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Page 1035 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
Haase’s idea is strongly related to an affine representation of de Casteljau’s algorithm for rational curves and surfaces, and even to de Boor’s algorithm for rational splines.”  ...  {For the entire collection see MR 94c:65008.} 95b:65024 65D17 41A15 Boehm, Wolfgang (D-BRNS-GC; Braunschweig) An affine representation of de Casteljau’s and de Boor’s rational algorithms.  ... 

Computing with geometry as an undergraduate course

John L. Lowther, Ching-Kuang Shene
2001 Proceedings of the thirty-second SIGCSE technical symposium on Computer Science Education - SIGCSE '01  
Unfortunately, in a typical computer science curriculum, computing with geometry is virtually missing in spite of its impact on computer science and other fields, and its importance to increase students  ...  Furthermore, many educators still believe computing with geometry, especially curves, surfaces and solids, belongs to engineering and is not part of computer science curricula, despite the need in graphics  ...  Finally, we thank a number of reviewers in the past three years whose constructive comments have not only made this controversial paper better but also helped us further polish our work.  ... 
doi:10.1145/364447.364558 dblp:conf/sigcse/LowtherS01 fatcat:zopc6yop75cwdhkoopc7swt75y

Computing with geometry as an undergraduate course

John L. Lowther, Ching-Kuang Shene
2001 ACM SIGCSE Bulletin  
Unfortunately, in a typical computer science curriculum, computing with geometry is virtually missing in spite of its impact on computer science and other fields, and its importance to increase students  ...  Furthermore, many educators still believe computing with geometry, especially curves, surfaces and solids, belongs to engineering and is not part of computer science curricula, despite the need in graphics  ...  Finally, we thank a number of reviewers in the past three years whose constructive comments have not only made this controversial paper better but also helped us further polish our work.  ... 
doi:10.1145/366413.364558 fatcat:keq2jtvnpzesxilrwmvtvzwxdm

A History of Curves and Surfaces in CAGD [chapter]

Gerald Farin
2002 Handbook of Computer Aided Geometric Design  
We adopt the definition that CAGD deals with the construction and representation of free-form curves, surfaces, or volumes.  ...  This article provides a historical account of the major developments in the area of curves and surfaces as they entered the area of CAGD -Computer Aided Geometric Designuntil the middle 1980s.  ...  He found out about de Casteljau's technical reports and coined the term "de Casteljau algorithm" in the late seventies.  ... 
doi:10.1016/b978-044451104-1/50002-2 fatcat:thb7qb27ebdwdbcshgnbzxvxq4

A Blossoming Development of Splines

Stephen Mann
2006 Synthesis Lectures on Computer Graphics and Animation  
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  ...  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  ...  steps). de Casteljau's algorithm, on the other hand, takes n(n + 1)/2 affine combinations, each of which requires two multiplications and one addition.  ... 
doi:10.2200/s00041ed1v01200607cgr001 fatcat:5shteg26izdvdj4ndz2xb6xv2m

Interactive Design of Developable Surfaces

Chengcheng Tang, Pengbo Bo, Johannes Wallner, Helmut Pottmann
2016 ACM Transactions on Graphics  
We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami.  ...  Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.  ...  Kilian, and E. Vouga. We want to thank Le Shi (KAUST) for the design of Figure 18 .  ... 
doi:10.1145/2832906 fatcat:7ljzrbbqwfds5cbv4k4x4jv6d4

Page 1276 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
G. see Brown, Joanna Mary; et al., (951:65008) Boehm, Wolfgang An affine representation of de Casteljau’s and de Boor’s rational algorithms. (English summary) 95b:65024 Bonneau, G.-P.  ...  An implicitization algorithm with fewer variables. (English summary) 95k:65014 Andersson, Roger K.-E. Surfaces with prescribed curvature. I.  ... 

Page 726 of Mathematical Reviews Vol. 27, Issue Index [page]

Mathematical Reviews  
(English summary) 95a:41002 Boehm, Wolfgang An affine representation of de Casteljau’s and de Boor’s rational algorithms. (English summary) 95b:65024 de Boor, Carl * Splinefunktionen. (German.  ...  Conic sections—an introduction to the rational splines.  ... 

Pythagorean-Hodograph B-Spline Curves [article]

Gudrun Albrecht, Carolina Vittoria Beccari, Jean-Charles Canonne, Lucia Romani
2016 arXiv   pre-print
An important consequence of this special property is that the offsets of Pythagorean-Hodograph B-Spline curves are non-uniform rational B-Spline (NURBS) curves.  ...  They can be seen as a generalization of the well-known class of planar Pythagorean-Hodograph (PH) B\'ezier curves, presented by R. Farouki and T.  ...  De Boor's algorithm thus degenerates to de Casteljau's algorithm yielding the first equation of condition (16) . The first equation of condition (17) is obtained analogously.  ... 
arXiv:1609.07888v1 fatcat:jgmq6nlnh5h3lh246bhzaovpmm

Design with Nonlinear Constraints

Mark Pauly, Pengbo Bo, Caigui Jiang, Yongliang Yang, Xin Zhao, Xiang Sun, Alexandra Gomes, Marko Tomiči´tomiči´c
2015 unpublished
He is also an excellent mentor who has greatly helped my research and a good friend who shares many interests.  ...  Then, with a formulation bridging mesh-based and spline-based representations, the application is extended to developable surfaces including origami with curved creases.  ...  When n = 1, B-spline curves reduce to Bézier curves with single parameter intervals, and de Boor's algorithm reduces to de Casteljau's algorithm.  ... 
fatcat:zssv5xvizbcczom5auj4wtjqfa