Shape Information of Curves and its Visualization using Two-tone Pseudo Coloring

This paper presents a method for computing and visualizing the shape information of differentiable parametric curves. The shape information is the slope α of the logarithmic curvature graph and the slope β of the logarithmic torsion graph. We derive the equations for computing α and β in terms of curvature and torsion, respectively. The value of α is related to the specific curvature function, such as the linear function when α = −1. For space curves, the value of β is also related to the specific torsion function. Using the two-tone pseudo coloring for the visualization of the shape information, users can read out the approximate value of α and β for each point of the curve. For some planar curves, we clarify the similarities with log-aesthetic curves by taking the limit of α as the parameter approaches the limit value. © 2024 CAD Solutions.