fix(math): align deterministic Bezier operations

Core/GameEngine/Include/Common/BezierSegment.h

@@ -40,7 +40,34 @@
 
 #define USUAL_TOLERANCE 1.0f
 
-#ifndef SAGE_USE_GLM
+#ifdef SAGE_USE_GLM
+// GeneralsX @bugfix Copilot 15/08/2026 Match D3DX operation ordering for deterministic Bezier trajectories.
+class BezierMath
+{
+public:
+	static glm::vec4 GLMVec4Transform(const glm::vec4& v, const glm::mat4& m)
+	{
+#if USE_DETERMINISTIC_MATH
+		return glm::vec4(
+			((v.x * m[0][0] + v.y * m[1][0]) + v.z * m[2][0]) + v.w * m[3][0],
+			((v.x * m[0][1] + v.y * m[1][1]) + v.z * m[2][1]) + v.w * m[3][1],
+			((v.x * m[0][2] + v.y * m[1][2]) + v.z * m[2][2]) + v.w * m[3][2],
+			((v.x * m[0][3] + v.y * m[1][3]) + v.z * m[2][3]) + v.w * m[3][3]);
+#else
+		return m * v;
+#endif
+	}
+
+	static float GLMVec4Dot(const glm::vec4& a, const glm::vec4& b)
+	{
+#if USE_DETERMINISTIC_MATH
+		return ((a.x * b.x + a.y * b.y) + a.z * b.z) + a.w * b.w;
+#else
+		return glm::dot(a, b);
+#endif
+	}
+};
+#else
 class BezierMath
 {
 public:

Core/GameEngine/Source/Common/Bezier/BezFwdIterator.cpp

@@ -73,9 +73,9 @@ void BezFwdIterator::start()
 	glm::vec4 pz(mBezSeg.m_controlPoints[0].z, mBezSeg.m_controlPoints[1].z, mBezSeg.m_controlPoints[2].z, mBezSeg.m_controlPoints[3].z);
 
 	glm::vec4 cVec[3];
-	cVec[0] = BezierSegment::s_bezBasisMatrix * px;
-	cVec[1] = BezierSegment::s_bezBasisMatrix * py;
-	cVec[2] = BezierSegment::s_bezBasisMatrix * pz;
+	cVec[0] = BezierMath::GLMVec4Transform(px, BezierSegment::s_bezBasisMatrix);
+	cVec[1] = BezierMath::GLMVec4Transform(py, BezierSegment::s_bezBasisMatrix);
+	cVec[2] = BezierMath::GLMVec4Transform(pz, BezierSegment::s_bezBasisMatrix);
 #endif
 
 	mCurrPoint = mBezSeg.m_controlPoints[0];
@@ -129,4 +129,3 @@ void BezFwdIterator::next()
 
 	++mStep;
 }
-

Core/GameEngine/Source/Common/Bezier/BezierSegment.cpp

@@ -128,11 +128,11 @@ void BezierSegment::evaluateBezSegmentAtT(Real tValue, Coord3D *outResult) const
 	glm::vec4 yCoords(m_controlPoints[0].y, m_controlPoints[1].y, m_controlPoints[2].y, m_controlPoints[3].y);
 	glm::vec4 zCoords(m_controlPoints[0].z, m_controlPoints[1].z, m_controlPoints[2].z, m_controlPoints[3].z);
 
-	glm::vec4 tResult = BezierSegment::s_bezBasisMatrix * tVec;
+	glm::vec4 tResult = BezierMath::GLMVec4Transform(tVec, BezierSegment::s_bezBasisMatrix);
 
-	outResult->x = glm::dot(xCoords, tResult);
-	outResult->y = glm::dot(yCoords, tResult);
-	outResult->z = glm::dot(zCoords, tResult);
+	outResult->x = BezierMath::GLMVec4Dot(xCoords, tResult);
+	outResult->y = BezierMath::GLMVec4Dot(yCoords, tResult);
+	outResult->z = BezierMath::GLMVec4Dot(zCoords, tResult);
 #endif
 }
 

docs/WORKLOG/2026-08-DIARY.md

@@ -1,5 +1,10 @@
 # August 2026
 
+## 15/08/2026
+### Match Cross-Platform Bezier Trajectories
+- Fixed deterministic projectile paths using GLM's platform-dependent matrix and dot-product evaluation order while Windows used explicitly ordered D3DX-compatible scalar operations.
+- Applied the same operation order to GLM transforms and dot products so projectile positions remain bit-identical across macOS and Windows.
+
 ## 14/08/2026
 ### Restore Windows LAN Map Compatibility
 - Kept spaces literal when serializing map names so TheSuperHackers Windows builds can resolve official maps such as Twilight Flame.