Planar Hermite quintic interpolants with prescribed arc length

This work is inspired by the method proposed in [1], where planar G2 interpolants based on seventh-degree PH biarcs were constructed to interpolate prescribed points, tangent directions, and curvature values while enforcing a desired arc length. Our aim is to investigate the possibility of achieving analogous results using quintic PH curves. The construction of the quintic biarc model with prescribed arc length is presented, along with the derivation of the associated equations and the strategies used to reduce the degrees of freedom. Numerical experiments are reported to show the validity, limitations, and general applicability of the proposed quintic approach.