Vector Analysis for Computer Graphics by John Vince

Author:John Vince
Language: eng
Format: epub, pdf
ISBN: 9781447175056
Publisher: Springer London

Fig. 7.11Three unit tangent and normal vectors for

Differentiating :

whose magnitude is

Therefore,

Let’s find for three values of t:

as shown in Fig. 7.11.

This time, let’s differentiate and normalise it:

Note that this is one of the options if we had taken the easy route!

Therefore,

as shown in Fig. 7.11.

Using the grad operator, we can find the unit normal vector as follows:

which gives the same result as before.

7.3.7 Unit Tangent and Normal Vectors to a Helix

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