tiny.geometry.tolerance

1pub const tolerance = @import("tolerance.zig");

1//! Every tolerance the package compares against, in one place.2//!3//! Primitive queries are exact computations in strict float mode that reject4//! only degenerate input through the floors below. Tree queries add5//! one relative slack to their box tests so a node box never culls a triangle6//! that the primitive test would accept.7const std = @import("std");89/// Two directions whose angle has a sine at or below this are parallel. A10/// cross or triple product this small next to its factors' lengths is mostly11/// rounding, which is about 2^-22 of those lengths in f32, so every answer12/// built on one would be noise. The test is relative, so it reads the same at13/// every coordinate scale.14pub const sine_floor: f32 = 0x1p-16;1516/// A squared length at or below this has no direction, so a segment this17/// short is a point.18pub const length_sq_floor: f32 = 1e-20;1920/// A ray direction component at or below this magnitude is parallel to the21/// matching slab, so its reciprocal is never formed.22pub const direction_component_floor: f32 = 1e-30;2324/// Whether a product of squared magnitude `product_sq` is parallel noise next25/// to `factors_sq`, the product of its factors' squared lengths. A triangle26/// is degenerate when its area normal is parallel noise next to its two27/// edges, and a ray grazes a triangle when their determinant is parallel28/// noise next to the ray and both edges.29pub fn isParallel(product_sq: f32, factors_sq: f32) bool {30    return product_sq <= sine_floor * sine_floor * factors_sq;31}3233/// A closing speed squared at or below this cannot reach a feature within the34/// sweep, so the feature contributes no contact.35pub const closing_sq_floor: f32 = 1e-24;3637/// The margin tree box tests add on every side, for coordinates no larger than38/// `magnitude` in absolute value. Sixteen units in the last place of the39/// largest coordinate bound the rounding of a slab or closest-point test.40pub fn boxSlack(magnitude: f32) f32 {41    std.debug.assert(magnitude >= 0);42    return 16 * std.math.floatEps(f32) * magnitude;43}4445test "parallel noise is judged relative to the factors" {46    try std.testing.expect(isParallel(0, 0));47    try std.testing.expect(isParallel(1, 1e12));48    try std.testing.expect(!isParallel(1e-6, 1));49    try std.testing.expect(!isParallel(1e6, 1e12));50}5152test "box slack scales with the coordinate magnitude" {53    try std.testing.expectEqual(@as(f32, 0), boxSlack(0));54    try std.testing.expect(boxSlack(1000) > boxSlack(1));55    try std.testing.expect(boxSlack(1) < 1e-5);56}