Module length 

Arc length, and distributing points along a curve by it.

A curve’s parameter is not its length. A B-spline traverses its own parameter at whatever speed its knots imply; a cone’s slant runs at a rate set by its half angle. So “a point every two millimetres” and “twenty evenly spaced points” are questions about length, and answering them from parameter values is answering a different question.

Two operations, one of them an inversion

Length is an integral: the speed |c'(u)| integrated over the range. That is curve_length, and it is exact to a stated tolerance rather than summed from a polyline.

Placing a point at a length is the inverse of that integral, which has no closed form for anything but a line and a circle. It is solved rather than approximated: the length from the start is strictly increasing wherever the parameterization is regular, so a bracketed root find always converges, and there is no risk of the multiple-root trouble a general solve would have.

This is not tessellation

ogeom_mesh::discretize() places points where the curve bends, which is what a mesh wants and what a drawing wants. These place points where the caller asked, evenly along the curve, which is what a toolpath, a dimension chain or a sampling pattern wants. Neither substitutes for the other: an evenly spaced polyline through a tight corner misses it, and a deflection-driven one has no even spacing to speak of.

Functions

curve_length

The arc length of a curve over range.

parameter_at_length

The parameter at which a given arc length from the start of range is reached.

points_by_count

count points evenly spaced by arc length along a curve, ends included.

points_by_spacing

Points along a curve at a fixed arc-length spacing.