The Quasi‐Cubic Trigonometric Cardinal Spline With Local Shape Adjustability

The cubic Cardinal spline curve is a fundamental tool in the field of interpolation curve design. However, the cubic Cardinal spline curve cannot adjust its shape locally through the free parameters, and it struggles to accurately represent common engineering curves such as elliptical arcs, circular arcs, and parabolic arcs. To overcome these limitations, a novel quasi‐cubic trigonometric Cardinal spline curve is developed. This new spline curve retains the core advantages of the cubic Cardinal spline curve while introducing significant enhancements. It incorporates free parameters that enable local shape adjustment and is capable of accurately representing elliptical arcs, circular arcs, and parabolic arcs. Additionally, the cubic Cardinal spline surface is introduced, and the schemes for creating fair quasi‐cubic trigonometric Cardinal spline curve and surface are provided.