The biarc UI above demonstrates how biarcs work but it’s not a great UI for players to build roads. A better UI would constrain the control point to lie on the circle, or automatically choose a control point based on some heuristics.Cognitive learning pdf in the biarc literature there’s no one best heuristic that everyone agrees on, so you might want to try several and see which is best for your game.Cognitive learning pdf also, my guess is that you wouldn’t even want to give players a control over the tangents. You can easily choose tangents that lead to gigantic arcs.Cognitive learning pdf in a game it’s likely you’re connecting the road to an existing road, so the tangent is already determined. Conclusions #

For roads and railroad tracks though, I think circular arcs are an interesting alternative.Cognitive learning pdf they have some nice properties when it comes to representation and simulation, with a possible issue with very large radii. Railroad tycoon 3 and sid meier’s railroads use them.Cognitive learning pdf racing games use them. I think train fever [14] uses them. Are there other building games that use circular arcs?

• approximating curves and their offsets using biarcs and pythagorean hodograph quintics [29] (by sir, feichtinger, juttler) helped me understand how to represent biarcs, how to calculate and use the circle of valid control points, and also helped correct a misunderstanding I had — a misunderstanding that had led me astray when writing my code.Cognitive learning pdf it also goes into curve fitting, which could be useful but something I didn’t explore.

How can we calculate intersections? I believe we can intersect the left/right offset curves of two roads to find four points for a quadrilateral.Cognitive learning pdf for bezier curves we’d need to convert to a piecewise linear form; for circular arcs we can calculate the intersections directly. However I haven’t tried implementing intersections for curved roads, and there are probably many corner cases to work out (no pun intended!).Cognitive learning pdf in the real world

In real life, roads and railroad tracks use circular arcs [32], not bezier curves. However arcs are not G 2 continuous. This means you have to abruptly shift your steering wheel when transitioning from a straight segment to a curved segment.Cognitive learning pdf to solve this, they use clothoid connectors [33]. (clothoids are also called “ euler spirals [34]” or “cornu spirals”.) however, clothoids have complicated distances/interpolations and unlikely to have clean offset curves.Cognitive learning pdf they might be useful in racing games but I wouldn’t use them in a city-building game. (see the next section for some references.) other curves

cognitive learning pdf

• sketching piecewise clothoid curves [40] (by mccrae and singh) is about clothoid curves in road design for games, including curve fitting, and also includes a video showing a UI in which players can draw a curved line and the system will figure out how to turn it into a piecewise circular curve, then render a road.Cognitive learning pdf be sure to watch the video! I didn’t play with any of this on this page; I focused on circular arcs, not clothoids, and I haven’t explored the UI aspects.Cognitive learning pdf they also include a windows demo and source code.

For a few weeks I got distracted by geometric algebra [45], which seemed like it might be a nice way to represent lines and curves.Cognitive learning pdf there are a lot of cool ideas in there, and it explained things that really bothered me about the usual vector representation in 3D graphics.Cognitive learning pdf however, I didn’t learn enough of it to be able to say whether I could use it in my 2D setting. I should’ve probably tried implementing circular arcs with geometric algebra; that would’ve made me learn it faster.Cognitive learning pdf