187 lines
4.4 KiB
Lua
187 lines
4.4 KiB
Lua
--[[
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Copyright (c) 2012-2013 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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local sqrt, cos, sin, atan2 = math.sqrt, math.cos, math.sin, math.atan2
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local function str(x, y)
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return '(' .. tonumber(x) .. ',' .. tonumber(y) .. ')'
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end
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local function mul(s, x, y)
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return s * x, s * y
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end
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local function div(s, x, y)
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return x / s, y / s
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end
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local function add(x1, y1, x2, y2)
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return x1 + x2, y1 + y2
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end
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local function sub(x1, y1, x2, y2)
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return x1 - x2, y1 - y2
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end
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local function permul(x1, y1, x2, y2)
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return x1 * x2, y1 * y2
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end
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local function dot(x1, y1, x2, y2)
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return x1 * x2 + y1 * y2
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end
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local function det(x1, y1, x2, y2)
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return x1 * y2 - y1 * x2
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end
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local function eq(x1, y1, x2, y2)
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return x1 == x2 and y1 == y2
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end
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local function lt(x1, y1, x2, y2)
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return x1 < x2 or (x1 == x2 and y1 < y2)
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end
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local function le(x1, y1, x2, y2)
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return x1 <= x2 and y1 <= y2
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end
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local function len2(x, y)
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return x * x + y * y
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end
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local function len(x, y)
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return sqrt(x * x + y * y)
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end
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local function fromPolar(angle, radius)
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radius = radius or 1
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return cos(angle) * radius, sin(angle) * radius
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end
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local function randomDirection(len_min, len_max)
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len_min = len_min or 1
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len_max = len_max or len_min
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assert(len_max > 0, 'len_max must be greater than zero')
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assert(len_max >= len_min, 'len_max must be greater than or equal to len_min')
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return fromPolar(math.random() * 2 * math.pi,
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math.random() * (len_max - len_min) + len_min)
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end
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local function toPolar(x, y)
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return atan2(y, x), len(x, y)
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end
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local function dist2(x1, y1, x2, y2)
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return len2(x1 - x2, y1 - y2)
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end
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local function dist(x1, y1, x2, y2)
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return len(x1 - x2, y1 - y2)
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end
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local function normalize(x, y)
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local l = len(x, y)
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if l > 0 then
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return x / l, y / l
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end
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return x, y
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end
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local function rotate(phi, x, y)
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local c, s = cos(phi), sin(phi)
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return c * x - s * y, s * x + c * y
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end
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local function perpendicular(x, y)
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return -y, x
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end
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local function project(x, y, u, v)
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local s = (x * u + y * v) / (u * u + v * v)
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return s * u, s * v
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end
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local function mirror(x, y, u, v)
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local s = 2 * (x * u + y * v) / (u * u + v * v)
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return s * u - x, s * v - y
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end
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-- ref.: http://blog.signalsondisplay.com/?p=336
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local function trim(maxLen, x, y)
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local s = maxLen * maxLen / len2(x, y)
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s = s > 1 and 1 or math.sqrt(s)
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return x * s, y * s
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end
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local function angleTo(x, y, u, v)
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if u and v then
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return atan2(y, x) - atan2(v, u)
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end
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return atan2(y, x)
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end
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-- the module
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return {
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str = str,
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fromPolar = fromPolar,
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toPolar = toPolar,
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randomDirection = randomDirection,
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-- arithmetic
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mul = mul,
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div = div,
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idiv = idiv,
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add = add,
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sub = sub,
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permul = permul,
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dot = dot,
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det = det,
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cross = det,
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-- relation
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eq = eq,
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lt = lt,
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le = le,
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-- misc operations
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len2 = len2,
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len = len,
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dist2 = dist2,
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dist = dist,
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normalize = normalize,
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rotate = rotate,
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perpendicular = perpendicular,
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project = project,
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mirror = mirror,
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trim = trim,
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angleTo = angleTo,
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}
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