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Python: Added more rotation functions and unit tests.
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Don Cross
@@ -626,6 +626,20 @@ Equatorial coordinates in the specified frame of reference.
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---
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<a name="EquatorFromVector"></a>
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### EquatorFromVector(vec)
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**Given an equatorial vector, calculates equatorial angular coordinates.**
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Vector`](#Vector) | `vec` | A vector in an equatorial coordinate system. |
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### Returns: Equatorial
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Angular coordinates expressed in the same equatorial system as `vec`.
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---
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<a name="GeoMoon"></a>
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### GeoMoon(time)
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@@ -962,6 +976,25 @@ A rotation matrix that converts ECL to EQJ.
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---
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<a name="Rotation_EQD_EQJ"></a>
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### Rotation_EQD_EQJ(time)
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**Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).**
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This is one of the family of functions that returns a rotation matrix
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for converting from one orientation to another.
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Source: EQD = equatorial system, using equator of the specified date/time.
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Target: EQJ = equatorial system, using equator at J2000 epoch.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Time`](#Time) | `time` | The date and time at which the Earth's equator defines the source orientation. |
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### Returns: RotationMatrix
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A rotation matrix that converts EQD at `time` to EQJ.
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---
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<a name="Rotation_EQJ_ECL"></a>
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### Rotation_EQJ_ECL()
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@@ -977,6 +1010,25 @@ A rotation matrix that converts EQJ to ECL.
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---
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<a name="Rotation_EQJ_EQD"></a>
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### Rotation_EQJ_EQD(time)
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**Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).**
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This is one of the family of functions that returns a rotation matrix
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for converting from one orientation to another.
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Source: EQJ = equatorial system, using equator at J2000 epoch.
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Target: EQD = equatorial system, using equator of the specified date/time.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Time`](#Time) | `time` | The date and time at which the Earth's equator defines the target orientation. |
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### Returns: RotationMatrix
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A rotation matrix that converts EQJ to EQD at `time`.
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---
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<a name="Search"></a>
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### Search(func, context, t1, t2, dt_tolerance_seconds)
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@@ -1334,6 +1386,22 @@ of winter in the southern hemisphere.
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---
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<a name="SphereFromVector"></a>
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### SphereFromVector(vector)
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**Converts Cartesian coordinates to spherical coordinates.**
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Given a Cartesian vector, returns latitude, longitude, and distance.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Vector`](#Vector) | `vector` | Cartesian vector to be converted to spherical coordinates. |
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### Returns: Spherical
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Spherical coordinates that are equivalent to the given vector.
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---
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<a name="SunPosition"></a>
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### SunPosition(time)
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@@ -1359,3 +1427,37 @@ In fact, the function #Seasons does use this function for that purpose.
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### Returns: #EclipticCoordinates
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The ecliptic coordinates of the Sun using the Earth's true equator of date.
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---
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<a name="VectorFromEquator"></a>
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### VectorFromEquator(equ, time)
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**Given angular equatorial coordinates in `equ`, calculates equatorial vector.**
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Equatorial`](#Equatorial) | `equ` | Angular equatorial coordinates to be converted to a vector. |
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| [`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. |
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### Returns: Vector
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A vector in the equatorial system.
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---
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<a name="VectorFromSphere"></a>
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### VectorFromSphere(sphere, time)
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**Converts spherical coordinates to Cartesian coordinates.**
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Given spherical coordinates and a time at which they are valid,
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returns a vector of Cartesian coordinates. The returned value
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includes the time, as required by all `Time` objects.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Spherical`](#Spherical) | `sphere` | Spherical coordinates to be converted. |
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| [`Time`](#Time) | `time` | The time that should be included in the returned vector. |
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### Returns: Vector
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The vector form of the supplied spherical coordinates.
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@@ -5083,6 +5083,107 @@ def NextLunarApsis(apsis):
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raise InternalError()
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return next
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def VectorFromSphere(sphere, time):
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"""Converts spherical coordinates to Cartesian coordinates.
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Given spherical coordinates and a time at which they are valid,
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returns a vector of Cartesian coordinates. The returned value
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includes the time, as required by all `Time` objects.
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Parameters
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----------
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sphere : Spherical
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Spherical coordinates to be converted.
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time : Time
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The time that should be included in the returned vector.
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Returns
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-------
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Vector
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The vector form of the supplied spherical coordinates.
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"""
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radlat = math.radians(sphere.lat)
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radlon = math.radians(sphere.lon)
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rcoslat = sphere.dist * math.cos(radlat)
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return Vector(
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rcoslat * math.cos(radlon),
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rcoslat * math.sin(radlon),
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sphere.dist * math.sin(radlat),
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time
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)
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def VectorFromEquator(equ, time):
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"""Given angular equatorial coordinates in `equ`, calculates equatorial vector.
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Parameters
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----------
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equ : Equatorial
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Angular equatorial coordinates to be converted to a vector.
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time : Time
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The date and time of the observation. This is needed because the returned
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vector object requires a valid time value when passed to certain other functions.
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Returns
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-------
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Vector
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A vector in the equatorial system.
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"""
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return VectorFromSphere(Spherical(equ.dec, 15.0 * equ.ra, equ.dist), time)
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def EquatorFromVector(vec):
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"""Given an equatorial vector, calculates equatorial angular coordinates.
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Parameters
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----------
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vec : Vector
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A vector in an equatorial coordinate system.
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Returns
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-------
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Equatorial
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Angular coordinates expressed in the same equatorial system as `vec`.
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"""
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sphere = SphereFromVector(vec)
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return Equatorial(sphere.lon / 15.0, sphere.lat, sphere.dist)
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def SphereFromVector(vector):
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"""Converts Cartesian coordinates to spherical coordinates.
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Given a Cartesian vector, returns latitude, longitude, and distance.
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Parameters
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----------
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vector : Vector
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Cartesian vector to be converted to spherical coordinates.
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Returns
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-------
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Spherical
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Spherical coordinates that are equivalent to the given vector.
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"""
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xyproj = vector.x*vector.x + vector.y*vector.y
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dist = math.sqrt(xyproj + vector.z*vector.z)
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if xyproj == 0.0:
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if vector.z == 0.0:
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raise Exception('Zero-length vector not allowed.')
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lon = 0.0
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if vector.z < 0.0:
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lat = -90.0
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else:
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lat = +90.0
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else:
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lon = math.degrees(math.atan2(vector.y, vector.x))
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if lon < 0.0:
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lon += 360.0
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lat = math.degrees(math.atan2(vector.z, math.sqrt(xyproj)))
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return Spherical(lat, lon, dist)
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def InverseRotation(rotation):
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"""Calculates the inverse of a rotation matrix.
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@@ -5220,3 +5321,48 @@ def Rotation_ECL_EQJ():
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[ 0, +c, +s],
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[ 0, -s, +c]
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])
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def Rotation_EQJ_EQD(time):
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"""Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).
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This is one of the family of functions that returns a rotation matrix
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for converting from one orientation to another.
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Source: EQJ = equatorial system, using equator at J2000 epoch.
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Target: EQD = equatorial system, using equator of the specified date/time.
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Parameters
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----------
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time : Time
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The date and time at which the Earth's equator defines the target orientation.
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Returns
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-------
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RotationMatrix
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A rotation matrix that converts EQJ to EQD at `time`.
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"""
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prec = _precession_rot(0.0, time.tt)
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nut = _nutation_rot(time, 0)
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return CombineRotation(prec, nut)
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def Rotation_EQD_EQJ(time):
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"""Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).
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This is one of the family of functions that returns a rotation matrix
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for converting from one orientation to another.
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Source: EQD = equatorial system, using equator of the specified date/time.
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Target: EQJ = equatorial system, using equator at J2000 epoch.
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Parameters
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----------
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time : Time
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The date and time at which the Earth's equator defines the source orientation.
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Returns
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-------
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RotationMatrix
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A rotation matrix that converts EQD at `time` to EQJ.
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"""
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nut = _nutation_rot(time, 1)
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prec = _precession_rot(time.tt, 0.0)
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return CombineRotation(nut, prec)
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