317 lines
9.1 KiB
Lua
317 lines
9.1 KiB
Lua
--[[
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Copyright (c) 2010-2013 Matthias Richter
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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Except as contained in this notice, the name(s) of the above copyright holders
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shall not be used in advertising or otherwise to promote the sale, use or
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other dealings in this Software without prior written authorization.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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]]--
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-- Modified to include 3D capabilities by Bill Shillito, April 2014
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-- Various bug fixes by Colby Klein, October 2014
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--- 3 dimensional vectors.
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-- @module vec3
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-- @alias vector
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local assert = assert
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local sqrt, cos, sin, atan2, acos = math.sqrt, math.cos, math.sin, math.atan2, math.acos
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local vector = {}
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vector.__index = vector
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--- Instance a new vec3.
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-- @param x X value, table containing 3 elements, or another vector.
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-- @param y Y value
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-- @param z Z value
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-- @return vec3
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local function new(x,y,z)
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-- allow construction via vec3(a, b, c), vec3 { a, b, c } or vec3 { x = a, y = b, z = c }
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if type(x) == "table" then
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return setmetatable({x=x.x or x[1] or 0, y=x.y or x[2] or 0, z=x.z or x[3] or 0}, vector)
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end
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return setmetatable({x = x or 0, y = y or 0, z = z or 0}, vector)
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end
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local function isvector(v)
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return getmetatable(v) == vector or (type(v) == "table" and type(v.x) == "number" and type(v.y) == "number" and type(v.z) == "number")
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end
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local zero = new(0,0,0)
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local unit_x = new(1,0,0)
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local unit_y = new(0,1,0)
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local unit_z = new(0,0,1)
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--- Create a new vector containing the same data.
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-- @return vec3
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function vector:clone()
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return new(self.x, self.y, self.z)
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end
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--- Unpack the vector into its components.
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-- @return number
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-- @return number
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-- @return number
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function vector:unpack()
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return self.x, self.y, self.z
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end
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function vector:__tostring()
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return string.format("(%+0.3f,%+0.3f,%+0.3f)", self.x, self.y, self.z)
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end
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function vector.__unm(a)
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return new(-a.x, -a.y, -a.z)
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end
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function vector.__add(a,b)
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if type(a) == "number" then
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return new(a+b.x, a+b.y, a+b.z)
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elseif type(b) == "number" then
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return new(a.x+b, a.y+b, a.z+b)
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else
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assert(isvector(a) and isvector(b), "Add: wrong argument types (<vector> expected)")
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return new(a.x+b.x, a.y+b.y, a.z+b.z)
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end
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end
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function vector.__sub(a,b)
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if type(a) == "number" then
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return new(a-b.x, a-b.y, a-b.z)
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elseif type(b) == "number" then
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return new(a.x-b, a.y-b, a.z-b)
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else
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assert(isvector(a) and isvector(b), "Sub: wrong argument types (<vector> expected)")
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return new(a.x-b.x, a.y-b.y, a.z-b.z)
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end
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end
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function vector.__mul(a,b)
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if type(a) == "number" then
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return new(a*b.x, a*b.y, a*b.z)
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elseif type(b) == "number" then
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return new(b*a.x, b*a.y, b*a.z)
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else
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assert(isvector(a) and isvector(b), "Mul: wrong argument types (<vector> or <number> expected)")
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return new(a.x*b.x, a.y*b.y, a.z*b.z)
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end
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end
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function vector.__div(a,b)
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if type(a) == "number" then
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return new(a / b.x, a / b.y, a / b.z)
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elseif type(b) == "number" then
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return new(a.x / b, a.y / b, a.z / b)
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else
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assert(isvector(a) and isvector(b), "Div: wrong argument types (<vector> or <number> expected)")
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return new(a.x/b.x, a.y/b.y, a.z/b.z)
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end
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end
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function vector.__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 vector.__lt(a,b)
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-- This is a lexicographical order.
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return a.x < b.x or (a.x == b.x and a.y < b.y) or (a.x == b.x and a.y == b.y and a.z < b.z)
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end
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function vector.__le(a,b)
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-- This is a lexicographical order.
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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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--- Dot product.
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-- @param a first vec3 to dot with
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-- @param b second vec3 to dot with
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-- @return number
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function vector.dot(a,b)
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assert(isvector(a) and isvector(b), "dot: wrong argument types (<vector> expected)")
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return a.x*b.x + a.y*b.y + a.z*b.z
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end
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function vector:len2()
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return self.x * self.x + self.y * self.y + self.z * self.z
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end
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--- Vector length/magnitude.
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-- @return number
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function vector:len()
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return sqrt(self.x * self.x + self.y * self.y + self.z * self.z)
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end
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--- Distance between two points.
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-- @param a first point
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-- @param b second point
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-- @return number
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function vector.dist(a, b)
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assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
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local dx = a.x - b.x
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local dy = a.y - b.y
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local dz = a.z - b.z
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return sqrt(dx * dx + dy * dy + dz * dz)
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end
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--- Squared distance between two points.
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-- @param a first point
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-- @param b second point
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-- @return number
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function vector.dist2(a, b)
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assert(isvector(a) and isvector(b), "dist: wrong argument types (<vector> expected)")
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local dx = a.x - b.x
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local dy = a.y - b.y
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local dz = a.z - b.z
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return (dx * dx + dy * dy + dz * dz)
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end
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--- Normalize vector.
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-- Scales the vector in place such that its length is 1.
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-- @return vec3
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function vector:normalize_inplace()
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local l = self:len()
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if l > 0 then
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self.x, self.y, self.z = self.x / l, self.y / l, self.z / l
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end
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return self
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end
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--- Normalize vector.
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-- Returns a copy of the vector scaled such that its length is 1.
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-- @return vec3
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function vector:normalize()
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return self:clone():normalize_inplace()
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end
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--- Rotate vector about an axis.
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-- @param phi Amount to rotate, in radians
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-- @param axis Axis to rotate by
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-- @return vec3
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function vector:rotate(phi, axis)
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if axis == nil then return self end
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local u = axis:normalize() or Vector(0,0,1) -- default is to rotate in the xy plane
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local c, s = cos(phi), sin(phi)
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-- Calculate generalized rotation matrix
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local m1 = new((c + u.x * u.x * (1-c)), (u.x * u.y * (1-c) - u.z * s), (u.x * u.z * (1-c) + u.y * s))
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local m2 = new((u.y * u.x * (1-c) + u.z * s), (c + u.y * u.y * (1-c)), (u.y * u.z * (1-c) - u.x * s))
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local m3 = new((u.z * u.x * (1-c) - u.y * s), (u.z * u.y * (1-c) + u.x * s), (c + u.z * u.z * (1-c)) )
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-- Return rotated vector
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return new( m1:dot(self), m2:dot(self), m3:dot(self) )
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end
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function vector:rotate_inplace(phi, axis)
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self = self:rotated(phi, axis)
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end
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function vector:perpendicular()
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return new(-self.y, self.x, 0)
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end
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function vector:project_on(v)
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assert(isvector(v), "invalid argument: cannot project vector on " .. type(v))
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-- (self * v) * v / v:len2()
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local s = (self.x * v.x + self.y * v.y + self.z * v.z) / (v.x * v.x + v.y * v.y + v.z * v.z)
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return new(s * v.x, s * v.y, s * v.z)
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end
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function vector:project_from(v)
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assert(isvector(v), "invalid argument: cannot project vector on " .. type(v))
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-- Does the reverse of projectOn.
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local s = (v.x * v.x + v.y * v.y + v.z * v.z) / (self.x * v.x + self.y * v.y + self.z * v.z)
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return new(s * v.x, s * v.y, s * v.z)
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end
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function vector:mirror_on(v)
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assert(isvector(v), "invalid argument: cannot mirror vector on " .. type(v))
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local s = 2 * (self.x * v.x + self.y * v.y + self.z * v.z) / (v.x * v.x + v.y * v.y + v.z * v.z)
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return new(s * v.x - self.x, s * v.y - self.y, s * v.z - self.z)
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end
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--- Cross product.
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-- @param v vec3 to cross with
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-- @return vec3
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function vector:cross(v)
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assert(isvector(v), "cross: wrong argument types (<vector> expected)")
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return 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)
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end
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-- @return vec3
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function vector:trim_inplace(maxLen)
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-- ref.: http://blog.signalsondisplay.com/?p=336
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local s = maxLen * maxLen / self:len2()
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s = (s > 1 and 1) or math.sqrt(s)
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self.x, self.y, self.z = self.x * s, self.y * s, self.z * s
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return self
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end
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-- @return vec3
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function vector:trim(maxLen)
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return self:clone():trim_inplace(maxLen)
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end
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-- @return number
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function vector:angle_to(other)
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-- Only makes sense in 2D.
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if other then
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return atan2(self.y-other.y, self.x-other.x)
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end
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return atan2(self.y, self.x)
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end
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-- @return number
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function vector:angle_between(other)
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if other then
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return acos(self:dot(other) / (self:len() * other:len()))
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end
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return 0
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end
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-- @return vec3
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function vector:orientation_to_direction(orientation)
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orientation = orientation or new(0, 1, 0)
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return orientation
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:rotated(self.z, unit_z)
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:rotated(self.y, unit_y)
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:rotated(self.x, unit_x)
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end
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-- http://keithmaggio.wordpress.com/2011/02/15/math-magician-lerp-slerp-and-nlerp/
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function vector.lerp(a, b, s)
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return a + s * (b - a)
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end
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-- the module
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return setmetatable(
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{
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new = new,
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lerp = lerp,
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isvector = isvector,
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zero = zero,
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unit_x = unit_x,
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unit_y = unit_y,
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unit_z = unit_z
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}, {
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__call = function(_, ...) return new(...) end
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}
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)
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