Software-engineering approach to degree elevation of B-spline curves
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Degree elevation of B-spline curves
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Cited by (37)
Collision-free and smooth motion planning of dual-arm Cartesian robot based on B-spline representation
2023, Robotics and Autonomous SystemsA New Framework for Joint Trajectory Planning Based on Time-Parameterized B-Splines
2023, CAD Computer Aided DesignGeometric conditions of non-self-intersecting NURBS surfaces
2017, Applied Mathematics and ComputationCitation Excerpt :Theorem 1 will be used in the proof of Theorem 2. The degree elevation algorithm of NURBS curves is studied in [22–25]. In 2007, Wang and Deng proved that the degree elevation of B-spline curve is the corner cutting procedure of its control polygon (Theorem 4, Section 4, [26]).
Hybrid-degree weighted T-splines and their application in isogeometric analysis
2016, Computers and FluidsInjectivity of NURBS curves
2016, Journal of Computational and Applied MathematicsCitation Excerpt :The degree elevation algorithm is also an important algorithm of NURBS curves. There are several methods studied on the degree elevation of B-spline curves, such as Refs. [26–29]. In 2007, Wang and Deng proved that the degree elevation of B-spline curve is the corner cutting procedure of its control polygon (Theorem 4, Section 4, [30]).
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Les A Piegle is a professor of computer science and engineering at the University of South Florida, USA. His research interests are in CAD/CAM, geometric modelling, user-interface design, data structures and algorithms, and computer graphics. He spent many years researching and implementing NURBS routines in academia as well as in industry.
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Wayne Tiller is an independent consultant specializing in geometric modelling and computational geometry for CAD/CAM. He has 21 years experience in applied mathematics, computer science, and software development. From 1981 to 1990, he worked at Structural Dynamics Research Corporation, USA, conducting research and developing software for their NURBS-based geometry products. He served on the IGES Geometry Sub-committee from 1981 to 1984. He has taught courses and conducted seminars in computational geometry at the University of Cincinnati, USA, the University of Texas at Tyler, USA, and in government and industry. He received a BS in mathematics in 1968 from Louisiana State University at Baton Rouge, USA, and a PhD in mathematics in 1972 from Texas Christian University in Forth Worth, USA.