The simple geometry behind any road

2 days ago

Profiles serve as control points for interpolating road geometry, similar to Bezier splines' anchor points.
The road geometry problem involves connecting profiles with smooth parallel arcs using lines and circular arcs.
A single circular arc can't always connect two points with prescribed tangents, so a two-line fillet construction is used: a line segment followed by a tangent circular arc.
When profiles' continuation lines don't intersect (e.g., in an S-shift), an intermediary profile is introduced, found via a cubic Hermite spline approximation.
Special cases include parallel continuation lines, solved with a half-circle and straight segment, and constraints to avoid unsolvable profile arrangements.

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