Simplify vector calculation for Straight

- Simplify vector calculation
- Place commonly used values outside the loop for calculation
- Fix doc typo

docs/New-or-Enhanced-Logics.md

@@ -757,15 +757,15 @@ Trajectory.Speed=100.0  ; floating point value
   - `Trajectory.Straight.PassDetonate` enables extra detonations when the projectile is traveling. (You can use this when you want the projectile to detonate warheads every other distance/time during the flight.)
     - `Trajectory.Straight.PassDetonateWarhead` defines the warhead detonated by `Trajectory.Straight.PassDetonate`, and `Trajectory.Straight.PassDetonateDamage` defines the damage caused by `Trajectory.Straight.PassDetonateWarhead`.
     - `Trajectory.Straight.PassDetonateDelay` controls the delay for detonating the warhead defined by `Trajectory.Straight.Warhead`.
-    - `Trajectory.Straight.PassDetonateInitialDelay` controls the initial delay for detonating the warhead defined by `Trajectory.Straight.Warhead`.
+    - `Trajectory.Straight.PassDetonateInitialDelay` controls the initial delay for detonating the warhead defined by `Trajectory.Straight.PassDetonateWarhead`.
     - `Trajectory.Straight.PassDetonateLocal` controls whether `Trajectory.Straight.PassDetonateWarhead` and weapon's `Warhead` are always detonate at ground level. It will also no longer restrict vertical velocity of the projectile when using `Trajectory.Straight.ConfineAtHeight`.
   - `Trajectory.Straight.LeadTimeCalculate` controls whether the projectile need to calculate the lead time of the target when firing. Note that this will not affect the facing of the turret.
   - `Trajectory.Straight.OffsetCoord` controls the offsets of the target. Projectile will aim at this position to attack. It also supports `Inaccurate=yes` and `Trajectory.Straight.LeadTimeCalculate=true` on this basis.
     - `Trajectory.Straight.RotateCoord` controls whether to rotate the projectile's firing direction within the angle bisector of `Trajectory.Straight.OffsetCoord` according to the weapon's `Burst`. Set to 0 to disable this function.
     - `Trajectory.Straight.MirrorCoord` controls whether `Trajectory.Straight.OffsetCoord` need to mirror the lateral value to adapt to the current burst index. At the same time, the rotation direction calculated by `Trajectory.Straight.RotateCoord` will also be reversed, and the rotation angle between each adjacent projectile on each side will not change as a result.
     - `Trajectory.Straight.UseDisperseBurst` controls whether the calculation of `Trajectory.Straight.RotateCoord` is based on its superior's `Trajectory.Disperse.WeaponBurst` of the dispersed trajectory, rather than `Burst` of the weapon. If this value is not appropriate, it will result in unsatisfactory visual displays.
     - `Trajectory.Straight.AxisOfRotation` controls the rotation axis when calculating `Trajectory.Straight.RotateCoord`. The axis will rotates with the unit orientation or the vector that from target position to the source position.
-  - `Trajectory.Straight.ProximityImpact` controls the initial proximity fuse times. When there are enough remaining times and the projectile approaches another valid target, it will detonate a warhead defined by `Trajectory.Straight.Warhead` on it. If the times is about to run out, it will also detonate itself at its location. This function can be cancelled by setting to 0. A negative integer means unlimited times. By the way, you can use the weapon's `Warhead` with low versus only to aim at the target, and use the `Trajectory.Straight.ProximityWarhead` to causing actual harm. (You can use this to cause non repeated damage to all units encountered during the flight of the projectile.)
+  - `Trajectory.Straight.ProximityImpact` controls the initial proximity fuse times. When there are enough remaining times and the projectile approaches another valid target, it will detonate a warhead defined by `Trajectory.Straight.ProximityWarhead` on it. If the times is about to run out, it will also detonate itself at its location. This function can be cancelled by setting to 0. A negative integer means unlimited times. By the way, you can use the weapon's `Warhead` with low versus only to aim at the target, and use the `Trajectory.Straight.ProximityWarhead` to causing actual harm. (You can use this to cause non repeated damage to all units encountered during the flight of the projectile.)
     - `Trajectory.Straight.ProximityWarhead` defines the warhead detonated by `Trajectory.Straight.ProximityImpact`, and `Trajectory.Straight.ProximityDamage` defines the damage caused by `Trajectory.Straight.ProximityWarhead`.
     - `Trajectory.Straight.ProximityRadius` controls the range of proximity fuse. It can NOT be set as a negative integer.
     - `Trajectory.Straight.ProximityDirect` controls whether let the target receive damage instead of detonating the warhead.

src/Ext/Bullet/Trajectories/StraightTrajectory.cpp

@@ -787,7 +787,8 @@ void StraightTrajectory::PrepareForDetonateAt(BulletClass* pBullet, HouseClass*
 		return;
 
 	// Step 1: Find valid targets on the ground within range.
-	std::vector<CellClass*> recCellClass = PhobosTrajectoryType::GetCellsInProximityRadius(pBullet, pType->ProximityRadius.Get());
+	const auto radius = pType->ProximityRadius.Get();
+	std::vector<CellClass*> recCellClass = PhobosTrajectoryType::GetCellsInProximityRadius(pBullet, radius);
 	const size_t cellSize = recCellClass.size() * 2;
 	size_t vectSize = cellSize;
 	size_t thisSize = 0;
@@ -798,10 +799,11 @@ void StraightTrajectory::PrepareForDetonateAt(BulletClass* pBullet, HouseClass*
 		static_cast<int>(pBullet->Velocity.Y),
 		static_cast<int>(pBullet->Velocity.Z)
 	};
+	const auto velocitySq = velocityCrd.MagnitudeSquared();
+	const auto pTarget = pBullet->Target;
 
 	std::vector<TechnoClass*> validTechnos;
 	validTechnos.reserve(vectSize);
-	const auto pTarget = pBullet->Target;
 
 	for (const auto& pRecCell : recCellClass)
 	{
@@ -824,19 +826,23 @@ void StraightTrajectory::PrepareForDetonateAt(BulletClass* pBullet, HouseClass*
 			if (!pType->ProximityAllies && pOwner && pOwner->IsAlliedWith(pTechno->Owner) && pTechno != pTarget)
 				continue;
 
-			const auto distanceCrd = pTechno->GetCoords() - pBullet->SourceCoords;
-			const auto locationCrd = (velocityCrd + (pBullet->Location - pBullet->SourceCoords));
-			const auto terminalCrd = distanceCrd - locationCrd;
-			auto distance = locationCrd.MagnitudeSquared(); // Not true distance yet.
+			// Check distance
+			const auto targetCrd = pTechno->GetCoords();
+			const auto pathCrd = targetCrd - pBullet->SourceCoords;
+
+			if (pathCrd * velocityCrd < 0) // In front of the techno
+				continue;
+
+			const auto distanceCrd = targetCrd - pBullet->Location;
+			const auto nextDistanceCrd = distanceCrd - velocityCrd;
 
-			// Between front and back
-			if (distanceCrd * velocityCrd < 0 || terminalCrd * velocityCrd > 0)
+			if (nextDistanceCrd * velocityCrd > 0) // Behind the bullet
 				continue;
 
-			distance = (distance > 1e-10) ? sqrt(distanceCrd.CrossProduct(terminalCrd).MagnitudeSquared() / distance) : distanceCrd.Magnitude();
+			const auto cross = distanceCrd.CrossProduct(nextDistanceCrd).MagnitudeSquared();
+			const auto distance = (velocitySq > 1e-10) ? sqrt(cross / velocitySq) : distanceCrd.Magnitude();
 
-			// Between left and right (cylindrical)
-			if (technoType != AbstractType::Building && distance > pType->ProximityRadius.Get())
+			if (technoType != AbstractType::Building && distance > radius) // In the cylinder
 				continue;
 
 			if (thisSize >= vectSize)
@@ -854,26 +860,35 @@ void StraightTrajectory::PrepareForDetonateAt(BulletClass* pBullet, HouseClass*
 	if (pType->ProximityFlight)
 	{
 		const auto airTracker = &AircraftTrackerClass::Instance;
-		airTracker->FillCurrentVector(MapClass::Instance->GetCellAt(pBullet->Location + velocityCrd * 0.5), static_cast<int>((pType->ProximityRadius.Get() + pType->Trajectory_Speed / 2) / Unsorted::LeptonsPerCell));
+		airTracker->FillCurrentVector(MapClass::Instance->GetCellAt(pBullet->Location + velocityCrd * 0.5),
+			Game::F2I(sqrt(radius * radius + (velocitySq / 4)) / Unsorted::LeptonsPerCell));
 
 		for (auto pTechno = airTracker->Get(); pTechno; pTechno = airTracker->Get())
 		{
 			if (!pTechno->IsAlive || !pTechno->IsOnMap || pTechno->Health <= 0 || pTechno->InLimbo || pTechno->IsSinking)
 				continue;
 
+			// Not directly harming friendly forces
 			if (!pType->ProximityAllies && pOwner && pOwner->IsAlliedWith(pTechno->Owner) && pTechno != pTarget)
 				continue;
 
-			const auto distanceCrd = pTechno->GetCoords() - pBullet->Location;
-			const auto terminalCrd = distanceCrd - velocityCrd;
-			auto distance = velocityCrd.MagnitudeSquared(); // Not true distance yet.
+			// Check distance
+			const auto targetCrd = pTechno->GetCoords();
+			const auto pathCrd = targetCrd - pBullet->SourceCoords;
+
+			if (pathCrd * velocityCrd < 0) // In front of the techno
+				continue;
+
+			const auto distanceCrd = targetCrd - pBullet->Location;
+			const auto nextDistanceCrd = distanceCrd - velocityCrd;
 
-			if (distanceCrd * velocityCrd < 0 || terminalCrd * velocityCrd > 0)
+			if (nextDistanceCrd * velocityCrd > 0) // Behind the bullet
 				continue;
 
-			distance = (distance > 1e-10) ? sqrt(distanceCrd.CrossProduct(terminalCrd).MagnitudeSquared() / distance) : distanceCrd.Magnitude();
+			const auto cross = distanceCrd.CrossProduct(nextDistanceCrd).MagnitudeSquared();
+			const auto distance = (velocitySq > 1e-10) ? sqrt(cross / velocitySq) : distanceCrd.Magnitude();
 
-			if (distance > pType->ProximityRadius.Get())
+			if (distance > radius) // In the cylinder
 				continue;
 
 			if (thisSize >= vectSize)