Entry Sanchez-Reyes:1997:SAP from tog.bib

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BibTeX entry

@Article{Sanchez-Reyes:1997:SAP,
  author =       "J. S{\'a}nchez-Reyes",
  title =        "The symmetric analogue of the polynomial power basis",
  journal =      j-TOG,
  volume =       "16",
  number =       "3",
  pages =        "319--357",
  month =        jul,
  year =         "1997",
  CODEN =        "ATGRDF",
  ISSN =         "0730-0301",
  bibdate =      "Fri Sep 26 10:19:42 1997",
  bibsource =    "http://www.acm.org/pubs/toc/",
  URL =          "http://www.acm.org/pubs/citations/journals/tog/1997-16-3/p319-sanchez-reyes/",
  abstract =     "A new polynomial basis over the unit interval $t \in
                 [0,1]$ is proposed. The work is motivated by the fact
                 that the monomial (power) form is not suitable in CAGD,
                 as it suffers from serious numerical problems, and the
                 monomial coefficients have no geometric meaning. The
                 new form is the symmetric analogue of the power form,
                 because it can be regarded as an ``Hermite two-point
                 expansion'' instead of a Taylor expansion. This form
                 enjoys good numerical properties and admits a
                 Horner-like evaluation algorithm that is almost as fast
                 as that of the power form. In addition, the symmetric
                 power coefficients convey a geometric meaning, and
                 therefore they can be used as shape handles. A
                 polynomial expressed in the symmetric power basis is
                 decomposed into linear, cubic quintic, and successive
                 components. In consequence, this basis is bbetter
                 suited to handle polynomials of different degrees than
                 the Bernstein basis, and those algorithms involving
                 degree operations have extremely simple formulations.
                 The minimum degree of a polynomial is immediately
                 obtained by inspecting its coefficients. Degree
                 reduction of a curve or surface reduces to dropping the
                 desired high degree terms",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms; design; measurement; performance; theory",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis. {\bf G.1.1}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation. {\bf I.3.5} Computing Methodologies,
                 COMPUTER GRAPHICS, Computational Geometry and Object
                 Modeling, Curve, surface, solid, and object
                 representations. {\bf J.6} Computer Applications,
                 COMPUTER-AIDED ENGINEERING. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices",
}

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