polydf — Distance queries for parametric curves (2D & 3D)

polydf provides fast nearest-point queries from points to differentiable parametric curves:

• 2D curves: nearest parameter, closest point, unsigned distance, and a normal-based signed distance.
• 3D curves: nearest parameter, closest point, and unsigned distance.
• Optional conservative early-out when you have an upper bound on curve speed.

Highlights

• Works with closures and analytic functions; derivative is optional for 2D signing.
• Robust multi-start 1D minimization (Brent-like) over a user-provided t range.
• Tuple-friendly helpers and simple options for accuracy/performance tradeoffs.

Quick start (2D)

use nalgebra::{Vector2, vector};
use polydf::{NearestOptions, nearest_t};

fn circle(t: f32) -> Vector2<f32> { vector![t.cos(), t.sin()] }

let p = vector![1.5, 0.0];
let res = nearest_t(p, circle, 0.0..=std::f32::consts::TAU, NearestOptions::default());
assert!((res.distance - 0.5).abs() < 1e-3);

Quick start (3D)

use nalgebra::{Vector3, vector};
use polydf::{NearestOptions, nearest_t_3d};

fn helix(t: f32) -> Vector3<f32> { vector![t.cos(), t.sin(), 0.5 * t] }

let p = vector![2.0, 0.0, 0.0];
let res = nearest_t_3d(p, helix, -10.0..=10.0, NearestOptions::default());
println!("t* = {} d = {}", res.t, res.distance);

Early-out (needs speed upper bound)

use polydf::is_definitely_far_3d;
let threshold = 5.0f32;
let speed_ub = Some(1.2f32); // for helix
let far = is_definitely_far_3d(p, helix, -10.0..=10.0, threshold, speed_ub, 64);

Examples

• cargo run --example render_curve (2D image)
• cargo run --example render_curve_with_derivative (2D image with derivative)
• cargo run --example nearest_helix_3d (3D console demo)