“Normal Vector”的概念、定义、习题解题方法及翻译-数学辞典

单词

Normal Vector

释义

Normal Vector

The normal to a Plane specified by

(1)

is given by

(2)

The normal vector at a point

on a surface

(3)

In the Plane, the unit normal vector is defined by

(4)

where

is the unit Tangent Vector and

is the polar angle. Given a unit Tangent Vector

(5)

with

, the normal is

(6)

For a function given parametrically by

, the normal vector relative to the point

istherefore given by

			(7)
			(8)

To actually place the vector normal to the curve, it must be displaced by

In 3-D Space, the unit normal is

(9)

where

is the Curvature. Given a 3-D surface

(10)

If the surface is defined parametrically in the form

			(11)
			(12)
			(13)

define the Vectors

(14)

(15)

Then the unit normal vector is

(16)

Let

be the discriminant of the Metric Tensor. Then

(17)

See also Binormal Vector, Curvature, Frenet Formulas, Tangent Vector

References

Gray, A. ``Tangent and Normal Lines to Plane Curves.'' §5.5 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 85-90, 1993.

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