Go: added some vector and angle functions.

Added functions:
    DegreesFromRadians
    RadiansFromDegrees
    AngleBetween
    StateVector.Position
    StateVector.Velocity

Changed existing functions to pass structs by value,
just like we do in the C code. This is a safety feature
to signal value semantics and a contract not to mutate the
argument state.

Run Go tests with the -v option to log more info about what's happening.

generate/template/astronomy.go

@@ -240,7 +240,7 @@ func TimeFromTerrestrialDays(tt float64) AstroTime {
 	return makeTime(universalTime(tt), tt)
 }
 
-func (time *AstroTime) AddDays(days float64) AstroTime {
+func (time AstroTime) AddDays(days float64) AstroTime {
 	return TimeFromUniversalDays(time.Ut + days)
 }
 
@@ -260,6 +260,11 @@ type AstroVector struct {
 	T AstroTime
 }
 
+// Returns the length of vec expressed in the same distance units as vec's components.
+func (vec AstroVector) Length() float64 {
+	return math.Sqrt(vec.X*vec.X + vec.Y*vec.Y + vec.Z*vec.Z)
+}
+
 type StateVector struct {
 	X  float64
 	Y  float64
@@ -270,6 +275,16 @@ type StateVector struct {
 	T  AstroTime
 }
 
+// Position returns the position vector inside a state vector.
+func (state StateVector) Position() AstroVector {
+	return AstroVector{state.X, state.Y, state.Z, state.T}
+}
+
+// Position returns the velocity vector inside a state vector.
+func (state StateVector) Velocity() AstroVector {
+	return AstroVector{state.Vx, state.Vy, state.Vz, state.T}
+}
+
 type Spherical struct {
 	Lat  float64
 	Lon  float64
@@ -433,4 +448,34 @@ type constelBoundary struct {
 	decLo float64
 }
 
+// DegreesFromRadians converts an angle expressed in radians to an angle expressed in degrees.
+func DegreesFromRadians(radians float64) float64 {
+	return radians * (180.0 / math.Pi)
+}
+
+// RadiansFromDegrees converts an angle expressed in degrees to an angle expressed in radians.
+func RadiansFromDegrees(degrees float64) float64 {
+	return degrees * (math.Pi / 180.0)
+}
+
+// AngleBetween calculates the angle in degrees between two vectors.
+// Given a pair of vectors avec and bvec, this function returns the
+// angle in degrees between the vectors in 3D space.
+// The angle is measured in the plane that contains both vectors.
+// The returned value is in the closed range [0, 180].
+func AngleBetween(avec AstroVector, bvec AstroVector) float64 {
+	r := avec.Length() * bvec.Length()
+	if r < 1.0e-8 {
+		panic("Cannot find angle between vectors because they are too short.")
+	}
+	dot := (avec.X*bvec.X + avec.Y*bvec.Y + avec.Z*bvec.Z) / r
+	if dot <= -1.0 {
+		return 180.0
+	}
+	if dot >= +1.0 {
+		return 0.0
+	}
+	return DegreesFromRadians(math.Acos(dot))
+}
+
 //$ASTRO_CONSTEL()

generate/unit_test_golang

@@ -10,7 +10,7 @@ Fail()
 go version || Fail "Cannot find Go compiler."
 
 cd ../source/golang
-go test || Fail "Failure in Go unit tests."
+go test -v || Fail "Failure in Go unit tests."
 cd ../../generate
 echo "unit_test_golang: success"
 exit 0

source/golang/README.md

@@ -13,13 +13,17 @@ It provides a suite of well\-tested functions for calculating positions of the S
 ## Index
 
 - [Constants](<#constants>)
+- [func AngleBetween\(avec AstroVector, bvec AstroVector\) float64](<#AngleBetween>)
+- [func DegreesFromRadians\(radians float64\) float64](<#DegreesFromRadians>)
+- [func RadiansFromDegrees\(degrees float64\) float64](<#RadiansFromDegrees>)
 - [type AstroMoonQuarter](<#AstroMoonQuarter>)
 - [type AstroSearchFunc](<#AstroSearchFunc>)
 - [type AstroTime](<#AstroTime>)
   - [func TimeFromTerrestrialDays\(tt float64\) AstroTime](<#TimeFromTerrestrialDays>)
   - [func TimeFromUniversalDays\(ut float64\) AstroTime](<#TimeFromUniversalDays>)
-  - [func \(time \*AstroTime\) AddDays\(days float64\) AstroTime](<#AstroTime.AddDays>)
+  - [func \(time AstroTime\) AddDays\(days float64\) AstroTime](<#AstroTime.AddDays>)
 - [type AstroVector](<#AstroVector>)
+  - [func \(vec AstroVector\) Length\(\) float64](<#AstroVector.Length>)
 - [type AtmosphereInfo](<#AtmosphereInfo>)
 - [type AxisInfo](<#AxisInfo>)
 - [type Body](<#Body>)
@@ -37,6 +41,8 @@ It provides a suite of well\-tested functions for calculating positions of the S
 - [type SeasonsInfo](<#SeasonsInfo>)
 - [type Spherical](<#Spherical>)
 - [type StateVector](<#StateVector>)
+  - [func \(state StateVector\) Position\(\) AstroVector](<#StateVector.Position>)
+  - [func \(state StateVector\) Velocity\(\) AstroVector](<#StateVector.Velocity>)
 - [type TimeFormat](<#TimeFormat>)
 - [type Topocentric](<#Topocentric>)
 
@@ -118,8 +124,35 @@ const (
 )
 ```
 
+<a name="AngleBetween"></a>
+## func [AngleBetween](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L466>)
+
+```go
+func AngleBetween(avec AstroVector, bvec AstroVector) float64
+```
+
+AngleBetween calculates the angle in degrees between two vectors. Given a pair of vectors avec and bvec, this function returns the angle in degrees between the vectors in 3D space. The angle is measured in the plane that contains both vectors. The returned value is in the closed range \[0, 180\].
+
+<a name="DegreesFromRadians"></a>
+## func [DegreesFromRadians](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L452>)
+
+```go
+func DegreesFromRadians(radians float64) float64
+```
+
+DegreesFromRadians converts an angle expressed in radians to an angle expressed in degrees.
+
+<a name="RadiansFromDegrees"></a>
+## func [RadiansFromDegrees](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L457>)
+
+```go
+func RadiansFromDegrees(degrees float64) float64
+```
+
+RadiansFromDegrees converts an angle expressed in degrees to an angle expressed in radians.
+
 <a name="AstroMoonQuarter"></a>
-## type [AstroMoonQuarter](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L357-L360>)
+## type [AstroMoonQuarter](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L372-L375>)
 
 
 
@@ -131,7 +164,7 @@ type AstroMoonQuarter struct {
 ```
 
 <a name="AstroSearchFunc"></a>
-## type [AstroSearchFunc](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L371>)
+## type [AstroSearchFunc](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L386>)
 
 
 
@@ -206,10 +239,10 @@ func TimeFromUniversalDays(ut float64) AstroTime
 
 
 <a name="AstroTime.AddDays"></a>
-### func \(\*AstroTime\) [AddDays](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L243>)
+### func \(AstroTime\) [AddDays](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L243>)
 
 ```go
-func (time *AstroTime) AddDays(days float64) AstroTime
+func (time AstroTime) AddDays(days float64) AstroTime
 ```
 
 
@@ -228,8 +261,17 @@ type AstroVector struct {
 }
 ```
 
+<a name="AstroVector.Length"></a>
+### func \(AstroVector\) [Length](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L264>)
+
+```go
+func (vec AstroVector) Length() float64
+```
+
+Returns the length of vec expressed in the same distance units as vec's components.
+
 <a name="AtmosphereInfo"></a>
-## type [AtmosphereInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L344-L348>)
+## type [AtmosphereInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L359-L363>)
 
 
 
@@ -242,7 +284,7 @@ type AtmosphereInfo struct {
 ```
 
 <a name="AxisInfo"></a>
-## type [AxisInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L384-L389>)
+## type [AxisInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L399-L404>)
 
 
 
@@ -256,7 +298,7 @@ type AxisInfo struct {
 ```
 
 <a name="Body"></a>
-## type [Body](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L279>)
+## type [Body](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L294>)
 
 
 
@@ -281,7 +323,7 @@ type CalendarDateTime struct {
 ```
 
 <a name="DeltaTimeFunc"></a>
-## type [DeltaTimeFunc](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L373>)
+## type [DeltaTimeFunc](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L388>)
 
 
 
@@ -290,7 +332,7 @@ type DeltaTimeFunc func(ut float64) float64
 ```
 
 <a name="Ecliptic"></a>
-## type [Ecliptic](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L319-L323>)
+## type [Ecliptic](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L334-L338>)
 
 
 
@@ -303,7 +345,7 @@ type Ecliptic struct {
 ```
 
 <a name="Equatorial"></a>
-## type [Equatorial](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L312-L317>)
+## type [Equatorial](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L327-L332>)
 
 
 
@@ -317,7 +359,7 @@ type Equatorial struct {
 ```
 
 <a name="JupiterMoonsInfo"></a>
-## type [JupiterMoonsInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L417-L422>)
+## type [JupiterMoonsInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L432-L437>)
 
 
 
@@ -331,7 +373,7 @@ type JupiterMoonsInfo struct {
 ```
 
 <a name="LibrationInfo"></a>
-## type [LibrationInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L375-L382>)
+## type [LibrationInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L390-L397>)
 
 
 
@@ -347,7 +389,7 @@ type LibrationInfo struct {
 ```
 
 <a name="NodeEventInfo"></a>
-## type [NodeEventInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L399-L402>)
+## type [NodeEventInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L414-L417>)
 
 
 
@@ -359,7 +401,7 @@ type NodeEventInfo struct {
 ```
 
 <a name="NodeEventKind"></a>
-## type [NodeEventKind](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L391>)
+## type [NodeEventKind](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L406>)
 
 
 
@@ -368,7 +410,7 @@ type NodeEventKind int
 ```
 
 <a name="Observer"></a>
-## type [Observer](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L306-L310>)
+## type [Observer](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L321-L325>)
 
 
 
@@ -381,7 +423,7 @@ type Observer struct {
 ```
 
 <a name="Refraction"></a>
-## type [Refraction](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L336>)
+## type [Refraction](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L351>)
 
 
 
@@ -400,7 +442,7 @@ const (
 ```
 
 <a name="RotationMatrix"></a>
-## type [RotationMatrix](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L332-L334>)
+## type [RotationMatrix](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L347-L349>)
 
 
 
@@ -411,7 +453,7 @@ type RotationMatrix struct {
 ```
 
 <a name="SeasonsInfo"></a>
-## type [SeasonsInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L350-L355>)
+## type [SeasonsInfo](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L365-L370>)
 
 
 
@@ -425,7 +467,7 @@ type SeasonsInfo struct {
 ```
 
 <a name="Spherical"></a>
-## type [Spherical](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L273-L277>)
+## type [Spherical](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L288-L292>)
 
 
 
@@ -438,7 +480,7 @@ type Spherical struct {
 ```
 
 <a name="StateVector"></a>
-## type [StateVector](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L263-L271>)
+## type [StateVector](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L268-L276>)
 
 
 
@@ -454,8 +496,26 @@ type StateVector struct {
 }
 ```
 
+<a name="StateVector.Position"></a>
+### func \(StateVector\) [Position](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L279>)
+
+```go
+func (state StateVector) Position() AstroVector
+```
+
+Position returns the position vector inside a state vector.
+
+<a name="StateVector.Velocity"></a>
+### func \(StateVector\) [Velocity](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L284>)
+
+```go
+func (state StateVector) Velocity() AstroVector
+```
+
+Position returns the velocity vector inside a state vector.
+
 <a name="TimeFormat"></a>
-## type [TimeFormat](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L362>)
+## type [TimeFormat](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L377>)
 
 
 
@@ -475,7 +535,7 @@ const (
 ```
 
 <a name="Topocentric"></a>
-## type [Topocentric](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L325-L330>)
+## type [Topocentric](<https://github.com/cosinekitty/astronomy/blob/golang/source/golang/astronomy.go#L340-L345>)