Use DouglasPeucker with squaredEuclideanDistance

include/engine/douglas_peucker.hpp

@@ -12,26 +12,47 @@ namespace engine
 {
 namespace detail
 {
-const constexpr int DOUGLAS_PEUCKER_THRESHOLDS[19] = {
-    512440, // z0
-    256720, // z1
-    122560, // z2
-    56780,  // z3
-    28800,  // z4
-    14400,  // z5
-    7200,   // z6
-    3200,   // z7
-    2400,   // z8
-    1000,   // z9
-    600,    // z10
-    120,    // z11
-    60,     // z12
-    45,     // z13
-    36,     // z14
-    20,     // z15
-    8,      // z16
-    6,      // z17
-    4,      // z18
+
+// This is derived from the following formular:
+// x = b * (1 + lon/180) => dx = b * dlon/180
+// y = b * (1 - lat/180) => dy = b * dlat/180
+// dx^2 + dy^2 < min_pixel^2
+// => dlon^2 + dlat^2 < min_pixel^2 / b^2 * 180^2
+inline std::vector<std::uint64_t> generateThreshold(double min_pixel, unsigned number_of_zoomlevels)
+{
+    std::vector<std::uint64_t> thresholds(number_of_zoomlevels);
+    for (unsigned zoom = 0; zoom < number_of_zoomlevels; ++zoom)
+    {
+        const double shift = (1u << zoom) * 256;
+        const double b = shift / 2.0;
+        const double pixel_to_deg = 180. / b;
+        const std::uint64_t min_deg = min_pixel * pixel_to_deg * COORDINATE_PRECISION;
+        thresholds[zoom] = min_deg * min_deg;
+    }
+
+    return thresholds;
+}
+
+const constexpr std::uint64_t DOUGLAS_PEUCKER_THRESHOLDS[19] = {
+    49438476562500, // z0
+    12359619140625, // z1
+    3089903027344,  // z2
+    772475756836,   // z3
+    193118939209,   // z4
+    48279515076,    // z5
+    12069878769,    // z6
+    3017414761,     // z7
+    754326225,      // z8
+    188567824,      // z9
+    47141956,       // z10
+    11785489,       // z11
+    2944656,        // z12
+    736164,         // z13
+    184041,         // z14
+    45796,          // z15
+    11449,          // z16
+    2809,           // z17
+    676,            // z18
 };
 
 const constexpr auto DOUGLAS_PEUCKER_THRESHOLDS_SIZE =