feat: analytical turn waypoints

Make sure all Dubins and Reeds-Shepp turns have enough
waypoints, even with very small turning radius.

#1025

Author: Peter Vaiko

scripts/pathfinder/Dubins.lua

@@ -46,7 +46,7 @@ function DubinsSolution:getLength(turnRadius)
 end
 
 function DubinsSolution:getWaypoints(start, turnRadius)
-    return dubins_path_sample_many(self.pathDescriptor, 1)
+    return dubins_path_sample_many(self.pathDescriptor, math.min(1, turnRadius * math.pi / 12))
 end
 
 local twoPi = 2 * math.pi

scripts/pathfinder/ReedsShepp.lua

@@ -174,7 +174,10 @@ function ReedsShepp.ActionSet:getWaypoints(start, turnRadius)
     local waypoints = {}
     table.insert(waypoints, prev)
     for _, action in ipairs(self.actions) do
-        local n = math.ceil(action.length * turnRadius)
+        -- waypoints are 1 m apart, but make sure there are at least 12 waypoints per half circle
+        -- even with very small radii
+        local n = math.ceil(math.max(action.length * turnRadius, action.length / math.pi * 12))
+        print(action, n)
         if action.steer ~= Steer.Straight then
             local pieceAngle = action.length / n