Basic usage

This package extends Unitful.jl and the new dimension of angle inherits a lot of default behavior from Unitful.jl. You should read the Unitful.jl documentation first.

At its core, DimensionfulAngles defines:

the angle dimension DimensionfulAngles.𝐀
the reference unit radian DimensionfulAngles.radᵃ (SI unit of angle)
the degree DimensionfulAngles.°ᵃ (SI-accepted unit of angle)
the "defining constant" θ₀ equal to one radian.
the @ua_str macro for easily recalling units in the package
extensions to uconvert to convert between Unitful and DimensionfulAngles quantities.

The unit radᵃ is prefixable, and therefore defines many other units, which are documented in Prefixed units.

The units in this package are appended the superscript ᵃ to differentiate them from the units in Unitful.jl and UnitfulAngles.jl, which have the same name but are non-dimensional. The @ua_str provides an easier way to access these units without having to type the superscript ᵃ. For example, both of these are equivalent:

julia> using Unitful

julia> using DimensionfulAngles

julia> 1.3u"radᵃ"
1.3 rad

julia> 1.3ua"rad"
1.3 rad

The default u string can still be more convenient when defining quantities with mixed units, such as

julia> using Unitful

julia> using DimensionfulAngles

julia> 2.1u"radᵃ/s"
2.1 rad s⁻¹

Alternatively it might be convenient to import the units you are using directly, renaming units from DimensionfulAngles to remove the superscript ᵃ. For example:

julia> using Unitful

julia> using Unitful: m, s, kg

julia> using DimensionfulAngles: radᵃ as rad, °ᵃ as °

julia> 2.1rad / s
2.1 rad s⁻¹

Yet another way to import units is to import the default set of units, which includes all the default units from Unitful.jl but with angle units from DimensionfulAngles.jl. The units from DimensionfulAngles.jl are imported without the superscript ᵃ in their names. This is done as:

julia> using DimensionfulAngles.DefaultSymbols

One of the main advantage of defining an angle dimension is to be able to dispatch on angles. This behavior and useful aliases are completely inherited from Unitful.jl. The most basic usage uses the automatically defined alias DimensionfulAngles.Angle:

julia> using Unitful

julia> using DimensionfulAngles

julia> what_am_i(::Unitful.Length) = "I am a length."
what_am_i (generic function with 1 method)

julia> what_am_i(::DimensionfulAngles.Angle) = "I am an angle."
what_am_i (generic function with 2 methods)

julia> my_height = 6u"ft" + 1.0u"inch"
1.8542 m

julia> angle = 1.2ua"rad"
1.2 rad

julia> what_am_i(my_height)
"I am a length."

julia> what_am_i(angle)
"I am an angle."

Finally, we can convert quantities to or from Unitful (including UnitfulAngles) using an extension of uconvert with first argument :Unitful or :DimensionfulAngles.

Unitful.uconvert — Method

uconvert(s::Symbol, x::Quantity)

Convert between DimensionfulAngles and Unitful angles (non-dimensional, SI). The Symbol s is either :Unitful, to convert to Unitful angles, or DimensionfulAngles to convert to DimensionfulAngles angles. It converts angle units and the following derived units: sr, rpm, rps).

Astronomical units are not equivalent between these two packages

Astronomical units in DimensionfulAngles and UnitfulAngles are not equivalent, and are converted to compatible units first. See documentation for more information.

Example

julia> using Unitful, DimensionfulAngles

julia> ω = 3.2u"radᵃ/s"
3.2 rad s⁻¹

julia> ω̄ = uconvert(:Unitful, ω)
3.2 rad s⁻¹

julia> dimension(ω)
𝐀 𝐓⁻¹

julia> dimension(ω̄)
𝐓⁻¹

julia> dimension(uconvert(:DimensionfulAngles, ω̄))
𝐀 𝐓⁻¹

Basic usage

Syntax

Syntax provided by Unitful.jl

Prefixed units