MathAssertions.TUnit 0.3.0

MathAssertions.TUnit

Scope: Test projects only. Not intended for production code.

TUnit-native math assertion library for .NET. Covers tolerance comparisons, sequences, statistics, linear algebra, number theory, and 3D geometry. NaN-aware, infinity-aware, AOT-compatible, no runtime reflection in the assertion path.

Full documentation, "Why component-wise rather than Euclidean", cookbook, design notes, and roadmap: github.com/JohnVerheij/MathAssertions.TUnit

Status: v0.3.0 (pose renderer)

The mathematical-assertion surface is exposed as fluent extensions over TUnit's Assert.That(value).Method(...). ~85 fluent entry points across twelve adapter classes covering scalar tolerance comparisons, the System.Numerics compound types (vector / quaternion / matrix / plane / complex), double[] / float[] element-wise comparison with null-array guards, sequence properties, descriptive statistics, linear-algebra invariants, integer number theory, and a complete 3D-geometry primitive surface (containment / closest-point distance / intersection / pointcloud aggregates). v0.2.0 adds rich per-component / per-cell delta rendering to every compound IsApproximatelyEqualTo failure message plus HasAxisAngleApproximately on Quaternion. v0.3.0 adds the MathAssertions.Render namespace with PoseRenderer for turning a position / orientation pose into deterministic, snapshot-friendly text.

Install

dotnet add package MathAssertions.TUnit

MathAssertions (the framework-agnostic core) comes transitively. Requirements: TUnit 1.43.11 or later, .NET 10.

The source-generated entry point (IsApproximatelyEqualTo on Vector3) auto-imports via TUnit.Assertions.Extensions. The only additional using you typically need is System.Numerics for the value type itself. If you call MathTolerance.IsApproximatelyEqual directly from a [GenerateAssertion] extension on a private domain type, add MathAssertions to your GlobalUsings.cs:

global using MathAssertions;

Quick start

using System.Numerics;

[Test]
public async Task ComputedPositionIsApproximatelyAtTarget(CancellationToken ct)
{
    Vector3 target = new(0.300f, 0.150f, 0.450f);
    Vector3 actual = SolveTrajectory(input);

    await Assert.That(actual).IsApproximatelyEqualTo(target, tolerance: 1e-3);
}

Entry points

The fluent surface, organized by adapter class:

IsFinite() for double/float is provided by TUnit's built-in DoubleAssertionExtensions/SingleAssertionExtensions; this package does not duplicate it.

Cookbook

Pattern: comparing quaternions

IsApproximatelyEqualTo is component-wise. Two unit quaternions q and -q represent the same physical rotation but fail component-wise comparison. If the production code may emit either sign of a unit quaternion (calibration outputs, slerp interpolation, normalization that picks a sign), use IsRotationallyEquivalentTo:

[Test]
public async Task RotationOutputMatchesExpected(CancellationToken ct)
{
    Quaternion expected = Quaternion.CreateFromAxisAngle(Vector3.UnitY, MathF.PI / 4);
    Quaternion actual = SolveOrientation(input);  // may emit ±expected

    // Component-wise: fails if SolveOrientation returned -expected
    // await Assert.That(actual).IsApproximatelyEqualTo(expected, tolerance: 1e-6);

    // Rotational: treats q and -q as the same rotation
    await Assert.That(actual).IsRotationallyEquivalentTo(expected, tolerance: 1e-6);
}

Use IsApproximatelyEqualTo when component identity matters (serialization roundtrips, exact storage formats). Use IsRotationallyEquivalentTo when geometric meaning matters (physical orientations, rotations applied to vectors).

Pattern: comparing planes

IsApproximatelyEqualTo is component-wise on the plane equation (n.X, n.Y, n.Z, d). The same geometric plane has two valid representations: (n, d) and (-n, -d). If the production code constructs planes via different paths (three-point, normal-and-distance, normal-and-point), the sign of the normal may differ between expected and actual without changing the plane. Use IsGeometricallyEquivalentTo:

[Test]
public async Task GroundPlaneMatchesExpected(CancellationToken ct)
{
    Plane expected = new(Vector3.UnitY, -1.0f);  // y = 1
    Plane actual = ComputeGroundPlane(input);    // could be (UnitY, -1) or (-UnitY, 1)

    await Assert.That(actual).IsGeometricallyEquivalentTo(expected, tolerance: 1e-6);
}

Use IsApproximatelyEqualTo when normal direction is observable in the consumer (winding-aware shading, half-space convention). Use IsGeometricallyEquivalentTo when only the plane's geometry is observable.

Verifying invertible transformations: HasRoundtripIdentity

When a transformation is invertible, the framework-agnostic MathTolerance.HasRoundtripIdentity(double input, Func<double,double> forward, Func<double,double> backward, double tolerance) checks that backward(forward(input)) lands back at input within tolerance. The primitive is double-only on purpose; consumers wrap their own typed inputs.

// Sin / Asin compose back to the input.
await Assert.That(MathTolerance.HasRoundtripIdentity(
    0.42, Math.Sin, Math.Asin, tolerance: 1e-12)).IsTrue();

// Degree / radian conversion.
await Assert.That(MathTolerance.HasRoundtripIdentity(
    45.0,
    d => d * Math.PI / 180.0,
    r => r * 180.0 / Math.PI,
    tolerance: 1e-12)).IsTrue();

For typed inputs (vector / quaternion / serializer pair), compose [GenerateAssertion] on your own type rather than chaining HasRoundtripIdentity. The primitive is intentionally double-only so the family does not lock in a particular cross-type roundtrip surface.

Pattern: detecting an unpopulated zero quaternion

A zero-valued quaternion (all four components zero, length zero) is a valid in-memory state but not a valid rotation. Common cases: a protobuf default for an unpopulated Quaternion field, an in-construction calibration output that has not yet been written, an explicit "no rotation set" sentinel.

The BCL exposes Quaternion.Zero. The existing component-wise comparison handles the assertion without a specialized API:

[Test]
public async Task UnpopulatedRotationIsZeroSentinel(CancellationToken ct)
{
    Quaternion actual = ReadRotationFromMessage(message);

    await Assert.That(actual).IsApproximatelyEqualTo(Quaternion.Zero, tolerance: 1e-9);
}

This reads as "the quaternion is approximately the zero quaternion" and fails for any rotation including the identity rotation Quaternion.Identity (which has W = 1).

NaN and infinity semantics

The fluent extensions match the underlying MathTolerance semantics, which match TUnit's IsCloseTo primitive:

For compound types (Vector2/Vector3/Vector4, Quaternion, Matrix4x4, Plane, Complex), every component pair is evaluated against this table; the assertion passes iff every pair passes.

Extending to your own types

Add tolerance assertions for your own domain types via a one-line [GenerateAssertion] extension calling MathTolerance.IsApproximatelyEqual on each component. The package never sees your private types.

using MathAssertions;
using TUnit.Assertions.Attributes;

file static class PositionAssertions
{
    [GenerateAssertion(
        ExpectationMessage = "to be approximately equal to {expected} within tolerance {tolerance}",
        InlineMethodBody = true)]
    public static bool IsApproximatelyEqualTo(this MyPosition value, MyPosition expected, double tolerance)
        => MathTolerance.IsApproximatelyEqual(value.AsVector3(), expected.AsVector3(), tolerance);
}

Failure diagnostics

On a failed assertion, the exception message renders the actual Vector3 against the expected and the supplied tolerance:

Expected:
  to be approximately equal to <1, 2, 99> component-wise within tolerance 0.001

Actual:
  <1, 2, 3>

Full failure-diagnostics examples, design notes, stability intent, and roadmap on GitHub.

Family

Part of an assertion family for TUnit:

• LogAssertions.TUnit
• SnapshotAssertions.TUnit
• TimeAssertions.TUnit

License

MIT. Copyright (c) 2026 John Verheij.