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|
--[[ Lua Missing Math functions
/***************************************************************************
* __________ __ ___.
* Open \______ \ ____ ____ | | _\_ |__ _______ ___
* Source | _// _ \_/ ___\| |/ /| __ \ / _ \ \/ /
* Jukebox | | ( <_> ) \___| < | \_\ ( <_> > < <
* Firmware |____|_ /\____/ \___ >__|_ \|___ /\____/__/\_ \
* \/ \/ \/ \/ \/
* $Id$
*
* Copyright (C) 2017 William Wilgus
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY
* KIND, either express or implied.
*
****************************************************************************/
]]
--[[ Exposed Functions
_math.clamp
_math.clamp_roll
_math.d_sin
_math.d_cos
_math.d_tan
_math.i_sqrt
]]
local _math = {} do
-- internal constants
local _NIL = nil -- _NIL placeholder
-- clamps value to >= min and <= max
local function clamp(iVal, iMin, iMax)
if iMin > iMax then
local swap = iMin
iMin, iMax = iMax, swap
end
if iVal < iMin then
return iMin
elseif iVal < iMax then
return iVal
end
return iMax
end
-- clamps value to >= min and <= max rolls over to opposite
local function clamp_roll(iVal, iMin, iMax)
if iMin > iMax then
local swap = iMin
iMin, iMax = iMax, swap
end
if iVal < iMin then
iVal = iMax
elseif iVal > iMax then
iVal = iMin
end
return iVal
end
local function i_sqrt(n)
-- Newtons square root approximation
if n < 2 then return n end
local g = n / 2
local l = 1
for c = 1, 25 do -- if l,g haven't converged after 25 iterations quit
l = (n / g + g)/ 2
g = (n / l + l)/ 2
if g == l then return g end
end
-- check for period-two cycle between g and l
if g - l == 1 then
return l
elseif l - g == 1 then
return g
end
return _NIL
end
local function d_sin(iDeg, bExtraPrecision)
--[[ values are returned multiplied by 10000
II | I 180-90 | 90-0
---(--)--- -------(--)-------
III | IV 180-270 | 270-360
sine is only positive in quadrants I , II => 0 - 180 degrees
sine 180-360 degrees is a reflection of sine 0-180
Bhaskara I's sine approximation formula isn't overly accurate
but it is close enough for rough image work.
]]
local sign, x
-- no negative angles -10 degrees = 350 degrees
if iDeg < 0 then
x = 360 + (iDeg % 360)
else --keep rotation in 0-360 range
x = iDeg % 360
end
-- reflect II & I onto III & IV
if x > 180 then
sign = -1
x = x % 180
else
sign = 1
end
local x1 = x * (180 - x)
if bExtraPrecision then -- ~halves the largest errors
if x <= 22 or x >= 158 then
return sign * 39818 * x1 / (40497 - x1)
elseif (x >= 40 and x <= 56) or (x > 124 and x < 140) then
return sign * 40002 * x1 / (40450 - x1)
elseif (x > 31 and x < 71) or (x > 109 and x < 150) then
return sign * 40009 * x1 / (40470 - x1)
end
end
--multiplied by 10000 so no decimal in results (RB LUA is integer only)
return sign * 40000 * x1 / (40497 - x1)
end
local function d_cos(iDeg, bExtraPrecision)
--cos is just sine shifed by 90 degrees CCW
return d_sin(90 - iDeg, bExtraPrecision)
end
local function d_tan(iDeg, bExtraPrecision)
--tan = sin0 / cos0
return (d_sin(iDeg, bExtraPrecision) * 10000 / d_sin(90 - iDeg, bExtraPrecision))
end
--expose functions to the outside through _math table
_math.clamp = clamp
_math.clamp_roll = clamp_roll
_math.i_sqrt = i_sqrt
_math.d_sin = d_sin
_math.d_cos = d_cos
_math.d_tan = d_tan
end -- missing math functions
return _math
|
