I'm developing an iPhone app that allows users to cut out part of an image from its background. In order to do this, they'll connect a bunch of bezier curves together to form the clipping path. Rather than have them move the control points of the curves in order to change the curve, I'd like them to be able to move a point on the curve itself. At this point, I'm not set on using quadratic rather than cubic beziers, or vice versa. The rest of this post will discuss the issue from the point of view of quadratic curves, but I would love an answer that provides solutions to both.
It seems to me that there are two possible methods for accomplishing this:
By determining the relationship between the point on the curve and the true control point. If this can be done, then the new location of the control point can be calculated based on the new location of the point on the curve.
By using an equation that can estimate a bezier curve based on two end points and a third point on the curve (if cubic, then a third and fourth point on the curve).
Are either of these possible? I've been googling this for a while and have come across a couple potential solutions using method #2, but I don't fully understand either:
Solution 1 (click here): I think I understand the code in this example well enough, but I don't know how to calculate t.
Solution 2 (click here): This code is written in C#. I tried converting it to Objective-C (the language used for iPhone apps), but ultimately got stuck on the "solvexy()" function because I don't see how i or j are used after calculating their values.
In regards to method #1, it seems to me that there should be some mathematical relationship between the control point, and the point on the curve through which a tangent to the curve at that point would be perpendicular to a line drawn from the control point to that point.
The idea is that this point which lies on the curve, through which the perpendicular tangent is drawn, is the point that users would be dragging in order to modify the curve.