Computational geometry deals with the construction of algorithms and their complexity related to problems in geometry arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographic information systems. Digital geometry deals with geometric properties of subsets of digital images or, equivalently, with geometric properties of finite sets of lattice points. Digital geometry can anticipate progress in imaging technology allowing higher and higher spatial resolution. It seems that the input data in both fields will "converge" to data embedded in digital arrays of very high spatial resolution. This book covers the important developments in digital and computational geometry including methods of approximating geometric objects.