H
(
x
)
=
0forx< 0
1forx> 0
This is defined as a function with
Define H(x)=when(x<0,0,when(x=0,undef,1))
Sometimes the Heaviside function is defined as
H
(
x
)
=
0forx< 0
1
2
for x = 0
1forx> 0
The function definition for this case is
Define H(x)=when(x<0,0,when(x=0,1/2,1))
[6.30] Spherical coordinate conventions
Spherical coordinates specifiy a point or ray in 3D space with three measurements:
! The magnitude, which is the length of the ray, or the distance from the origin to the point
! The zenith angle, which is measured from the z-axis to the ray
! The azimuth angle, which is measured from the x-axis to the projection of the ray in the xy-plane.
For a picture, refer to the
▶sphere command in your 89/92+ manual.
This definition is unambiguous. However, there is considerable ambiguity when the three
measurements are grouped to specify the point. The two possibilities are
(magnitude, azimuth, zenith) used by the 89/92+
(magnitude, zenith, azimuth) used in other references
This can cause confusing results on the 89/92+, if you are used to the second specification.
Sam Jordan adds:
Also note that the mapping from rectangular to spherical coordinates is not exactly
one-to-one since the rectangular vector [0,0,1] can be represented by any spherical
vector of the form [1,<A,<0].
In this case,
[0,0,1]▶sphere returns [1, ∠R▶Pθ(0,0), ∠0]
(Credit to Gp and Sam Jordan)
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