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hmm I dont know what to do

I am making some kind of a platform sidescroller game in source. So far I have moved the camera to thirdperson so it is placed perpendicular to the character 1000 units away so the character is seen from the side. The character controlled by the player is some kind of a plane which can only move left, right, up and down. At the moment when the character-plane moves left and right it follows a straight line. I want the the plane to follow a predefined function (for example a Sinus curve) instead of just a straight line.

I hope you understand what my problem is. Another way to describe what I want is to make the character follow a function when he moves forward instead of just moving straigt ahead.

What is the easiest way to solve this.