Visualization of curvature on curve and surface by tangential angle parametrization

TL;DR

This paper introduces a unified visualization method for curvature on planar curves and surfaces of revolution using tangential angle parametrization, revealing geometric features clearly without arbitrary tuning.

Contribution

It presents a novel, unified approach to visualize curvature on curves and surfaces using tangential angle steps, enhancing geometric understanding.

Findings

Markers at equal tangential angle steps reveal local bending and inflection points.

Curvature lines at equal tangential angle steps reflect principal curvature variations.

The method provides clear visualizations without arbitrary parameter tuning.

Abstract

We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal increments of the tangential angle reveals local bending features and naturally highlights inflection points and vertices. This approach extends to surfaces of revolution, where curvature lines drawn at equal tangential angle steps reflect principal curvature variations and naturally expose ridge and parabolic curves. Our method provides clear, consistent visualizations without arbitrary parameter tuning, offering geometric insight for both analysis and design applications.