ABSTRACT
At first glance, curves do not appear to be a central topic in building a game en-gine. Many game engines concentrate on taking polygonal models and processing them for display by the renderer. If objects must change position or orientation during game play, the standard approach has been just to move the objects in a simple fashion, using translation by constant vector offset and rotation by a constant anglesomething that requires only vector and matrix algebra (i.e., linear algebra, emphasis on line). But curves are actually quite useful when you think about it. For example, if a flight simulator wishes to support realistic flight dynamics, such as the correct banking of a plane as it makes a tight turn, curves can be of assistance. The bank angle is related to how much bending there is in the curve that represents the flight path, requiring the concept of curvature of a curve. Moreover, if the plane is required to travel at a constant speed along the curved path, the calculations involve knowing something about arc length and the concept of reparameterization by arc length.
