spherical coordinates

[Bram Stolk]

Hi there,


Which module could I use if I want to do spherical coordinates in Python?

parnassus, google, and groups.google.com did not give me a good pointer.


Thanks,

Bram


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Bram Stolk, VR Engineer.
SARA Academic Computing Services Amsterdam, PO Box 94613, 1090 GP AMSTERDAM
email: (e-mail address removed) Phone +31-20-5923059 Fax +31-20-6683167

"For the costs of subsidized agriculture in the EU, we can have all 56 million
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[Peter Maas]

Which module could I use if I want to do spherical coordinates in Python?

math. Formulas:

--- 2D

r = sqrt(x**2 + y**2)
phi = atan(y/x)

x = r*cos(phi)
y = r*sin(phi)

--- 3D

r = sqrt(x**2 + y**2 + z**2)
phi = atan(y/x)
theta = atan(z/sqrt(x**2+y**2)

x = r*cos(phi)*cos(theta)
y = r*sin(phi)*cos(theta)
z = r*sin(theta)

Mit freundlichen Gruessen,

Peter Maas

 

[project2501]

what do you want to do with spherical coordinates? surely they are simply
a transform from cartesian coordinates?

 

[Paul Rubin]

r = sqrt(x**2 + y**2)
phi = atan(y/x)

Better use phi=atan2(y,x) in case x=0. Similarly for the other atan calls.

 

[Paul McGuire]

Better use phi=atan2(y,x) in case x=0. Similarly for the other atan

calls.

These are formulas for cylindrical coordinates. The OP was asking for
spherical coordinates rho, theta, and phi, where:

rho = distance from origin (similar to r in cylindrical coords)
theta = angle from the positive x axis of the xyz vector projection onto the
x-y plane (just like theta in cylindrical coords)
phi = angle of the xyz vector from the x-y plane

To convert from spherical to Cartesian:

x = rho * sin(phi) * cos(theta)
y = rho * sin(phi) * sin(theta)
z = rho * cos(phi)

From Cartesian to spherical:

rho = sqrt(x**2 + y**2 + z**2)
theta = atan2(y, x)
if rho != 0.0:
phi = acos( z / rho )
else:
phi = pi / 2 * sgn(z)

I can imagine that all these conversions could be a performance killer if
done entirely in Python, and could stand to be done as a C extension. This
is probably why the OP was asking if such a package already exists.

-- Paul

(Hmm, the math module doesn't have a sgn() function. Is this difficult to
add?)

 

[Paul McGuire]

calls.

These are formulas for cylindrical coordinates. The OP was asking for
spherical coordinates rho, theta, and phi, where:

rho = distance from origin (similar to r in cylindrical coords)
theta = angle from the positive x axis of the xyz vector projection onto the
x-y plane (just like theta in cylindrical coords)
phi = angle of the xyz vector from the x-y plane

To convert from spherical to Cartesian:

x = rho * sin(phi) * cos(theta)
y = rho * sin(phi) * sin(theta)
z = rho * cos(phi)

From Cartesian to spherical:

rho = sqrt(x**2 + y**2 + z**2)
theta = atan2(y, x)
if rho != 0.0:
phi = acos( z / rho )
else:
phi = pi / 2 * sgn(z)

I can imagine that all these conversions could be a performance killer if
done entirely in Python, and could stand to be done as a C extension. This
is probably why the OP was asking if such a package already exists.

-- Paul

(Hmm, the math module doesn't have a sgn() function. Is this difficult to
add?)

D'oh - that's what I get for pulling formulas off the web and not reviewing
the material!!!

phi = angle of the xyz vector from the positive z-axis

phi = acos( z / rho)

Sorry!

http://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/spherical/body.htm

 

[Bram Stolk]

I can imagine that all these conversions could be a performance killer if
done entirely in Python, and could stand to be done as a C extension. This
is probably why the OP was asking if such a package already exists.

Well, performance is not my first concern.
I just want encapsulated classes for convenience, that handle all
sorts of spherical coordinate specifics.

For instance... interpolation between spherical coordinates. You can avoid
going to/from cartesian if you properly handle the wrap-around at 180 and 360
degrees.

Also, I want to be able to recursively subdivide the theta,phy space, and
do stratification in theta,phy space, and al sorts of other operations, on
the surface of a given sphere.

An encapsulating class for these kind of coordinates would be a help, I
thought.

Bram

--
------------------------------------------------------------------------------
Bram Stolk, VR Engineer.
SARA Academic Computing Services Amsterdam, PO Box 94613, 1090 GP AMSTERDAM
email: (e-mail address removed) Phone +31-20-5923059 Fax +31-20-6683167

"For the costs of subsidized agriculture in the EU, we can have all 56 million
European cows fly around the world. First Class." - J. Norberg
------------------------------------------------------------------------------

 

[Peter Maas]

calls.

These are formulas for cylindrical coordinates.

r and phi are 2D spherical coordinates. You have to add a 3rd coordinate
(usually called z) to get cylindrical coordinates.

The OP was asking for
spherical coordinates rho, theta, and phi, where:

The OP was asking for spherical coordinates without mentioning
variables or dimensions. I posted the raw 2D and 3D formulas without
bothering about error handling or other implementation issues.

Mit freundlichen Gruessen,

Peter Maas

 

[Bram Stolk]

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I can imagine that all these conversions could be a performance killer if
done entirely in Python, and could stand to be done as a C extension. This
is probably why the OP was asking if such a package already exists.

Well, performance is not my first concern.
I just want encapsulated classes for convenience, that handle all
sorts of spherical coordinate specifics.

For instance... interpolation between spherical coordinates. You can avoid
going to/from cartesian if you properly handle the wrap-around at 180 and 360
degrees.

Also, I want to be able to recursively subdivide the theta,phy space, and
do stratification in theta,phy space, and al sorts of other operations, on
the surface of a given sphere.

An encapsulating class for these kind of coordinates would be a help, I
thought.

Bram

--
------------------------------------------------------------------------------
Bram Stolk, VR Engineer.
SARA Academic Computing Services Amsterdam, PO Box 94613, 1090 GP AMSTERDAM
email: (e-mail address removed) Phone +31-20-5923059 Fax +31-20-6683167

"For the costs of subsidized agriculture in the EU, we can have all 56 million
European cows fly around the world. First Class." - J. Norberg
------------------------------------------------------------------------------