The representation of non-quadrilateral surfaces is an important topic of computer-aided geometric design. Conventional methods include trimming and splitting, but there are also genuine multi-sided surfaces that can be used for curve network based design or hole filling applications.

Most of these non-standard representations are either (i) restricted to (rational) polynomial boundaries, or (ii) lacking an interior control mechanism. Here I propose a multi-sided patch that can interpolate arbitrary boundary curves, and provides an intuitive, control point based approach to interior modifications, similar to that of generalized Bézier patches, while ensuring smooth connections to adjacent surfaces, as well.