diff --git a/src/g_heretic/a_hereticweaps.cpp b/src/g_heretic/a_hereticweaps.cpp
index 711bbd960..247ccb03f 100644
--- a/src/g_heretic/a_hereticweaps.cpp
+++ b/src/g_heretic/a_hereticweaps.cpp
@@ -1099,7 +1099,7 @@ DEFINE_ACTION_FUNCTION(AActor, A_HideInCeiling)
 		F3DFloor * rover = self->Sector->e->XFloor.ffloors[i];
 		if(!(rover->flags & FF_SOLID) || !(rover->flags & FF_EXISTS)) continue;
 		 
-		if ((foo = rover->bottom.plane->ZatPoint(self->x, self->y)) >= (self->z + self->height))
+		if ((foo = rover->bottom.plane->ZatPoint(self)) >= (self->z + self->height))
 		{
 			self->z = foo + 4*FRACUNIT;
 			self->bouncecount = i;
diff --git a/src/g_strife/a_strifestuff.cpp b/src/g_strife/a_strifestuff.cpp
index 05f6367dc..9f3ebb272 100644
--- a/src/g_strife/a_strifestuff.cpp
+++ b/src/g_strife/a_strifestuff.cpp
@@ -628,7 +628,7 @@ DEFINE_ACTION_FUNCTION(AActor, A_CheckTerrain)
 {
 	sector_t *sec = self->Sector;
 
-	if (self->z == sec->floorplane.ZatPoint (self->x, self->y))
+	if (self->z == sec->floorplane.ZatPoint(self))
 	{
 		if (sec->special == Damage_InstantDeath)
 		{
diff --git a/src/p_map.cpp b/src/p_map.cpp
index 5feff237e..78a17df10 100644
--- a/src/p_map.cpp
+++ b/src/p_map.cpp
@@ -593,8 +593,8 @@ int P_GetFriction(const AActor *mo, int *frictionfactor)
 				if (!(rover->flags & FF_EXISTS)) continue;
 				if (!(rover->flags & FF_SWIMMABLE)) continue;
 
-				if (mo->z > rover->top.plane->ZatPoint(mo->x, mo->y) ||
-					mo->z < rover->bottom.plane->ZatPoint(mo->x, mo->y))
+				if (mo->z > rover->top.plane->ZatPoint(mo) ||
+					mo->z < rover->bottom.plane->ZatPoint(mo))
 					continue;
 
 				newfriction = secfriction(rover->model, rover->top.isceiling);
@@ -623,13 +623,13 @@ int P_GetFriction(const AActor *mo, int *frictionfactor)
 				if (rover->flags & FF_SOLID)
 				{
 					// Must be standing on a solid floor
-					if (mo->z != rover->top.plane->ZatPoint(mo->x, mo->y)) continue;
+					if (mo->z != rover->top.plane->ZatPoint(mo)) continue;
 				}
 				else if (rover->flags & FF_SWIMMABLE)
 				{
 					// Or on or inside a swimmable floor (e.g. in shallow water)
-					if (mo->z > rover->top.plane->ZatPoint(mo->x, mo->y) ||
-						(mo->z + mo->height) < rover->bottom.plane->ZatPoint(mo->x, mo->y))
+					if (mo->z > rover->top.plane->ZatPoint(mo) ||
+						(mo->z + mo->height) < rover->bottom.plane->ZatPoint(mo))
 						continue;
 				}
 				else
@@ -650,9 +650,9 @@ int P_GetFriction(const AActor *mo, int *frictionfactor)
 			}
 			newfriction = secfriction(sec);
 			if ((newfriction < friction || friction == ORIG_FRICTION) &&
-				(mo->z <= sec->floorplane.ZatPoint(mo->x, mo->y) ||
+				(mo->z <= sec->floorplane.ZatPoint(mo) ||
 				(sec->GetHeightSec() != NULL &&
-				mo->z <= sec->heightsec->floorplane.ZatPoint(mo->x, mo->y))))
+				mo->z <= sec->heightsec->floorplane.ZatPoint(mo))))
 			{
 				friction = newfriction;
 				movefactor = secmovefac(sec);
@@ -1798,10 +1798,10 @@ static void CheckForPushSpecial(line_t *line, int side, AActor *mobj, bool windo
 		if (windowcheck && !(ib_compatflags & BCOMPATF_NOWINDOWCHECK) && line->backsector != NULL)
 		{ // Make sure this line actually blocks us and is not a window
 			// or similar construct we are standing inside of.
-			fixed_t fzt = line->frontsector->ceilingplane.ZatPoint(mobj->x, mobj->y);
-			fixed_t fzb = line->frontsector->floorplane.ZatPoint(mobj->x, mobj->y);
-			fixed_t bzt = line->backsector->ceilingplane.ZatPoint(mobj->x, mobj->y);
-			fixed_t bzb = line->backsector->floorplane.ZatPoint(mobj->x, mobj->y);
+			fixed_t fzt = line->frontsector->ceilingplane.ZatPoint(mobj);
+			fixed_t fzb = line->frontsector->floorplane.ZatPoint(mobj);
+			fixed_t bzt = line->backsector->ceilingplane.ZatPoint(mobj);
+			fixed_t bzb = line->backsector->floorplane.ZatPoint(mobj);
 			if (fzt >= mobj->z + mobj->height && bzt >= mobj->z + mobj->height &&
 				fzb <= mobj->z && bzb <= mobj->z)
 			{
@@ -1812,8 +1812,8 @@ static void CheckForPushSpecial(line_t *line, int side, AActor *mobj, bool windo
 
 					if (!(rover->flags & FF_SOLID) || !(rover->flags & FF_EXISTS)) continue;
 
-					fixed_t ff_bottom = rover->bottom.plane->ZatPoint(mobj->x, mobj->y);
-					fixed_t ff_top = rover->top.plane->ZatPoint(mobj->x, mobj->y);
+					fixed_t ff_bottom = rover->bottom.plane->ZatPoint(mobj);
+					fixed_t ff_top = rover->top.plane->ZatPoint(mobj);
 
 					if (ff_bottom < mobj->z + mobj->height && ff_top > mobj->z)
 					{
@@ -2083,8 +2083,8 @@ bool P_TryMove(AActor *thing, fixed_t x, fixed_t y,
 	{
 		fixed_t eyez = oldz + viewheight;
 
-		oldAboveFakeFloor = eyez > oldsec->heightsec->floorplane.ZatPoint(thing->x, thing->y);
-		oldAboveFakeCeiling = eyez > oldsec->heightsec->ceilingplane.ZatPoint(thing->x, thing->y);
+		oldAboveFakeFloor = eyez > oldsec->heightsec->floorplane.ZatPoint(thing);
+		oldAboveFakeCeiling = eyez > oldsec->heightsec->ceilingplane.ZatPoint(thing);
 	}
 
 	// Borrowed from MBF: 
@@ -2743,14 +2743,14 @@ const secplane_t * P_CheckSlopeWalk(AActor *actor, fixed_t &xmove, fixed_t &ymov
 	}
 
 	const secplane_t *plane = &actor->floorsector->floorplane;
-	fixed_t planezhere = plane->ZatPoint(actor->x, actor->y);
+	fixed_t planezhere = plane->ZatPoint(actor);
 
 	for (unsigned int i = 0; i<actor->floorsector->e->XFloor.ffloors.Size(); i++)
 	{
 		F3DFloor * rover = actor->floorsector->e->XFloor.ffloors[i];
 		if (!(rover->flags & FF_SOLID) || !(rover->flags & FF_EXISTS)) continue;
 
-		fixed_t thisplanez = rover->top.plane->ZatPoint(actor->x, actor->y);
+		fixed_t thisplanez = rover->top.plane->ZatPoint(actor);
 
 		if (thisplanez>planezhere && thisplanez <= actor->z + actor->MaxStepHeight)
 		{
@@ -2768,7 +2768,7 @@ const secplane_t * P_CheckSlopeWalk(AActor *actor, fixed_t &xmove, fixed_t &ymov
 			F3DFloor * rover = actor->Sector->e->XFloor.ffloors[i];
 			if (!(rover->flags & FF_SOLID) || !(rover->flags & FF_EXISTS)) continue;
 
-			fixed_t thisplanez = rover->top.plane->ZatPoint(actor->x, actor->y);
+			fixed_t thisplanez = rover->top.plane->ZatPoint(actor);
 
 			if (thisplanez>planezhere && thisplanez <= actor->z + actor->MaxStepHeight)
 			{
diff --git a/src/p_mobj.cpp b/src/p_mobj.cpp
index bcaa77855..1c5105235 100644
--- a/src/p_mobj.cpp
+++ b/src/p_mobj.cpp
@@ -2077,7 +2077,7 @@ explode:
 					if (tm.ceilingline &&
 						tm.ceilingline->backsector &&
 						tm.ceilingline->backsector->GetTexture(sector_t::ceiling) == skyflatnum &&
-						mo->z >= tm.ceilingline->backsector->ceilingplane.ZatPoint (mo->x, mo->y))
+						mo->z >= tm.ceilingline->backsector->ceilingplane.ZatPoint(mo))
 					{
 						// Hack to prevent missiles exploding against the sky.
 						// Does not handle sky floors.
@@ -2161,7 +2161,7 @@ explode:
 	{ // Don't stop sliding if halfway off a step with some velocity
 		if (mo->velx > FRACUNIT/4 || mo->velx < -FRACUNIT/4 || mo->vely > FRACUNIT/4 || mo->vely < -FRACUNIT/4)
 		{
-			if (mo->floorz > mo->Sector->floorplane.ZatPoint (mo->x, mo->y))
+			if (mo->floorz > mo->Sector->floorplane.ZatPoint(mo))
 			{
 				if (mo->dropoffz != mo->floorz) // 3DMidtex or other special cases that must be excluded
 				{
@@ -2407,7 +2407,7 @@ void P_ZMovement (AActor *mo, fixed_t oldfloorz)
 	{	// Hit the floor
 		if ((!mo->player || !(mo->player->cheats & CF_PREDICTING)) &&
 			mo->Sector->SecActTarget != NULL &&
-			mo->Sector->floorplane.ZatPoint (mo->x, mo->y) == mo->floorz)
+			mo->Sector->floorplane.ZatPoint(mo) == mo->floorz)
 		{ // [RH] Let the sector do something to the actor
 			mo->Sector->SecActTarget->TriggerAction (mo, SECSPAC_HitFloor);
 		}
@@ -2509,7 +2509,7 @@ void P_ZMovement (AActor *mo, fixed_t oldfloorz)
 	{ // hit the ceiling
 		if ((!mo->player || !(mo->player->cheats & CF_PREDICTING)) &&
 			mo->Sector->SecActTarget != NULL &&
-			mo->Sector->ceilingplane.ZatPoint (mo->x, mo->y) == mo->ceilingz)
+			mo->Sector->ceilingplane.ZatPoint(mo) == mo->ceilingz)
 		{ // [RH] Let the sector do something to the actor
 			mo->Sector->SecActTarget->TriggerAction (mo, SECSPAC_HitCeiling);
 		}
@@ -2564,7 +2564,7 @@ void P_CheckFakeFloorTriggers (AActor *mo, fixed_t oldz, bool oldz_has_viewheigh
 	if (sec->heightsec != NULL && sec->SecActTarget != NULL)
 	{
 		sector_t *hs = sec->heightsec;
-		fixed_t waterz = hs->floorplane.ZatPoint (mo->x, mo->y);
+		fixed_t waterz = hs->floorplane.ZatPoint(mo);
 		fixed_t newz;
 		fixed_t viewheight;
 
@@ -2599,7 +2599,7 @@ void P_CheckFakeFloorTriggers (AActor *mo, fixed_t oldz, bool oldz_has_viewheigh
 
 		if (!(hs->MoreFlags & SECF_FAKEFLOORONLY))
 		{
-			waterz = hs->ceilingplane.ZatPoint (mo->x, mo->y);
+			waterz = hs->ceilingplane.ZatPoint(mo);
 			if (oldz <= waterz && newz > waterz)
 			{ // View went above fake ceiling
 				sec->SecActTarget->TriggerAction (mo, SECSPAC_EyesAboveC);
@@ -5493,7 +5493,7 @@ bool P_HitFloor (AActor *thing)
 	// don't splash if landing on the edge above water/lava/etc....
 	for (m = thing->touching_sectorlist; m; m = m->m_tnext)
 	{
-		if (thing->z == m->m_sector->floorplane.ZatPoint (thing->x, thing->y))
+		if (thing->z == m->m_sector->floorplane.ZatPoint(thing))
 		{
 			break;
 		}
@@ -5505,7 +5505,7 @@ bool P_HitFloor (AActor *thing)
 			if (!(rover->flags & FF_EXISTS)) continue;
 			if (rover->flags & (FF_SOLID|FF_SWIMMABLE))
 			{
-				if (rover->top.plane->ZatPoint(thing->x, thing->y) == thing->z)
+				if (rover->top.plane->ZatPoint(thing) == thing->z)
 				{
 					return P_HitWater (thing, m->m_sector);
 				}
diff --git a/src/p_spec.cpp b/src/p_spec.cpp
index 36d5f3bab..baec6d9e1 100644
--- a/src/p_spec.cpp
+++ b/src/p_spec.cpp
@@ -430,7 +430,7 @@ void P_PlayerInSpecialSector (player_t *player, sector_t * sector)
 	{
 		// Falling, not all the way down yet?
 		sector = player->mo->Sector;
-		if (player->mo->z != sector->floorplane.ZatPoint (player->mo->x, player->mo->y)
+		if (player->mo->z != sector->floorplane.ZatPoint(player->mo)
 			&& !player->mo->waterlevel)
 		{
 			return;
@@ -507,7 +507,7 @@ static void DoSectorDamage(AActor *actor, sector_t *sec, int amount, FName type,
 	if (!(flags & DAMAGE_PLAYERS) && actor->player != NULL)
 		return;
 
-	if (!(flags & DAMAGE_IN_AIR) && actor->z != sec->floorplane.ZatPoint(actor->x, actor->y) && !actor->waterlevel)
+	if (!(flags & DAMAGE_IN_AIR) && actor->z != sec->floorplane.ZatPoint(actor) && !actor->waterlevel)
 		return;
 
 	if (protectClass != NULL)
@@ -544,8 +544,8 @@ void P_SectorDamage(int tag, int amount, FName type, const PClass *protectClass,
 			{
 				next = actor->snext;
 				// Only affect actors touching the 3D floor
-				fixed_t z1 = sec->floorplane.ZatPoint(actor->x, actor->y);
-				fixed_t z2 = sec->ceilingplane.ZatPoint(actor->x, actor->y);
+				fixed_t z1 = sec->floorplane.ZatPoint(actor);
+				fixed_t z2 = sec->ceilingplane.ZatPoint(actor);
 				if (z2 < z1)
 				{
 					// Account for Vavoom-style 3D floors
@@ -2281,7 +2281,7 @@ void DPusher::Tick ()
 			}
 			else // special water sector
 			{
-				ht = hsec->floorplane.ZatPoint (thing->x, thing->y);
+				ht = hsec->floorplane.ZatPoint(thing);
 				if (thing->z > ht) // above ground
 				{
 					xspeed = m_Xmag; // full force
@@ -2310,7 +2310,7 @@ void DPusher::Tick ()
 			{ // special water sector
 				floor = &hsec->floorplane;
 			}
-			if (thing->z > floor->ZatPoint (thing->x, thing->y))
+			if (thing->z > floor->ZatPoint(thing))
 			{ // above ground
 				xspeed = yspeed = 0; // no force
 			}
diff --git a/src/po_man.cpp b/src/po_man.cpp
index 98fbbcbcb..fb1d12519 100644
--- a/src/po_man.cpp
+++ b/src/po_man.cpp
@@ -1238,8 +1238,8 @@ bool FPolyObj::CheckMobjBlocking (side_t *sd)
 							}
 							// [BL] See if we hit below the floor/ceiling of the poly.
 							else if(!performBlockingThrust && (
-									mobj->z < ld->sidedef[!side]->sector->GetSecPlane(sector_t::floor).ZatPoint(mobj->x, mobj->y) ||
-									mobj->z + mobj->height > ld->sidedef[!side]->sector->GetSecPlane(sector_t::ceiling).ZatPoint(mobj->x, mobj->y)
+									mobj->z < ld->sidedef[!side]->sector->GetSecPlane(sector_t::floor).ZatPoint(mobj) ||
+									mobj->z + mobj->height > ld->sidedef[!side]->sector->GetSecPlane(sector_t::ceiling).ZatPoint(mobj)
 								))
 							{
 								performBlockingThrust = true;