1 files changed, 10 insertions, 1 deletions
diff --git a/advtrains/helpers.lua b/advtrains/helpers.lua
index a2eabb5..9afe72d 100644
--- a/advtrains/helpers.lua
+++ b/advtrains/helpers.lua
@@ -398,13 +398,22 @@ function advtrains.decode_pos(pts)
 	return vector.new(dec(strx), dec(stry), dec(strz))
 end
 
+-- Solve quadratic equations (i.e. a*x^2 + b*x + c = 0)
 function advtrains.solve_quadratic_equation(a, b, c)
 	if not (a and b and c) then return nil end
+	if a == 0 then return {-c/b, -c/b} end -- avoid division by zero
 	local delta = (b*b - 4*a*c)
-	if delta < 0 then return nil end
+	if delta < 0 then return {-b/2/a,-b/2/a} end -- ignore imaginary part
 	return {((-b+math.sqrt(delta))/2/a),((-b-math.sqrt(delta))/2/a)}
 end
 
+-- safe square root
+-- Negative return values indicate imaginary numbers.
+function advtrains.safesqrt(a)
+	if a >= 0 then return math.sqrt(a) end
+	return 0 - math.sqrt(-a)
+end
+
 --[[ Benchmarking code
 local tdt = {}
 local tlt = {}