Make circle drawing more scalable

[albinahlback]

By usage of trigonometric function, I was able to reduce the computational complexity of the algorithm from O(r^2) to O(r). Further note the lack of if statements within the for loops.

Note that some smaller circles (r ~= 2), the appearance is somewhat wierd. Maybe someone can see if one should use ceil or floor instead of round. However, I think this is worth the performance gain.

Resolves #7

[aviks]

Thanks for this. I presume you have seen #13 to check the history of this code?

Can you provide some screenshots with the new algorithm for different sizes of circles, as well as some timings for the old and new code?

[albinahlback]

I added the testfile in test/. Here's the result, which clearly proves that this way is faster:

# Starting julia

julia> include("circleperformance.jl")
testnew (generic function with 1 method)

# Running every test, so everything gets compiled before timing

julia> ren = myinit()
Ptr{SimpleDirectMediaLayer.Renderer} @0x0000000004768490

julia> @time testold(ren, circles, 1000, false)
  1.325373 seconds

julia> ren = myinit()
Ptr{SimpleDirectMediaLayer.Renderer} @0x0000000004bfd2d0

julia> @time testold(ren, circles, 1000, true)
  2.234989 seconds

julia> ren = myinit()
Ptr{SimpleDirectMediaLayer.Renderer} @0x000000006cdce890

julia> @time testnew(ren, circles, 1000, false)
  0.898482 seconds (40.00 k allocations: 3.662 MiB)

julia> ren = myinit()
Ptr{SimpleDirectMediaLayer.Renderer} @0x000000006cd6e8a0

julia> @time testnew(ren, circles, 1000, true)
  0.596087 seconds (40.00 k allocations: 3.662 MiB)

[albinahlback]

The first sequence of circles on the left have the radius 1 to 7. The ones to the right have the radius 49 to 81.

As you can see, the smaller ones have a somewhat odd shape. But in my opinion, this is fine when considering that the code is smaller and faster.