Featured Map for24 March 2023:
Introducing Bézier Paths

The Featured Mapten days agointroduced rhumb lines as a new path type, as an alternative to the usualgeodesic ("great circle") paths. As noted then, rhumb lines may not seemuch use as more than a curiosity. Today's Featured Map introduces anothernew path type, one which is likely to have greater utility.

TheFeatured Map on 11 January 2023included a trio of routes which sat atop each other. From the notes onthat Featured Map:

One quirk of the map is that it looks like Alaska might fly the A321neofromChicago O'Hareto New York, either toJFKor toNewark or even to both.That's an illusion due to the geodesic ("great circle") path fromSan Francisco toNew Yorkpassing almost directly over O'Hare.(That might be a topic for a future Featured Map!)

This is that future Featured Map.

Although geodesic paths depict the shortest path on the globe,they may not resemble the paths actually flown (due to winds andother factors), and they can do a truly poor job of portraying anairline's network. A classic example of the latter dichotomy is thediagram of the London Underground (the Tube Map)that Harry Beck created in 1931: although it is severely distortedfrom physical reality, it is brilliantly useful.

Enter Bézier curves, named for French automotive engineer Pierre Bézier,which in their cubic form augment the end points of a path withtwo control points to define a smooth curve, arbitrary other thanwith regard to the four points. Depending upon the chosen controlpoints, this curve might resemble the geodesic path,or might be wildly different.

Over 20 years ago, Brian Reid, then at the Digital Equipment Corp. (DEC)Western Research Laboraoties (WRL) in Palo Alto, Califoria, produced aseries of maps (er, diagrams) of traffic flows in both the Usenet and UUCPnetworks. They used Bézier curves, and he was kind enough to share his codefor choosing the control points. It turned out to be difficult to integrateinto theoriginal Great Circle Mapper,one of many problems which led to a rewrite of the site (known as GC2if you're amongst the one people, er, person, in-the-know)to the current web site.

Several years after thedebut of GC2 in 2010,the idea of using Brian's work was revived. Brian is really smart butwith a dullard like yours truly at the helm it worked for some casesbut failed miserably for others and was again set aside.

January's Alaska Airbus map again ignitedthat desire to find a different way of portraying paths. Rather than"boiling the ocean" with automatic selection of Bézier control points,it seemed like user-definable control points might offer a useful stepeven if the ease of use falls short of the goals of theGreat Circle Mapper.My flights fromSan Francisco toPhoenix (and return)for the Cranky Network Awards provided time to enhance the software tosupport Bézier curves as a path type.

(Many thanks to everyone who expressed enthusiasm and supportat that event!)

Bézier paths are still a work-in-progress in that the defaultparameters are useless but after over 20 years it's time torelease it despite the warts.

Today's Featured Map again shows Alaska Airlines' Airbus flights fromSan Francisco toChicago,New York (JFK), andNewark,with the geodesic paths in red even though it looks like just one path,and with the three routes diagrammed in green using Bézier pathsto clearly show what Alaska Airlines flies. More information aboutBézier paths andhow to configure themis in the FAQ.

References and additional information:

• Tube map –Transport for London
• When Topology Trumped Topography: Celebrating 90 Years of Beck's Underground Map
• The Birth of Bézier Curves & How It Shaped Graphic Design (28 October 2022)
• Flowing From Site to Site: Brian Reid's USENET Traffic Flow Maps (circa 1986-95)
• Alaska Airlines
• 2023 Cranky Network Awards
  
  
• Featured Map: Pi(rates) and Rhumb (14 March 2023)
• Featured Map: Alaska's Dwindling Airbus Fleet (11 January 2023)
• Featured Map: The First 24 Hours (14 January 2010)