diff --git a/src/actor.h b/src/actor.h
index 18d4cf155d..2de96d84c8 100644
--- a/src/actor.h
+++ b/src/actor.h
@@ -818,22 +818,28 @@ public:
 		return ( abs(X() - other->X()) < blockdist && abs(Y() - other->Y()) < blockdist);
 	}
 
-	// 'absolute' is reserved for a linked portal implementation which needs
-	// to distinguish between portal-aware and portal-unaware distance calculation.
-	fixed_t AproxDistance(AActor *other, bool absolute = false)
-	{
-		return P_AproxDistance(X() - other->X(), Y() - other->Y());
-	}
-
-	// same with 'ref' here.
-	fixed_t AproxDistance(fixed_t otherx, fixed_t othery, AActor *ref = NULL)
+	fixed_t AproxDistance(fixed_t otherx, fixed_t othery)
 	{
 		return P_AproxDistance(X() - otherx, Y() - othery);
 	}
 
+	fixed_t AngleTo(fixed_t otherx, fixed_t othery)
+	{
+		return R_PointToAngle2(X(), Y(), otherx, othery);
+	}
+
+	// 'absolute' is reserved for a linked portal implementation which needs
+	// to distinguish between portal-aware and portal-unaware distance calculation.
+	fixed_t AproxDistance(AActor *other, bool absolute = false)
+	{
+		fixedvec3 otherpos = absolute ? other->Pos() : other->PosRelative(this);
+		return P_AproxDistance(X() - otherpos.x, Y() - otherpos.y);
+	}
+
 	fixed_t AproxDistance(AActor *other, fixed_t xadd, fixed_t yadd, bool absolute = false)
 	{
-		return P_AproxDistance(X() - other->X() + xadd, Y() - other->Y() + yadd);
+		fixedvec3 otherpos = absolute ? other->Pos() : other->PosRelative(this);
+		return P_AproxDistance(X() - otherpos.x + xadd, Y() - otherpos.y + yadd);
 	}
 
 	fixed_t AproxDistance3D(AActor *other, bool absolute = false)
@@ -844,18 +850,21 @@ public:
 	// more precise, but slower version, being used in a few places
 	fixed_t Distance2D(AActor *other, bool absolute = false)
 	{
-		return xs_RoundToInt(TVector2<double>(X() - other->X(), Y() - other->Y()).Length());
+		fixedvec3 otherpos = absolute ? other->Pos() : other->PosRelative(this);
+		return xs_RoundToInt(TVector2<double>(X() - otherpos.x, Y() - otherpos.y).Length());
 	}
 
 	// a full 3D version of the above
 	fixed_t Distance3D(AActor *other, bool absolute = false)
 	{
-		return xs_RoundToInt(TVector3<double>(X() - other->X(), Y() - other->Y(), Z() - other->Z()).Length());
+		fixedvec3 otherpos = absolute ? other->Pos() : other->PosRelative(this);
+		return xs_RoundToInt(TVector3<double>(X() - otherpos.x, Y() - otherpos.y, Z() - otherpos.z).Length());
 	}
 
-	angle_t AngleTo(AActor *other, bool absolute = false) const
+	angle_t AngleTo(AActor *other, bool absolute = false)
 	{
-		return R_PointToAngle2(X(), Y(), other->X(), other->Y());
+		fixedvec3 otherpos = absolute ? other->Pos() : other->PosRelative(this);
+		return R_PointToAngle2(X(), Y(), otherpos.x, otherpos.y);
 	}
 
 	angle_t AngleTo(AActor *other, fixed_t oxofs, fixed_t oyofs, bool absolute = false) const
@@ -863,53 +872,71 @@ public:
 		return R_PointToAngle2(X(), Y(), other->X() + oxofs, other->Y() + oyofs);
 	}
 
-	fixed_t AngleTo(fixed_t otherx, fixed_t othery, AActor *ref = NULL)
-	{
-		return R_PointToAngle2(X(), Y(), otherx, othery);
-	}
-
-	fixed_t AngleXYTo(fixed_t myx, fixed_t myy, AActor *other, bool absolute = false)
-	{
-		return R_PointToAngle2(myx, myy, other->X(), other->Y());
-	}
-
 	fixedvec2 Vec2To(AActor *other) const
 	{
-		fixedvec2 ret = { other->X() - X(), other->Y() - Y() };
+		fixedvec3 otherpos = other->PosRelative(this);
+		fixedvec2 ret = { otherpos.x - X(), otherpos.y - Y() };
 		return ret;
 	}
 
 	fixedvec3 Vec3To(AActor *other) const
 	{
-		fixedvec3 ret = { other->X() - X(), other->Y() - Y(), other->Z() - Z() };
+		fixedvec3 otherpos = other->PosRelative(this);
+		fixedvec3 ret = { otherpos.x - X(), otherpos.y - Y(), otherpos.z - Z() };
 		return ret;
 	}
 
-	fixedvec2 Vec2Offset(fixed_t dx, fixed_t dy, bool absolute = false) const
+	fixedvec2 Vec2Offset(fixed_t dx, fixed_t dy, bool absolute = false)
 	{
-		fixedvec2 ret = { X() + dx, Y() + dy };
-		return ret;
+		if (absolute)
+		{
+			fixedvec2 ret = { X() + dx, Y() + dy };
+			return ret;
+		}
+		else return P_GetOffsetPosition(this, dx, dy);
 	}
 
 
-	fixedvec2 Vec2Angle(fixed_t length, angle_t angle, bool absolute = false) const
+	fixedvec2 Vec2Angle(fixed_t length, angle_t angle, bool absolute = false)
 	{
-		fixedvec2 ret = { X() + FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]),
-						  Y() + FixedMul(length, finesine[angle >> ANGLETOFINESHIFT]) };
-		return ret;
+		if (absolute)
+		{
+			fixedvec2 ret = { X() + FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]),
+							  Y() + FixedMul(length, finesine[angle >> ANGLETOFINESHIFT]) };
+			return ret;
+		}
+		else return P_GetOffsetPosition(this, FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]), FixedMul(length, finesine[angle >> ANGLETOFINESHIFT]));
 	}
 
-	fixedvec3 Vec3Offset(fixed_t dx, fixed_t dy, fixed_t dz, bool absolute = false) const
+	fixedvec3 Vec3Offset(fixed_t dx, fixed_t dy, fixed_t dz, bool absolute = false)
 	{
-		fixedvec3 ret = { X() + dx, Y() + dy, Z() + dz };
-		return ret;
+		if (absolute)
+		{
+			fixedvec3 ret = { X() + dx, Y() + dy, Z() + dz };
+			return ret;
+		}
+		else
+		{
+			fixedvec2 op = P_GetOffsetPosition(this, dx, dy);
+			fixedvec3 pos = { op.x, op.y, Z() + dz };
+			return pos;
+		}
 	}
 
-	fixedvec3 Vec3Angle(fixed_t length, angle_t angle, fixed_t dz, bool absolute = false) const
+	fixedvec3 Vec3Angle(fixed_t length, angle_t angle, fixed_t dz, bool absolute = false)
 	{
-		fixedvec3 ret = { X() + FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]),
+		if (absolute)
+		{
+			fixedvec3 ret = { X() + FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]),
 						  Y() + FixedMul(length, finesine[angle >> ANGLETOFINESHIFT]), Z() + dz };
-		return ret;
+			return ret;
+		}
+		else
+		{
+			fixedvec2 op = P_GetOffsetPosition(this, FixedMul(length, finecosine[angle >> ANGLETOFINESHIFT]), FixedMul(length, finesine[angle >> ANGLETOFINESHIFT]));
+			fixedvec3 pos = { op.x, op.y, Z() + dz };
+			return pos;
+		}
 	}
 
 	void ClearInterpolation();
@@ -1190,7 +1217,7 @@ public:
 		return __pos;
 	}
 
-	fixedvec3 PosRelative(AActor *other) const;
+	fixedvec3 PosRelative(const AActor *other) const;
 	fixedvec3 PosRelative(sector_t *sec) const;
 	fixedvec3 PosRelative(line_t *line) const;
 
diff --git a/src/g_hexen/a_korax.cpp b/src/g_hexen/a_korax.cpp
index b0e57b618e..c68fce87b4 100644
--- a/src/g_hexen/a_korax.cpp
+++ b/src/g_hexen/a_korax.cpp
@@ -513,7 +513,7 @@ AActor *P_SpawnKoraxMissile (fixed_t x, fixed_t y, fixed_t z,
 	z -= source->floorclip;
 	th = Spawn (type, x, y, z, ALLOW_REPLACE);
 	th->target = source; // Originator
-	an = source->AngleXYTo(x, y, dest);
+	an = th->AngleTo(dest);
 	if (dest->flags & MF_SHADOW)
 	{ // Invisible target
 		an += pr_kmissile.Random2()<<21;
@@ -522,7 +522,7 @@ AActor *P_SpawnKoraxMissile (fixed_t x, fixed_t y, fixed_t z,
 	an >>= ANGLETOFINESHIFT;
 	th->velx = FixedMul (th->Speed, finecosine[an]);
 	th->vely = FixedMul (th->Speed, finesine[an]);
-	dist = dest->AproxDistance (x, y, source) / th->Speed;
+	dist = dest->AproxDistance (th) / th->Speed;
 	if (dist < 1)
 	{
 		dist = 1;
diff --git a/src/namedef.h b/src/namedef.h
index 83f4aca9b0..fc0ebad243 100644
--- a/src/namedef.h
+++ b/src/namedef.h
@@ -284,8 +284,18 @@ xx(FRandom)
 xx(Random2)
 xx(RandomPick)
 xx(FRandomPick)
+xx(Exp)
+xx(Log10)
+xx(Ceil)
+xx(ACos)
+xx(ASin)
+xx(ATan)
 xx(Cos)
 xx(Sin)
+xx(Tan)
+xx(CosH)
+xx(SinH)
+xx(TanH)
 xx(Alpha)
 xx(Angle)
 xx(Args)
@@ -322,6 +332,7 @@ xx(Radius)
 xx(ReactionTime)
 xx(MeleeRange)
 xx(Speed)
+xx(Clamp)
 
 // Various actor names which are used internally
 xx(MapSpot)
diff --git a/src/p_maputl.cpp b/src/p_maputl.cpp
index eee5167ce8..67c2303e79 100644
--- a/src/p_maputl.cpp
+++ b/src/p_maputl.cpp
@@ -856,7 +856,7 @@ bool FMultiBlockLinesIterator::Next(FMultiBlockLinesIterator::CheckResult *item)
 
 void FMultiBlockLinesIterator::startIteratorForGroup(int group)
 {
-	offset = Displacements(basegroup, group);
+	offset = Displacements.getOffset(basegroup, group);
 	offset.x += checkpoint.x;
 	offset.y += checkpoint.y;
 	bbox.setBox(offset.x, offset.y, checkpoint.z);
@@ -1088,7 +1088,7 @@ bool FMultiBlockThingsIterator::Next(FMultiBlockThingsIterator::CheckResult *ite
 	if (thing != NULL)
 	{
 		item->thing = thing;
-		item->position = checkpoint + Displacements(basegroup, thing->Sector->PortalGroup);
+		item->position = checkpoint + Displacements.getOffset(basegroup, thing->Sector->PortalGroup);
 		item->portalflags = portalflags;
 		return true;
 	}
@@ -1127,7 +1127,7 @@ bool FMultiBlockThingsIterator::Next(FMultiBlockThingsIterator::CheckResult *ite
 
 void FMultiBlockThingsIterator::startIteratorForGroup(int group)
 {
-	fixedvec2 offset = Displacements(basegroup, group);
+	fixedvec2 offset = Displacements.getOffset(basegroup, group);
 	offset.x += checkpoint.x;
 	offset.y += checkpoint.y;
 	bbox.setBox(offset.x, offset.y, checkpoint.z);
diff --git a/src/p_sectors.cpp b/src/p_sectors.cpp
index 756495ac81..8c21ff5fff 100644
--- a/src/p_sectors.cpp
+++ b/src/p_sectors.cpp
@@ -897,9 +897,9 @@ fixed_t sector_t::HighestCeilingAt(fixed_t x, fixed_t y, sector_t **resultsec)
 	// Continue until we find a blocking portal or a portal below where we actually are.
 	while (!check->PortalBlocksMovement(ceiling) && planeheight < check->SkyBoxes[ceiling]->threshold)
 	{
-		FDisplacement &disp = check->CeilingDisplacement();
-		x += disp.pos.x;
-		y += disp.pos.y;
+		fixedvec2 pos = check->CeilingDisplacement();
+		x += pos.x;
+		y += pos.y;
 		planeheight = check->SkyBoxes[ceiling]->threshold;
 		check = P_PointInSector(x, y);
 	}
@@ -921,9 +921,9 @@ fixed_t sector_t::LowestFloorAt(fixed_t x, fixed_t y, sector_t **resultsec)
 	// Continue until we find a blocking portal or a portal above where we actually are.
 	while (!check->PortalBlocksMovement(floor) && planeheight > check->SkyBoxes[floor]->threshold)
 	{
-		FDisplacement &disp = check->FloorDisplacement();
-		x += disp.pos.x;
-		y += disp.pos.y;
+		fixedvec2 pos = check->FloorDisplacement();
+		x += pos.x;
+		y += pos.y;
 		planeheight = check->SkyBoxes[floor]->threshold;
 		check = P_PointInSector(x, y);
 	}
@@ -960,9 +960,9 @@ fixed_t sector_t::NextHighestCeilingAt(fixed_t x, fixed_t y, fixed_t z, int flag
 		}
 		else
 		{
-			FDisplacement &disp = sec->CeilingDisplacement();
-			x += disp.pos.x;
-			y += disp.pos.y;
+			fixedvec2 pos = sec->CeilingDisplacement();
+			x += pos.x;
+			y += pos.y;
 			planeheight = sec->SkyBoxes[ceiling]->threshold;
 			sec = P_PointInSector(x, y);
 		}
@@ -1003,9 +1003,9 @@ fixed_t sector_t::NextLowestFloorAt(fixed_t x, fixed_t y, fixed_t z, int flags,
 		}
 		else
 		{
-			FDisplacement &disp = sec->FloorDisplacement();
-			x += disp.pos.x;
-			y += disp.pos.y;
+			fixedvec2 pos = sec->FloorDisplacement();
+			x += pos.x;
+			y += pos.y;
 			planeheight = sec->SkyBoxes[floor]->threshold;
 			sec = P_PointInSector(x, y);
 		}
diff --git a/src/p_things.cpp b/src/p_things.cpp
index 357fdcef6c..82fe0d5a24 100644
--- a/src/p_things.cpp
+++ b/src/p_things.cpp
@@ -786,7 +786,7 @@ int P_Thing_Warp(AActor *caller, AActor *reference, fixed_t xofs, fixed_t yofs,
 			if (flags & WARPF_WARPINTERPOLATION)
 			{
 				// This just translates the movement but doesn't change the vector
-				fixedvec3 displacedold  = old + Displacements(oldpgroup, caller->Sector->PortalGroup);
+				fixedvec3 displacedold  = old + Displacements.getOffset(oldpgroup, caller->Sector->PortalGroup);
 				caller->PrevX += caller->X() - displacedold.x;
 				caller->PrevY += caller->Y() - displacedold.y;
 				caller->PrevZ += caller->Z() - displacedold.z;
@@ -795,8 +795,8 @@ int P_Thing_Warp(AActor *caller, AActor *reference, fixed_t xofs, fixed_t yofs,
 			else if (flags & WARPF_COPYINTERPOLATION)
 			{
 				// Map both positions of the reference actor to the current portal group
-				fixedvec3 displacedold = old + Displacements(reference->PrevPortalGroup, caller->Sector->PortalGroup);
-				fixedvec3 displacedref = old + Displacements(reference->Sector->PortalGroup, caller->Sector->PortalGroup);
+				fixedvec3 displacedold = old + Displacements.getOffset(reference->PrevPortalGroup, caller->Sector->PortalGroup);
+				fixedvec3 displacedref = old + Displacements.getOffset(reference->Sector->PortalGroup, caller->Sector->PortalGroup);
 				caller->PrevX = caller->X() + displacedold.x - displacedref.x;
 				caller->PrevY = caller->Y() + displacedold.y - displacedref.y;
 				caller->PrevZ = caller->Z() + displacedold.z - displacedref.z;
diff --git a/src/portal.cpp b/src/portal.cpp
index 8446b3151a..2a920f74c0 100644
--- a/src/portal.cpp
+++ b/src/portal.cpp
@@ -121,6 +121,11 @@ static void BuildBlockmap()
 				{
 					PortalBlockmap.containsLines = true;
 					block.portallines.Push(ld);
+					block.neighborContainsLines = true;
+					if (x > 0) PortalBlockmap(x - 1, y).neighborContainsLines = true;
+					if (y > 0) PortalBlockmap(x, y - 1).neighborContainsLines = true;
+					if (x < PortalBlockmap.dx - 1) PortalBlockmap(x + 1, y).neighborContainsLines = true;
+					if (y < PortalBlockmap.dy - 1) PortalBlockmap(x, y + 1).neighborContainsLines = true;
 				}
 			}
 		}
@@ -691,15 +696,23 @@ void P_NormalizeVXVY(fixed_t& vx, fixed_t& vy)
 
 fixedvec2 P_GetOffsetPosition(AActor *actor, fixed_t dx, fixed_t dy)
 {
-	fixedvec3 dest = { actor->X() + dx, actor->Y() + dy };
+	fixedvec2 dest = { actor->X() + dx, actor->Y() + dy };
 	if (PortalBlockmap.containsLines)
 	{
 		fixed_t actx = actor->X(), acty = actor->Y();
+		// Try some easily discoverable early-out first. If we know that the trace cannot possibly find a portal, this saves us from calling the traverser completely for vast parts of the map.
+		if (dx < 128 * FRACUNIT && dy < 128 * FRACUNIT)
+		{
+			fixed_t blockx = GetSafeBlockX(actx - bmaporgx);
+			fixed_t blocky = GetSafeBlockX(acty - bmaporgy);
+			if (blockx < 0 || blocky < 0 || blockx >= bmapwidth || blocky >= bmapheight || !PortalBlockmap(blockx, blocky).neighborContainsLines) return dest;
+		}
+
 		FLinePortalTraverse it;
 		bool repeat;
 		do
 		{
-			it.init(actx, acty, dx, dy, PT_ADDLINES);
+			it.init(actx, acty, dx, dy, PT_ADDLINES|PT_DELTA);
 			intercept_t *in;
 
 			repeat = false;
@@ -1159,9 +1172,9 @@ bool P_CollectConnectedGroups(int startgroup, const fixedvec3 &position, fixed_t
 	while (!wsec->PortalBlocksMovement(sector_t::ceiling) && upperz > wsec->SkyBoxes[sector_t::ceiling]->threshold)
 	{
 		sector_t *othersec = wsec->SkyBoxes[sector_t::ceiling]->Sector;
-		FDisplacement &disp = Displacements(startgroup, othersec->PortalGroup);
-		fixed_t dx = position.x + disp.pos.x;
-		fixed_t dy = position.y + disp.pos.y;
+		fixedvec2 pos = Displacements.getOffset(startgroup, othersec->PortalGroup);
+		fixed_t dx = position.x + pos.x;
+		fixed_t dy = position.y + pos.y;
 		processMask.setBit(othersec->PortalGroup);
 		out.Add(othersec->PortalGroup|FPortalGroupArray::UPPER);
 		wsec = P_PointInSector(dx, dy);	// get upper sector at the exact spot we want to check and repeat
@@ -1171,9 +1184,9 @@ bool P_CollectConnectedGroups(int startgroup, const fixedvec3 &position, fixed_t
 	while (!wsec->PortalBlocksMovement(sector_t::floor) && position.z < wsec->SkyBoxes[sector_t::floor]->threshold)
 	{
 		sector_t *othersec = wsec->SkyBoxes[sector_t::floor]->Sector;
-		FDisplacement &disp = Displacements(startgroup, othersec->PortalGroup);
-		fixed_t dx = position.x + disp.pos.x;
-		fixed_t dy = position.y + disp.pos.y;
+		fixedvec2 pos = Displacements.getOffset(startgroup, othersec->PortalGroup);
+		fixed_t dx = position.x + pos.x;
+		fixed_t dy = position.y + pos.y;
 		processMask.setBit(othersec->PortalGroup|FPortalGroupArray::LOWER);
 		out.Add(othersec->PortalGroup);
 		wsec = P_PointInSector(dx, dy);	// get lower sector at the exact spot we want to check and repeat
diff --git a/src/portal.h b/src/portal.h
index 942a44c4ac..ef8cec98af 100644
--- a/src/portal.h
+++ b/src/portal.h
@@ -30,10 +30,6 @@ struct FDisplacement
 	bool isSet;
 	BYTE indirect;	// just for illustration.
 
-	operator fixedvec2()
-	{
-		return pos;
-	}
 };
 
 struct FDisplacementTable
@@ -55,9 +51,18 @@ struct FDisplacementTable
 
 	FDisplacement &operator()(int x, int y)
 	{
-		if (x == y) return data[0];	// shortcut for the most common case
 		return data[x + size*y];
 	}
+
+	fixedvec2 getOffset(int x, int y) const
+	{
+		if (x == y)
+		{
+			fixedvec2 nulvec = { 0,0 };
+			return nulvec;	// shortcut for the most common case
+		}
+		return data[x + size*y].pos;
+	}
 };
 
 extern FDisplacementTable Displacements;
@@ -72,7 +77,13 @@ extern FDisplacementTable Displacements;
 
 struct FPortalBlock
 {
+	bool neighborContainsLines;	// this is for skipping the traverser and exiting early if we can quickly decide that there's no portals nearby.
 	TArray<line_t*> portallines;
+
+	FPortalBlock()
+	{
+		neighborContainsLines = false;
+	}
 };
 
 struct FPortalBlockmap
@@ -187,5 +198,6 @@ void P_TranslatePortalAngle(line_t* src, line_t* dst, angle_t& angle);
 void P_TranslatePortalZ(line_t* src, line_t* dst, fixed_t& z);
 void P_NormalizeVXVY(fixed_t& vx, fixed_t& vy);
 fixed_t P_PointLineDistance(line_t* line, fixed_t x, fixed_t y);
+fixedvec2 P_GetOffsetPosition(AActor *actor, fixed_t dx, fixed_t dy);
 
 #endif
\ No newline at end of file
diff --git a/src/r_defs.h b/src/r_defs.h
index cac0215aaf..34ba653e61 100644
--- a/src/r_defs.h
+++ b/src/r_defs.h
@@ -838,14 +838,14 @@ struct sector_t
 	}
 
 	// These may only be called if the portal has been validated
-	FDisplacement &FloorDisplacement()
+	fixedvec2 FloorDisplacement()
 	{
-		return Displacements(PortalGroup, SkyBoxes[sector_t::floor]->Sector->PortalGroup);
+		return Displacements.getOffset(PortalGroup, SkyBoxes[sector_t::floor]->Sector->PortalGroup);
 	}
 
-	FDisplacement &CeilingDisplacement()
+	fixedvec2 CeilingDisplacement()
 	{
-		return Displacements(PortalGroup, SkyBoxes[sector_t::ceiling]->Sector->PortalGroup);
+		return Displacements.getOffset(PortalGroup, SkyBoxes[sector_t::ceiling]->Sector->PortalGroup);
 	}
 
 	int GetTerrain(int pos) const;
@@ -1375,24 +1375,24 @@ inline sector_t *P_PointInSector(fixed_t x, fixed_t y)
 	return P_PointInSubsector(x, y)->sector;
 }
 
-inline fixedvec3 AActor::PosRelative(AActor *other) const
+inline fixedvec3 AActor::PosRelative(const AActor *other) const
 {
-	return __pos + Displacements(Sector->PortalGroup, other->Sector->PortalGroup);
+	return __pos + Displacements.getOffset(Sector->PortalGroup, other->Sector->PortalGroup);
 }
 
 inline fixedvec3 AActor::PosRelative(sector_t *sec) const
 {
-	return __pos + Displacements(Sector->PortalGroup, sec->PortalGroup);
+	return __pos + Displacements.getOffset(Sector->PortalGroup, sec->PortalGroup);
 }
 
 inline fixedvec3 AActor::PosRelative(line_t *line) const
 {
-	return __pos + Displacements(Sector->PortalGroup, line->frontsector->PortalGroup);
+	return __pos + Displacements.getOffset(Sector->PortalGroup, line->frontsector->PortalGroup);
 }
 
 inline fixedvec3 PosRelative(const fixedvec3 &pos, line_t *line, sector_t *refsec = NULL)
 {
-	return pos + Displacements(refsec->PortalGroup, line->frontsector->PortalGroup);
+	return pos + Displacements.getOffset(refsec->PortalGroup, line->frontsector->PortalGroup);
 }
 
 inline void AActor::ClearInterpolation()
diff --git a/src/r_utility.cpp b/src/r_utility.cpp
index a97ebc65ec..628310fcec 100644
--- a/src/r_utility.cpp
+++ b/src/r_utility.cpp
@@ -583,7 +583,7 @@ void R_InterpolateView (player_t *player, fixed_t frac, InterpolationViewer *ivi
 	}
 	int oldgroup = R_PointInSubsector(iview->oviewx, iview->oviewy)->sector->PortalGroup;
 	int newgroup = R_PointInSubsector(iview->nviewx, iview->nviewy)->sector->PortalGroup;
-	fixedvec2 disp = Displacements(oldgroup, newgroup);
+	fixedvec2 disp = Displacements.getOffset(oldgroup, newgroup);
 	viewx = iview->oviewx + FixedMul (frac, iview->nviewx - iview->oviewx - disp.x);
 	viewy = iview->oviewy + FixedMul (frac, iview->nviewy - iview->oviewy - disp.y);
 	viewz = iview->oviewz + FixedMul (frac, iview->nviewz - iview->oviewz);
diff --git a/src/thingdef/thingdef_codeptr.cpp b/src/thingdef/thingdef_codeptr.cpp
index e03d674c78..ec876da15e 100644
--- a/src/thingdef/thingdef_codeptr.cpp
+++ b/src/thingdef/thingdef_codeptr.cpp
@@ -323,6 +323,40 @@ DEFINE_ACTION_FUNCTION_PARAMS(AActor, GetDistance)
 	return 0;
 }
 
+//==========================================================================
+//
+// GetSpawnHealth
+//
+//==========================================================================
+DEFINE_ACTION_FUNCTION_PARAMS(AActor, GetSpawnHealth)
+{
+	if (numret > 0)
+	{
+		PARAM_PROLOGUE;
+		PARAM_OBJECT(self, AActor);
+		ret->SetInt(self->SpawnHealth());
+		return 1;
+	}
+	return 0;
+}
+
+//==========================================================================
+//
+// GetGibHealth
+//
+//==========================================================================
+DEFINE_ACTION_FUNCTION_PARAMS(AActor, GetGibHealth)
+{
+	if (numret > 0)
+	{
+		PARAM_PROLOGUE;
+		PARAM_OBJECT(self, AActor);
+		ret->SetInt(self->GetGibHealth());
+		return 1;
+	}
+	return 0;
+}
+
 //===========================================================================
 //
 // __decorate_internal_state__
@@ -5147,7 +5181,7 @@ DEFINE_ACTION_FUNCTION_PARAMS(AActor, A_WolfAttack)
 			if (spawnblood)
 			{
 				P_SpawnBlood(bloodpos, angle, newdam > 0 ? newdam : damage, self->target);
-				P_TraceBleed(newdam > 0 ? newdam : damage, self->target, self->AngleTo(dx, dy, self->target), 0);
+				P_TraceBleed(newdam > 0 ? newdam : damage, self->target, self);
 			}
 		}
 	}
diff --git a/src/thingdef/thingdef_exp.cpp b/src/thingdef/thingdef_exp.cpp
index 7ef93563c1..8cfd737b95 100644
--- a/src/thingdef/thingdef_exp.cpp
+++ b/src/thingdef/thingdef_exp.cpp
@@ -57,6 +57,7 @@ static FxExpression *ParseRandomPick(FScanner &sc, FName identifier, PClassActor
 static FxExpression *ParseRandom2(FScanner &sc, PClassActor *cls);
 static FxExpression *ParseAbs(FScanner &sc, PClassActor *cls);
 static FxExpression *ParseMinMax(FScanner &sc, FName identifier, PClassActor *cls);
+static FxExpression *ParseClamp(FScanner &sc, PClassActor *cls);
 
 //
 // ParseExpression
@@ -381,6 +382,8 @@ static FxExpression *ParseExpression0 (FScanner &sc, PClassActor *cls)
 			case NAME_Min:
 			case NAME_Max:
 				return ParseMinMax(sc, identifier, cls);
+			case NAME_Clamp:
+				return ParseClamp(sc, cls);
 			case NAME_Abs:
 				return ParseAbs(sc, cls);
 			default:
@@ -521,3 +524,23 @@ static FxExpression *ParseMinMax(FScanner &sc, FName identifier, PClassActor *cl
 	}
 	return new FxMinMax(list, identifier, sc);
 }
+
+static FxExpression *ParseClamp(FScanner &sc, PClassActor *cls)
+{
+	FxExpression *src = ParseExpressionM(sc, cls);
+	sc.MustGetToken(',');
+	FxExpression *min = ParseExpressionM(sc, cls);
+	sc.MustGetToken(',');
+	FxExpression *max = ParseExpressionM(sc, cls);
+	sc.MustGetToken(')');
+
+	// Build clamp(a,x,y) as min(max(a,x),y)
+	TArray<FxExpression *> list(2);
+	list.Reserve(2);
+	list[0] = src;
+	list[1] = min;
+	FxExpression *maxexpr = new FxMinMax(list, NAME_Max, sc);
+	list[0] = maxexpr;
+	list[1] = max;
+	return new FxMinMax(list, NAME_Min, sc);
+}
diff --git a/src/thingdef/thingdef_exp.h b/src/thingdef/thingdef_exp.h
index 294399d791..62640e7e13 100644
--- a/src/thingdef/thingdef_exp.h
+++ b/src/thingdef/thingdef_exp.h
@@ -830,19 +830,19 @@ public:
 
 //==========================================================================
 //
-//	FxGlobalFunctionCall
+//	FxFlopFunctionCall
 //
 //==========================================================================
 
-class FxGlobalFunctionCall : public FxExpression
+class FxFlopFunctionCall : public FxExpression
 {
-	FName Name;
+	int Index;
 	FArgumentList *ArgList;
 
 public:
 
-	FxGlobalFunctionCall(FName fname, FArgumentList *args, const FScriptPosition &pos);
-	~FxGlobalFunctionCall();
+	FxFlopFunctionCall(int index, FArgumentList *args, const FScriptPosition &pos);
+	~FxFlopFunctionCall();
 	FxExpression *Resolve(FCompileContext&);
 	ExpEmit Emit(VMFunctionBuilder *build);
 };
diff --git a/src/thingdef/thingdef_expression.cpp b/src/thingdef/thingdef_expression.cpp
index 833f3a3d5b..2ac41f7a8b 100644
--- a/src/thingdef/thingdef_expression.cpp
+++ b/src/thingdef/thingdef_expression.cpp
@@ -54,6 +54,36 @@
 #include "vmbuilder.h"
 #include "v_text.h"
 
+struct FLOP
+{
+	ENamedName Name;
+	int Flop;
+	double (*Evaluate)(double);
+};
+
+// Decorate operates on degrees, so the evaluate functions need to convert
+// degrees to radians for those that work with angles.
+static const FLOP FxFlops[] =
+{
+	{ NAME_Exp,		FLOP_EXP,		[](double v) { return exp(v); } },
+	{ NAME_Log,		FLOP_LOG,		[](double v) { return log(v); } },
+	{ NAME_Log10,	FLOP_LOG10,		[](double v) { return log10(v); } },
+	{ NAME_Sqrt,	FLOP_SQRT,		[](double v) { return sqrt(v); } },
+	{ NAME_Ceil,	FLOP_CEIL,		[](double v) { return ceil(v); } },
+	{ NAME_Floor,	FLOP_FLOOR,		[](double v) { return floor(v); } },
+
+	{ NAME_ACos,	FLOP_ACOS_DEG,	[](double v) { return acos(v) * (180.0 / M_PI); } },
+	{ NAME_ASin,	FLOP_ASIN_DEG,	[](double v) { return asin(v) * (180.0 / M_PI); } },
+	{ NAME_ATan,	FLOP_ATAN_DEG,	[](double v) { return atan(v) * (180.0 / M_PI); } },
+	{ NAME_Cos,		FLOP_COS_DEG,	[](double v) { return cos(v * (M_PI / 180.0)); } },
+	{ NAME_Sin,		FLOP_SIN_DEG,	[](double v) { return sin(v * (M_PI / 180.0)); } },
+	{ NAME_Tan,		FLOP_TAN_DEG,	[](double v) { return tan(v * (M_PI / 180.0)); } },
+
+	{ NAME_CosH,	FLOP_COSH,		[](double v) { return cosh(v); } },
+	{ NAME_SinH,	FLOP_SINH,		[](double v) { return sinh(v); } },
+	{ NAME_TanH,	FLOP_TANH,		[](double v) { return tanh(v); } },
+};
+
 ExpEmit::ExpEmit(VMFunctionBuilder *build, int type)
 : RegNum(build->Registers[type].Get(1)), RegType(type), Konst(false), Fixed(false)
 {
@@ -3146,20 +3176,21 @@ FxFunctionCall::~FxFunctionCall()
 
 FxExpression *FxFunctionCall::Resolve(FCompileContext& ctx)
 {
-	// There's currently only 3 global functions.
-	// If this changes later, it won't be here!
-	if (MethodName == NAME_Sin || MethodName == NAME_Cos || MethodName == NAME_Sqrt)
+	for (int i = 0; i < countof(FxFlops); ++i)
 	{
-		if (Self != NULL)
+		if (MethodName == FxFlops[i].Name)
 		{
-			ScriptPosition.Message(MSG_ERROR, "Global functions cannot have a self pointer");
+			if (Self != NULL)
+			{
+				ScriptPosition.Message(MSG_ERROR, "Global functions cannot have a self pointer");
+				delete this;
+				return NULL;
+			}
+			FxExpression *x = new FxFlopFunctionCall(i, ArgList, ScriptPosition);
+			ArgList = NULL;
 			delete this;
-			return NULL;
+			return x->Resolve(ctx);
 		}
-		FxExpression *x = new FxGlobalFunctionCall(MethodName, ArgList, ScriptPosition);
-		ArgList = NULL;
-		delete this;
-		return x->Resolve(ctx);
 	}
 
 	int min, max, special;
@@ -3483,10 +3514,11 @@ ExpEmit FxVMFunctionCall::Emit(VMFunctionBuilder *build, bool tailcall)
 //
 //==========================================================================
 
-FxGlobalFunctionCall::FxGlobalFunctionCall(FName fname, FArgumentList *args, const FScriptPosition &pos)
+FxFlopFunctionCall::FxFlopFunctionCall(int index, FArgumentList *args, const FScriptPosition &pos)
 : FxExpression(pos)
 {
-	Name = fname;
+	assert(index >= 0 && index < countof(FxFlops) && "FLOP index out of range");
+	Index = index;
 	ArgList = args;
 }
 
@@ -3496,18 +3528,18 @@ FxGlobalFunctionCall::FxGlobalFunctionCall(FName fname, FArgumentList *args, con
 //
 //==========================================================================
 
-FxGlobalFunctionCall::~FxGlobalFunctionCall()
+FxFlopFunctionCall::~FxFlopFunctionCall()
 {
 	SAFE_DELETE(ArgList);
 }
 
-FxExpression *FxGlobalFunctionCall::Resolve(FCompileContext& ctx)
+FxExpression *FxFlopFunctionCall::Resolve(FCompileContext& ctx)
 {
 	CHECKRESOLVED();
 
 	if (ArgList == NULL || ArgList->Size() != 1)
 	{
-		ScriptPosition.Message(MSG_ERROR, "%s only has one parameter", Name.GetChars());
+		ScriptPosition.Message(MSG_ERROR, "%s only has one parameter", FName(FxFlops[Index].Name).GetChars());
 		delete this;
 		return NULL;
 	}
@@ -3528,15 +3560,7 @@ FxExpression *FxGlobalFunctionCall::Resolve(FCompileContext& ctx)
 	if ((*ArgList)[0]->isConstant())
 	{
 		double v = static_cast<FxConstant *>((*ArgList)[0])->GetValue().GetFloat();
-		if (Name == NAME_Sqrt)
-		{
-			v = sqrt(v);
-		}
-		else
-		{
-			v *= M_PI / 180.0;		// convert from degrees to radians
-			v = (Name == NAME_Sin) ? sin(v) : cos(v);
-		}
+		v = FxFlops[Index].Evaluate(v);
 		FxExpression *x = new FxConstant(v, ScriptPosition);
 		delete this;
 		return x;
@@ -3554,15 +3578,12 @@ FxExpression *FxGlobalFunctionCall::Resolve(FCompileContext& ctx)
 //
 //==========================================================================
 
-ExpEmit FxGlobalFunctionCall::Emit(VMFunctionBuilder *build)
+ExpEmit FxFlopFunctionCall::Emit(VMFunctionBuilder *build)
 {
 	ExpEmit v = (*ArgList)[0]->Emit(build);
 	assert(!v.Konst && v.RegType == REGT_FLOAT);
 
-	build->Emit(OP_FLOP, v.RegNum, v.RegNum,
-		(Name == NAME_Sqrt) ?	FLOP_SQRT :
-		(Name == NAME_Sin) ?	FLOP_SIN_DEG :
-								FLOP_COS_DEG);
+	build->Emit(OP_FLOP, v.RegNum, v.RegNum, FxFlops[Index].Flop);
 	return v;
 }
 
diff --git a/wadsrc/static/actors/actor.txt b/wadsrc/static/actors/actor.txt
index 642269f283..34fbd5cef7 100644
--- a/wadsrc/static/actors/actor.txt
+++ b/wadsrc/static/actors/actor.txt
@@ -42,6 +42,8 @@ ACTOR Actor native //: Thinker
 	native bool IsPointerEqual(int ptr_select1, int ptr_select2);
 	native int	CountInv(class<Inventory> itemtype, int ptr_select = AAPTR_DEFAULT);
 	native float GetDistance(bool checkz, int ptr = AAPTR_DEFAULT);
+	native int GetSpawnHealth();
+	native int GetGibHealth();
 
 	// Action functions
 	// Meh, MBF redundant functions. Only for DeHackEd support.