Blending toward the nearest point on a path creases wherever the nearest point flips

Fact

The usual way to stamp a path into a field is: find the closest point on the polyline, take its value, blend by distance. The blend weight is continuous, but the value is not: on the inside of a sharp corner there is a bisector where the closest point jumps from one leg to the other, and the two legs hold different values.

At a hairpin the two legs differ by whatever the path climbed around the corner, so the stamped field gets a step of exactly that size running down the middle of its own corridor. Everything looks correct until a corner is tight enough for both legs to be inside one blend radius.

Averaging over every sample within range instead — Σ w_i·v_i / Σ w_i, with w_i the same distance window — is continuous everywhere, and on a straight stretch the symmetric weights reproduce the local value unchanged.

Why it matters

The defect is invisible in the thing you are looking at: the path's own centre line measures correct, the corner geometry is correct, and the surface normals are smooth. What breaks is a narrow band a few units wide, so it is found by something walking into it rather than by looking.

It generalises past terrain to anything stamped along a curve — a road's material, a river's depth, a corridor's lighting, a brush stroke's width.

How to apply

• Use a weighted average of all samples in range for the value, and the nearest-point distance only for the weight.
• Sample the path densely enough that several samples are always in range; spacing well under the blend radius is enough.
• To test it, walk the centre line and measure the field's gradient. A crease is a gradient jump that does not shrink when you halve the probe step — a genuine curvature does.