The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. 

The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of curvature as the central angle subtended by an arc of length 30.48 meters. This method also provides a way to compute the radius of the curve, essential in designing curves for different applications.

The radius of curvature provides a measure of the curve's sharpness. A smaller radius corresponds to a sharper curve, while a larger radius indicates a gentler curve. 

In practical use, the chord basis is often preferred in railroad engineering due to its alignment with long, gradual curves where arc lengths are approximated to chord lengths. On the other hand, highway engineering and property boundary design frequently rely on the arc basis for precision in defining curved paths.

These concepts are critical in civil engineering, ensuring safe and efficient designs in infrastructure like railroads, highways, and property layouts.