Module fj_core::algorithms::approx::path

Path approximation

Since paths are infinite (even circles have an infinite coordinate space, even though they connect to themselves in global coordinates), a range must be provided to approximate them. The approximation then returns points within that range.

The boundaries of the range are not included in the approximation. This is done, to give the caller (who knows the boundary anyway) more options on how to further process the approximation.

Determinism

Path approximation is carefully designed to produce a deterministic result for the combination of a given path and a given tolerance, regardless of what the range is. This is done to prevent invalid meshes from being generated.

In specific terms, this means there is an infinite set of points that approximates a path, and that set is deterministic for a given combination of path and tolerance. The range that defines where the path is approximated only influences the result in two ways:

1. It controls which points from the infinite set are actually computed.
2. It defines the order in which the computed points are returned.

As a result, path approximation is guaranteed to generate points that can fit together in a valid mesh, no matter which ranges of a path are being approximated, and how many times.