diff --git a/main.py b/main.py
index 0276c28..0581f41 100644
--- a/main.py
+++ b/main.py
@@ -1,3 +1,4 @@
+import math
 from typing import List, Tuple
 
 import matplotlib.pyplot as plt
@@ -54,7 +55,11 @@
         if abs(xs[0] - xs[1]) < 1e-6 and abs(ys[0] - ys[1]) < 1e-6:
             return
         self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
-        super().draw(renderer)
+        try:
+            super().draw(renderer)
+        except Exception:
+            # If patch drawing fails (e.g., degenerate path), skip drawing the arrow
+            return
 
     def do_3d_projection(self, renderer=None):
         xs3d, ys3d, zs3d = self._verts3d
@@ -108,6 +113,28 @@
     return data_list
 
 
+def compute_and_format_angle(pts: List[Tuple[float, float, float]]) -> str:
+    if len(VECTOR_PAIRS) < 2:
+        return "Angle v1-v2: N/A"
+    (a1, b1) = VECTOR_PAIRS[0]
+    (a2, b2) = VECTOR_PAIRS[1]
+    p1s = pts[a1]
+    p1e = pts[b1]
+    p2s = pts[a2]
+    p2e = pts[b2]
+    v1 = (p1e[0] - p1s[0], p1e[1] - p1s[1], p1e[2] - p1s[2])
+    v2 = (p2e[0] - p2s[0], p2e[1] - p2s[1], p2e[2] - p2s[2])
+    norm1 = math.sqrt(v1[0] ** 2 + v1[1] ** 2 + v1[2] ** 2)
+    norm2 = math.sqrt(v2[0] ** 2 + v2[1] ** 2 + v2[2] ** 2)
+    if norm1 < 1e-9 or norm2 < 1e-9:
+        return "Angle v1-v2: N/A"
+    dot = v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2]
+    cos_val = max(-1.0, min(1.0, dot / (norm1 * norm2)))
+    angle_rad = math.acos(cos_val)
+    angle_deg = math.degrees(angle_rad)
+    return f"Angle v1-v2: {angle_deg:.2f}°"
+
+
 # Function to visualize thumb data with a slider
 def visualize_thumb_data(data: List[ThumbFrameData]):
     if not data:
@@ -193,6 +220,10 @@
         )
         arrow_labels.append(lbl)
 
+    # Angle display between v1 and v2 (figure-relative text)
+    angle_text = fig.text(0.02, 0.95, "", fontsize=12, weight="bold")
+    angle_text.set_text(compute_and_format_angle(points))
+
     ax.set_xlabel("X")
     ax.set_ylabel("Y")
     ax.set_zlabel("Z")
@@ -243,6 +274,9 @@
             mid_z = 0.5 * (z1 + z2) + LABEL_OFFSET_Z_FACTOR * (z_max - z_min)
             arrow_labels[i_pair].set_position((mid_x, mid_y, mid_z))
 
+        # Update angle text between v1 and v2
+        angle_text.set_text(compute_and_format_angle(points))
+
         ax.set_title(f"Frame {data[frame_idx].frame_number}")
         fig.canvas.draw_idle()