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NP-Incompleteness

Understanding std::call_once() in C++

01 Mar 2024
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In this post, we’ll delve into the function std::call_once() in the C++ STL: why it’s useful, how efficient it is and how it can be implemented. We’ll provide an simple implementation based on locks and a more advanced one based on futexes.

Finally we do a benchmark to compare their performance vs. libraries such as GCC, Clang and Folly.

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Bipolar Coordinates and Möbius Transformations

10 Feb 2024
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In this post we’ll discuss the bipolar coordinate system and how it can be used to simplify Möbius transformations. It puts together a bunch of concepts we studied in prior posts, so being familiar with the series is helpful.

This is the last post of the series based on holomorphic functions, which correspond to Chapter 3 (Analytic Functions as Mappings) in Ahlfors’ Complex Analysis [1].

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Symmetry Points of a Circle

03 Feb 2024
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In this post we study the Symmetry Points of a Circle in the context of Complex Analysis. It builds on concepts and results discussed in prior section, so it’s worth getting familiar with the series:

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Circles of Apollonius

20 Jan 2024
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In this post we study the circles of Apollonius or Apollonian circles from a geometric perspective. Later we relate it with concepts from complex analysis.

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Cross Ratio

13 Jan 2024
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In this post we’ll discuss the concept of the cross-ratio which has its origins in geometry, but we’ll mainly consider it in the context of complex analysis.

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