math.floor(self.x * 10^decimals + 0.5) / 10^decimals
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self.y = math.floor(self.y * 10^decimals + 0.5) / 10^decimals
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return self
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end
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-- magnitude (length) vec
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function vector2:len()
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return math.sqrt(self.x * self.x + self.y * self.y)
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end
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-- normalize vector
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function vector2:norm()
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local length_vectors = self:len()
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return vector2:new(self.x / length_vectors, self.y / length_vectors)
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end
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-- dot product
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function vector2:dot(v)
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if type(v) == "number" then
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error("Invalid input argument. Expected a vector2 object")
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end
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return self.x * v.x + self.y * v.y
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end
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-- linear interpolation
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function vector2:lerp(b, t)
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if type(b) ~= "vector2" then
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error("Invalid input argument. Expected a vector2 object")
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end
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if type(t) ~= "number" or t < 0 or t > 1 then
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error("Invalid input argument. Expected a number between 0 and 1")
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end
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return vector2:new(self.x + t * (b.x - self.x), self.y + t * (b.y - self.y));
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end
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-- rot vec2
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-- @param angle -> float (radians)
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-- @param axis -> string || nil .. if nil => rot axis z
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-- @param convert2deg -> bool .. if true => deg2rad
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-- @return vec2
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function vector2:rot(angle, axis, convert2deg)
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if convert2deg == true then
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angle = math.rad(angle)
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end
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if type(axis) == "string" then
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if axis == "x" then
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local x_new = self.x
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local y_new = self.y * math.cos(angle) - self.y * math.sin(angle)
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self.y = y_new
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elseif axis == "y" then
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local x_new = self.x * math.cos(angle) + self.x * math.sin(angle)
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local y_new = self.y
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self.x = x_new
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elseif axis == "z" then
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local x_new = self.x * math.cos(angle) - self.y * math.sin(angle)
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local y_new = self.x * math.sin(angle) + self.y * math.cos(angle)
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self.x, self.y = x_new, y_new
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end
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elseif axis == nil then
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local x_new = self.x * math.cos(angle) - self.y * math.sin(angle)
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local y_new = self.x * math.sin(angle) + self.y * math.cos(angle)
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self.x, self.y = x_new, y_new
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end
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return self:round(15)
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end
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-- add vec
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function vector2.__add(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return vector2:new(value_2.x, value_2.y)
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else
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return vector2:new(value_2.x + value_1, value_2.y + value_1)
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end
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return vector2:new(value_1.x, value_1.y)
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else
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return vector2:new(value_1.x + value_2, value_1.y + value_2)
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end
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else
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return vector2:new(value_1.x + value_2.x, value_1.y + value_2.y)
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end
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end
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end
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-- mul vec
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function vector2.__mul(value_1, value_2)
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if type(value_1) == "number" then
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return vector2:new(value_2.x * value_1, value_2.y * value_1)
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else
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if type(value_2) == "number" then
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return vector2:new(value_1.x * value_2, value_1.y * value_2)
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else
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return vector2:new(value_1.x * value_2.x, value_1.y * value_2.y)
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end
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end
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end
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-- pow vec
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function vector2.__pow(value_1, value_2)
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if type(value_1) == "number" then
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return vector2:new(value_1.x ^ value_2, value_2.y ^ value_1)
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else
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if type(value_2) == "number" then
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return vector2:new(value_1.x ^ value_2, value_1.y ^ value_2)
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else
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return vector2:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y)
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end
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end
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end
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-- div vec
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function vector2.__div(value_1, value_2)
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if type(value_1) == "number" then
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return vector2:new(value_2.x / value_1, value_2.y / value_1)
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else
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if type(value_2) == "number" then
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return vector2:new(value_1.x / value_2, value_1.y / value_2)
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else
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return vector2:new(value_1.x / value_2.x, value_1.y / value_2.y)
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end
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end
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end
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-- eq vec
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function vector2.__eq(a, b)
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return a.x == b.x and a.y == b.y
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end
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-- eq vec
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function vector2.__eq(a, b)
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return a.x == b.x and a.y == b.y
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end
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function vector2.__tostring(vcrt)
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return vcrt:strvec2()
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end
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-- vec3 construct
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function vector3:new(x, y, z)
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if type(x) ~= "number" or type(y) ~= "number" or type(z) ~= "number" then
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print("\n(( TypeError : new vec3))\nType arg vec3(x, y, z) = " .. "(" .. type(x) .. ", " .. type(y) .. ", " .. type(z) .. ")")
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error("Invalid input argument. Expected a vector obj. [ vec3(scalar, scalar, scalar) ]\n\n")
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end
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local obj = {
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x = x or 0,
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y = y or 0,
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z = z or 0
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}
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setmetatable(obj, self)
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return obj
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end
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-- str vec
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function vector3:strvec3()
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return "(" .. self.x .. ", " .. self.y .. ", " .. self.z .. ")"
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end
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-- dot product
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function vector3:dot(v)
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if type(v) == "number" then
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print("\n(( TypeError : dot ))\nType arg dot(vector3), your arg: " .. "dot(" .. type(v) .. ")")
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error("Invalid input argument. Expected a vector3 obj.\n")
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end
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return self.x * v.x + self.y * v.y + self.z * v.z
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end
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-- cross product
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function vector3:cross(v)
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if type(v) == "number" then
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print("\n(( TypeError : cross ))\nType arg cross(vector3), your arg: " .. "cross(" .. type(v) .. ")")
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error("Invalid input argument. Expected a vector3 obj.\n")
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end
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return vector3:new(
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self.y * v.z - self.z * v.y,
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self.z * v.x - self.x * v.z,
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self.x * v.y - self.y * v.x
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)
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end
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-- round vector components
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function vector3:round(decimals)
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decimals = decimals or 0
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self.x = math.floor(self.x * 10^decimals + 0.5) / 10^decimals
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self.y = math.floor(self.y * 10^decimals + 0.5) / 10^decimals
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self.z = math.floor(self.z * 10^decimals + 0.5) / 10^decimals
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return self
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end
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-- check if two vectors are parallel
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function vector3:is_parallel(v)
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if type(v) ~= "vector3" then
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error("Invalid input argument. Expected a vector3 object.")
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end
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return self:cross(v):len() < 1e-6
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end
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-- magnitude (length) vec
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function vector3:len()
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return math.sqrt(self.x * self.x + self.y * self.y + self.z * self.z)
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end
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-- normalize vector
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function vector3:norm()
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local length_vectors = self:len()
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return vector3:new(self.x / length_vectors, self.y / length_vectors, self.z / length_vectors)
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end
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-- linear interpolation (lerp) for vector3
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function vector3:lerp(b, t)
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if type(b) ~= "vector3" then
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error("Invalid input argument. Expected a vector3 object")
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end
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if type(t) ~= "number" or t < 0 or t > 1 then
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error("Invalid input argument. Expected a number between 0 and 1")
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end
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return vector3:new(self.x + t * (b.x - self.x), self.y + t * (b.y - self.y), self.z + t * (b.z - self.z));
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end
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-- rot vec3
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-- @param angle -> float
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-- @param axis -> string || nil .. if nil => rot axis z
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-- @param convert2deg -> bool || nil .. if true => deg2rad
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-- @return vec3
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function vector3:rot(angle, axis, convert2deg)
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if convert2deg == true then
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angle = math.rad(angle)
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end
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if type(axis) == "string" then
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local cx, sx = math.cos(angle), math.sin(angle)
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if axis == "x" then
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local x, y, z = self.x, self.y, self.z
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self.y = cx * y - sx * z
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self.z = sx * y + cx * z
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elseif axis == "y" then
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local x, y, z = self.x, self.y, self.z
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self.x = cx * x + sx * z
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self.z = -sx * x + cx * z
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elseif axis == "z" then
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local x, y, z = self.x, self.y, self.z
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self.x = cx * x - sx * y
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self.y = sx * x + cx * y
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end
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elseif axis == nil then
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local cosx, sx, cy, sy = math.cos(angle), math.sin(angle), math.cos(angle), math.sin(angle)
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local x, y, z = self.x, self.y, self.z
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self.x = cx * x - sx * y
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self.y = sx * x + cx * y
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self.z = cy * z - sy * self:len()
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local len = self:len()
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if len ~= 0 then
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self.z = self.z / len
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end
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end
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return self:round(15)
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end
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-- add vec
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function vector3.__add(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return value_2
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end
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return vector3:new(value_2.x + value_1, value_2.y + value_1, value_2.z + value_1)
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return value_1
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end
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return vector3:new(value_1.x + value_2, value_1.y + value_2, value_1.z + value_2)
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else
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if value_1.z ~= nil and value_2.z ~= nil then
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return vector3:new(value_1.x + value_2.x, value_1.y + value_2.y, value_1.z + value_2.z)
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else
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return vector3:new(value_1.x + value_2.x, value_1.y + value_2.y)
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end
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end
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end
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end
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function vector3.__sub(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return value_2
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end
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return vector3:new(value_2.x - value_1, value_2.y - value_1, value_2.z - value_1)
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return value_1
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end
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return vector3:new(value_1.x - value_2, value_1.y - value_2, value_1.z - value_2)
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else
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if value_1.z ~= nil and value_2.z ~= nil then
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return vector3:new(value_1.x - value_2.x, value_1.y - value_2.y, value_1.z - value_2.z)
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else
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return vector3:new(value_1.x - value_2.x, value_1.y - value_2.y)
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end
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end
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end
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end
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-- mul vec
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function vector3.__mul(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return value_2
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end
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return vector3:new(value_2.x * value_1, value_2.y * value_1, value_2.z * value_1)
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return value_1
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end
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return vector3:new(value_1.x * value_2, value_1.y * value_2, value_1.z * value_2)
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else
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if value_1.z ~= nil and value_2.z ~= nil then
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return vector3:new(value_1.x * value_2.x, value_1.y * value_2.y, value_1.z * value_2.z)
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else
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return vector3:new(value_1.x * value_2.x, value_1.y * value_2.y)
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end
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end
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end
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end
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function vector3.__pow(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return value_2
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end
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return vector3:new(value_2.x ^ value_1, value_2.y ^ value_1, value_2.z ^ value_1)
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return value_1
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end
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return vector3:new(value_1.x ^ value_2, value_1.y ^ value_2, value_1.z ^ value_2)
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else
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if value_1.z ~= nil and value_2.z ~= nil then
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return vector3:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y, value_1.z ^ value_2.z)
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else
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return vector3:new(value_1.x ^ value_2.x, value_1.y ^ value_2.y)
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end
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end
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end
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end
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-- div vec
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function vector3.__div(value_1, value_2)
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if type(value_1) == "number" then
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if value_1 == 0 then
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return value_2
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end
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return vector3:new(value_2.x / value_1, value_2.y / value_1, value_2.z / value_1)
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else
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if type(value_2) == "number" then
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if value_2 == 0 then
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return value_1
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end
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return vector3:new(value_1.x / value_2, value_1.y / value_2, value_1.z / value_2)
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else
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if value_1.z ~= nil and value_2.z ~= nil then
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return vector3:new(value_1.x / value_2.x, value_1.y / value_2.y, value_1.z / value_2.z)
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else
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return vector3:new(value_1.x / value_2.x, value_1.y / value_2.y)
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end
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end
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end
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end
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-- eq vec
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function vector3.__eq(a, b)
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return a.x == b.x and a.y == b.y and a.z == b.z
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end
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function vector3.__tostring(vcrt3)
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return vcrt3:strvec3()
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end
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