=== SAVED CAST: hawking_4_s41 ===
Normalized points: 64
Raw points: N/A

--- NORMALIZED STROKE POINTS (x, y in [0,1], top-left origin) ---
  [ 0]  (0.8659, 0.8332)
  [ 1]  (0.8785, 0.8344)
  [ 2]  (0.8273, 0.7437)
  [ 3]  (0.7643, 0.6608)
  [ 4]  (0.7011, 0.5780)
  [ 5]  (0.6379, 0.4952)
  [ 6]  (0.5747, 0.4124)
  [ 7]  (0.5236, 0.3227)
  [ 8]  (0.4840, 0.2264)
  [ 9]  (0.4444, 0.1301)
  [10]  (0.4882, 0.0763)
  [11]  (0.5894, 0.0521)
  [12]  (0.6907, 0.0278)
  [13]  (0.7930, 0.0096)
  [14]  (0.8967, 0.0001)
  [15]  (0.9384, 0.0069)
  [16]  (0.8659, 0.4836)
  [17]  (0.9334, 0.5049)
  [18]  (0.9203, 0.5138)
  [19]  (0.8495, 0.5137)
  [20]  (0.7787, 0.5142)
  [21]  (0.7079, 0.5152)
  [22]  (0.6371, 0.5162)
  [23]  (0.5663, 0.5171)
  [24]  (0.4955, 0.5181)
  [25]  (0.4248, 0.5191)
  [26]  (0.3540, 0.5200)
  [27]  (0.2832, 0.5210)
  [28]  (0.2124, 0.5216)
  [29]  (0.1416, 0.5213)
  [30]  (0.0708, 0.5210)
  [31]  (0.0000, 0.5208)
  [32]  (0.8659, 0.1167)
  [33]  (0.9000, 0.1358)
  [34]  (0.9341, 0.1549)
  [35]  (0.9682, 0.1740)
  [36]  (1.0000, 0.1927)
  [37]  (0.9615, 0.1992)
  [38]  (0.9229, 0.2058)
  [39]  (0.8844, 0.2123)
  [40]  (0.8458, 0.2188)
  [41]  (0.8073, 0.2254)
  [42]  (0.7895, 0.1911)
  [43]  (0.7866, 0.1607)
  [44]  (0.8208, 0.1417)
  [45]  (0.8540, 0.1453)
  [46]  (0.8863, 0.1672)
  [47]  (0.9186, 0.1892)
  [48]  (0.8659, 0.9999)
  [49]  (0.7948, 0.9398)
  [50]  (0.7259, 0.8771)
  [51]  (0.6570, 0.8144)
  [52]  (0.5881, 0.7518)
  [53]  (0.5184, 0.6900)
  [54]  (0.4459, 0.6314)
  [55]  (0.3735, 0.5729)
  [56]  (0.3010, 0.5143)
  [57]  (0.2286, 0.4558)
  [58]  (0.2015, 0.3979)
  [59]  (0.2758, 0.3417)
  [60]  (0.3583, 0.3090)
  [61]  (0.4515, 0.3065)
  [62]  (0.5446, 0.3040)
  [63]  (0.6377, 0.3015)

--- KEY VERTICES (corners with angle < 120 degrees) ---
  V0  (0.8785, 0.8344)  angle=124.7 deg
  V1  (0.4444, 0.1301)  angle=61.5 deg
  V2  (0.4882, 0.0763)  angle=37.4 deg
  V3  (0.9384, 0.0069)  angle=89.3 deg
  V4  (0.8659, 0.4836)  angle=81.1 deg
  V5  (0.9334, 0.5049)  angle=128.4 deg
  V6  (0.9203, 0.5138)  angle=34.1 deg
  V7  (0.0000, 0.5208)  angle=154.8 deg
  V8  (0.8659, 0.1167)  angle=54.3 deg
  V9  (1.0000, 0.1927)  angle=139.9 deg
  V10  (0.8073, 0.2254)  angle=72.1 deg
  V11  (0.7866, 0.1607)  angle=66.2 deg
  V12  (0.8208, 0.1417)  angle=35.2 deg
  V13  (0.9186, 0.1892)  angle=59.5 deg
  V14  (0.8659, 0.9999)  angle=126.5 deg
  V15  (0.2015, 0.3979)  angle=77.9 deg

--- SUGGESTED DOT TEMPLATE FORMAT ---
// Paste into SpellGestureTracker.java getDotTemplates():
new DotTemplate(DetectedPattern.SPELL_NAME, "description",
    new double[][] {
        // pick key dots from vertices above
    },
    new int[][] {
        // define connections between dots
    }
),
