Question

In my application, I have few screen coordinates through which I draw a Bezier Spline and I need to find the average Velocity and acceleration through that spline.

How should I go about it ?

I will find it in terms of pixel/sec and pixels/square-sec.
and then convert it to m/sec and m/sec sq once the User provides pixel-meter mapping.

But How will I get the velocity or accn as I cant just take start point and end point, It has to be thru that curve.

Answer 1

Ughh, leave the pixel/sex and the pixels/square-sec approach aside for now.

I’m assuming from your question that you have an x-y plot with some sort of Bezier spline, some sort of curve which represents way over time. The x axis usually represents time, while the y axis represents way (length) s.

Velocity is the derivation of length over time, and acceleration the derivation of that. A derivation is simply the ratio of dy/dx in a (preferably) close pair of points.

So, what you need for a start is to interpolate and gather as many points from that Bezier spline. Leaving that up to you. From there,

dy = y(i+1) - yi
dx = x(i+1) - xi
velocity = dy/dx

So a graph of velocity over time would be that plotted on a time basis. Same goes for accelleration, just repeat the process.