Drawing Cubic Bézier Curves with Curvature and Radius Calculations

After drawing a cubic Bézier curve, we can compute the curvature and radius at each point along the curve. These calculations are crucial for designing roads and railway tracks. The implementation typically involves using parametric equations to represent the Bézier curve, followed by mathematical derivatives to determine the curvature formula. For curvature calculation, we utilize the first and second derivatives of the Bézier curve's parametric equations. The radius of curvature is then derived as the reciprocal of the curvature value. These geometric properties enable engineers to determine optimal vehicle speeds for maintaining safety and comfort during turns. By analyzing curvature and radius distributions, we can optimize curve designs to enhance both safety and efficiency in transportation infrastructure. The algorithm can be implemented using vector mathematics and differentiation techniques, with key functions including curve parameterization, derivative calculations, and curvature-radius conversions.