Add - Tics Function (#8)

*  Add - Tics Function

* TODO.md: remove 'tics' from list.
* docs/src/ref.md: add "tics" entry to the manual.
* src/utils.jl: Add tics entry to "utils".
* src/tics.jl: Contains tics function.
* test/util-tests.jl: Include tests

Note - The test and examples values are random dummy values,
as I couldn't find any proper example sets to use.

* Small fix for readibility

* src/tics.jl: Re-added spacing in the function info section for readibility,
which had somehow gotten lost in transition.

* Improvements, fixes and increasing test coverage

* src/tics.jl: Removed float for numeric literals
	       Fixed indentation, added promt pasting
* test/utils-tests.jl: In brief, brute forced for test coverage

* Use T() to convert numeric literals to type T

* src/tics.jl: Implemented T(number) for accuracy and type stabiltiy
* test/utils-tests.jl: Edited tests to accommodate changes in tics.jl

Author: TestSubjector

TODO.md

@@ -418,7 +418,6 @@ Missing in AstroLib.jl
 * `ticlabels`
 * `tic_one`
 * `ticpos`
-* `tics`
 * `t_nstar`
 * `tnx_eval`
 * `tpv_eval`

docs/src/ref.md

@@ -152,6 +152,7 @@ julia> AstroLib.planets["saturn"].mass
 [`sixty()`](@ref),
 [`sphdist()`](@ref),
 [`ten()`](@ref),
+[`tics()`](@ref).
 [`trueanom()`](@ref),
 [`vactoair()`](@ref)
 

src/tics.jl

@@ -0,0 +1,116 @@
+function _tics{T<:AbstractFloat}(radec_min::T, radec_max::T, numx::T, ticsize::T, ra::Bool)
+
+    numtics = numx/ticsize
+    if ra
+        mul = T(4)
+    else
+        mul = T(60)
+    end
+    mins = abs(radec_min - radec_max)*mul
+    rapix = (numx - 1)/mins
+    incr = mins/numtics
+
+    if incr >= 120
+        incr = T(480)
+    elseif incr >= 60
+        incr = T(120)
+    elseif incr >= 30
+        incr = T(60)
+    elseif incr >= 15
+        incr = T(30)
+    elseif incr >= 10
+        incr = T(15)
+    elseif incr >= 5
+        incr = T(10)
+    elseif incr >= 2
+        incr = T(5)
+    elseif incr >= 1
+        incr = T(2)
+    elseif incr >= 1//2
+        incr = T(1)
+    elseif incr >= 1//4
+        incr = T(1//2)
+    elseif incr >= 10//60
+        incr = T(1//4)
+    elseif incr >= 5//60
+        incr = T(10//60)
+    elseif incr >= 2//60
+        incr = T(5//60)
+    elseif incr >= 1//60
+        incr = T(2//60)
+    elseif incr >= 5//600
+        incr = T(1//60)
+    elseif incr >= 2//600
+        incr = T(5//600)
+    elseif incr >= 1//600
+        incr = T(2//600)
+    elseif incr >= 5//6000
+        incr = T(1//600)
+    elseif incr >= 2//6000
+        incr = T(5//6000)
+    elseif incr >= 1//6000
+        incr = T(2//6000)
+    else incr >= 0
+        incr = T(1//6000)
+    end
+
+    ticsize = rapix * incr
+
+    if ra && incr == 480
+        incr = T(240)
+    end
+    if radec_min > radec_max
+        incr = -incr
+    end
+    return ticsize, incr
+end
+
+"""
+    tics(radec_min, radec_max, numx, ticsize[, ra=true]) -> ticsize, incr
+
+### Purpose ###
+
+Compute a nice increment between tic marks for astronomical images.
+
+### Explanation ###
+
+For use in labelling a displayed image with right ascension or declination
+axes.  An approximate distance between tic marks is input, and a new value
+is computed such that the distance between tic marks is in simple increments
+of the tic label values.
+
+### Arguements ###
+
+* `radec_min` : minimum axis value (degrees).
+* `radec_min` : maximum axis value (degrees).
+* `numx` : number of pixels in x direction.
+* `ticsize` : distance between tic marks (pixels).
+* `ra` (optional boolean keyword): if true, incremental value would
+  be in minutes of time. Default is false.
+
+### Output ###
+
+A 2-tuple `(ticsize, incr)`:
+* `ticsize` : distance between tic marks (pixels).
+* `incr` : incremental value for tic labels.  The format is dependent
+  on the optional keyword. If true (i.e for right ascension), it's in minutes
+  of time, else it's in minutes of arc (for declination).
+
+### Example ###
+
+``` julia
+julia> tics(55, 60, 100.0, 1/2)
+(0.66, 2)
+
+julia> tics(30, 60, 12, 2, true)
+(2.75, 30)
+```
+
+### Notes ###
+
+Code of this function is based on IDL Astronomy User's Library.
+"""
+tics(radec_min::Real, radec_max::Real, numx::Real,
+     ticsize::Real, ra::Bool=false) =
+         _tics(promote(float(radec_min), float(radec_max), float(numx),
+                       float(ticsize))..., ra)

src/utils.jl

@@ -148,6 +148,9 @@ export sunpos
 include("ten.jl")
 export ten
 
+include("tics.jl")
+export tics
+
 include("trueanom.jl")
 export trueanom
 

test/utils-tests.jl

@@ -544,6 +544,38 @@ end
     [-0.37388888888888894, -1.0, -3.0]
 @test ten.([12.0, -0.0], [24, 30]) == ten.([" 12::24", " -0:30: "]) == [12.4, -0.5]
 
+#Test tics
+@test tics(30, 90, 30, 1) == (3.8666666666666667, 480)
+@test tics(30, 90, 3, 3, true) == (4.0, 240)
+@test tics(30, 70, 3, 1, true) == (0.75, 60)
+@test tics.([30,50],[70,60], [6,12], [3,0.5], [true, false]) ==
+            [(3.75,120), (0.55,30)]
+@test tics(45, 55, 30, 0.5) == (0.725, 15)
+@test tics(45, 60, 10, 0.1) == (0.1, 10)
+@test tics(55, 60, 100.0, 1/2) == (0.66, 2)
+@test tics(25, 30, 50, 2, true) == (2.45, 1)
+@test tics(20, 80, 600, 0.03) == (0.04159722222222222, 0.25)
+@test tics(25, 75, 500, 0.02) == (0.02772222222222222, 0.16666666666666666)
+@test tics(10, 12, 25, 0.01) == (0.016666666666666666, 0.08333333333333333)
+@test tics(20, 80, 6000, 0.03) == (0.055546296296296295, 0.03333333333333333)
+@test tics(30, 60, 200, 0.02, true) == (0.02763888888888889, 0.016666666666666666)
+@test tics(60, 70, 125, 0.001) == (0.0017222222222222222, 0.008333333333333333)
+@test tics(10, 12, 25, 0.01, true) == (0.01, 0.0033333333333333335)
+@test tics(130, 180, 1000, 0.0004) == (0.000555, 0.0016666666666666668)
+@test tics(60, 70, 5500//2, 0.003) == (0.003818055555555556, 0.0008333333333333334)
+@test tics(30, 150, 4000, 0.002, true) == (0.0027770833333333337, 0.0003333333333333333)
+@test tics(9.5, 14.5, 5000, 0.002) == (0.002777222222222222, 0.00016666666666666666)
+@test tics(90, 45, 1000, 10) == (11.1, -30)
+let
+    local ticsize, incr
+    ticsize, incr = tics(30, 70, 50, 0.1)
+    @test ticsize ≈ 0.10208333333333333
+    @test incr ≈ 5
+    ticsize, incr = tics(pi/3, pi/2, 60.0, 7.5, true)
+    @test ticsize ≈ 14.085212463632736
+    @test incr ≈ 0.5
+end
+
 # Test kepler_solver
 @test trueanom(8pi/3, 0.7)              ≈ 2.6657104039293764
 @test trueanom.([pi/4, pi/6, 8pi/3], 0) ≈ [pi/4, pi/6, 2pi/3]