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-- Taken from luapower.com (Public domain)
--basic math for the cartesian plane.
--angles are expressed in degrees, not radians.
local sqrt, abs, min, max, sin, cos, radians, degrees, atan2 =
math.sqrt, math.abs, math.min, math.max, math.sin, math.cos, math.rad, math.deg, math.atan2
--hypotenuse function: computes sqrt(a^2 + b^2) without underflow / overflow problems.
local function hypot(a, b)
if a == 0 and b == 0 then return 0 end
a, b = abs(a), abs(b)
a, b = max(a,b), min(a,b)
return a * sqrt(1 + (b / a)^2)
end
--distance between two points. avoids underflow and overflow.
local function distance(x1, y1, x2, y2)
return hypot(x2-x1, y2-y1)
end
--distance between two points squared.
local function distance2(x1, y1, x2, y2)
return (x2-x1)^2 + (y2-y1)^2
end
--point at a specified angle on a circle.
local function point_around(cx, cy, r, angle)
angle = radians(angle)
return
cx + cos(angle) * r,
cy + sin(angle) * r
end
--rotate point (x,y) around origin (cx,cy) by angle.
local function rotate_point(x, y, cx, cy, angle)
if angle == 0 then return x, y end
angle = radians(angle)
x, y = x-cx, y-cy
local c, s = cos(angle), sin(angle)
return cx + x*c - y*s, cy + y*c + x*s
end
--angle between two points in -360..360 degree range.
local function point_angle(x, y, cx, cy)
return degrees(atan2(y - cy, x - cx))
end
--reflect point through origin (i.e. rotate point 180deg around another point).
local function reflect_point(x, y, cx, cy)
return 2 * cx - x, 2 * cy - y
end
--reflect point through origin at a specified distance.
local function reflect_point_distance(x, y, cx, cy, length)
local d = distance(x, y, cx, cy)
if d == 0 then return cx, cy end
local scale = length / d
return
cx + (cx - x) * scale,
cy + (cy - y) * scale
end
return {
hypot = hypot,
distance = distance,
distance2 = distance2,
point_around = point_around,
rotate_point = rotate_point,
point_angle = point_angle,
reflect_point = reflect_point,
reflect_point_distance = reflect_point_distance,
}
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