A deep dive into the geometry behind procedurally generated roads using only lines and circular arcs. Starting from the problem of connecting two road profiles at arbitrary positions and orientations, the author walks through a two-line fillet construction (arc + straight line) as the core building block. For cases where continuation lines don't intersect (S-curve transitions), a cubic Hermite spline is used to find an intermediary profile position and tangent. Special edge cases like parallel continuation lines are handled with half-circle constructions, while truly unsolvable arrangements are prevented through design constraints in the placement tool.
Table of contents
The Geometry ProblemA Single Arc Won’t Do The TrickThe Geometrical SolutionProfiles InterpolationThe Next ProblemThe Intermediary ProfileBack to Splines?Special CasesConstraining by DesignWhat’s next?FootnotesSort: