By David F. Rogers
For one week after receiving this ebook I agreed with an prior very severe evaluation. I replaced my brain. the topic isn't effortless yet written by means of an individual who understands his company. Having received used to his notation i locate this publication a growing number of precious and refer again to it every time an issue arises and typically uncover the answer or a few pointer to the reply.
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Additional resources for An Introduction to NURBS: With Historical Perspective (The Morgan Kaufmann Series in Computer Graphics)
1 B(~zier Curve Definition A Bdzier curve, which is a special case of a NURBS curve, is determined by a control polygon, such as shown in Fig. 2. Because the Bdzier basis is also the Bernstein basis, several properties of Bdzier curves are immediately known. For example: The basis functions are real. The degree of the polynomial defining the curve segment is one less than the number of control polygon points. The curve generally follows the shape of the control polygon. The first and last points on the curve are coincident with the first and last points of the control polygon.
The cutting volume was approximately 20 x 14 x 10 inches. 6 in/sec, with a maximum speed of 16 in/sec on all three axes. The machine was used to cut rigid foam, wood and rigid, high-density polyethylene models, two examples of which, produced on the earlier Mark I machine, are held by Robin Forrest in the picture on page 13. A PDP11/45, running the GINO-F software, was used as the controller. (David F. Rogers) B( zier C u r v e s We begin our discussion of NURBS (NonUniform Rational B-Spline) curves and surfaces by looking at their antecedents, specifically B~zier curves.
B-splines were not fully exploited until years later, when subdivision and the Oslo Algorithm became available and they became a commodity. Today they have probably become the most common surface representation in modern CAD systems. Rich Riesenfeld Salt Lake City, January 2000 This Page Intentionally Left Blank B-spline Curves From a mathematical point of view, a curve generated by using the vertices of a control polygon is dependent oil some interpolation or approximation scheme to establish the relationship between the curve and the control polygon.