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JuliaApproximation / DomainSets.jl

A Julia package for describing domains as continuous sets of elements
MIT License
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Add arclength #20

Open dlfivefifty opened 6 years ago

dlfivefifty commented 6 years ago

I'm not sure what the conclusion was what to call it, but there should be some version of arclength for an interval.

It could be called lebesguemeasure, though that's a bit confusing for intervals embedded in the complex plane, as the measure with respect to dx*dy would be zero....

daanhb commented 6 years ago

I'm fine with arclength, but the cases you mention can also be distinguished. Any Interval{T} where T <: Real has non-zero Lebesgue measure, and the current way to embed an interval in the complex plane is to explicitly use an embedding: i = embedding_map(Float64, Complex128) * interval(). (Nicer syntax would be welcome.) One could probably make it so that the lebesgue measure of i is zero in this case, since the embedding map knows the difference in dimension of the spaces.

dlfivefifty commented 6 years ago

I usre Segment(a::Complex,b::Complex) for line segments in the complex plane, so don't need embedding_map.

dlfivefifty commented 5 years ago

IntervalSets.jl uses width(d), which I think is fine.