How can I convert curveTo() to a list of Points?

Question

Take the following AS3 that will draw a curved line using curveTo():

var line:Shape = new Shape();

line.x = line.y = 20;
line.graphics.lineStyl         


        

Answer 1

A Bezier curve is a parametric function. A quadratic Bezier curve (i.e. three control points) can be expressed as: F(t) = A(1 - t)^2 + B(1 - t)t + Ct^2 where A, B and C are points and t goes from zero to one.

This will give you two equations:

x = a(1 - t)^2 + b(1 - t)t + ct^2

y = d(1 - t)^2 + e(1 - t)t + ft^2

If you add for instance the line equation (y = kx + m) to that, you'll end up with three equations and three unknowns (x, y and t).

from: How to find the mathematical function defining a bezier curve

using this equation, you can create an array of x and y coordinates