Comparison of Group and Hull Results

With the functions to grab a group's concave hull up and running, now seems a good time to stop and compare the results of the holistic group grabbing functions versus those of the hull grabbing functions. To preface, none of the results were in the least bit surprising, and they have shown me that further modifications are needed to accurately represent a group with the least amount of data possible. If, however, only the hull is needed, the hull functions provide no more or less than the tightest concave hull possible.

Below is the numeric output representation of one of the groups I used to compare the two function sets. This group was made by cupping my left and and placing it horizontally on the sensor, pinky-side down. It took several tries to get the shape just right such that the top was a straight horizontal line, one of the necessary testing conditions for determining whether or not the hull functions perform to my specifications.

0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   135228141617349 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   427 1153168628043562224115  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   240838351020442 56  474 15641568598 17  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   43  1394920 0   0   0   0   28  904 1249870 357 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   115910410   0   0   0   0   0   0   559 125214151153725 3   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   317 52  0   0   0   0   0   0   0   0   1247185614361648124538  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   434 1597196417731189369 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   905 190718851292353 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   834 14161579117623  0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   20  691 1317124134  0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   15  27  23  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   


   Center: 22.099086 14.843965

I'll begin by describing the reason for creating this particular shape. As mentioned above, the top of the shape contains a stretch of linear, horizontal hull points. As only the end points of that line are necessary to determine its shape, the algorithm checks for and excludes these kinds of points. It does so by excluding points that contain a linear sequence of adjacent edge points wherein the excluded points are adjacent to exactly three zero-points and those three zero-points are vertically or horizontally linear. If a point is adjacent to exactly three linear zero-points, then it is guaranteed to have one edge-point neighbor on each side in the same direction; thus, that point lies within a linear edge. If, on the other hand, the point has four adjacent zero-points, it is guaranteed to be an end point. If the edge is adjacent to exactly one or exactly two points, then it is in a concave portion of the shape. The only case that needs be excluded is the case in which a point is adjacent to exactly three linear zero-points.

This shape also affords the opportunity to determine whether or not the hull-grabbing algorithm truly generates a concave hull, due to the curvature on the bottom. Convex hull wrapping would ignore the entire concave portion of the shape, leaving too many extraneous zero-points in the group data set. It would also give an inaccurate impression of the group's shape. This particular group allowed me to see if the algorithm actually did what I intended: picking up the concave hull of the group.

Since only one group was picked up from this pressure array, the results are easy to see side-by-side. The group centers and points within the group are listed below.

  Holistic Group Grab  Hull Grab
  
Centers (x y):
  22.099086 14.843965  17.866549 13.251164

Data Points (x y data):
  13 15 1159           13 15 1159
  13 16 317            13 16 317
  14 14 434            14 14 434
  14 15 1041           14 15 1041
  14 16 52             14 16 52
  15 13 2408           15 13 2408
  15 14 1394           15 14 1394
  16 13 3835           16 13 3835
  16 14 920            16 14 920
  17 12 427            17 12 427
  17 13 1020           17 13 1020
  18 12 1153
  18 13 442            18 13 442
  19 11 1352           19 11 1352
  19 12 1686
  19 13 56             19 13 56
  20 11 2814           20 11 2814
  20 12 2804
  20 13 474
  21 11 1617           21 11 1617
  21 12 3562
  21 13 1564
  21 14 28             21 14 28
  22 11 349            22 11 349
  22 12 2241
  22 13 1568
  22 14 904
  22 15 559            22 15 559
  23 12 15             23 12 15
  23 13 598
  23 14 1249
  23 15 1252
  23 16 1247
  23 17 434            23 17 434
  24 13 17             24 13 17
  24 14 870
  24 15 1415
  24 16 1856
  24 17 1597
  24 18 905            24 18 905
  25 14 357            25 14 357
  25 15 1153
  25 16 1436
  25 17 1964
  25 18 1907
  25 19 834
  25 20 20             25 20 20
  26 15 725
  26 16 1648
  26 17 1773
  26 18 1885
  26 19 1416
  26 20 691
  26 21 15             26 21 15
  27 15 3              27 15 3
  27 16 1245
  27 17 1189
  27 18 1292
  27 19 1579
  27 20 1317
  27 21 27             27 21 27
  28 16 38             28 16 38
  28 17 369            28 17 369
  28 18 353
  28 19 1176
  28 20 1241
  28 21 23             28 21 23
  29 19 23             29 19 23
  29 20 34             29 20 34

The blank lines were intentionally place in the hull group point list to underscore the difference between these two point lists. The hull point set is, as expected, much smaller than the holistic set (33 points, as compared to 69).