This article continues the series about approximating circles using Bézier curves. Preceding parts analysed linear and quadratic curves. This entry examines cubic Bézier curves. It presents a construction of a spline which approximates a circle and derives practical formulæ based on different optimisation criteria.

Cubic Bézier curves are available in many popular tools. They are widely used in vector graphics editing and animation software, and provide flexibility while remaining intuitive to edit. For example, Fig. 1 presents Inkscape’s Node Tool highlighting a joint and two control points adjacent to it. Dragging the points offers a user-friendly way to modify the shape.

A cubic Bézier curve uses four control points: \(\def\P{\mathbf P}\P_0\) through \(\P_3\) and is defined by the following parametric function: $$\def\tau2k{\frac τ{2k}} \def\D{Δ\mathbf P} \def\O{\mathbf O} \def\R2{\mathtt{R2}} \def\V{\mathbf V} \def\VR{\mathbf V^⟂} \def\argmin{\operatorname*{arg\,min}} \def\lerp{\operatorname{lerp}} B(t)=(1-t)^3\P_0 + 3(1-t)^2t\P_1 + 3(1-t)t^2\P_2 + t^3\P_3$$

When Linux desktop adoption is discussed, some point out the lack of graphical user interfaces (GUI) and the necessity of using command-line interface (CLI) tools or editing text files as a reason more people don’t use Linux-based systems. Such characterisation misses how much Linux has changed. The notion that the terminal is a major barrier is outdated and ignores the fact that most users never need to touch it. An assertion that users should not need the terminal for common tasks is different from a claim Linux distributions lack GUIs.

The Good

First, let’s recognise how Linux has improved. In the ’90s and ’00s one had to manually edit cryptic modelines to get their display working. A mistake could lead to a damaged monitor. Nowadays, the main complication is picking a distribution which includes Nvidia drivers.

And that’s not the only thing that has changed. Installing software often required interacting with the CLI; now graphical software managers — which work not unlike app stores many users are familiar with — are common. Handling WiFi used to require messing with wpa_supplicant; now it’s done through an icon in the system tray.

Bambu Lab, a company once celebrated for its high-quality and user-friendly 3D printers, has recently hit a trifecta of questionable behaviour: enshittification of their products, threatening legal action to silence critics and violation of free software licences. Fortunately, several organisations have stepped in to fight for customer rights and free software. Among those, Software Freedom Conservancy (SFC) is asking for volunteers and donations to help fight Bambu’s corporate overreach.

It is unclear why Americans write dates in month-day-year format. What is clear is that it makes little sense and differs from the way most of the world writes dates resulting in confusion. While human puzzlement is well-documented (something I’ve written about as well), equally critical is how screen readers and machine translation behave.

When handling dates in a free-form text, software relies on fragile heuristics. For example, DeepL and Google Translate decide seemingly randomly whether to treat dates the British or American way as demonstrated on figure below. The behaviour can change depending on the use of padding zero, existence of other dates in the translated fragment or surrounding text.

W opinii opubilkowanej w Poradni językowej PWN, dr Adam Wolański bezapelacyjnie odrzucił zapis dat w formie RRRR-MM-DD tłumacząc, iż „w korespondencji z Wielką Brytanią datę zapiszemy cyfrowo jako 21/6/2009 lub 21/06/2009, lub 21.6.2009, a z USA — jako 6/21/2009 lub 06/21/2009.” Jest to opinia, która pomija istotę problemu i sens komentarza czytelnika Poradni. Z założenia jestem zwolennikiem reguł językowych, jednak w tym przypadku jasno trzeba przyjąć, iż po angielsku, daty w formie cyfrowej piszemy jako RRRR-MM-DD (lub ewentualnie RRRR/MM/DD).

Szczególnie w międzynarodowych projektach tożsamość i kompetencja językowa odbiorcy często są nieznane. Bywa to Brytyjczyk w Nowym Jorku, Amerykanin w Zurychu, Japończyk w Sydney itp. Dodatkowo czytelnik skłonny jest zgadywać co autor miał na myśli, np. Amerykanin może rozumować, że Europejczyk stosuje zapis dzień/miesiąc. Sytuacje komplikuje fakt, że wiadomość bywa powielana zatracając informację o oryginalnym autorze i odbiorcy. Do tego dochodzą czytniki ekranowe i narzędzia do maszynowego tłumaczenia, które mają swoje niejednoznaczne heurystyki (o czym napisałem osobny artykuł).

Podstawową funkcją języka jest komunikacja. Tymczasem zapis XX/YY/RRRR (czy też XX/YY bez określenia roku) komunikacji nie sprzyja. Wręcz przeciwnie; jest on źródłem nieporozumień i opóźnień. Z tego powodu powinien być odrzucony.

Even though using Linux has never been easier, newcomers often hit a confusing roadblock: the overwhelming choice of a distribution. Someone coming from Windows or MacOS will find the very concept of a ‘distribution’ to be alien, and the endless listicles and user arguments about which one is ‘best’ only make the confusion worse.

This article aims to clear up that confusion by providing a better way to think about Linux choices, so you won’t be overwhelmed by all the different options if you’re thinking of switching.

The chilly afternoon in Łódź was no match for the warm welcome Andrzej Sapkowski and Adam Badowski received as they entered the stage. The author of the Witcher book series and co-CEO of CD Projekt Red (CDPR) arrived at the 36th International Festival of Comics and Games to explore a simple but elusive question:

What makes a Witcher story?

The panel was moderated by Michał Giersz, who wasted no time to start the conversation. According to him, having Geralt, Ciri, Yennefer or Triss by itself doesn’t make a Witcher story. Narratives without those characters may still feel like Witcher tales. In trying to find the essence of the Witcher stories, he asked about aspects that Sapkowski focuses on first when writing.

Updated on the 31st of July to reflect the fact deadline for both petitions have now passed.

The dystopian interpretation of the ‘you’ll own nothing and be happy’ phrase feels increasingly prescient.¹ As corporations hide behind lengthy Terms of Service and End User License Agreements,² the concept of ownership becomes alarmingly ambiguous. This erosion of consumer rights has given rise to the Stop Killing Games (SKG) movement.

In 2015 I’ve stumbled upon the Classic Tetris World Cham­pion­ship. Even though I’d never played NES Tetris, I started following the event with interest. I keenly remember watching the historic 2018 final which was a prelude to the next generation of players picking up the game.

In contrast, world of racing games offer an example of fleeting ownership. While generations continue to enjoy NES Tetris, with a 13-year-old famously ‘beating’ the game 34 years after its release,³ Ubisoft’s 2014 game The Crew didn’t even last a decade. In 2024, Ubisoft didn’t just shut down the servers; it began revoking players’ licenses, seemingly doing everything in its power to ensure the game couldn’t be preserved or revived by the community.

Przeglądając archiwa swoich starych dysków, natknąłem się na niesłychanie ciekawy artykuł z Gazety Praca. Czas zrobił swoje i na stronie Gazety już go niestety nie ma,¹ a szkoda aby zniknął po nim ślad. Pozwolę więc sobie go zacytować w całości, aby przetrwał dla potomności:

Informatycy najgorzej ubrani

Michał Stangret, 2005-11-25

Są przepoceni, rzadko myją włosy i noszą flanelowe koszule wciągnięte w spodnie. Komputerowcy zajęli pierwsze miejsce w rankingu najgorzej ubranych zawodów. Dostało się też księgowym, urzędnikom i dziennikarzom.

In September 2022, ‘Théâtre D’opéra Spatial’, a work submitted by Jason Allen, won Colorado State Fair’s annual fine art competition in the digital art category. What made the success noteworthy was that the image had been AI-generated. Mr Allen eventually tried to register the work with the US Copyright Office but his attempts turned out fruitless. In September 2023 the Office refused his registration.

I didn’t think much of it at the time. I wasn’t that invested in the consideration of what kind of ‘two-dimensional artworks’ are protected by copyright and, more notably, I somewhat agreed with the decision. Perhaps the prompt was protected, but if only minor manual edits were made to the image, it felt like a stretch to say the image as a whole could be covered by copyright law.