Yuan Cao
Telescope Control Library
Diff: CelestialMath.h
- Revision:
- 0:6cb2eaf8b133
- Child:
- 18:3ea58b079adc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/CelestialMath.h Sun Aug 19 05:21:20 2018 +0000
@@ -0,0 +1,310 @@
+/*
+ * CelestialMath.h
+ *
+ * Created on: Feb 21, 2018
+ * Author: Yuan
+ */
+
+#ifndef CELESTIALMATH_H_
+#define CELESTIALMATH_H_
+
+#include <time.h>
+#include <math.h>
+
+static const double sidereal_speed = 0.00417807462; /* deg / s */
+
+struct EquatorialCoordinates
+{
+ double dec; // Declination
+ double ra; // Right ascension
+ EquatorialCoordinates(double d = 0, double r = 0) :
+ dec(d), ra(r)
+ {
+ }
+};
+
+struct LocalEquatorialCoordinates
+{
+ double dec; // Declination
+ double ha; // Hour angle
+ LocalEquatorialCoordinates(double d = 0, double h = 0) :
+ dec(d), ha(h)
+ {
+ }
+ LocalEquatorialCoordinates operator+(
+ const LocalEquatorialCoordinates &b) const
+ {
+ return LocalEquatorialCoordinates(remainder(dec + b.dec, 360),
+ remainder(ha + b.ha, 360));
+ }
+ LocalEquatorialCoordinates operator-(
+ const LocalEquatorialCoordinates &b) const
+ {
+ return LocalEquatorialCoordinates(remainder(dec - b.dec, 360),
+ remainder(ha - b.ha, 360));
+ }
+};
+
+struct AzimuthalCoordinates
+{
+ double alt; // Altitude
+ double azi; // Azimuth
+ AzimuthalCoordinates(double a1 = 0, double a2 = 0) :
+ alt(a1), azi(a2)
+ {
+ }
+};
+
+struct LocationCoordinates
+{
+ double lat; // Latitude
+ double lon; // Longtitude
+ LocationCoordinates(double l1 = 0, double l2 = 0) :
+ lat(l1), lon(l2)
+ {
+ }
+};
+
+struct Transformation;
+
+struct CartesianVector
+{
+ double x, y, z;
+ CartesianVector(double x = 0, double y = 0, double z = 0) :
+ x(x), y(y), z(z)
+ {
+ }
+ CartesianVector operator*(const Transformation &t);
+};
+
+struct Transformation
+{
+ double a11, a12, a13;
+ double a21, a22, a23;
+ double a31, a32, a33;
+ CartesianVector operator*(const CartesianVector &vec);
+ void transpose()
+ {
+ double temp = a12;
+ a12 = a21;
+ a21 = temp;
+ temp = a13;
+ a13 = a31;
+ a31 = temp;
+ temp = a32;
+ a32 = a23;
+ a23 = temp;
+ }
+};
+
+typedef enum
+{
+ PIER_SIDE_EAST, PIER_SIDE_WEST, PIER_SIDE_AUTO = 0
+} pierside_t;
+
+struct IndexOffset
+{
+ double dec_off; // Offset of the index position in DEC
+ double ra_off; // Offset of the index position in RA/HA axis
+ IndexOffset(double d = 0, double r = 0) :
+ dec_off(d), ra_off(r)
+ {
+ }
+};
+
+struct MountCoordinates
+{
+ double dec_delta; // Displacement from index position in DEC axis
+ double ra_delta; // Displacement from index position in RA/HA axis
+ pierside_t side;
+ MountCoordinates(double dec = 0, double ra = 0, pierside_t s =
+ PIER_SIDE_AUTO) :
+ dec_delta(dec), ra_delta(ra), side(s)
+ {
+ }
+ MountCoordinates operator+(const IndexOffset &offset) const
+ {
+ return MountCoordinates(remainder(dec_delta + offset.dec_off, 360),
+ remainder(ra_delta + offset.ra_off, 360), side);
+ }
+ MountCoordinates operator-(const IndexOffset &offset) const
+ {
+ return MountCoordinates(remainder(dec_delta - offset.dec_off, 360),
+ remainder(ra_delta - offset.ra_off, 360), side);
+ }
+};
+/**
+ * Alignment star object
+ */
+struct AlignmentStar
+{
+ EquatorialCoordinates star_ref; /// Reference position of the star in the sky (in current epoch)
+ MountCoordinates star_meas; /// Measured position of the star in mount coordinates
+ time_t timestamp; /// UTC timestamp of the measurement
+ AlignmentStar()
+ {
+ timestamp = 0;
+ }
+ AlignmentStar(const EquatorialCoordinates & ref, MountCoordinates meas,
+ time_t t) :
+ star_ref(ref), star_meas(meas), timestamp(t)
+ {
+ }
+ LocalEquatorialCoordinates star_ref_local(
+ const LocationCoordinates &loc) const;
+};
+
+struct EqCalibration
+{
+ IndexOffset offset;
+ AzimuthalCoordinates pa;
+ double cone;
+ double error;
+ EqCalibration() :
+ cone(0), error(0)
+ {
+ }
+ EqCalibration(const IndexOffset &off, const AzimuthalCoordinates p,
+ double c, double e) :
+ offset(off), pa(p), cone(c), error(e)
+ {
+ }
+};
+/**
+ * Utility functions for doing math on coordinates of the celestial sphere
+ */
+class CelestialMath
+{
+public:
+ CelestialMath()
+ {
+ }
+ ~CelestialMath()
+ {
+ }
+
+ /*Basic conversion between reference frames*/
+ static AzimuthalCoordinates localEquatorialToAzimuthal(
+ const LocalEquatorialCoordinates &a,
+ const LocationCoordinates &loc);
+ static LocalEquatorialCoordinates azimuthalToLocalEquatorial(
+ const AzimuthalCoordinates &b, const LocationCoordinates &loc);
+ static double getGreenwichMeanSiderealTime(time_t timestamp);
+ static double getLocalSiderealTime(time_t timestamp,
+ const LocationCoordinates &loc);
+ static LocalEquatorialCoordinates equatorialToLocalEquatorial(
+ const EquatorialCoordinates &e, time_t timestamp,
+ const LocationCoordinates &loc);
+ static EquatorialCoordinates localEquatorialToEquatorial(
+ const LocalEquatorialCoordinates &a, time_t timestamp,
+ const LocationCoordinates &loc);
+
+ /*Misalignment correction functions*/
+ static Transformation &getMisalignedPolarAxisTransformation(
+ Transformation &t, const AzimuthalCoordinates &mpa,
+ const LocationCoordinates &loc);
+ static LocalEquatorialCoordinates applyMisalignment(const Transformation &t,
+ const LocalEquatorialCoordinates &a);
+ static LocalEquatorialCoordinates applyMisalignment(
+ const LocalEquatorialCoordinates &a,
+ const AzimuthalCoordinates &mpa, const LocationCoordinates &loc);
+ static LocalEquatorialCoordinates applyConeError(
+ const LocalEquatorialCoordinates &a, double cone);
+ static LocalEquatorialCoordinates deapplyMisalignment(
+ const Transformation &t, const LocalEquatorialCoordinates &a);
+ static LocalEquatorialCoordinates deapplyMisalignment(
+ const LocalEquatorialCoordinates &a,
+ const AzimuthalCoordinates &mpa, const LocationCoordinates &loc);
+ static LocalEquatorialCoordinates deapplyConeError(
+ const LocalEquatorialCoordinates &a, double cone);
+
+ /*Convert to and from Mount coordinates*/
+ static MountCoordinates localEquatorialToMount(
+ const LocalEquatorialCoordinates &a, pierside_t side =
+ PIER_SIDE_AUTO);
+ static LocalEquatorialCoordinates mountToLocalEquatorial(
+ const MountCoordinates &m);
+
+ /*Alignment procedures*/
+
+ /**
+ * One-star alignment (only for testing), to find the PA misalignment
+ */
+ static AzimuthalCoordinates alignOneStar(
+ const LocalEquatorialCoordinates &star_ref,
+ const LocalEquatorialCoordinates &star_meas,
+ const LocationCoordinates &loc,
+ const AzimuthalCoordinates &pa_start);
+
+ static IndexOffset alignOneStarForOffset(
+ const LocalEquatorialCoordinates &star_ref,
+ const MountCoordinates &star_meas);
+
+ /*static AzimuthalCoordinates alignOneStar(const LocalEquatorialCoordinates &star_ref, const LocalEquatorialCoordinates &star_meas,
+ const LocationCoordinates &loc, const AzimuthalCoordinates &pa_start);*/
+ /**
+ * Two-star alignment for finding PA misalignment as well as offset in both axis
+ * @param star_ref Reference stars (array of 2)
+ * @param star_meas Measured stars (array of 2)
+ * @param loc Location
+ * @param pa Initial PA alt-az coordinates. This parameter will be updated with new values
+ * @param offset Initial offset values. This parameter will be updated with new values
+ */
+ static void alignTwoStars(const LocalEquatorialCoordinates star_ref[],
+ const LocalEquatorialCoordinates star_meas[],
+ const LocationCoordinates &loc, AzimuthalCoordinates &pa,
+ LocalEquatorialCoordinates &offset);
+ static void alignTwoStars(const LocalEquatorialCoordinates star_ref[],
+ const MountCoordinates star_meas[], const LocationCoordinates &loc,
+ AzimuthalCoordinates &pa, IndexOffset &offset, bool &diverge);
+
+ /**
+ * N-star alignment for finding PA misalignment, offset, and cone error
+ * This function will first call alignTwoStars with the first two stars assuming no cone error, then run an optimization algorithm to minimize the residual error by tweaking all 5 parameters.
+ * @param N number of alignment stars
+ * @param star_ref Reference stars
+ * @param star_meas Measured stars
+ * @param loc Location
+ * @param pa Initial PA alt-az coordinates. This parameter will be updated with new values
+ * @param offset Initial offset values. This parameter will be updated with new values
+ * @param cone Initial cone error. This parameter will be updated with new values
+ */
+ static void alignNStars(const int N,
+ const LocalEquatorialCoordinates star_ref[],
+ const LocalEquatorialCoordinates star_meas[],
+ const LocationCoordinates &loc, AzimuthalCoordinates &pa,
+ LocalEquatorialCoordinates &offset, double &cone);
+ static void alignNStars(const int N,
+ const LocalEquatorialCoordinates star_ref[],
+ const MountCoordinates star_meas[], const LocationCoordinates &loc,
+ AzimuthalCoordinates &pa, IndexOffset &offset, double &cone,
+ bool &diverge);
+
+ /**
+ * Adaptor for EqMount
+ */
+ static EqCalibration align(const int N, const AlignmentStar stars[],
+ const LocationCoordinates &loc, bool &diverge);
+
+ static double alignmentError(const int N, const AlignmentStar stars[],
+ const EqCalibration &calib, const LocationCoordinates &loc);
+
+ /*Utility functions*/
+
+ /*
+ * Convert HMS notation such as 21h54m31.6s to degrees (counting from 0h0m0s = 0degree, from -180 ~ 180 degrees)
+ */
+ static double parseHMSAngle(char *hms);
+
+ static double parseDMSAngle(char *dms);
+
+ /**
+ * Calculate King tracking rate based on the star position and location
+ */
+ static double kingRate(EquatorialCoordinates eq, LocationCoordinates loc,
+ time_t time);
+
+};
+
+#endif /* CELESTIALMATH_H_ */
+