diff --git a/source/graphics/ModelDef.cpp b/source/graphics/ModelDef.cpp
index ea7f157da9..5be0cb61b4 100644
--- a/source/graphics/ModelDef.cpp
+++ b/source/graphics/ModelDef.cpp
@@ -1,4 +1,4 @@
-/* Copyright (C) 2021 Wildfire Games.
+/* Copyright (C) 2022 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -15,17 +15,14 @@
  * along with 0 A.D.  If not, see <http://www.gnu.org/licenses/>.
  */
 
-/*
- * Defines a raw 3d model.
- */
-
 #include "precompiled.h"
 
 #include "ModelDef.h"
+
 #include "graphics/SkeletonAnimDef.h"
 #include "lib/sysdep/arch/x86_x64/simd.h"
-#include "ps/FileIo.h"
 #include "maths/Vector4D.h"
+#include "ps/FileIo.h"
 
 #if COMPILER_HAS_SSE
 # include <xmmintrin.h>
@@ -203,10 +200,11 @@ static void SkinPointsAndNormalsSSE(
 		const CMatrix3D& mtx = newPoseMatrices[blendIndices[j]];
 
 		// Loads matrix to xmm registers.
-		col0 = _mm_load_ps(mtx._data);
-		col1 = _mm_load_ps(mtx._data + 4);
-		col2 = _mm_load_ps(mtx._data + 8);
-		col3 = _mm_load_ps(mtx._data + 12);
+		const float* data = mtx.AsFloatArray();
+		col0 = _mm_load_ps(data);
+		col1 = _mm_load_ps(data + 4);
+		col2 = _mm_load_ps(data + 8);
+		col3 = _mm_load_ps(data + 12);
 
 		// Loads and computes vertex coordinates.
 		vec0 = _mm_load1_ps(&vtx.m_Coords.X);	// v0 = [x, x, x, x]
diff --git a/source/graphics/TerrainTextureEntry.cpp b/source/graphics/TerrainTextureEntry.cpp
index 24a5521130..83fec62102 100644
--- a/source/graphics/TerrainTextureEntry.cpp
+++ b/source/graphics/TerrainTextureEntry.cpp
@@ -185,8 +185,3 @@ void CTerrainTextureEntry::BuildBaseColor()
 		m_BaseColorValid = true;
 	}
 }
-
-const float* CTerrainTextureEntry::GetTextureMatrix() const
-{
-	return &m_TextureMatrix._11;
-}
diff --git a/source/graphics/TerrainTextureEntry.h b/source/graphics/TerrainTextureEntry.h
index b6722dfba7..4ae1647b76 100644
--- a/source/graphics/TerrainTextureEntry.h
+++ b/source/graphics/TerrainTextureEntry.h
@@ -50,7 +50,7 @@ public:
 
 	// Returns a matrix of the form [c 0 -s 0; -s 0 -c 0; 0 0 0 0; 0 0 0 1]
 	// mapping world-space (x,y,z,1) coordinates onto (u,v,0,1) texcoords
-	const float* GetTextureMatrix() const;
+	const CMatrix3D& GetTextureMatrix() const { return m_TextureMatrix; }
 
 	// Used in Atlas to retrieve a texture for previews. Can't use textures
 	// directly because they're required on CPU side. Another solution is to
diff --git a/source/graphics/TerritoryTexture.cpp b/source/graphics/TerritoryTexture.cpp
index 836dcd800a..b84db8cd6c 100644
--- a/source/graphics/TerritoryTexture.cpp
+++ b/source/graphics/TerritoryTexture.cpp
@@ -63,10 +63,10 @@ Renderer::Backend::GL::CTexture* CTerritoryTexture::GetTexture()
 	return m_Texture.get();
 }
 
-const float* CTerritoryTexture::GetTextureMatrix()
+const CMatrix3D& CTerritoryTexture::GetTextureMatrix()
 {
 	ENSURE(!UpdateDirty());
-	return &m_TextureMatrix._11;
+	return m_TextureMatrix;
 }
 
 const CMatrix3D& CTerritoryTexture::GetMinimapTextureMatrix()
diff --git a/source/graphics/TerritoryTexture.h b/source/graphics/TerritoryTexture.h
index eddf4c71db..a61ab48cef 100644
--- a/source/graphics/TerritoryTexture.h
+++ b/source/graphics/TerritoryTexture.h
@@ -47,7 +47,7 @@ public:
 	 * coordinates, in the form expected by a matrix uniform.
 	 * This must only be called after UpdateIfNeeded.
 	 */
-	const float* GetTextureMatrix();
+	const CMatrix3D& GetTextureMatrix();
 
 	/**
 	 * Returns a matrix to map (0,0)-(1,1) texture coordinates onto texture
diff --git a/source/maths/Matrix3D.h b/source/maths/Matrix3D.h
index 92b77fd8a3..0cbea2b9a8 100644
--- a/source/maths/Matrix3D.h
+++ b/source/maths/Matrix3D.h
@@ -1,4 +1,4 @@
-/* Copyright (C) 2021 Wildfire Games.
+/* Copyright (C) 2022 Wildfire Games.
  * This file is part of 0 A.D.
  *
  * 0 A.D. is free software: you can redistribute it and/or modify
@@ -28,7 +28,6 @@
 
 class CQuaternion;
 
-/////////////////////////////////////////////////////////////////////////
 // CMatrix3D: a 4x4 matrix class for common operations in 3D
 class CMatrix3D
 {
@@ -37,8 +36,10 @@ public:
 	// or via a flat or 2d array
 	// NOTE: _xy means row x, column y in the mathematical notation of this matrix, so don't be
 	// fooled by the way they're listed below
-	union {
-		struct {
+	union
+	{
+		struct
+		{
 			float _11, _21, _31, _41;
 			float _12, _22, _32, _42;
 			float _13, _23, _33, _43;
@@ -320,6 +321,20 @@ public:
 	// rotate a vector by the transpose of this matrix
 	void RotateTransposed(const CVector3D& vector,CVector3D& result) const;
 	CVector3D RotateTransposed(const CVector3D& vector) const;
+
+	// Returns 16 element array of floats, e.g. for mat4 uniforms.
+	const float* AsFloatArray() const
+	{
+		// Additional check to prevent a weird compiler has a different
+		// alignement for an array and a class members.
+		static_assert(
+			sizeof(CMatrix3D) == sizeof(float) * 16u &&
+			offsetof(CMatrix3D, _data) == 0 &&
+			offsetof(CMatrix3D, _11) == 0 &&
+			offsetof(CMatrix3D, _44) == sizeof(float) * 15u,
+			"CMatrix3D should be properly layouted to use AsFloatArray");
+		return _data;
+	}
 };
 
 #endif // INCLUDED_MATRIX3D
diff --git a/source/renderer/backend/gl/ShaderProgram.cpp b/source/renderer/backend/gl/ShaderProgram.cpp
index 33fb33ce59..1ad59bda55 100644
--- a/source/renderer/backend/gl/ShaderProgram.cpp
+++ b/source/renderer/backend/gl/ShaderProgram.cpp
@@ -781,7 +781,7 @@ public:
 		if (id.first != -1)
 		{
 			if (id.second == GL_FLOAT_MAT4)
-				glUniformMatrix4fv(id.first, 1, GL_FALSE, &v._11);
+				glUniformMatrix4fv(id.first, 1, GL_FALSE, v.AsFloatArray());
 			else
 				LOGERROR("CShaderProgramGLSL::Uniform(): Invalid uniform type (expected mat4)");
 		}