This book explains the Beta-spline representation for curves and surfaces. This topic is important for the modeling of objects delineated by free-form curved surfaces. Such models are needed in the design and manufacture of three-dimensional parts, as well as in the generation of synthetic computer images. The Beta-spline technique follows from the earlier techniques of Bézier and B-spline curves and surfaces, and forms the latest method in this field. The utility of this technique is the capability of representing complex curved surface objects using natural input specifications. The Beta-spline technique combines powerful and general mathematics with an intuitive specification method. Mathematical underpinnings are sufficiently flexible to allow the representation of a wide class of complex shapes. At the same time, description of these shapes is achieved through the use of intuitive and meaningful specification parameters. In addition to a set of points in three-space, called control vertices, shape parameters are introduced which are parameters whose values indicate the shape of the object in terms of "sharpness" or "flatness".

Product Description: Can computers be turned into usable devices to communicate imagined 3D shapes? Can digital design be enhanced to provide the public with user-friendly freeform modeling tools, as well as enabling skilled artists to express any complex shape they can think of? These are the questions the authors address in this lecture...read more

Product Description: These papers are taken from the 8th Pacific Conference on Computer Graphics and Applications (PG 2000). They address topics such as: global illumination; text layout, rendering and visibility; modelling and simulation; meshes and contours; animation; techniques with video; and more...read more (view table of contents, read Amazon.com's description)