From f3fbc8b3cafa9656e0f12ac03b4ad82ea60b7f00 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Fri, 25 Apr 2025 22:42:30 +0200
Subject: [PATCH] Math: make Vector::isZero() equivalent to comparison to a
 zero vector.

The original behavior was extremely imprecise. I remember hitting this
in the UI library, where it was happily telling me that a vector is
zero, and I spent ages debugging only to replace it with an equality
comparison that behaved correctly. Let's fix that properly.
---
 doc/changelog.dox                   |  4 ++++
 src/Magnum/Math/Test/VectorTest.cpp | 13 +++++++++++--
 src/Magnum/Math/Vector.h            | 26 +++++++-------------------
 3 files changed, 22 insertions(+), 21 deletions(-)

diff --git a/doc/changelog.dox b/doc/changelog.dox
index cd146abc8..abd11a7bb 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -1252,6 +1252,10 @@ See also:
     @cpp transformation.rotationScaling().inverted().transposed() @ce every
     time, it's just corrected to return an inverse transpose instead of a
     @ref Math::Matrix::cofactor() of the upper 3x3 matrix.
+-   Changed @ref Math::Vector::isZero() to have exactly the same behavior as
+    comparing to a zero vector, as those operations should be interchangeable.
+    Before the function returned @cpp true @ce for values up to @cpp 0.003f @ce
+    in case of 32-bit floats which was extremely imprecise.
 -   Fixed an assertion when using @ref MeshTools::removeDuplicates() on an
     interleaved @ref Trade::MeshData that included padding at the beginning or
     end of each vertex
diff --git a/src/Magnum/Math/Test/VectorTest.cpp b/src/Magnum/Math/Test/VectorTest.cpp
index b325eba59..21970501b 100644
--- a/src/Magnum/Math/Test/VectorTest.cpp
+++ b/src/Magnum/Math/Test/VectorTest.cpp
@@ -415,9 +415,18 @@ void VectorTest::convert() {
 }
 
 void VectorTest::isZeroFloat() {
-    CORRADE_VERIFY(!Vector3(0.01f, 0.0f, 0.0f).isZero());
-    CORRADE_VERIFY(Vector3(0.0f, Math::TypeTraits<float>::epsilon()/2.0f, 0.0f).isZero());
+    /* Zero vector is zero */
     CORRADE_VERIFY(Vector3(0.0f, 0.0f, 0.0f).isZero());
+
+    /* Small vector is not */
+    CORRADE_VERIFY(!Vector3(0.01f, 0.0f, 0.0f).isZero());
+
+    /* Should behave the same as comparison to a zero Vector3 */
+    CORRADE_VERIFY(Vector3(0.0f, Math::TypeTraits<float>::epsilon()*0.9f, 0.0f).isZero());
+    CORRADE_VERIFY(Vector3(0.0f, Math::TypeTraits<float>::epsilon()*0.9f, 0.0f) == Vector3{});
+
+    CORRADE_VERIFY(!Vector3(0.0f, Math::TypeTraits<float>::epsilon(), 0.0f).isZero());
+    CORRADE_VERIFY(Vector3(0.0f, Math::TypeTraits<float>::epsilon(), 0.0f) != Vector3{});
 }
 
 void VectorTest::isZeroInteger() {
diff --git a/src/Magnum/Math/Vector.h b/src/Magnum/Math/Vector.h
index 400acf612..299804f99 100644
--- a/src/Magnum/Math/Vector.h
+++ b/src/Magnum/Math/Vector.h
@@ -81,20 +81,6 @@ namespace Implementation {
         return T((U(1) - t)*a + t*b);
     }
 
-    template<bool integral> struct IsZero;
-    template<> struct IsZero<false> {
-        template<std::size_t size, class T> bool operator()(const Vector<size, T>& vec) const {
-            /* Proper comparison should be with epsilon^2, but the value is not
-               representable in given precision. Comparing to epsilon instead. */
-            return std::abs(vec.dot()) < TypeTraits<T>::epsilon();
-        }
-    };
-    template<> struct IsZero<true> {
-        template<std::size_t size, class T> bool operator()(const Vector<size, T>& vec) const {
-            return vec == Vector<size, T>{};
-        }
-    };
-
     /* Used to make friends to speed up debug builds */
     template<std::size_t, class> struct MatrixDeterminant;
     /* To make gather() / scatter() faster */
@@ -360,13 +346,15 @@ template<std::size_t size, class T> class Vector {
         /**
          * @brief Whether the vector is zero
          *
-         * @f[
-         *      |\boldsymbol a \cdot \boldsymbol a - 0| < \epsilon^2 \cong \epsilon
-         * @f]
-         * @see @ref dot(), @ref normalized()
+         * Equivalent to @ref operator==() with a default-constructed vector.
+         * Done using @ref TypeTraits::equals(), i.e. with fuzzy compare for
+         * floating-point types.
          */
         bool isZero() const {
-            return Implementation::IsZero<std::is_integral<T>::value>{}(*this);
+            for(std::size_t i = 0; i != size; ++i)
+                if(!TypeTraits<T>::equals(_data[i], T()))
+                    return false;
+            return true;
         }
 
         /**