This chapter discusses geometric properties of curves and surfaces such as length, area, volume, and curvature. It reviews analytic representations, the construction of digital representations, and the estimation of geometric properties from digitized data, with emphasis on area estimation in 2D and volume estimation in 3D. Digital estimation of other curve and surface properties will be treated in later chapters.
Section 7.1.2 gave topologic definitions of curves and arcs. This section reviews analytic representations and properties of planar curves, including arc length, slope, curvature, and area, as well as geometric properties of isothetic grid polygons.