mirror of
https://github.com/cosinekitty/astronomy.git
synced 2026-05-19 06:17:03 -04:00
Python: Finished coding rotation functions. Need to finish test cases.
This commit is contained in:
Don Cross
@@ -760,6 +760,32 @@ for more details.
|
||||
|
||||
---
|
||||
|
||||
<a name="HorizonFromVector"></a>
|
||||
### HorizonFromVector(vector, refraction)
|
||||
|
||||
**Converts Cartesian coordinates to horizontal coordinates.**
|
||||
|
||||
Given a horizontal Cartesian vector, returns horizontal azimuth and altitude.
|
||||
*IMPORTANT:* This function differs from `SphereFromVector` in two ways:
|
||||
- `SphereFromVector` returns a `lon` value that represents azimuth defined counterclockwise
|
||||
from north (e.g., west = +90), but this function represents a clockwise rotation
|
||||
(e.g., east = +90). The difference is because `SphereFromVector` is intended
|
||||
to preserve the vector "right-hand rule", while this function defines azimuth in a more
|
||||
traditional way as used in navigation and cartography.
|
||||
- This function optionally corrects for atmospheric refraction, while `SphereFromVector` does not.
|
||||
The returned object contains the azimuth in `lon`.
|
||||
It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees.
|
||||
The altitude is stored in `lat`.
|
||||
The distance to the observed object is stored in `dist`,
|
||||
and is expressed in astronomical units (AU).
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Vector`](#Vector) | `vector` | Cartesian vector to be converted to horizontal angular coordinates. |
|
||||
| [`Refraction`](#Refraction) | `refraction` | See comments in the #RefractionAngle function. |
|
||||
|
||||
---
|
||||
|
||||
<a name="Illumination"></a>
|
||||
### Illumination(body, time)
|
||||
|
||||
@@ -976,6 +1002,25 @@ A rotation matrix that converts ECL to EQJ.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_EQD_ECL"></a>
|
||||
### Rotation_EQD_ECL(time)
|
||||
|
||||
**Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).**
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQD = equatorial system, using equator of date.
|
||||
Target: ECL = ecliptic system, using equator at J2000 epoch.
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Time`](#Time) | `time` | The date and time of the source equator. |
|
||||
|
||||
### Returns
|
||||
A rotation matrix that converts EQD to ECL.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_EQD_EQJ"></a>
|
||||
### Rotation_EQD_EQJ(time)
|
||||
|
||||
@@ -995,6 +1040,32 @@ A rotation matrix that converts EQD at `time` to EQJ.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_EQD_HOR"></a>
|
||||
### Rotation_EQD_HOR(time, observer)
|
||||
|
||||
**Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).**
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQD = equatorial system, using equator of the specified date/time.
|
||||
Target: HOR = horizontal system.
|
||||
Use #HorizonFromVector to convert the return value
|
||||
to a traditional altitude/azimuth pair.
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Time`](#Time) | `time` | The date and time at which the Earth's equator applies. |
|
||||
| [`Observer`](#Observer) | `observer` | A location near the Earth's mean sea level that defines the observer's location. |
|
||||
|
||||
### Returns: RotationMatrix
|
||||
A rotation matrix that converts EQD to HOR at `time` and for `observer`.
|
||||
The components of the horizontal vector are:
|
||||
x = north, y = west, z = zenith (straight up from the observer).
|
||||
These components are chosen so that the "right-hand rule" works for the vector
|
||||
and so that north represents the direction where azimuth = 0.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_EQJ_ECL"></a>
|
||||
### Rotation_EQJ_ECL()
|
||||
|
||||
@@ -1029,6 +1100,72 @@ A rotation matrix that converts EQJ to EQD at `time`.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_EQJ_HOR"></a>
|
||||
### Rotation_EQJ_HOR(time, observer)
|
||||
|
||||
**Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).**
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQJ = equatorial system, using the equator at the J2000 epoch.
|
||||
Target: HOR = horizontal system.
|
||||
Use #HorizonFromVector to convert the return value to
|
||||
a traditional altitude/azimuth pair.
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Time`](#Time) | `time` | The date and time of the desired horizontal orientation. |
|
||||
| [`Observer`](#Observer) | `observer` | A location near the Earth's mean sea level that defines the observer's horizon. |
|
||||
|
||||
### Returns: RotationMatrix
|
||||
A rotation matrix that converts EQJ to HOR at `time` and for `observer`.
|
||||
The components of the horizontal vector are:
|
||||
x = north, y = west, z = zenith (straight up from the observer).
|
||||
These components are chosen so that the "right-hand rule" works for the vector
|
||||
and so that north represents the direction where azimuth = 0.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_HOR_EQD"></a>
|
||||
### Rotation_HOR_EQD(time, observer)
|
||||
|
||||
**Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).**
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: HOR = horizontal system (x=North, y=West, z=Zenith).
|
||||
Target: EQD = equatorial system, using equator of the specified date/time.
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Time`](#Time) | `time` | The date and time at which the Earth's equator applies. |
|
||||
| [`Observer`](#Observer) | `observer` | A location near the Earth's mean sea level that defines the observer's horizon. |
|
||||
|
||||
### Returns: RotationMatrix
|
||||
A rotation matrix that converts HOR to EQD at `time` and for `observer`.
|
||||
|
||||
---
|
||||
|
||||
<a name="Rotation_HOR_EQJ"></a>
|
||||
### Rotation_HOR_EQJ(time, observer)
|
||||
|
||||
**Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).**
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: HOR = horizontal system (x=North, y=West, z=Zenith).
|
||||
Target: EQJ = equatorial system, using equator at the J2000 epoch.
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Time`](#Time) | `time` | The date and time of the observation. |
|
||||
| [`Observer`](#Observer) | `observer` | A location near the Earth's mean sea level that define's the observer's horizon. |
|
||||
|
||||
### Returns: RotationMatrix
|
||||
A rotation matrix that converts HOR to EQD at `time` and for `observer`.
|
||||
|
||||
---
|
||||
|
||||
<a name="Search"></a>
|
||||
### Search(func, context, t1, t2, dt_tolerance_seconds)
|
||||
|
||||
@@ -1444,6 +1581,22 @@ A vector in the equatorial system.
|
||||
|
||||
---
|
||||
|
||||
<a name="VectorFromHorizon"></a>
|
||||
### VectorFromHorizon(sphere, time, refraction)
|
||||
|
||||
**Given apparent angular horizontal coordinates in `sphere`, calculate horizontal vector.**
|
||||
|
||||
| Type | Parameter | Description |
|
||||
| --- | --- | --- |
|
||||
| [`Spherical`](#Spherical) | `sphere` | A structure that contains apparent horizontal coordinates: `lat` holds the refracted azimuth angle, `lon` holds the azimuth in degrees clockwise from north, and `dist` holds the distance from the observer to the object in AU. |
|
||||
| [`Time`](#Time) | `time` | The date and time of the observation. This is needed because the returned vector object requires a valid time value when passed to certain other functions. |
|
||||
| [`Refraction`](#Refraction) | `refraction` | See remarks in function #RefractionAngle. |
|
||||
|
||||
### Returns: Vector
|
||||
A vector in the horizontal system: `x` = north, `y` = west, and `z` = zenith (up).
|
||||
|
||||
---
|
||||
|
||||
<a name="VectorFromSphere"></a>
|
||||
### VectorFromSphere(sphere, time)
|
||||
|
||||
|
||||
@@ -5183,6 +5183,75 @@ def SphereFromVector(vector):
|
||||
return Spherical(lat, lon, dist)
|
||||
|
||||
|
||||
def _ToggleAzimuthDirection(az):
|
||||
az = 360.0 - az
|
||||
if az >= 360.0:
|
||||
az -= 360.0
|
||||
elif az < 0.0:
|
||||
az += 360.0
|
||||
return az
|
||||
|
||||
|
||||
def VectorFromHorizon(sphere, time, refraction):
|
||||
"""Given apparent angular horizontal coordinates in `sphere`, calculate horizontal vector.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
sphere : Spherical
|
||||
A structure that contains apparent horizontal coordinates:
|
||||
`lat` holds the refracted azimuth angle,
|
||||
`lon` holds the azimuth in degrees clockwise from north,
|
||||
and `dist` holds the distance from the observer to the object in AU.
|
||||
time : Time
|
||||
The date and time of the observation. This is needed because the returned
|
||||
vector object requires a valid time value when passed to certain other functions.
|
||||
refraction : Refraction
|
||||
See remarks in function #RefractionAngle.
|
||||
|
||||
Returns
|
||||
-------
|
||||
Vector
|
||||
A vector in the horizontal system: `x` = north, `y` = west, and `z` = zenith (up).
|
||||
"""
|
||||
lon = _ToggleAzimuthDirection(sphere.lon)
|
||||
lat = sphere.lat + InverseRefractionAngle(refraction, sphere.lat)
|
||||
xsphere = Spherical(lat, lon, sphere.dist)
|
||||
return VectorFromSphere(xsphere, time)
|
||||
|
||||
|
||||
def HorizonFromVector(vector, refraction):
|
||||
"""Converts Cartesian coordinates to horizontal coordinates.
|
||||
|
||||
Given a horizontal Cartesian vector, returns horizontal azimuth and altitude.
|
||||
|
||||
*IMPORTANT:* This function differs from `SphereFromVector` in two ways:
|
||||
- `SphereFromVector` returns a `lon` value that represents azimuth defined counterclockwise
|
||||
from north (e.g., west = +90), but this function represents a clockwise rotation
|
||||
(e.g., east = +90). The difference is because `SphereFromVector` is intended
|
||||
to preserve the vector "right-hand rule", while this function defines azimuth in a more
|
||||
traditional way as used in navigation and cartography.
|
||||
- This function optionally corrects for atmospheric refraction, while `SphereFromVector` does not.
|
||||
|
||||
The returned object contains the azimuth in `lon`.
|
||||
It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees.
|
||||
|
||||
The altitude is stored in `lat`.
|
||||
|
||||
The distance to the observed object is stored in `dist`,
|
||||
and is expressed in astronomical units (AU).
|
||||
|
||||
Parameters
|
||||
----------
|
||||
vector : Vector
|
||||
Cartesian vector to be converted to horizontal angular coordinates.
|
||||
refraction : Refraction
|
||||
See comments in the #RefractionAngle function.
|
||||
"""
|
||||
sphere = SphereFromVector(vector)
|
||||
sphere.lon = _ToggleAzimuthDirection(sphere.lon)
|
||||
sphere.lat += RefractionAngle(refraction, sphere.lat)
|
||||
return sphere
|
||||
|
||||
|
||||
def InverseRotation(rotation):
|
||||
"""Calculates the inverse of a rotation matrix.
|
||||
@@ -5366,3 +5435,151 @@ def Rotation_EQD_EQJ(time):
|
||||
nut = _nutation_rot(time, 1)
|
||||
prec = _precession_rot(time.tt, 0.0)
|
||||
return CombineRotation(nut, prec)
|
||||
|
||||
|
||||
def Rotation_EQD_HOR(time, observer):
|
||||
"""Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQD = equatorial system, using equator of the specified date/time.
|
||||
Target: HOR = horizontal system.
|
||||
|
||||
Use #HorizonFromVector to convert the return value
|
||||
to a traditional altitude/azimuth pair.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
time : Time
|
||||
The date and time at which the Earth's equator applies.
|
||||
observer: Observer
|
||||
A location near the Earth's mean sea level that defines the observer's location.
|
||||
|
||||
Returns
|
||||
-------
|
||||
RotationMatrix
|
||||
A rotation matrix that converts EQD to HOR at `time` and for `observer`.
|
||||
The components of the horizontal vector are:
|
||||
x = north, y = west, z = zenith (straight up from the observer).
|
||||
These components are chosen so that the "right-hand rule" works for the vector
|
||||
and so that north represents the direction where azimuth = 0.
|
||||
"""
|
||||
sinlat = math.sin(math.radians(observer.latitude))
|
||||
coslat = math.cos(math.radians(observer.latitude))
|
||||
sinlon = math.sin(math.radians(observer.longitude))
|
||||
coslon = math.cos(math.radians(observer.longitude))
|
||||
uze = [coslat * coslon, coslat * sinlon, sinlat]
|
||||
une = [-sinlat * coslon, -sinlat * sinlon, coslat]
|
||||
uwe = [sinlon, -coslon, 0.0]
|
||||
spin_angle = -15.0 * _sidereal_time(time)
|
||||
uz = _spin(spin_angle, uze)
|
||||
un = _spin(spin_angle, une)
|
||||
uw = _spin(spin_angle, uwe)
|
||||
return RotationMatrix([
|
||||
[un[0], uw[0], uz[0]],
|
||||
[un[1], uw[1], uz[1]],
|
||||
[un[2], uw[2], uz[2]],
|
||||
])
|
||||
|
||||
|
||||
def Rotation_HOR_EQD(time, observer):
|
||||
"""Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: HOR = horizontal system (x=North, y=West, z=Zenith).
|
||||
Target: EQD = equatorial system, using equator of the specified date/time.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
time : Time
|
||||
The date and time at which the Earth's equator applies.
|
||||
observer : Observer
|
||||
A location near the Earth's mean sea level that defines the observer's horizon.
|
||||
|
||||
Returns
|
||||
-------
|
||||
RotationMatrix
|
||||
A rotation matrix that converts HOR to EQD at `time` and for `observer`.
|
||||
"""
|
||||
rot = Rotation_EQD_HOR(time, observer)
|
||||
return InverseRotation(rot)
|
||||
|
||||
|
||||
def Rotation_HOR_EQJ(time, observer):
|
||||
"""Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: HOR = horizontal system (x=North, y=West, z=Zenith).
|
||||
Target: EQJ = equatorial system, using equator at the J2000 epoch.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
time : Time
|
||||
The date and time of the observation.
|
||||
observer : Observer
|
||||
A location near the Earth's mean sea level that define's the observer's horizon.
|
||||
|
||||
Returns
|
||||
-------
|
||||
RotationMatrix
|
||||
A rotation matrix that converts HOR to EQD at `time` and for `observer`.
|
||||
"""
|
||||
hor_eqd = Rotation_HOR_EQD(time, observer)
|
||||
eqd_eqj = Rotation_EQD_EQJ(time)
|
||||
return CombineRotation(hor_eqd, eqd_eqj)
|
||||
|
||||
|
||||
def Rotation_EQJ_HOR(time, observer):
|
||||
"""Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQJ = equatorial system, using the equator at the J2000 epoch.
|
||||
Target: HOR = horizontal system.
|
||||
|
||||
Use #HorizonFromVector to convert the return value to
|
||||
a traditional altitude/azimuth pair.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
time : Time
|
||||
The date and time of the desired horizontal orientation.
|
||||
observer : Observer
|
||||
A location near the Earth's mean sea level that defines the observer's horizon.
|
||||
|
||||
Returns
|
||||
-------
|
||||
RotationMatrix
|
||||
A rotation matrix that converts EQJ to HOR at `time` and for `observer`.
|
||||
The components of the horizontal vector are:
|
||||
x = north, y = west, z = zenith (straight up from the observer).
|
||||
These components are chosen so that the "right-hand rule" works for the vector
|
||||
and so that north represents the direction where azimuth = 0.
|
||||
"""
|
||||
rot = Rotation_HOR_EQJ(time, observer)
|
||||
return InverseRotation(rot)
|
||||
|
||||
|
||||
def Rotation_EQD_ECL(time):
|
||||
"""Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).
|
||||
|
||||
This is one of the family of functions that returns a rotation matrix
|
||||
for converting from one orientation to another.
|
||||
Source: EQD = equatorial system, using equator of date.
|
||||
Target: ECL = ecliptic system, using equator at J2000 epoch.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
time : Time
|
||||
The date and time of the source equator.
|
||||
|
||||
Returns
|
||||
-------
|
||||
A rotation matrix that converts EQD to ECL.
|
||||
"""
|
||||
eqd_eqj = Rotation_EQD_EQJ(time)
|
||||
eqj_ecl = Rotation_EQJ_ECL()
|
||||
return CombineRotation(eqd_eqj, eqj_ecl)
|
||||
|
||||
|
||||
Reference in New Issue
Block a user