Closed spline curves bounding maximal area.
Closed-form expressions for the approximation of arclength parameterization for Bézier curves
In applications such as CNC machining, highway and railway design, manufacturing industry and animation, there is a need to systematically generate sets of reference points with prescribed arclengths along parametric curves, with sufficient accuracy and real-time performance. Thus, mechanisms to produce a parameter set that yields the coordinates of the reference points along the curve Q(t) = {x(t), y(t)} are sought. Arclength parameterizable expressions usually yield a parameter set that is necessary...
Computing homology.
Curvature computations on surfaces in -space
Curve mesh fairing and surface interpolation
Curves from variational principles