Overview
Part of the book series: Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging (SLVCCGACPI)
Part of the book sub series: Synthesis Lectures on Computer Graphics and Animation (SLCGA)
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About this book
In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the author
Stephen Mann is an Associate Professor in the David R. Cheriton School of Computer Science and cross-appointed to the Mechanical Engineering Department at the University of Waterloo, Waterloo, Ontario, Canada. He received a B.A. in computer science and pure mathematics at the University of California, Berkeley, and has a Masters in Computer Science and Ph.D. in Computer Science and Engineering from the University of Washington in Seattle. His research interests include CAGD, geometric modeling, computer graphics, and the mathematical foundations of computer graphics.
Bibliographic Information
Book Title: Blossoming Development of Splines
Authors: Stephen Mann
Series Title: Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography and Imaging
DOI: https://doi.org/10.1007/978-3-031-79516-9
Publisher: Springer Cham
eBook Packages: Synthesis Collection of Technology (R0), eBColl Synthesis Collection 1
Copyright Information: Springer Nature Switzerland AG 2006
Softcover ISBN: 978-3-031-79515-2Published: 31 December 2007
eBook ISBN: 978-3-031-79516-9Published: 31 May 2022
Series ISSN: 2469-4215
Series E-ISSN: 2469-4223
Edition Number: 1
Number of Pages: IX, 97
Topics: Mathematics, general, Computer Imaging, Vision, Pattern Recognition and Graphics