Representation of Curves on a Plane

  • Buntara S. Gan
Chapter

Abstract

In this chapter, we will discuss in detail several methods of representing curves in geometric modeling. Unlike the other books which usually start from the standard basic theories behind the equations, this chapter will lead us directly on how to find equations or functions from a given set of data points. This following and connected subsection will reveal the techniques of representing the curves in real applications of beam geometric modeling. The objective of this chapter is to bring the reader to understand the concept of the nonuniform rational B-spline (NURBS) which is the basis foundation for the construction of beam element formulations in the Isogeometric approach.

Keywords

Curve Polynomial Bernstein Bézier B-spline NURBS Isogeometric 

References

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Further Reading

  1. Beach RC (1991) An introduction to the curves and surfaces of computer-aided design. Van Nostrand Reinhold, New YorkGoogle Scholar
  2. Bézier PE (1972) Numerical control: mathematics and applications. Wiley, New YorkMATHGoogle Scholar
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  4. Farin GE (1993) Curves and surfaces for computer aided geometric design – a practical guide, 3rd edn. Academic Press, BostonMATHGoogle Scholar
  5. Faux ID, Pratt MJ (1981) Computational geometry for design and manufacture. Ellis Horwood Ltd., ChichesterMATHGoogle Scholar
  6. Hoffmann CM (1989) Geometric & solid modeling. Morgan Kaufmann, San MateoGoogle Scholar
  7. Hoschek J, Lasser D (1993) Fundamentals of computer aided geometric design. AK Peters Ltd., WellesleyMATHGoogle Scholar
  8. Lorentz GG (1986) Bernstein polynomials. Chelsea Publishing Co., New YorkMATHGoogle Scholar
  9. Mortenson ME (1985) Geometric modeling. Wiley, New YorkGoogle Scholar
  10. Piegl L, Tiller W (1997) The NURBS book. Springer, BerlinCrossRefMATHGoogle Scholar
  11. Rogers DF, Adams JA (1990) Mathematical elements for computer graphics, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  12. Yamaguchi F (1988) Curves and surfaces in computer aided geometric design. Springer, New YorkCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Buntara S. Gan
    • 1
  1. 1.College of Engineering, Department of ArchitectureNihon UniversityKoriyamaJapan

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