Visualization of the Curvature Monotonicity Region of Planar Polynomial Bézier Curves

Abstract

In this research, we propose a method for visualizing the curvature monotonicity regions of planar polynomial Bezier curves using a GPU. The curvature of curves does not change by translation or rotation. Scaling the curves inversely scales the curvature. The curvature monotonicity does not change by translation, rotation, or scaling. Using this property, we propose a method to efficiently visualize the curvature monotonicity regions by introducing the standard form.