Sample codes

https://github.com/NorimasaYoshida/CurveToolWithCMRegion/

A curve tool similar to Adobe Illustrator, but it includes a visualization of the curvature monotonicity region. When a control point is placed within its corresponding region, the curvature of the curve will vary monotonically.

Try  the online demo.

[1] Takafumi Saito and Norimasa Yoshida, Curvature monotonicity evaluation functions on rational Bézier curves. Computers & Graphics, Vol. 114, pp.219-229, Aug. 2023. https://doi.org/10.1016/j.cag.2023.05.019

[2] Norimasa Yoshida, Seiya Sakurai, Hikaru Yasuda, Taisei Inoue and Takafumi Saito, Visualization of the Curvature Monotonicity Regions of Polynomial Curves and its Application to Curve Design, Computer-Aided Design and Applications, Vol. 21, No.1, pp.75-87, Jan. 2024. https://doi.org/10.14733/cadaps.2024.75-87

https://notebookarchive.org/2024-06-1xe104l

The upper left figure is a cubic Bezier curve.  The upper right is the curvature plot. The lower left is the CMEF, whereas the lower right is the dk/ds.

Takafumi Saito and Norimasa Yoshida, Curvature monotonicity evaluation functions on rational Bézier curves. Computers & Graphics, Vol. 114, pp.219-229, Aug. 2023. doi: https://doi.org/10.1016/j.cag.2023.05.019. 

https://notebookarchive.org/2024-06-1ucl8i6

The left figure shows how alpha (the slope of LCG) of a hyperbolic spiral varies with respect to the parameter t.

Norimasa Yoshida and Takafumi Saito, Shape Information of Curves and its Visualization using Two-tone Pseudo Coloring, Computer-Aided Design and Applications, Vol. 21, No.1, pp.11-28, Jan. 2024. doi: 10.14733/cadaps.2024.11-28