Velocity Control

To control velocity along a spline motion path,

• Let s = f(t) specify distance along the spline as a function of time t.
• The function f(t), being just a scalar value, can be supported with a functional animation technique (i.e. another spline).
• The function f(t) may be specifed as the integral of yet another function, v(t) = df(t)/dt, the velocity. Note that the integral of a spline function can be found analytically, through a manipulation of the control points.
• The motion path as a function of time is thus given by .