Computer Science at Narvik University College (NUC), 2012. — 325 p.Geometry – from Ancient Greek, earth measurement – has been an important ingredient of the development of science and later also industry, design and production. In modern time, the Geometric modeling community is established, and has now a 50-year-old history. The first pioneers were motivated by the introduction of computers in design, construction and manufacturing. The goal was basically to provide methods and algorithms for curve and surface representations and calculations on these, and to combine curve and surface methods in computer graphics and simulations. By doing this, they started the develop of a new discipline called geometric modeling, including computer aided geometric design, solid modeling, algebraic geometry, and computational geometry.
Computer aided geometric design (CAGD) is the central part of the field. It started with the development of methods and algorithms for CAD/CAM. Today, however, is support for virtual reality/design and computer games, simulators and animations in movies and TV productions as important areas.
Curves and surfaces for computer aided geometric design started with classical geometric objects as line, arc, plane, sphere, cylinder etc. The next step in the development of freeform geometry was Bezier, Hermite, B-spline and rational variants as rational Bezier and NURBS and subdivision surfaces. The development began in earnest in the 1960s and went with full force until 1990. It is, however, still an ongoing development that includes T-splines and other improvement as Multivariate splines. New results also includes the introduction of generalized B-splines and thus it is still a long way to go. This way of constructing curves and surface is the most important today and will probably be it as far as we can see. It is the defacto industrial standard. What we can call a 2nd generation curve and surface construction started around year 2000, and it is just in its initial phase. It includes different types of curves and surfaces constructed by blending technics.
