diff --git a/Source/scrollrt.cpp b/Source/scrollrt.cpp
index 3ec6aac92..10f146d49 100644
--- a/Source/scrollrt.cpp
+++ b/Source/scrollrt.cpp
@@ -943,11 +943,11 @@ void DrawFloor(const Surface &out, Point tilePosition, Point targetBufferPositio
 			} else {
 				world_draw_black_tile(out, targetBufferPosition.x, targetBufferPosition.y);
 			}
-			ShiftGrid(&tilePosition.x, &tilePosition.y, 1, 0);
+			tilePosition += DIR_E;
 			targetBufferPosition.x += TILE_WIDTH;
 		}
 		// Return to start of row
-		ShiftGrid(&tilePosition.x, &tilePosition.y, -columns, 0);
+		tilePosition += Displacement::fromDirection(DIR_W) * columns;
 		targetBufferPosition.x -= columns * TILE_WIDTH;
 
 		// Jump to next row
@@ -999,11 +999,11 @@ void DrawTileContent(const Surface &out, Point tilePosition, Point targetBufferP
 					DrawDungeon(out, tilePosition, targetBufferPosition);
 				}
 			}
-			ShiftGrid(&tilePosition.x, &tilePosition.y, 1, 0);
+			tilePosition += DIR_E;
 			targetBufferPosition.x += TILE_WIDTH;
 		}
 		// Return to start of row
-		ShiftGrid(&tilePosition.x, &tilePosition.y, -columns, 0);
+		tilePosition += Displacement::fromDirection(DIR_W) * columns;
 		targetBufferPosition.x -= columns * TILE_WIDTH;
 
 		// Jump to next row
@@ -1109,23 +1109,23 @@ void DrawGame(const Surface &fullOut, Point position)
 	if (CanPanelsCoverView()) {
 		if (zoomflag) {
 			if (chrflag || QuestLogIsOpen) {
-				ShiftGrid(&position.x, &position.y, 2, 0);
+				position += Displacement::fromDirection(DIR_E) * 2;
 				columns -= 4;
 				sx += SPANEL_WIDTH - TILE_WIDTH / 2;
 			}
 			if (invflag || sbookflag) {
-				ShiftGrid(&position.x, &position.y, 2, 0);
+				position += Displacement::fromDirection(DIR_E) * 2;
 				columns -= 4;
 				sx += -TILE_WIDTH / 2;
 			}
 		} else {
 			if (chrflag || QuestLogIsOpen) {
-				ShiftGrid(&position.x, &position.y, 1, 0);
+				position += DIR_E;
 				columns -= 2;
 				sx += -TILE_WIDTH / 2 / 2; // SPANEL_WIDTH accounted for in Zoom()
 			}
 			if (invflag || sbookflag) {
-				ShiftGrid(&position.x, &position.y, 1, 0);
+				position += DIR_E;
 				columns -= 2;
 				sx += -TILE_WIDTH / 2 / 2;
 			}
@@ -1138,12 +1138,12 @@ void DrawGame(const Surface &fullOut, Point position)
 	switch (ScrollInfo._sdir) {
 	case SDIR_N:
 		sy -= TILE_HEIGHT;
-		ShiftGrid(&position.x, &position.y, 0, -1);
+		position += DIR_N;
 		rows += 2;
 		break;
 	case SDIR_NE:
 		sy -= TILE_HEIGHT;
-		ShiftGrid(&position.x, &position.y, 0, -1);
+		position += DIR_N;
 		columns++;
 		rows += 2;
 		break;
@@ -1159,13 +1159,13 @@ void DrawGame(const Surface &fullOut, Point position)
 		break;
 	case SDIR_SW:
 		sx -= TILE_WIDTH;
-		ShiftGrid(&position.x, &position.y, -1, 0);
+		position += DIR_W;
 		columns++;
 		rows++;
 		break;
 	case SDIR_W:
 		sx -= TILE_WIDTH;
-		ShiftGrid(&position.x, &position.y, -1, 0);
+		position += DIR_W;
 		columns++;
 		break;
 	case SDIR_NW:
@@ -1530,7 +1530,8 @@ void CalcViewportGeometry()
 	int lrow = tileRows - RowsCoveredByPanel();
 
 	// Center player tile on screen
-	ShiftGrid(&tileShift.deltaX, &tileShift.deltaY, -tileColums / 2, -lrow / 2);
+	tileShift += Displacement::fromDirection(DIR_W) * (tileColums / 2);
+	tileShift += Displacement::fromDirection(DIR_N) * (lrow / 2);
 
 	tileRows *= 2;
 
@@ -1544,7 +1545,7 @@ void CalcViewportGeometry()
 		}
 	} else if ((tileColums & 1) != 0 && (lrow & 1) != 0) {
 		// Offset tile to vertically align the player when both rows and colums are odd
-		ShiftGrid(&tileShift.deltaX, &tileShift.deltaY, 0, -1);
+		tileShift += Displacement::fromDirection(DIR_N);
 		tileRows++;
 		tileOffset.deltaY -= TILE_HEIGHT / 2;
 	}