Interactive modeler of clothoid-arc-clothoid (SCS) transitions - smooth, curvature-continuous paths that route a road around circular obstacles(cities).
Direction handles and obstacles are draggable, paths are recomputed live. Hovering a path shows its parameters; the minimal-energy candidate is highlighted.
Given a sequence of road directions (anchored vectors) and a circular banned zone between each consecutive pair, connect the roads with a path that:
- is tangent to both roads,
- has continuous curvature everywhere (no curvature jumps, unlike simple line-arc-line paths),
- stays outside the obstacle,
- minimizes bending energy (integral of squared curvature).
The transition used is the classic road and railway design primitive: straight, clothoid, circular arc, clothoid, straight. The clothoid (also well known as Euler spiral) has linear curvature change, which is what makes the curvature profile continuous.
For each obstacle, the construction is solved symmetrically - a fraction of the total turn (q) is assigned to the clothoids and the rest to the arc, then the arc radius (R) is searched until the path clears the obstacle. Valid candidates are scored by a bending-energy (E).
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