diff --git a/common.ts b/common.ts
index 96c6237..880b214 100644
--- a/common.ts
+++ b/common.ts
@@ -25,28 +25,30 @@ export function lerp(a: number, b: number, t: number) {
 }
 
 export function quadraticBezier(a: Point, b: Point, c: Point, res=0.05) {
-    const eps = 0.001; // to prevent issues with float comparaison (p <= 1)
+    const steps = Math.max(1, Math.ceil(1 / res))
     const curve = [];
-    for (let p = 0; p - 1 < eps; p += res) {
-        const ab = lerpPoint(a, b, p);
-        const bc = lerpPoint(b, c, p);
-        const abc = lerpPoint(ab, bc, p);
-        curve.push(abc);
+    for (let i = 0; i <= steps; i++) {
+      const p = i / steps;
+      const ab = lerpPoint(a, b, p);
+      const bc = lerpPoint(b, c, p);
+      const abc = lerpPoint(ab, bc, p);
+      curve.push(abc);
     }
     return curve;
 }
 
 export function cubicBezier(a: Point, b: Point, c: Point, d: Point, res=0.05) {
-    const eps = 0.001; // to prevent issues with float comparaison (p <= 1)
+    const steps = Math.max(1, Math.ceil(1 / res))
     const curve = [];
-    for (let p = 0; p - 1 < eps; p += res) {
-        const ab = lerpPoint(a, b, p);
-        const bc = lerpPoint(b, c, p);
-        const cd = lerpPoint(c, d, p);
-        const abc = lerpPoint(ab, bc, p);
-        const bcd = lerpPoint(bc, cd, p);
-        const abcd = lerpPoint(abc, bcd, p);
-        curve.push(abcd);
+    for (let i = 0; i <= steps; i++) {
+      const p = i / steps;
+      const ab = lerpPoint(a, b, p);
+      const bc = lerpPoint(b, c, p);
+      const cd = lerpPoint(c, d, p);
+      const abc = lerpPoint(ab, bc, p);
+      const bcd = lerpPoint(bc, cd, p);
+      const abcd = lerpPoint(abc, bcd, p);
+      curve.push(abcd);
     }
     return curve;
 }
diff --git a/snake.ts b/snake.ts
index e5d5abd..38b4fbb 100644
--- a/snake.ts
+++ b/snake.ts
@@ -84,7 +84,7 @@ function update(ctx: CanvasRenderingContext2D, time: number) {
   if (lastTime == null) lastTime = time;
   const dt = (time - lastTime) / 1000; // s
   lastTime = time;
-  apple = apple as Vec2d;
+  if (apple == null) return;
 
   if (!paused) {
     // update head position