how understand if a segment is inside a lissajous curve

i am a programmer and not a math guru, but i like geometry. so if i'm not accurate in math terminology or i have folly question please sorry me.

i'm drawing with a programming language the lissajous curve ( http://en.wikipedia.org/wiki/Lissajous_curve ), sampling 100 points.

i want to consider all segments formed by any two points. how can i understand if the segment is "inside" (i don't know how to explain it with right math words) the trigonometric curve?

here is an example:

the black segment is "outside", the blue one is "inside".

EDIT: - segment P1-P3 is considered "outside" - in wikipedia there is a general form but i consider only closed curve where a/b is rational

• What about a segment such as from p3 to p0, which has parts both inside and outside the curve? – Isaac Apr 17 '11 at 17:52
• How high are the frequencies you're expecting for your Lissajous curves? – J. M. is a poor mathematician Apr 17 '11 at 17:54
• @Isaac: Do you mean from p3 to p1? – Américo Tavares Apr 17 '11 at 18:03
• @Américo: er, oops... p3 to p1 is more likely to work than p3 to p0, yeah... it isn't entirely clear to me that p3 to p1 is actually both inside and outside, but clearly p3 to p0 is entirely inside. – Isaac Apr 17 '11 at 18:06
• segment p1-p3 is considered outside – nkint Apr 17 '11 at 20:25