Everything about Normal Vector totally explained
A
surface normal, or simply
normal, to a
flat surface is a
vector which is
perpendicular to that surface. A normal to a non-flat surface at a
point P on the surface is a vector perpendicular to the
tangent plane to that surface at
P. The word "normal" is also used as an adjective: a
line normal to a
plane, the normal component of a
force, the
normal vector, etc. The concept of
normality generalizes to
orthogonality.
Calculating a surface normal
For a
polygon (such as a
triangle), a surface normal can be calculated as the vector
cross product of two (non-parallel) edges of the polygon.
For a
plane given by the equation
, the vector
is a normal. For a plane given by the equation
r =
a + α
b + β
c, where
a is a vector to get onto the plane and
b and
c are non-parallel vectors lying on the plane, the normal to the plane defined is given by
b ×
c (the cross product of the vectors lying on the plane).
If a (possibly non-flat) surface
S is
parametrized by a system of
curvilinear coordinates x(
s,
t), with
s and
t real variables, then a normal is given by the cross product of the
partial derivatives
»
Uniqueness of the normal
A normal to a surface doesn't have a unique direction; the vector pointing in the opposite direction of a surface normal is also a surface normal. For a surface which is the
topological boundary of a set in three dimensions, one can distinguish between the
inward-pointing normal and
outer-pointing normal, which can help define the normal in a unique way. For an
oriented surface, the surface normal is usually determined by the
right-hand rule. If the normal is constructed as the cross product of tangent vectors (as described in the text above), it's a
pseudovector.
Uses
Normal in geometric optics
The
normal is an imaginary line
perpendicular to the surface of an
optical medium. The word normal is used here in the mathematical sense, meaning perpendicular. In
reflection of light, the
angle of incidence is the angle between the normal and the
incident ray. The
angle of reflection is the angle between the normal and the
reflected ray.
Further Information
Get more info on 'Normal Vector'.
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