Abstract
Surfaces are a way of representing 3D models in space; however, in general, a surface may not enclose a volume. In many aspects, surfaces can be seen as an extension to curves (Chap. 6) where a surface point is determined using two parameters. A surface may interpolate data points or be controlled by space points that may reside on different planes. In this chapter, we will discuss some surface representations.
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Notes
- 1.
Curves shaping along the surface are called isoparametric curves. An isoparametric curve has a fixed \(u\) value and a varying \(v\) value or a fixed \(v\) value and a varying \(u\) value.
- 2.
Recall that degree (\(p, q\)) is equivalent to order (\(p+1, q+1\)).
References
Bézier, P. 1972. Numerical control: Mathematics and applications. Wiley series in computing London: Wiley.
Bézier, P. 1974. Computer aided geometric design, chapter mathematical and practical possibilities of UNISURF. New York: Academic Press.
Forrest, R.A. 1980. The twisted cubic curve: A computer-aided geometric design approach. Computer Aided Design 12(4): 165–172.
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Elias, R. (2014). Surfaces. In: Digital Media. Springer, Cham. https://doi.org/10.1007/978-3-319-05137-6_7
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DOI: https://doi.org/10.1007/978-3-319-05137-6_7
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