Instrumented version - to look at timings

Including:
- replacing guassian with simpler triangle distribution
- Timing calculations -resulting in using only 50 points.
- Changes (which may need to be reconsidered) for optimization. These are likely to be simplified back.

ch-13/full-version/robot/arena.py

@@ -30,14 +30,14 @@ def point_is_inside_arena(x, y):
   return True
 
 ## intention - we can use a distance squared function to avoid the square root, and just square the distance sensor readings too.
-def get_ray_distance_to_segment_squared(ray, segment):
+def get_ray_distance_to_segment_squared(ray_x, ray_y, ray_tan, ray_heading, segment):
   """Return the distance squared from the ray origin to the intersection point along the given ray heading.
   The segments are boundary lines, which will be horizontal or vertical, and have known lengths.
   The ray can have any heading, and will be infinite in length.
   Ray -> (x, y, heading)
+  ray_tan -> tangent of the heading (optimization)
   Segment -> ((x1, y1), (x2, y2))
   """
-  ray_x, ray_y, ray_heading = ray
   segment_x1, segment_y1 = segment[0]
   segment_x2, segment_y2 = segment[1]
   # if the segment is horizontal, the ray will intersect it at a known y value
@@ -46,7 +46,7 @@ def get_ray_distance_to_segment_squared(ray, segment):
     if ray_heading == 0:
       return None
     # calculate the x value of the intersection point
-    intersection_x = ray_x + (segment_y1 - ray_y) / math.tan(ray_heading)
+    intersection_x = ray_x + (segment_y1 - ray_y) / ray_tan
     # is the intersection point on the segment?
     if intersection_x > max(segment_x1, segment_x2) or intersection_x < min(segment_x1, segment_x2):
       return None
@@ -58,7 +58,7 @@ def get_ray_distance_to_segment_squared(ray, segment):
     if ray_heading == math.pi / 2:
       return None
     # calculate the y value of the intersection point 
-    intersection_y = ray_y + (segment_x1 - ray_x) * math.tan(ray_heading)
+    intersection_y = ray_y + (segment_x1 - ray_x) * ray_tan
     # is the intersection point on the segment?
     if intersection_y > max(segment_y1, segment_y2) or intersection_y < min(segment_y1, segment_y2):
       return None
@@ -75,8 +75,10 @@ def get_ray_distance_squared_to_nearest_boundary_segment(ray):
   """
   # find the distance to each segment
   distances = []
+  ray_x, ray_y, ray_heading = ray
+  ray_tan = math.tan(ray_heading)
   for segment in boundary_lines:
-    distance_squared = get_ray_distance_to_segment_squared(ray, segment)
+    distance_squared = get_ray_distance_to_segment_squared(ray_x, ray_y, ray_tan, ray_heading, segment)
     if distance_squared is not None:
       distances.append(distance_squared)
   # return the minimum distance