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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: enter image description here

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

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    ohu, yes! just updated2011-04-20

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