This document discusses different representations of surfaces in 3D modeling, including polygon meshes, parametric surfaces, and quadric surfaces. Polygon meshes represent surfaces as sets of connected planar polygons, and are suitable for boxes and buildings but not curved surfaces. Parametric surfaces represent points on 3D curves or surfaces as polynomial functions of parameters, allowing more accurate curved representations using fewer data points than polygon meshes. Higher-order parametric curves are more compact and easier to manipulate than polylines.