fix(gtx): extractRealComponent returns the canonical (non-negative) real part

[Osamaali313]

Problem

glm::extractRealComponent reconstructs a quaternion's real component from its imaginary parts as sqrt(1 - x² - y² - z²), but it returns the negative root:

template<typename T, qualifier Q>
GLM_FUNC_QUALIFIER T extractRealComponent(qua<T, Q> const& q)
{
    T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
    if(w < T(0))
        return T(0);   // clamp: keep the result non-negative...
    else
        return -sqrt(w);   // ...then negate it (?)
}

The function is internally contradictory: it clamps the radicand with if (w < 0) return 0 — signalling a non-negative magnitude — and then returns -sqrt(w), which is always ≤ 0. So for any canonical unit quaternion (w ≥ 0) it returns the wrong sign:

quaternion (w, x, y, z)	true real part	extractRealComponent
60° about X → (0.8660254, 0.5, 0, 0)	+0.8660254	−0.8660254
identity → (1, 0, 0, 0)	+1	−1

This contradicts the documented purpose ("Extract the real component of a quaternion") and the standard reconstruction convention (the canonical real part of a unit quaternion is the non-negative root — the same w = sqrt(1 - x² - y² - z²) used when reconstructing a quaternion stored as x/y/z only).

Fix

Return the positive root (sqrt(w)).

Tests

The function had no test coverage (which is why the sign error went unnoticed). Added test_extractRealComponent to test/gtx/gtx_quaternion.cpp: it builds a canonical unit quaternion, extracts the real component, and asserts it recovers the true w and is non-negative. (Fails on the old -sqrt, passes on the fix.)

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Fixes the sign of glm::extractRealComponent so it returns the canonical (non-negative) real component, and adds a regression test to prevent returning the negated value.

Changes:

• Corrected extractRealComponent to return sqrt(w) instead of -sqrt(w) for valid inputs.
• Added a new unit test validating that extraction returns a non-negative w and matches the canonical quaternion.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.

File	Description
test/gtx/gtx_quaternion.cpp	Adds a regression test covering extractRealComponent’s expected (non-negative) output.
glm/gtx/quaternion.inl	Fixes the sign bug in extractRealComponent by removing the unintended negation.

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[Osamaali313]

Thanks @copilot — done in 8b954a7. The test now builds the quaternion with glm::angleAxis(glm::radians(60.0f), glm::vec3(1, 0, 0)) and compares the extracted real component against glm::cos(Angle * 0.5f), so there are no magic-number literals and the intent is self-describing. (angleAxis is already used elsewhere in this test file, so no new include is needed.)