diff --git a/main.cpp b/main.cpp
index 9461681..b13066e 100644
--- a/main.cpp
+++ b/main.cpp
@@ -89,6 +89,7 @@ int process_faces(const world_t* world, const TextureList& textures)
 
 		// Traverse the list of face edges to collect all of the face's vertices
 		Vec3 vertexSum;
+		std::vector<Vec3> faceVertices;
 		for (int edgeListIdx = 0; edgeListIdx < face->ledge_num; ++edgeListIdx)
 		{
 			int edgeIdx = world->edgeList[face->ledge_id + edgeListIdx];
@@ -97,8 +98,10 @@ int process_faces(const world_t* world, const TextureList& textures)
 				world->edges[edgeIdx].vertex0 :
 				world->edges[-edgeIdx].vertex1;
 
+			// TODO: some faces have redundant/degenerate vertices. We could optimize those by passing their polygons through GPC.
 			const vertex_t* vertex = &world->vertices[vertIndex];
 			Vec3 vertexPoint = vertex->toVec();
+			faceVertices.push_back(vertexPoint);
 
 			// Calculate bounding boxes of this face
 			Vec3 texturePoint = bounds.textureTransform.TransformPoint(vertexPoint);
@@ -117,6 +120,30 @@ int process_faces(const world_t* world, const TextureList& textures)
 		//if (face->ledge_num >= 10)
 		//	export_lightmap(world, face, bounds, faceIdx);
 
+		// Determine the face's bounding rectangle in world space (only four vertices, on the face's plane)
+		switch (faceVertices.size())
+		{
+		case 3:	// Special case: a triangle
+			for (int i = 0; i < 3; ++i)
+				outFace.bounds[i] = (unsigned short)tesselator.addVertex(faceVertices[i]);
+
+			outFace.bounds[3] = outFace.bounds[2];
+			break;
+		case 4:	// Special case: a quad
+			for (int i = 0; i < 4; ++i)
+				outFace.bounds[i] = (unsigned short)tesselator.addVertex(faceVertices[i]);
+
+			break;
+		default:
+			// TODO: this is far from optimal. We don't need a bounding rectangle, but a minimal bounding quad of any shape. Solve this problem: https://mathoverflow.net/questions/11580/minimum-area-bounding-quadrilateral-algorithm
+			bounds.textureTransform.Invert();
+			outFace.bounds[0] = (unsigned short)tesselator.addVertex(bounds.textureTransform.TransformPoint(Vec3(bounds.textureBounds.min.x, bounds.textureBounds.min.y, 0.0f)));
+			outFace.bounds[1] = (unsigned short)tesselator.addVertex(bounds.textureTransform.TransformPoint(Vec3(bounds.textureBounds.min.x, bounds.textureBounds.max.y, 0.0f)));
+			outFace.bounds[2] = (unsigned short)tesselator.addVertex(bounds.textureTransform.TransformPoint(Vec3(bounds.textureBounds.max.x, bounds.textureBounds.max.y, 0.0f)));
+			outFace.bounds[3] = (unsigned short)tesselator.addVertex(bounds.textureTransform.TransformPoint(Vec3(bounds.textureBounds.max.x, bounds.textureBounds.min.y, 0.0f)));
+			break;
+		}
+
 		outFace.numFaceVertices = (unsigned char)(outFaceVertices.size() - outFace.firstFaceVertex);
 		outFace.center = (vertexSum / face->ledge_num).convertWorldPosition();
 		double area = face_computeArea(world, face);
@@ -124,7 +151,7 @@ int process_faces(const world_t* world, const TextureList& textures)
 		outFaces.push_back(outFace);
 	}
 
-	printf("Tesselating faces...\n");
+	printf("Tessellating faces...\n");
 
 	std::vector<ps1bsp_polyvertex_t> outPolyVertices;
 	std::vector<ps1bsp_polygon_t> outPolygons;
@@ -248,7 +275,7 @@ int process_faces(const world_t* world, const TextureList& textures)
 			outPoly.numPolyVertices = (unsigned short)(outPolyVertices.size() - outPoly.firstPolyVertex);
 			outPolygons.push_back(outPoly);
 
-			outFace->totalQuads += (outPoly.numPolyVertices - 1) / 2;
+			outFace->totalPrimitives += (outPoly.numPolyVertices - 1) / 2;
 		}
 
 		outFace->numPolygons = (unsigned char)(outPolygons.size() - outFace->firstPolygon);
diff --git a/ps1bsp.h b/ps1bsp.h
index c87932a..ab0f07d 100644
--- a/ps1bsp.h
+++ b/ps1bsp.h
@@ -106,10 +106,14 @@ typedef struct ps1bsp_face_s
 	unsigned short planeId;
 	unsigned char side;
 
+	// TODO: not sure if we should make separate lists for triangles and non-triangle polygons here
+	// Could potentially improve drawing performance but at the cost of more memory use per face
+
 	// Used for high-quality tesselated textured drawing
 	unsigned short firstPolygon;
 	unsigned char numPolygons;
-	unsigned char totalQuads;
+
+	unsigned char totalPrimitives;	// Used for early primitive buffer checks
 
 	// Used for low-quality untextured vertex colored drawing
 	unsigned short firstFaceVertex;
@@ -120,6 +124,7 @@ typedef struct ps1bsp_face_s
 
 	// Used for backface culling
 	SVECTOR center;
+	unsigned short bounds[4];
 
 	// Run-time data
 	const struct ps1bsp_face_s* nextFace;	// For chaining faces in drawing order