Bezier Curves 2: higher order polynomials
Bezier curve written as a polynomial: each point is weighted; the curve is the sum of weighted points. The weights vary with t. For example, at t=0, the curve is at A, and the contribution of points B, C, D... is zero. A influences the curve less and less as t increases.
"Show All Point Weights" displays a vector in the direction of each point; the length of each vector show how far the curve is pushed in that direction.
A tool for giving a nth order Bézier from n+1 control points: http://www.geogebratube.org/material/show/id/83845