diff --git a/demo2/geometry.ts b/demo2/geometry.ts
index 45838bfc..f3881876 100644
--- a/demo2/geometry.ts
+++ b/demo2/geometry.ts
@@ -20,8 +20,8 @@ export class Point2D {
         Object.freeze(this);
     }
 
-    approxEq(other: Point2D): boolean {
-        return approxEq(this.x, other.x) && approxEq(this.y, other.y);
+    approxEq(other: Point2D, epsilon: number | undefined): boolean {
+        return approxEq(this.x, other.x, epsilon) && approxEq(this.y, other.y, epsilon);
     }
 
     lerp(other: Point2D, t: number): Point2D {
@@ -107,8 +107,8 @@ export class Matrix2D {
     }
 }
 
-export function approxEq(a: number, b: number): boolean {
-    return Math.abs(a - b) <= EPSILON;
+export function approxEq(a: number, b: number, epsilon: number | undefined): boolean {
+    return Math.abs(a - b) <= (epsilon == null ? EPSILON : epsilon);
 }
 
 export function lerp(a: number, b: number, t: number): number {
diff --git a/demo2/pathfinder.ts b/demo2/pathfinder.ts
index 9512f690..95e04c1a 100644
--- a/demo2/pathfinder.ts
+++ b/demo2/pathfinder.ts
@@ -324,6 +324,10 @@ class App {
             const pathTileStrips = scene.pathTileStrips[pathIndex];
             for (const tileStrip of pathTileStrips) {
                 for (const tile of tileStrip.tiles) {
+                    // TODO(pcwalton)
+                    if (tile.isFilled())
+                        continue;
+
                     for (const edge of tile.edges) {
                         let ctrl;
                         if (edge.ctrl == null)
diff --git a/demo2/tiling.ts b/demo2/tiling.ts
index 1c0a39b6..6456b6a2 100644
--- a/demo2/tiling.ts
+++ b/demo2/tiling.ts
@@ -264,7 +264,7 @@ export class Tiler {
     }
 
     private clipEdgeX(edge: Edge, x: number): ClippedEdgesX {
-        const EPSILON: number = 0.001;
+        const EPSILON: number = 0.00001;
 
         if (edge.from.x < x && edge.to.x < x)
             return {left: edge, right: null};
@@ -291,7 +291,7 @@ export class Tiler {
     }
 
     private clipEdgeY(edge: Edge, y: number): ClippedEdgesY {
-        const EPSILON: number = 0.001;
+        const EPSILON: number = 0.00001;
 
         if (edge.from.y < y && edge.to.y < y)
             return {upper: edge, lower: null};
@@ -473,6 +473,19 @@ export class Tile {
     isEmpty(): boolean {
         return this.edges.length === 0;
     }
+
+    isFilled(): boolean {
+        if (this.edges.length !== 1)
+            return false;
+        const edge = this.edges[0];
+        if (edge.ctrl != null)
+            return false;
+        //console.log("single edge:", JSON.stringify(edge));
+        const left = edge.from.x < edge.to.x ? edge.from : edge.to;
+        const right = edge.from.x < edge.to.x ? edge.to : edge.from;
+        return left.approxEq(new Point2D(0, 0), 0.1) &&
+            right.approxEq(new Point2D(TILE_SIZE.width, 0), 0.1);
+    }
 }
 
 interface ClippedEdgesX {