Treffer: Curves.

Representing curves is a main and important topic in different fields such as computer aided geometric design (CAGD) (Farin in Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann Publishers Inc., San Francisco, 2002; Goldman in An integrated introduction to computer graphics and geometric modeling, Chapman&Hall/CRC Computer Graphics, London, 2009) and computer graphics (Mukundan in Advanced methods in computer graphics: with examples in OpenGL. Springer, Berlin, 2012; McConnell in Computer graphics: theory into practice. Jones & Bartlett, Boston, 2005; Lengyel in Mathematics for 3D game programming and computer graphics, Course Technology PTR, 2011; Salomon in Curves and surfaces for computer graphics. Springer, Berlin, 2006; Buss in 3D computer graphics: a mathematical introduction with OpenGL. Cambridge University Press, New York, 2003). Given a set of points, a curve may be constructed to pass through (i.e., <italic>interpolate</italic>) those points. Alternatively, points can be used to <italic>approximate</italic> the shape of the curve. The number of points used to construct the curve affects its degree; and consequently, its shape. Curves may be created using functions of degree 2 (i.e. of order 3) and higher. Lines created through linear equations of degree 1 may be considered as a special case of curves although other methods are usually used to create lines (see Chap. 2 ). Points in 2D space create planar curve while 3D points are used to create 3D curves passing through different planes in 3D space. Different equations used to generate 2D curves can easily be extended to 3D space. In this chapter, we explore different curves representations. We discuss various methods and equations to construct curves. [ABSTRACT FROM AUTHOR]

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