A new Procedure of Computing the Minimum Radii of Bézier Curves and Applications in Designing a Bike Trail

Abstract

The paper presents a new procedure for finding the minimum radius of a Bézier Curves. The authors choose to use the theoretical procedure for a practical application. For this purpose, the authors find the minimum radii of a Bézier Curve consisting of 16 Cubic Bézier Curves on a bike trail situated in Mălini, Romania. In the design of the bike route, the authors consider elevations to design a bike trail on level curves. This decision is made to obtain a slope of less than 20%, for a relaxing route for the family. The route is created on a length of about 5 km completely respecting the design norms of a cycling track, according to the Methodological Guide for regulating the design. Authors choose to present a comparison for the procedure between hand-drawn horizontal curves, and approximating the trail using Cubic Bézier Curves and Python

Keywords

• bézier curves
• b-spline
• cubic bézier curves
• minimum radius
• interpolation
• approximation
• elevations
• level curves