# B-Spline derivatives

This topic is 3824 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

A derivative of B-Spline at some parameter t is a vector with its magnitude and direction. This magnitude is changing is size over time. What I am interested is what this magnitude is a function of? Why is sometimes magnitude bigger and why is sometimes smaller?

##### Share on other sites
It's also function of 't'. That doesn't change when you take the derivative. The magnitude changes because the instantaneous rate-of-change at every point on the spline changes as a function of 't'. If you have dx/dt, dy/dt, and dz/dt for each direction, then combined you get [dx,dy,dz]/dt, or dP/dt, which you can think of as velocity. Then magnitude would be speed.

##### Share on other sites
Thx, very much.
So I assume another derivative and it would be acceleration?

##### Share on other sites
Yes, the rate of change of the rate of change would be the acceleration.

X(t) = spline function
d/dt[X(t)] = V(t)
d/dt[V(t)] = d/dt[d/dt[X(t)]] = A(T)

• ### What is your GameDev Story?

In 2019 we are celebrating 20 years of GameDev.net! Share your GameDev Story with us.

• 10
• 11
• 13
• 9
• 11
• ### Forum Statistics

• Total Topics
634087
• Total Posts
3015445
×