arris_math/lib.rs
1//! Numeric foundation of the Arris kernel: points, vectors and unit vectors
2//! over `nalgebra`, frames, axes and rigid motions, intervals, exact orientation
3//! predicates over `robust`, polynomial and interval-guarded root finding,
4//! and `Precision`, the model-wide tolerance configuration.
5//!
6//! Guarantees: `f64` throughout, no allocation in evaluation, no panic on
7//! any finite input, and no numeric literal standing in for a tolerance —
8//! every tolerance is a `Precision` field, a [`Tolerance`] derived from it,
9//! or a named constant with a comment (`.agents/rules/kernel.md`). Depends
10//! on nothing in the workspace.
11//!
12//! The point and vector types are `nalgebra`'s by alias and `nalgebra` is
13//! re-exported (`docs/adr/0001-nalgebra-types-by-alias.md`), so a caller
14//! reaches every operator and solver `nalgebra` has and a `nalgebra` major
15//! bump is an Arris API change.
16#![forbid(unsafe_code)]
17#![warn(missing_docs)]
18
19mod aabb;
20mod axis;
21mod control;
22mod frame;
23mod interval;
24mod isometry;
25mod periodic;
26mod precision;
27pub mod predicates;
28mod reflection;
29pub mod roots;
30mod tolerance;
31
32pub use nalgebra;
33
34pub use aabb::Aabb;
35pub use axis::Axis;
36pub use control::{Control, Interrupted, Meter, Poll, Stop};
37pub use frame::{Frame, Frame2, FrameError, Handedness};
38pub use interval::{Interval, IntervalError};
39pub use isometry::Isometry;
40pub use periodic::{
41 period_end, shift_into_range, shift_nearest, shift_nearest_uv, wrap_angle, wrap_into,
42 wrap_offset, wrap_signed,
43};
44pub use precision::Precision;
45pub use reflection::{Reflection, ReflectionError};
46pub use tolerance::Tolerance;
47
48/// Relative rounding slack: a magnitude at or below this fraction of its
49/// natural scale is rounding noise, not a value. Eight ulps — what a
50/// handful of multiplications and one trigonometric evaluation leave
51/// behind, and orders of magnitude below any model tolerance. It is not a
52/// geometric tolerance and never decides whether two things are *the
53/// same*; it decides whether a computed quantity is zero *in floating
54/// point*: the radius of a sphere's parallel at the pole, `cos(π/2)`
55/// evaluated in `f64`, is `6e-17`, not `0`.
56pub const RELATIVE_ROUNDING: f64 = 8.0 * f64::EPSILON;
57
58/// The widest gap a file's entities may leave that a read closes by a
59/// tolerance, as a fraction of the part's size — the diameter of the ball
60/// holding its vertices and edges (ADR-0025 §4). A vertex or an edge whose
61/// measured gap is above it, or above `Precision::max_tolerance`, is
62/// refused as a gap: closing it would be sewing, which is healing, and a
63/// solid grown to cover it would be a wrong one.
64///
65/// Evidence: an exact writer leaves gaps at the rounding of its decimal
66/// digits, around `1e-15` of the part (Arris's own files); a kernel's
67/// raised tolerances reach a few `1e-7` on a part of unit size (the
68/// corpus's `boolean/seam-a-tolerance-from-crossing-fuse`, `1.2e-7` on a
69/// part of size 7). Open CASCADE's own STEP of every corpus fixture
70/// (the corpus's read-back stage) measures at most `2.5e-6` of the part's
71/// diagonal on 201 of 202 files, and `8.5e-5` on the last — `7.4e-4` on a
72/// part `8.7` across, `boolean/seam-beside-crossing-fuse`, whose boolean
73/// Open CASCADE itself gets wrong by that much. Converted to B-splines
74/// (step 15), its `closed-form-band` variant measures `1.05e-3` on a part
75/// whose ball is `9.3` across, `1.13e-4` of it — exactly the tolerance
76/// Open CASCADE's own shape carries there, which its checker passes.
77/// Healing tools commonly default their sewing tolerance to `1e-6`–`1e-3`
78/// of the model's size, so `2e-4` admits every file an exporting kernel
79/// called valid by its own tolerances, the largest seen with `1.8×` to
80/// spare, and refuses the gaps a healer would have to sew. A tolerance
81/// policy, not a rounding slack. Over the real-part corpus it refuses
82/// gaps in 7 of NIST's 38 parts, which count for the healing cycle
83/// (ADR-0026 §5, `docs/ROADMAP.md` §C4).
84pub const READ_GAP_FRACTION: f64 = 2e-4;
85
86/// `|x| ≤ RELATIVE_ROUNDING · |scale|`: `x` is zero to rounding at
87/// `scale`. A zero `scale` makes only an exact zero negligible.
88///
89/// ```
90/// use arris_math::is_negligible;
91/// use core::f64::consts::FRAC_PI_2;
92///
93/// assert!(is_negligible(3.0 * FRAC_PI_2.cos(), 3.0));
94/// assert!(!is_negligible(3.0 * (FRAC_PI_2 - 1e-9).cos(), 3.0));
95/// ```
96pub fn is_negligible(x: f64, scale: f64) -> bool {
97 x.abs() <= RELATIVE_ROUNDING * scale.abs()
98}
99
100/// A position in 3D. `nalgebra::Point3<f64>` (ADR-0001).
101pub type Point3 = nalgebra::Point3<f64>;
102/// A displacement or direction in 3D, of any length.
103/// `nalgebra::Vector3<f64>` (ADR-0001).
104pub type Vec3 = nalgebra::Vector3<f64>;
105/// A direction in 3D: a [`Vec3`] of unit length, guaranteed by construction.
106/// `nalgebra::Unit<Vector3<f64>>` (ADR-0001).
107pub type UnitVec3 = nalgebra::Unit<Vec3>;
108/// A position in a surface's (u, v) plane. `nalgebra::Point2<f64>`
109/// (ADR-0001).
110pub type Point2 = nalgebra::Point2<f64>;
111/// A displacement in the (u, v) plane. `nalgebra::Vector2<f64>` (ADR-0001).
112pub type Vec2 = nalgebra::Vector2<f64>;
113/// A direction in the (u, v) plane: a [`Vec2`] of unit length.
114/// `nalgebra::Unit<Vector2<f64>>` (ADR-0001).
115pub type UnitVec2 = nalgebra::Unit<Vec2>;
116/// A 3x3 matrix, column-major: a rotation, or a tensor such as the
117/// inertia of a body. `nalgebra::Matrix3<f64>` (ADR-0001).
118pub type Matrix3 = nalgebra::Matrix3<f64>;
119
120#[cfg(test)]
121mod tests {
122 use super::*;
123 use core::f64::consts::{PI, TAU};
124
125 #[test]
126 fn wrap_angle_lands_in_the_half_open_turn() {
127 assert_eq!(wrap_angle(0.0), 0.0);
128 assert_eq!(wrap_angle(-1e-300), 0.0);
129 assert_eq!(wrap_angle(-1.0), TAU - 1.0);
130 assert_eq!(wrap_angle(PI), PI);
131 assert!(wrap_angle(-f64::EPSILON) < TAU);
132 assert_eq!(wrap_angle(3.0 * TAU + 1.0), 1.0);
133 assert_eq!(wrap_angle(-3.0 * TAU - 1.0), TAU - 1.0);
134 assert!(wrap_angle(f64::NAN).is_nan());
135 assert_eq!(wrap_angle(f64::INFINITY), f64::INFINITY);
136 }
137}