By David F. Rogers
For one week after receiving this publication I agreed with an previous very serious overview. I replaced my brain. the topic isn't really effortless yet written through anyone who is aware his company. Having acquired used to his notation i locate this ebook increasingly more helpful and refer again to it every time an issue arises and typically find the solution or a few pointer to the reply.
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Additional info for An Introduction to NURBS: With Historical Perspective (The Morgan Kaufmann Series in Computer Graphics)
The tangent vector at the end of the left-hand curve segment is equal in length to the longer tangent vector shown for the righthand curve segment. 4 Comparison of C 1 and G 1 continuity. 11 because both the direction and magnitude of the tangent vectors where the curve segments join are equal. The m a g n i t u d e of the tangent vector for the curve labeled G 1 is half t h a t of the curve labeled C 1. Notice the significant difference in the shape of the curves. A physical analog serves to clarify the fundamental difference between geometric and parametric continuity.
Steve Coons liked matrix formulations. The general case of the B-spline curve method that I was developing for my thesis did not easily fit that formulation. However, by considering only the special case of floating uniform knots, Steve was able to derive a matrix formulation. His efforts had the effect of making B-spline curves much easier to grasp and therefore more popular to use. However, this was a double-edged sword, for only the uniform floating B-splines lent themselves to this approach.
Automobile bodies, G 1 or even G 2 continuity is not adequate. For these applications, at least C 2 continuity is required to achieve the desired results. R o b i n Forrest In the early days of the development of surfaces for computer-aided design, there were relatively few players, scattered mainly around the United States and the United Kingdom. Information was available largely through technical reports, since there was no recognised place to publish such material. Fortunately, enthusiasm meant that papers and views were readily exchanged and commercial confidentiality did not intrude.