Struct SurfaceMidpoints 

pub struct SurfaceMidpoints { /* private fields */ }

A surface’s midpoints in f64 (see CurveMidpoints): for the searches on a surface whose answer is a free choice or a measurement in f64 — a seed for a projection, how far a point lies off the surface, where to draw it.

Implementations

impl SurfaceMidpoints

pub fn of(surface: &NurbSurface3D) -> Self

pub fn domain_u(&self) -> (f64, f64)

pub fn domain_v(&self) -> (f64, f64)

pub fn partials(&self, u: f64, v: f64) -> (P3, P3, P3)

The point at (u, v), clamped into the domain, and its partial derivatives there: (Scalar, S_u, S_v).

pub fn point(&self, u: f64, v: f64) -> P3

The point at (u, v), clamped into the domain.

pub fn project(&self, target: P3, u: f64, v: f64) -> (f64, f64)

The foot point of target on the surface by Newton from (u, v), on the first fundamental form, in the domain. A step is taken only where it makes progress: brings the point nearer target, or, no further from it, nearer meeting the foot point’s conditions r · S_u = r · S_v = 0 (r from the point to target) — near the foot point the distance changes too little to tell in f64, the conditions do not; but alone they also lead to points furthest from target. Where the full step makes none — at a pole, where one derivative vanishes up to the roundings of the midpoints and the system is as good as singular — the step along either derivative alone; and where neither does, the step along a derivative from the other parameter at its domain’s ends or middle, which at a pole is the same point on another meridian (as NurbSurface::project leaves a pole). Where none does, the search has arrived.