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Added quadratic_real_roots() and cubic_real_roots().

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Chris Palmer
2021-04-02 19:30:38 +01:00
parent f3376edaf1
commit b2d712bca9
3 changed files with 30 additions and 0 deletions
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25
utils/maths.scad
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@@ -162,3 +162,28 @@ function sumv(v) = reduce(v, function(a, b) a + b, 0); //! sum a vector of value
function xor(a,b) = (a && !b) || (!a && b); //! Logical exclusive OR
function cuberoot(x)= sign(x)*abs(x)^(1/3);
function quadratic_real_roots(a, b, c) = //! Returns real roots of a quadratic equation, biggest first. Returns empty list if no real roots
let(2a = 2 * a,
2c = 2 * c,
det = b^2 - 2a * 2c
) det < 0 ? [] :
let(r = sqrt(det),
x1 = b < 0 ? 2c / (-b + r) : (-b - r) / 2a,
x2 = b < 0 ? (-b + r) / 2a : 2c / (-b - r)
) [x2, x1];
function cubic_real_roots(a, b, c, d) = //! Returns real roots of cubic equation
let(b = b / a,
c = c / a,
d = d / a,
inflection = -b / 3,
p = c - b^2 / 3,
q = 2 * b^3 / 27 - b * c / 3 + d,
det = q^2 / 4 + p^3 / 27,
roots = !p && !q ? 1 : nearly_zero(det) ? 2 : det < 0 ? 3 : 1,
r = sqrt(det),
x = cuberoot(-q / 2 - r) + cuberoot(-q / 2 + r)
) roots == 1 ? [x] :
roots == 2 ? [3 * q /p + inflection, -3 * q / p / 2 + inflection] :
[for(i = [0 : roots - 1]) 2 * sqrt(-p / 3) * cos(acos(3 * q * sqrt(-3 / p) / p / 2) - i * 120) + inflection];