A class of cubic trigonometric pseudo B-spline functions combining multiple characteristics is proposed to address the deficiency of normal polynomial B-spline curves in shape control

the accurate representation of several engineering curves

and the construction of interpolation curves. A class of cubic trigonometric pseudo B-spline basis functions with two parameters is constructed. The parametric pseudo B-spline curve is defined based on the proposed basis functions

and the characteristics and fairness of the curve are discussed. Lastly

the corresponding algebraic pseudo B-spline is studied

and a method of determining the optimal algebraic pseudo B-spline is provided. The parametric pseudo B-spline curves can not only be C continuous

but can also automatically interpolate the given data points without solving the system equations. When the data points are fixed

the shape of the interpolation curves can be adjusted by the two parameters. Under appropriate conditions

the parametric pseudo B-spline curves can be precisely expressed as several engineering curves

such as circular arc

elliptical arc

and star line. The corresponding algebraic pseudo B-spline has properties similar to those of the parametric pseudo B-spline curve. The optimal algebraic pseudo B-spline can obtain satisfactory interpolation effects. The proposed pseudo B-spline simultaneously solves the deficiency of normal polynomial B-spline in shape control

the accurate representation of several engineering curves

and the construction of interpolation curves. Thus

it is a practical method for curve modeling.