Abstract
In this chapter I describe how to calculate tangent and normal vectors on various curves and surfaces. I begin with the notation used to describe vector-valued functions and definitions for a tangent and normal vector. This includes an introduction to the grad operator, and how it is used to compute the gradient of a scalar field. I then show how these vectors are computed for a line, parabola, circle, ellipse, sine curve, cosh curve, helix, Bézier curve, bilinear patch, quadratic Bézier patch, sphere and a torus.
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© 2019 Springer Nature Switzerland AG
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Vince, J. (2019). Tangent and Normal Vectors. In: Calculus for Computer Graphics. Springer, Cham. https://doi.org/10.1007/978-3-030-11376-6_13
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DOI: https://doi.org/10.1007/978-3-030-11376-6_13
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11375-9
Online ISBN: 978-3-030-11376-6
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