Suppose you have 5 points in zigzag A, B, C, D and E. You want to draw a smooth path through these that touches all of them. Get a piece of paper and follow along.
1) FAIL The first anyone would do would be to draw a curve from A to C using B as the control point of the curve -> A cB C (the middle one with a "c" is the control point) Then C cD E. As a result, you get 2 "hills" with a discontinuity at C. Not only you have the discontinuity, but you don't toucj B or D in your path. 2) FAIL You figure out how to remove the discontinuity by introducing mid points BC and CD. Then you do A cB BC, BC cC CD, CD cD E. Great! The curve is smooth but you still don't touch B, C and D. 3) GOTCHA You realize that the smoothness of the curve is based on the fact that wherever a point touches the curve, the tangent of the curve at that point determines a line, and if you follow that line, you will reach control points at both sides. This is the basic nature of a bezier curve. Hence, this implies that there are infinite solutions to your problem given that there could be any tangent at any point and hence the curve could have many shapes. So, you arbitrarily choose control points from a line projected at each non-end anchor point. The most obvious solution would be to (for each non-end anchor point like B, C or D) evaluate vectors to the previous and next anchor, add them, invert them (perpendicular), normalize and use an arbitrary factor. Then you just join the dots. Sounds abstract, but if you guide yourself through something visual, its only logical: http://www.codereflections.com/blog/archives/tag/bezier-curves-as3-flash hth, li
