docs: update benchmark with A*

Author: william-silversmith

README.md

@@ -115,13 +115,13 @@ python setup.py develop
 
 ## Performance
 
-I ran the algorithm on a field of ones from the bottom left corner to the top right corner of a 512x512x512 int8 image using a 3.7 GHz Intel i7-4920K CPU. Unidirectional search takes about 39.5 seconds (3.4 MVx/sec) with a maximum memory usage of about 1300 MB. In the unidirectional case, this test forces the algorithm to process nearly all of the volume (dijkstra aborts early when the target is found). In the bidirectional case, the volume is processed in about 11.5 seconds (11.7 MVx/sec) with a peak memory usage of about 2300 MB.
+I ran three algorithms on a field of ones from the bottom left corner to the top right corner of a 512x512x512 int8 image using a 3.7 GHz Intel i7-4920K CPU. Unidirectional search takes about 42 seconds (3.2 MVx/sec) with a maximum memory usage of about 1300 MB. In the unidirectional case, this test forces the algorithm to process nearly all of the volume (dijkstra aborts early when the target is found). In the bidirectional case, the volume is processed in about 11.8 seconds (11.3 MVx/sec) with a peak memory usage of about 2300 MB. The A* version processes the volume in 0.5 seconds (268.4 MVx/sec) with an identical memory profile to unidirectional search. A* works very well in this simple case, but may not be superior in all configurations.
 
 Theoretical unidirectional memory allocation breakdown: 128 MB source image, 512 MB distance field, 512 MB parents field (1152 MB). Theoretical bidirectional memory allocation breakdown: 128 MB source image, 2x 512 distance field, 2x 512 MB parental field (2176 MB).
 
 <p style="font-style: italics;" align="center">
-<img height=384 src="https://raw.githubusercontent.com/seung-lab/dijkstra3d/master/dijkstra3d.png" alt="Fig. 1: A benchmark of dijkstra.dijkstra run on a 512^3 voxel field of ones from bottom left source to top right target. (black) bidirectional search (blue) unidirectional search." /><br>
-Fig. 1: A benchmark of dijkstra.dijkstra run on a 512<sup>3</sup> voxel field of ones from bottom left source to top right target. (black) bidirectional search (blue) unidirectional search.
+<img height=384 src="https://raw.githubusercontent.com/seung-lab/dijkstra3d/master/dijkstra3d.png" alt="Fig. 1: A benchmark of dijkstra.dijkstra run on a 512<sup>3</sup> voxel field of ones from bottom left source to top right target. (black) unidirectional search (blue) bidirectional search (red) A* search aka compass=True." /><br>
+Fig. 1: A benchmark of dijkstra.dijkstra run on a 512<sup>3</sup> voxel field of ones from bottom left source to top right target. (black) unidirectional search (blue) bidirectional search (red) A* search aka <code>compass=True</code>.
 </p>
 
 ```python 
@@ -130,10 +130,12 @@ import time
 import dijkstra3d
 
 field = np.ones((512,512,512), order='F', dtype=np.int8)
+source = (0,0,0)
+target = (511,511,511)
 
-s = time.time()
-path = dijkstra3d.dijkstra(x, source=(0,0,0), target=(511, 511, 511), bidirectional=True) # or False 
-print(time.time() - s)
+path = dijkstra3d.dijkstra(field, source, target) # black line
+path = dijkstra3d.dijkstra(field, source, target, bidirectional=True) # blue line
+path = dijkstra3d.dijkstra(field, source, target, compass=True) # red line
 ```