An interface for use in a 3-D graphics system containing a parametric modelling unit for modelling objects as high order surfaces, and a polygon based rendering system for rendering polygon modelled objects for display. The interface comprises an input for receiving data and a subdivision unit coupled to the input for processing the data. The interface includes a converter coupled to the subdivision unit for determining from leaf patch data a first plurality of values representing vertices of tessellating polygons describing the leaf patch, and for determining from sub-leaf patch data a second plurality of values representing the vertices of tessellating polygons describing the sub-leaf patch. The interface also has a combiner, coupled to the converter, for combining the values to form leaf polygon data defining the polygon vertices at a first subdivision level, and an output coupled to the combiner for outputting the leaf polygon data.