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Smoothness is described in terms of normals. The term "normal" or "surface normal" to a plane is an imaginary vector line direction which is perpendicular to that plane. Thus, the perpendiculars across surface slopes are the normals to the surface. As you approach changes in slope across a smooth, continuous surface, the direction of the normals change their orientation gradually.
Two surfaces with different levels of smoothness are shown below. The first surface, represented by flat planar facets, is not smooth. The normal to the surface is constant throughout the extent of an individual facet. However, as the normal crosses an edge separating two adjacent facets, the normal abruptly changes.
Contrast this behavior with the surface on the right. The normal to the surface on the right varies continuously across the surface. The normal does not change abruptly as it crosses an edge in the surface.
Terrain surfaces vary in smoothness. Geologically young terrains typically have sharp ridges and valleys, in contrast to older terrains that have been smoothed by prolonged exposure to erosional forces. Statistical surfaces, such as a rainfall or air temperature surface, are generally smooth.