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 .

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab