Paper title:

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

Published in: Issue 1, (Vol. 17) / 2023
Publishing date: 2023-04-09
Pages: 35-41
Author(s): ȘOMÎTCĂ Ioana-Alexandra, DEACONU Ştefan-Eduard, ȘOMÎTCĂ Stelian-Alexandru
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

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