Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature

Eurographics Symposium on Geometry Processing 2022
Alexandre Binninger, Olga Sorkine-Hornung

Interpolating curves generated from the same control points (shown in red) using κ-curves [Yan et al. 2017], trigonometric blending [Yuksel 2020], our 3-arcs clothoids method and our clothoid-line-clothoid method. Our approach guarantees G2 continuity, has bounded local support and provides curvature monotonicity between control points of opposite curvature sign. The curvature normals are visualized with purple lines.


We propose a method for the construction of a planar curve based on piecewise clothoids and straight lines that intuitively interpolates a given sequence of control points. Our method has several desirable properties that are not simultaneously fulfilled by previous approaches: Our interpolating curves are C2 continuous, their computation does not rely on global optimization and has local support, enabling fast evaluation for interactive modeling. Further, the sign of the curvature at control points is consistent with the control polygon; the curvature attains its extrema at control points and is monotone between consecutive control points of opposite curvature signs. In addition, we can ensure that the curve has self-intersections only when the control polygon also self-intersects between the same control points. For more fine-grained control, the user can specify the desired curvature and tangent values at certain control points, though it is not required by our method. Our local optimization can lead to discontinuity w.r.t. the locations of control points, although the problem is limited by its locality. We demonstrate the utility of our approach in generating various curves and provide a comparison with the state of the art.





We thank the reviewers for their remarks. We also thank Ilya Baran for the insightful discussions and inspiration. This work was supported in party by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101003104, ERC CoG MYCLOTH).