Comments and answers for "Controlling the curvature of a Bézier curve"
http://answers.unity.com/questions/548023/controlling-the-curvature-of-a-bezier-curve.html
The latest comments and answers for the question "Controlling the curvature of a Bézier curve"Comment by The_Magical_Kiwi on The_Magical_Kiwi's answer
http://answers.unity.com/comments/758368/view.html
It was taking me to long to complete, so in the end, I created a system where if after trying a few different things(changing the distance of p1 and p2) to get a valid curve, if I haven't found one, it puts in extra points which cause the ship to stop and rotate on the spot before continuing on the curve.
Eventually, I'll come back to it when I have more time, the system I have isn't good enough, but for now it works.
TL;DR: Haven't found a solution, put in a placeholder system for now until I have more time to spend on it.Mon, 28 Jul 2014 15:58:42 GMTThe_Magical_KiwiAnswer by CHPedersen
http://answers.unity.com/answers/755500/view.html
As telcom_un mentioned, Bezier curves at their simplest aren't the easiest to control. But thankfully, you're in an area of math which has a very rich toolkit of other curve functions you can use which might make it easier for you to control the curve. :)
Bezier curves are actually just a special case of the more general ["Non-Uniform Rational Basis Spline", or NURBS curves for short.][1] NURBS curves allow you to specify weights for the control points which, in layman's terms, behaves like gravity in that they pull the curve further towards them the higher the weight. If a point's weight is infinite, the curve passes through that point, regardless of where it is.
There is also another type of curve function called ["Cubic Hermite Splines", which has a variant known as "Catmull-Rom Splines"][2]. These curves naturally pass through all the control points, and bend nicely in between.
Catmull-Rom splines is what Eric5h5 implemented for his [Vectrosity Library][3], which can draw this type of curve in Unity, and which I've used extensively. :)
(Don't take that last part as an ad, I don't work for Eric or am affiliated with him in any way, I just like his library and can recommend it.)
[1]: http://en.wikipedia.org/wiki/NURBS_curve
[2]: http://en.wikipedia.org/wiki/Cubic_Hermite_spline#Catmull.E2.80.93Rom_spline
[3]: http://www.starscenesoftware.com/vectrosity.htmlThu, 24 Jul 2014 08:22:52 GMTCHPedersenAnswer by telcom_un
http://answers.unity.com/answers/755434/view.html
In general it is not an easy task to control the curvature of a Bezier curve. If you look into the Bezier curvature formula you get, `k(t) = (px_d py_dd - py_d px_dd)/(px_d^2 + py_d^2)3/2.`
As you see you need second derivative to control the curvature. It means without acceleration constrains you don't have meaningful control over the curvature. So at least 4th order Bezier is necessary for your task. I don't know any a-z approach to give you Bezier though. If you got it by now please share it with me.Thu, 24 Jul 2014 08:11:50 GMTtelcom_un