fix: Use better algo (Meeus Ch.25) for estimating sun position when calculating prayer times

go.mod

@@ -31,6 +31,7 @@ require (
 	github.com/quic-go/quic-go v0.57.1 // indirect
 	github.com/refraction-networking/utls v1.8.2 // indirect
 	github.com/remyoudompheng/bigfft v0.0.0-20230129092748-24d4a6f8daec // indirect
+	github.com/samber/lo v1.52.0 // indirect
 	github.com/tinylib/msgp v1.6.3 // indirect
 	github.com/valyala/bytebufferpool v1.0.0 // indirect
 	github.com/valyala/fasthttp v1.69.0 // indirect

go.sum

@@ -73,6 +73,8 @@ github.com/rogpeppe/go-internal v1.10.0/go.mod h1:UQnix2H7Ngw/k4C5ijL5+65zddjncj
 github.com/rs/xid v1.4.0/go.mod h1:trrq9SKmegXys3aeAKXMUTdJsYXVwGY3RLcfgqegfbg=
 github.com/rs/zerolog v1.29.0 h1:Zes4hju04hjbvkVkOhdl2HpZa+0PmVwigmo8XoORE5w=
 github.com/rs/zerolog v1.29.0/go.mod h1:NILgTygv/Uej1ra5XxGf82ZFSLk58MFGAUS2o6usyD0=
+github.com/samber/lo v1.52.0 h1:Rvi+3BFHES3A8meP33VPAxiBZX/Aws5RxrschYGjomw=
+github.com/samber/lo v1.52.0/go.mod h1:4+MXEGsJzbKGaUEQFKBq2xtfuznW9oz/WrgyzMzRoM0=
 github.com/shamaton/msgpack/v3 v3.0.0 h1:xl40uxWkSpwBCSTvS5wyXvJRsC6AcVcYeox9PspKiZg=
 github.com/shamaton/msgpack/v3 v3.0.0/go.mod h1:DcQG8jrdrQCIxr3HlMYkiXdMhK+KfN2CitkyzsQV4uc=
 github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=

pkg/diyanetcalc/provider.go

@@ -9,77 +9,49 @@ import (
 
 	"prayertimes/pkg/hijricalendar"
 	"prayertimes/pkg/prayer"
+
+	"github.com/samber/lo"
 )
 
 const (
 	daysToGenerate = 30
 	degPerHour     = 15.0
+	j2000          = 2451545.0 // Julian Date of J2000.0 epoch (Jan 1.5, 2000)
 )
 
 var errNotSupported = errors.New("not supported in calculation provider")
 
-// Diyanet prayer times calculator.
-//
-// Implements the Turkish Presidency of Religious Affairs (Diyanet) methodology,
-// standardized in the 1983 reform. Prayer times are indexed to the Sun's apparent
-// altitude angle at the observer's location, solved via spherical trigonometry.
-
-// ---------------------------------------------------------------------------
 // Diyanet angular criteria (post-1983 reform)
-// ---------------------------------------------------------------------------
+//
-
+// imsakAngle: Sun 18° below horizon = start of astronomical twilight (Fajr).
-// Imsak (Fajr): Sun is 18deg below the horizon = start of astronomical twilight.
+// Pre-1983 used −19° + temkin buffer; now −18° with zero temkin.
-// Pre-1983 used -19deg plus a temkin buffer; now -18deg with zero temkin.
 const imsakAngle = -18.0
 
-// Isha (Yatsi): Sun is 17deg below the horizon = shafaq al-ahmar (red twilight)
+// ishaAngle: Sun 17° below horizon = shafaq al-ahmar (red twilight) gone.
-// has fully disappeared from the western sky.
 const ishaAngle = -17.0
 
-// Sunrise / Sunset (Tulu / Gurup): geometric horizon alone is insufficient.
+// sunAngle: combined refraction (~0.567°) + solar semi-diameter (~0.267°)
-// Two physical corrections are combined into a single -0.833deg value (50 arcmin):
+// correction applied at sunrise/sunset. Equivalent to 50 arcmin.
-//   - Atmospheric refraction: ~0.567deg — air bends sunlight over the horizon
-//   - Solar semi-diameter:    ~0.267deg — Sun is "up" when its upper limb clears
 const sunAngle = -0.833
 
-// ---------------------------------------------------------------------------
 // Temkin — precautionary time buffers (minutes, post-1983 standardized values)
 //
-// Temkin ensures a single published time remains valid across the full
+// Ensures a single published time remains valid across the full geographical
-// geographical extent of a city (highest peak to lowest valley, east to west).
+// extent of a city. Pre-1983 values were 10–20 min; the reform moderated them.
-// Pre-1983 values were often 10–20 min; the reform moderated them.
-//
-//	Imsak:   0 min — no buffer; avoids starting Fajr too early / fast too late
-//	Sunrise: -7 min — subtracted, ensuring the Sun has fully cleared the horizon
-//	Dhuhr:  +5 min — added, ensuring the Sun has clearly begun its descent
-//	Asr:    +4 min — accounts for local elevation and horizon obstacles
-//	Maghrib:+7 min — ensures the Sun has completely set before breaking fast
-//	Isha:    0 min — no buffer needed at this twilight stage
 //
-// ---------------------------------------------------------------------------
+//	Imsak:    0 — no buffer; avoids starting Fajr too early / fast too late
-type temkinMinutes struct {
+//	Sunrise: −7 — subtracted, ensuring the Sun has fully cleared the horizon
-	Imsak   float64
+//	Dhuhr:   +5 — Sun has clearly begun its descent
-	Sunrise float64
+//	Asr:     +4 — accounts for local elevation and horizon obstacles
-	Dhuhr   float64
+//	Maghrib: +7 — Sun has completely set before breaking fast
-	Asr     float64
+//	Isha:     0 — no buffer needed at this twilight stage
-	Maghrib float64
+var temkin = struct{ Imsak, Sunrise, Dhuhr, Asr, Maghrib, Isha float64 }{
-	Isha    float64
+	Imsak: 0, Sunrise: -7, Dhuhr: 5, Asr: 4, Maghrib: 7, Isha: 0,
-}
-
-var temkin = temkinMinutes{
-	Imsak:   0,
-	Sunrise: -7,
-	Dhuhr:   5,
-	Asr:     4,
-	Maghrib: 7,
-	Isha:    0,
 }
 
 type Provider struct{}
 
-func New() Provider {
+func New() Provider { return Provider{} }
-	return Provider{}
-}
 
 func (Provider) SearchLocations(_ context.Context, _ string) ([]prayer.Location, error) {
 	return nil, fmt.Errorf("failed to search locations: %w", errNotSupported)
@@ -90,241 +62,188 @@ func (Provider) Get(_ context.Context, _ string) (prayer.TimesResult, error) {
 }
 
 func (Provider) GetByCoords(_ context.Context, coords prayer.Coordinates) (prayer.TimesResult, error) {
-	offset := estimateUTCOffsetHours(coords.Longitude)
 	todayUTC := time.Now().UTC().Truncate(24 * time.Hour)
 
-	results := make([]prayer.Times, 0, daysToGenerate)
+	days := lo.Map(lo.Range(daysToGenerate), func(i, _ int) time.Time {
-	for i := 0; i < daysToGenerate; i++ {
+		return todayUTC.AddDate(0, 0, i)
-		day := todayUTC.AddDate(0, 0, i)
+	})
-		calculated := prayerTimes(coords.Latitude, coords.Longitude, day)
 
-		results = append(results, prayer.Times{
+	times := lo.Map(days, func(day time.Time, _ int) prayer.Times {
+		c := prayerTimes(coords.Latitude, coords.Longitude, day)
+		return prayer.Times{
 			Date:      day,
 			DateHijri: hijricalendar.ToISODate(day),
-			Fajr:      derefOrZero(calculated.Imsak),
+			Fajr:      lo.FromPtr(c.Imsak),
-			Sunrise:   derefOrZero(calculated.Sunrise),
+			Sunrise:   lo.FromPtr(c.Sunrise),
-			Dhuhr:     derefOrZero(calculated.Dhuhr),
+			Dhuhr:     lo.FromPtr(c.Dhuhr),
-			Asr:       derefOrZero(calculated.Asr),
+			Asr:       lo.FromPtr(c.Asr),
-			Sunset:    derefOrZero(calculated.Sunset),
+			Sunset:    lo.FromPtr(c.Sunset),
-			Maghrib:   derefOrZero(calculated.Maghrib),
+			Maghrib:   lo.FromPtr(c.Maghrib),
-			Isha:      derefOrZero(calculated.Isha),
+			Isha:      lo.FromPtr(c.Isha),
-		})
 		}
+	})
 
 	return prayer.TimesResult{
 		Location: prayer.Location{
 			Latitude:  coords.Latitude,
 			Longitude: coords.Longitude,
-			Timezone:  formatUTCOffsetTimezone(offset),
+			Timezone:  fmt.Sprintf("UTC%+d", int(math.Round(coords.Longitude/degPerHour))),
 		},
-		Times: results,
+		Times: times,
 	}, nil
 }
 
-// Convert a calendar date to a Julian Day Number.
+// julianDay converts a calendar date to a Julian Day Number.
 //
-// JDN is a continuous day count from Jan 1, 4713 BC used in astronomy to
+// JDN is a continuous day count from Jan 1, 4713 BC, used in astronomy to
-// avoid calendar-system ambiguities. The -1524.5 offset shifts the epoch to
+// avoid calendar-system ambiguities. January/February are treated as months
-// noon UT, Jan 1, 4713 BC (the standard astronomical Julian Date epoch).
+// 13/14 of the prior year. The Gregorian correction b = 2 − a + a/4 accounts
-// The Gregorian calendar correction term b = 2 - a + a//4 accounts for
+// for century-year leap-day rules introduced in 1582.
-// the century-year leap-day rules introduced in 1582.
 func julianDay(d time.Time) float64 {
 	y, m, day := d.Date()
 	if m <= 2 {
-		// January/February treated as months 13/14 of the prior year
 		y--
 		m += 12
 	}
 	a := y / 100
-	b := 2 - a + a/4 // Gregorian correction
+	b := 2 - a + a/4
-
+	return math.Floor(365.25*float64(y+4716)) +
-	return math.Floor(365.25*float64(y+4716)) + math.Floor(30.6001*float64(m+1)) + float64(day+b) - 1524.5
+		math.Floor(30.6001*float64(m+1)) +
+		float64(day+b) - 1524.5
 }
 
-// Compute solar declination and equation of time for a given Julian Day.
+// sunParams computes solar declination and equation of time via Meeus Ch.25
+// (~0.0003° accuracy — ~30× better than the USNO 6-term approximation).
 //
 // Returns:
-//
+//   - delta: solar declination in degrees (Sun's angular distance north/south
-//	delta — solar declination in degrees: the Sun's angular distance
+//     of the celestial equator; drives seasonal day length and noon altitude).
-//	        north (+) or south (-) of the celestial equator. Controls
+//   - eot: equation of time in minutes (difference between apparent solar time
-//	        seasonal day length and the Sun's maximum altitude.
+//     and mean solar time; caused by orbital eccentricity + axial tilt; ±16 min).
-//	eot   — equation of time in minutes: difference between apparent solar
+//
-//	        time (sundial) and mean solar time (clock). Caused by Earth's
+// Source: Jean Meeus, "Astronomical Algorithms" 2nd ed., Chapter 25.
-//	        elliptical orbit and axial tilt; ranges roughly ±16 min.
+//
-//
+// Variables (degrees unless noted):
-// Algorithm uses low-precision USNO solar coordinates (~0.01deg accuracy):
+//
-//
+//	T     — Julian centuries since J2000.0
-//	d  — days since J2000.0 epoch (Jan 1.5, 2000 = JD 2451545.0)
+//	L0    — geometric mean longitude of the Sun (Meeus eq. 25.2)
-//	g  — mean anomaly: Sun's angular position in its elliptical orbit
+//	M     — mean anomaly (Meeus eq. 25.3)
-//	q  — mean longitude of the Sun
+//	e     — orbital eccentricity (Meeus eq. 25.4)
-//	L  — ecliptic longitude: corrected for orbital eccentricity via the
+//	C     — equation of centre: true − mean anomaly (Meeus eq. 25.4)
-//	     equation of centre (1.915deg*sin g + 0.020deg*sin 2g)
+//	omega — Moon's ascending node longitude, used for nutation (Meeus eq. 25.11)
-//	e  — obliquity of the ecliptic: Earth's axial tilt (~23.44deg, slowly
+//	lam   — apparent longitude: true lon + nutation − aberration (Meeus eq. 25.9)
-//	     decreasing at 0.00000036deg/day)
+//	eps   — true obliquity of the ecliptic incl. nutation (Meeus eq. 22.2 / 25.8)
-func sunParams(jd float64) (delta float64, eot float64) {
+//	EoT   — Spencer/Meeus y-series (Meeus p.185), accurate to ~0.5 s
-	d := jd - 2451545.0 // days since J2000.0
+func sunParams(jd float64) (delta, eot float64) {
-
+	T := (jd - j2000) / 36525.0
-	g := toRadians(357.529 + 0.98560028*d) // mean anomaly
+
-	q := toRadians(280.459 + 0.98564736*d) // mean longitude
+	L0 := math.Mod(280.46646+T*(36000.76983+T*0.0003032), 360)
-
+	M := math.Mod(357.52911+T*(35999.05029-T*0.0001537), 360)
-	// Ecliptic longitude: equation of centre adds up to ~1.9deg correction for
+	Mr := rad(M)
-	// the difference between uniform circular and actual elliptical motion.
+	e := 0.016708634 - T*(0.000042037+T*0.0000001267)
-	L := q + toRadians(1.915*math.Sin(g)+0.020*math.Sin(2*g))
+
-	e := toRadians(23.439 - 0.00000036*d) // obliquity of ecliptic
+	// Equation of centre: corrects uniform circular → true elliptical motion.
-
+	C := (1.914602-T*(0.004817+T*0.000014))*math.Sin(Mr) +
-	// Declination: project ecliptic longitude onto the celestial equator.
+		(0.019993-T*0.000101)*math.Sin(2*Mr) +
-	delta = toDegrees(math.Asin(math.Sin(e) * math.Sin(L)))
+		0.000289*math.Sin(3*Mr)
-
+
-	// Right ascension in hours (atan2 handles all four quadrants correctly).
+	omega := 125.04 - 1934.136*T // Moon's ascending node: drives nutation
-	ra := toDegrees(math.Atan2(math.Cos(e)*math.Sin(L), math.Cos(L))) / degPerHour
+
-
+	// Apparent longitude: add nutation, subtract aberration (−0.00569°).
-	// EoT = mean sun hour angle minus apparent sun RA, normalized to ±30 min.
+	lam := rad(L0 + C - 0.00569 - 0.00478*math.Sin(rad(omega)))
-	// round() removes the large integer offset (q accumulates many full rotations)
+
-	// before converting to minutes; without it the raw difference is ~600 hours.
+	// True obliquity: Laskar (1986) mean obliquity + nutation in obliquity.
-	diff := toDegrees(q)/degPerHour - ra
+	eps0 := 84381.448 - T*(46.8150+T*(0.00059-T*0.001813)) // arcseconds
-	eot = (diff - math.Round(diff)) * 60
+	eps := rad(eps0/3600 + 0.00256*math.Cos(rad(omega)))
+
+	delta = deg(math.Asin(math.Sin(eps) * math.Sin(lam)))
+
+	// EoT via y-series (Spencer 1971 / Meeus p.185).
+	// y = tan²(ε/2); multiply degrees by 4 to get minutes (1° = 4 min).
+	y, L0r := math.Pow(math.Tan(eps/2), 2), rad(L0)
+	eot = deg(y*math.Sin(2*L0r)-
+		2*e*math.Sin(Mr)+
+		4*e*y*math.Sin(Mr)*math.Cos(2*L0r)-
+		0.5*y*y*math.Sin(4*L0r)-
+		1.25*e*e*math.Sin(2*Mr)) * 4
 
 	return delta, eot
 }
 
-// Solve for the hour angle H (hours) at which the Sun reaches a given altitude.
+// hourAngle solves for the hour angle H (hours) at which the Sun reaches
-//
+// the given altitude, using the spherical law of cosines:
-// Derived from the spherical law of cosines for the astronomical triangle:
 //
-//	sin(a) = sin(phi)*sin(delta) + cos(phi)*cos(delta)*cos(H)
+//	cos H = (sin a − sin φ·sin δ) / (cos φ·cos δ)
 //
-// Rearranged:
+// Returns (0, false) when |cos H| > 1 — the Sun never reaches that altitude
-//
+// (midnight sun / polar night). Diyanet resolves these via the Takdir method.
-//	cos(H) = (sin(a) − sin(phi)*sin(delta)) / (cos(phi)*cos(delta))
+func hourAngle(altDeg, lat, delta float64) (float64, bool) {
-//
+	cosH := (math.Sin(rad(altDeg)) - math.Sin(rad(lat))*math.Sin(rad(delta))) /
-// H is converted from degrees to hours by dividing by 15 (360deg/24h = 15deg/h).
+		(math.Cos(rad(lat)) * math.Cos(rad(delta)))
-// Returns false when |cos H| > 1, i.e. the Sun never reaches that altitude
-// (midnight sun or polar night) — Diyanet handles these with the Takdir method.
-func hourAngle(altitudeDeg, lat, delta float64) (hours float64, ok bool) {
-	cosH := (math.Sin(toRadians(altitudeDeg)) - math.Sin(toRadians(lat))*math.Sin(toRadians(delta))) /
-		(math.Cos(toRadians(lat)) * math.Cos(toRadians(delta)))
-
 	if math.Abs(cosH) > 1 {
 		return 0, false
 	}
-
+	return deg(math.Acos(cosH)) / degPerHour, true
-	return toDegrees(math.Acos(cosH)) / degPerHour, true
 }
 
-// Compute the solar altitude at which Asr begins (Asr-i Avval / First Asr).
+// asrAltitude returns the solar altitude at which Asr-i Avval begins.
 //
-// Diyanet follows the majority-school definition: Asr starts when an object's
+// Diyanet (majority school): Asr starts when shadow length = object height +
-// shadow length equals the object's height plus its shortest noon shadow (fey-i zeval).
+// its shortest noon shadow (fey-i zeval). Shadow factor = 1 (Hanafi uses 2).
-// The shadow factor is 1 (Asr-i Avval; Hanafi uses 2 for Asr-i Sani).
 //
-// The required altitude satisfies:  cot(a) = 1 + tan(|phi − delta|)
+//	cot a = 1 + tan|φ − δ|  →  a = atan(1 / (1 + tan|φ − δ|))
-// which is:  a = atan(1 / (1 + tan(|phi − delta|)))
-// where |phi − delta| is the Sun's angular distance from the zenith at solar noon.
 func asrAltitude(lat, delta float64) float64 {
-	return toDegrees(math.Atan(1.0 / (1.0 + math.Tan(toRadians(math.Abs(lat-delta))))))
+	return deg(math.Atan(1 / (1 + math.Tan(rad(math.Abs(lat-delta))))))
-}
-
-// Convert a decimal hour value (e.g. 10.5 = 10:30) to a UTC-aware datetime.
-func decimalHoursToUTC(hours float64, d time.Time) time.Time {
-	dayUTC := time.Date(d.Year(), d.Month(), d.Day(), 0, 0, 0, 0, time.UTC)
-	return dayUTC.Add(time.Duration(hours * float64(time.Hour)))
 }
 
 type computedTimes struct {
-	Imsak   *time.Time
+	Imsak, Sunrise, Dhuhr, Asr, Sunset, Maghrib, Isha *time.Time
-	Sunrise *time.Time
-	Dhuhr   *time.Time
-	Asr     *time.Time
-	Sunset  *time.Time
-	Maghrib *time.Time
-	Isha    *time.Time
 }
 
-// Compute Diyanet prayer times, returning UTC-aware datetimes.
+// prayerTimes computes all Diyanet prayer times for the given date, returned
-//
+// as UTC-aware values. Solar noon is the central reference:
-// Solar noon (Dhuhr) is the central reference. All other times are offsets:
-//
-//	Morning times (Imsak, Sunrise):               noon − H + temkin
-//	Afternoon/evening times (Asr, Maghrib, Isha): noon + H + temkin
 //
-// Internally computes solar noon at UTC (tz=0), so results are in UTC.
+//	T_noon(UTC) = 12 − λ/15 − EoT/60
 //
-// Solar noon formula:  T_noon = 12 + TZ − lambda/15 − EoT/60
+// Morning times (Imsak, Sunrise) = noon − H + temkin
-//
+// Afternoon/evening times        = noon + H + temkin
-//	lambda/15  converts longitude to hours (15deg/h)
-//	EoT        corrects the gap between mean solar time and apparent solar time
 func prayerTimes(lat, lon float64, d time.Time) computedTimes {
-	jd := julianDay(d)
+	delta, eot := sunParams(julianDay(d))
-	delta, eot := sunParams(jd)
+	noon := 12 - lon/degPerHour - eot/60
-
-	// UTC solar noon: tz=0, so T_noon = 12 − lambda/15 − EoT/60
-	noonUTC := 12 - lon/degPerHour - eot/60.0
 
-	compute := func(base, angle float64, sign int, temkinMinutes float64) *time.Time {
+	// offset converts a noon-relative hour angle to a UTC *time.Time,
-		h, ok := hourAngle(angle, lat, delta)
+	// applying the given temkin (minutes). Returns nil for polar night/day.
+	offset := func(h float64, ok bool, sign int, tk float64) *time.Time {
 		if !ok {
 			return nil
 		}
-		t := decimalHoursToUTC(base+float64(sign)*h+temkinMinutes/60.0, d)
+		t := utcTime(d, noon+float64(sign)*h+tk/60)
 		return &t
 	}
 
-	hAsr, hasAsr := hourAngle(asrAltitude(lat, delta), lat, delta)
+	hSun, okSun := hourAngle(sunAngle, lat, delta)
-	var asr *time.Time
+	hAsr, okAsr := hourAngle(asrAltitude(lat, delta), lat, delta)
-	if hasAsr {
+	hImsak, okImsak := hourAngle(imsakAngle, lat, delta)
-		t := decimalHoursToUTC(noonUTC+hAsr+temkin.Asr/60.0, d)
+	hIsha, okIsha := hourAngle(ishaAngle, lat, delta)
-		asr = &t
-	}
-
-	// Sunset for output is the geometric sunset without temkin offset.
-	geometricSunset := func(base, angle float64) *time.Time {
-		h, ok := hourAngle(angle, lat, delta)
-		if !ok {
-			return nil
-		}
-		t := decimalHoursToUTC(base+h, d)
-		return &t
-	}
 
-	tDhuhr := decimalHoursToUTC(noonUTC+temkin.Dhuhr/60.0, d)
+	tDhuhr := utcTime(d, noon+temkin.Dhuhr/60)
 
 	return computedTimes{
-		Imsak:   compute(noonUTC, imsakAngle, -1, temkin.Imsak),
+		Imsak:   offset(hImsak, okImsak, -1, temkin.Imsak),
-		Sunrise: compute(noonUTC, sunAngle, -1, temkin.Sunrise),
+		Sunrise: offset(hSun, okSun, -1, temkin.Sunrise),
 		Dhuhr:   &tDhuhr,
-		Asr:     asr,
+		Asr:     offset(hAsr, okAsr, +1, temkin.Asr),
-		Sunset:  geometricSunset(noonUTC, sunAngle),
+		Sunset:  offset(hSun, okSun, +1, 0), // geometric sunset, no temkin
-		Maghrib: compute(noonUTC, sunAngle, +1, temkin.Maghrib),
+		Maghrib: offset(hSun, okSun, +1, temkin.Maghrib),
-		Isha:    compute(noonUTC, ishaAngle, +1, temkin.Isha),
+		Isha:    offset(hIsha, okIsha, +1, temkin.Isha),
-	}
-}
-
-func derefOrZero(dt *time.Time) time.Time {
-	if dt == nil {
-		return time.Time{}
 	}
-	return dt.UTC()
 }
 
-func formatUTCOffsetTimezone(offset float64) string {
+// utcTime converts decimal hours (e.g. 10.5 = 10:30) to a UTC time.Time.
-	return fmt.Sprintf("UTC%+d", int(offset))
+func utcTime(d time.Time, hours float64) time.Time {
+	base := time.Date(d.Year(), d.Month(), d.Day(), 0, 0, 0, 0, time.UTC)
+	return base.Add(time.Duration(hours * float64(time.Hour)))
 }
 
-func estimateUTCOffsetHours(longitude float64) float64 {
+func rad(d float64) float64 { return d * math.Pi / 180 }
-	offset := math.Round(longitude / degPerHour)
+func deg(r float64) float64 { return r * 180 / math.Pi }
-	if offset < -12 {
-		return -12
-	}
-	if offset > 14 {
-		return 14
-	}
-	return offset
-}
-
-func toRadians(deg float64) float64 {
-	return deg * math.Pi / 180.0
-}
-
-func toDegrees(rad float64) float64 {
-	return rad * 180.0 / math.Pi
-}