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I have a series of points, as a list of pairs of real numbers, each multiple of a base value. So they represent a subset of a grid.
Given that this list, when represented with ListPlot, seems to delimit a 2D domain, I would like to know if there is a way to represent the boundaries of such a domain with polygonal or smooth interpolation functions.

Here is a sample image of my data:

enter image description here

These are my sample data:

{{0.02, 0.64}, {0.04, 0.64}, {0.06, 0.64}, {0.08, 0.64}, {
  0.08, 0.66}, {0.1, 0.64}, {0.1, 0.66}, {0.12, 0.64}, {0.12, 0.66}, {
    0.14, 0.64}, {0.14, 0.66}, {0.14, 0.68}, {
  0.16, 0.64}, {0.16, 0.66}, {0.16, 0.68}, {0.18, 0.64}, {0.18, 0.66}, {0.18, \
0.68}, {0.2, 0.66}, {0.2, 0.68}, {
  0.2, 0.7}, {0.22, 0.66}, {0.22, 0.68}, {0.22, 0.7}, {0.24, 0.66}, {
    0.24, 0.68}, {0.24, 0.7}, {0.26, 0.66}, {0.26, 0.68}, {0.26, 0.7}, {0.28,
   0.66}, {0.28, 0.68}, {0.28, 0.7}, {0.28, 0.72}, {0.3,
   0.66}, {0.3, 0.68}, {0.3, 0.7}, {0.3, 0.72}, {0.32, 0.66}, {0.32, 
    0.68}, {0.32,
   0.7}, {0.32, 0.72}, {0.34, 0.66}, {0.34, 0.68}, {0.34, 0.7}, {0.34,
     0.72}, {0.34,
   0.74}, {0.36, 0.66}, {0.36, 0.68}, {
    0.36, 0.7}, {0.36, 0.72}, {0.36, 0.74}, {0.38, 0.66}, {0.38, 0.68}, \
{0.38, 0.7}, {0.38, 0.72}, {0.38, 0.74}, {0.4, 0.66}, {0.4,
   0.68}, {0.4, 0.7}, {0.4, 0.72}, {0.4, 0.74}, {0.42,
   0.66}, {0.42, 0.68}, {0.42, 0.7}, {0.42, 0.72}, {0.42, 
  0.74}, {0.42, 0.76}, {
  0.44, 0.66}, {
    0.44, 0.68}, {0.44, 0.7}, {0.44, 0.72}, {0.44, 0.74}, {0.44, 0.76}, \
{0.46, 0.66}, {0.46, 0.68}, {0.46, 0.7}, {
  0.46, 0.72}, {
    0.46, 0.74}, {0.46, 0.76}, {0.48, 0.66}, {0.48, 0.68}, {0.48, 0.7}, \
{0.48, 0.72}, {0.48, 0.74}, {0.48, 0.76}, {0.48, 0.78}, {0.5, 0.66}, {
    0.5, 0.68}, {0.5, 0.7}, {0.5, 0.72}, {0.5, 0.74}, {0.5, 0.76}, {0.5,
   0.78}, {0.52, 0.66}, {0.52, 0.68}, {0.52, 0.7}, {0.52, 
  0.72}, {0.52, 0.74}, {0.52, 
  0.76}, {0.52, 0.78}, {0.54, 0.66}, {0.54, 0.68}, {0.54, 0.7}, {
    0.54, 0.72}, {0.54, 0.74}, {0.54, 0.76}, {0.54, 
    0.78}, {0.56, 0.68}, {0.56, 0.7}, {0.56, 0.72}, {0.56, 0.74}, {0.56, 
  0.76}, {0.56, 0.78}, {0.56, 0.8}, {0.58, 0.68}, {0.58,
   0.7}, {0.58, 0.72}, {0.58, 0.74}, {0.58, 0.76}, {0.58, 
  0.78}, {0.58, 0.8}, {0.6, 0.68}, {0.6, 
    0.7}, {0.6, 0.72}, {0.6, 0.74}, {0.6, 0.76}, {0.6, 0.78}, {
    0.6, 0.8}, {0.62, 0.68}, {0.62, 0.7}, {0.62, 0.72}, {
    0.62, 0.74}, {0.62, 0.76}, {0.62, 0.78}, {0.62, 0.8}, {0.62, 0.82}, \
{0.64, 0.68}, {0.64, 0.7}, {0.64, 0.72}, {0.64, 0.74}, {0.64, 0.76}, {0.64, \
0.78}, {0.64, 0.8}, {
  0.64, 0.82}, {
    0.66, 0.68}, {0.66, 0.7}, {0.66, 0.72}, {0.66, 0.74}, {0.66, 0.76}, \
{0.66, 0.78}, {0.66, 0.8}, {0.66, 0.82}, {0.68, 0.68}, {0.68, 
    0.7}, {0.68, 0.72}, {0.68, 0.74}, {0.68, 0.76}, {0.68, 0.78}, {0.68,
   0.8}, {0.68, 0.82}, {0.68, 0.84}, {0.7, 
    0.68}, {0.7, 0.7}, {0.7, 0.72}, {0.7, 0.74}, {0.7, 0.76}, {
    0.7, 0.78}, {0.7, 0.8}, {0.7, 0.82}, {0.7, 0.84}, {
    0.72, 0.68}, {0.72, 0.7}, {0.72, 0.72}, {0.72, 0.74}, {
    0.72, 0.76}, {0.72, 0.78}, {
    0.72, 0.8}, {0.72, 0.82}, {0.72, 0.84}, {0.74, 0.7}, {0.74, 0.72}, {0.74, 
    0.74}, {0.74, 0.76}, {0.74, 0.78}, {0.74, 
  0.8}, {0.74, 0.82}, {0.74, 0.84}, {0.76, 0.7}, {0.76, 0.72}, {0.76, 0.74}, {
  0.76, 0.76}, {0.76, 0.78}, {
  0.76, 0.8}, {0.76, 0.82}, {0.76, 0.84}, {0.76, 0.86}, {0.78, 0.7}, {
    0.78, 0.72}, {0.78, 0.74}, {0.78, 0.76}, {0.78, 0.78}, {0.78, 0.8}, {0.78,
   0.82}, {0.78, 0.84}, {0.78, 0.86}, {0.8, 0.7}, {0.8, 
  0.72}, {0.8, 0.74}, {0.8, 0.76}, {0.8, 0.78}, {0.8, 0.8}, {0.8, 0.82}, {0.8,
   0.84}, {0.8, 0.86}, {0.82, 
  0.7}, {0.82, 0.72}, {0.82, 0.74}, {0.82, 0.76}, {0.82, 0.78}, {0.82, 0.8}, {
  0.82, 0.82}, {0.82, 0.84}, {0.82, 0.86}, {0.82, 0.88}, {0.84, 
    0.7}, {0.84, 0.72}, {0.84, 0.74}, {0.84, 0.76}, {0.84, 0.78}, {0.84, \
0.8}, {0.84, 0.82}, {0.84, 0.84}, {0.84, 0.86}, {
  0.84, 0.88}, {
    0.86, 0.72}, {0.86, 0.74}, {0.86, 0.76}, {0.86, 0.78}, {0.86, 0.8}, \
{0.86, 0.82}, {0.86, 0.84}, {0.86, 0.86}, {0.86, 0.88}, {0.88, 0.72}, {0.88, \
0.74}, {0.88, 0.76}, {0.88, 0.78}, {0.88, 0.8}, {0.88, 0.82}, {
  0.88, 0.84}, {0.88, 0.86}, {
  0.88, 0.88}, {0.88, 0.9}, {0.9, 0.72}, {0.9, 0.74}, {0.9, 0.76}, {
    0.9, 0.78}, {0.9, 0.8}, {0.9, 0.82}, {0.9,
   0.84}, {0.9, 
    0.86}, {0.9, 0.88}, {0.9, 0.9}, {0.92, 0.72}, {0.92, 0.74}, {0.92, 0.76}, \
{0.92, 0.78}, {0.92, 0.8}, {0.92, 0.82}, {0.92, 0.84}, {0.92, 0.86}, {
  0.92, 0.88}, {
    0.92, 0.9}, {0.94, 0.74}, {0.94, 0.76}, {0.94, 0.78}, {0.94, 0.8}, {
  0.94, 0.82}, {0.94, 0.84}, {0.94, 0.86}, {0.94, 0.88}, {
  0.94, 0.9}, {0.96, 0.74}, {0.96, 0.76}, {0.96, 0.78}, {0.96, 0.8}, {
    0.96, 0.82}, {0.96, 0.84}, {0.96, 0.86}, {
  0.96, 0.88}, {0.96, 0.9}, {0.96, 0.92}, {
    0.98, 0.74}, {0.98, 0.76}, {0.98, 0.78}, {0.98, 0.8}, {0.98, 0.82}, {
  0.98, 0.84}, {0.98, 0.86}, {0.98, 0.88}, {0.98, 0.9}, {
    0.98, 0.92}, {1., 0.74}, {1., 0.76}, {1.,
   0.78}, {1., 0.8}, {1., 0.82}, {1., 0.84}, {1., 0.86}, {1., 
    0.88}, {1., 0.9}, {1., 0.92}, {1.02,
   0.76}, {1.02, 0.78}, {1.02, 0.8}, {1.02, 0.82}, {1.02, 
    0.84}, {1.02, 0.86}, {1.02, 0.88}, {1.02, 0.9}, {1.02, 0.92}, {1.02, 
    0.94}, {1.04, 0.76}, {1.04, 
    0.78}, {1.04, 0.8}, {1.04, 0.82}, {1.04, 0.84}, {1.04, 0.86}, {1.04, \
0.88}, {1.04, 0.9}, {1.04, 0.92}, {1.04, 0.94}, {1.06, 0.76}, {1.06, 
    0.78}, {1.06, 0.8}, {1.06, 0.82}, {1.06, 0.84}, {1.06, 0.86}, {1.06, \
0.88}, {1.06, 0.9}, {1.06, 0.92}, {1.06, 0.94}, {1.08, 0.76}, {1.08, 0.78}, \
{1.08, 0.8}, {1.08, 0.82}, {1.08, 0.84}, {1.08, 0.86}, {1.08, 0.88}, {1.08, \
0.9}, {1.08, 0.92}, {1.08, 0.94}, {1.08, 0.96}, {1.1, 0.76}, {1.1, 0.78}, \
{1.1, 0.8}, {1.1, 0.82}, {1.1, 0.84}, {1.1, 0.86}, {
  1.1, 0.88}, {1.1, 0.9}, {1.1, 0.92}, {1.1, 0.94}, {1.1, 
  0.96}, {1.12, 0.78}, {1.12, 0.8}, {1.12, 0.82}, {1.12,
   0.84}, {1.12, 0.86}, {1.12, 0.88}, {1.12, 0.9}, {1.12, 
  0.92}, {1.12, 0.94}, {1.12, 0.96}, {1.12, 0.98}, {1.14, 
  0.78}, {1.14, 0.8}, {1.14, 0.82}, {1.14, 0.84}, {1.14, 0.86}, {1.14, 
    0.88}, {1.14, 0.9}, {1.14, 0.92}, {1.14, 0.94}, {1.14, 0.96}, {1.14, \
0.98}, {1.16, 0.78}, {1.16, 0.8}, {1.16, 0.82}, {1.16, 0.84}, {1.16, 
    0.86}, {1.16, 0.88}, {1.16, 
    0.9}, {1.16, 0.92}, {1.16, 0.94}, {1.16, 0.96}, {1.16, 0.98}, {1.18, \
0.78}, {1.18, 0.8}, {1.18, 0.82}, {1.18, 0.84}, {1.18, 0.86}, {1.18, 
    0.88}, {1.18, 0.9}, {1.18, 0.92}, {1.18, 0.94}, {
  1.18, 0.96}, {1.18, 0.98}, {1.18, 1.}, {1.2, 0.8}, {1.2, 0.82}, {1.2, \
0.84}, {1.2, 0.86}, {1.2, 0.88}, {1.2, 0.9}, {1.2, 0.92}, {1.2, 0.94}, {1.2, \
0.96}, {1.2, 0.98}, {1.2, 1.}, {1.22, 0.8}, {1.22, 0.82}, {1.22, 0.84}, \
{1.22, 0.88}, {1.22, 0.9}, {1.22, 0.92}, {1.22, 0.94}, {1.22, 0.96}, {1.22, \
0.98}, {1.22, 1.}, {1.24, 0.8}, {
  1.24, 0.82}, {
    1.24, 0.84}, {1.24, 0.86}, {1.24, 0.88}, {1.24, 0.9}, {1.24, 0.92}, \
{1.24, 0.94}, {1.24, 0.96}, {1.24, 0.98}, {1.24, 1.}, {1.24, 1.02}, {
    1.26, 0.8}, {1.26, 0.82}, {1.26, 0.84}, {1.26, 0.86}, {1.26, 
  0.88}, {1.26, 0.9}, {1.26,
   0.92}, {1.26, 0.94}, {1.26, 0.96}, {1.26, 0.98}, {1.26, 1.}, {1.26,
     1.02}, {1.28, 0.82}, {1.28, 0.84}, {1.28, 0.86}, {
    1.28, 0.9}, {1.28, 0.92}, {1.28, 0.94}, {1.28, 0.96}, {
    1.28, 0.98}, {1.28, 1.}, {1.28, 1.02}, {1.3, 0.82}, {1.3, 0.84}, {1.3,
   0.86}, {1.3, 0.88}, {1.3,
   0.9}, {1.3, 0.92}, {1.3, 
  0.94}, {1.3, 0.96}, {1.3, 0.98}, {1.3, 1.}, {1.3, 1.02}, {1.3, 
    1.04}, {1.32, 0.82}, {1.32, 0.84}, {1.32, 0.86}, {1.32, 
    0.88}, {1.32, 0.92}, {1.32, 0.94}, {1.32, 0.96}, {1.32, 0.98}, {1.32,
   1.}, {1.32, 1.02}, {1.32, 1.04}, {
    1.34, 0.82}, {1.34, 0.84}, {1.34, 0.86}, {1.34, 0.88}, {1.34, 0.92}, \
{1.34, 0.94}, {1.34, 0.96}, {1.34, 0.98}, {1.34, 1.}, {
    1.34, 1.02}, {1.34, 1.04}, {1.34, 1.06}, {1.36, 0.84}, {
    1.36, 0.86}, {1.36, 0.88}, {1.36, 0.94}, {1.36, 0.96}, {
    1.36, 0.98}, {1.36, 1.}, {1.36, 1.02}, {1.36, 1.04}, {
    1.36, 1.06}, {1.38, 0.84}, {1.38, 0.86}, {1.38, 0.88}, {
    1.38, 0.9}, {1.38, 0.94}, {1.38, 0.96}, {1.38, 0.98}, {1.38, 1.}, {1.38, \
1.02}, {1.38, 1.04}, {1.38, 1.06}, {1.4, 0.84}, {1.4, 0.86}, {1.4,
     0.88}, {1.4, 
  0.9}, {1.4, 0.94}, {1.4, 0.96}, {1.4, 0.98}, {1.4, 1.}, {1.4, 1.02}, {
    1.4, 1.04}, {1.4, 1.06}, {1.4, 1.08}, {1.42, 0.86}, {
    1.42, 0.88}, {1.42, 0.9}, {1.42, 0.96}, {
  1.42, 0.98}, {1.42, 1.}, {1.42, 1.02}, {1.42, 1.04}, {1.42, 1.06}, {
    1.42, 1.08}, {1.44, 0.86}, {1.44, 0.88}, {
  1.44, 0.9}, {1.44, 0.96}, {1.44, 0.98}, {
    1.44, 1.}, {1.44, 1.02}, {1.44, 1.04}, {1.44, 1.06}, {1.44, 1.08}, {1.44, \
1.1}, {1.46, 0.86}, {
  1.46, 0.88}, {1.46, 0.9}, {1.46, 0.92}, {1.46, 0.98}, {1.46, 1.}, {
    1.46, 1.02}, {1.46, 1.04}, {1.46, 1.06}, {1.46, 1.08}, {
    1.46, 1.1}, {1.48, 0.86}, {1.48, 0.88}, {1.48, 0.9}, {
    1.48, 0.92}, {1.48, 0.98}, {1.48, 1.}, {1.48, 1.02}, {
    1.48, 1.04}, {1.48, 1.06}, {1.48, 1.08}, {1.48, 1.1}, {
    1.5, 0.88}, {1.5, 0.9}, {1.5, 0.92}, {1.5,
   1.}, {1.5, 
    1.02}, {1.5, 1.04}, {1.5, 1.06}, {1.5, 1.08}, {1.5, 1.1}, {1.5, 1.12}, \
{1.52, 0.88}, {1.52, 0.9}, {1.52, 0.92}, {1.52, 1.}, {1.52, 1.02}, {
    1.52, 1.04}, {1.52, 1.06}, {1.52, 1.08}, {1.52, 1.1}, {1.52, 1.12}, \
{1.54, 0.78}, {1.54, 0.8}, {1.54, 0.82}, {1.54, 0.84}, {1.54, 0.9}, {
    1.54, 0.92}, {1.54, 0.94}, {1.54, 1.02}, {1.54, 1.04}, {1.54, 1.06}, \
{1.54, 1.08}, {1.54, 1.1}, {1.54, 1.12}, {1.54,
   1.14}, {1.56, 0.76}, {1.56, 0.78}, {
    1.56, 0.8}, {1.56, 0.82}, {1.56, 0.84}, {1.56, 0.86}, {1.56, 0.9}, {1.56,
   0.92}, {1.56, 0.94}, {1.56,
   1.02}, {1.56, 1.04}, {1.56, 1.06}, {
    1.56, 1.08}, {1.56, 1.1}, {1.56, 1.12}, {1.56, 1.14}, {1.58, 0.76}, \
{1.58, 0.78}, {1.58, 0.8}, {1.58, 0.82}, {1.58, 0.84}, {1.58, 0.86}, {
    1.58, 0.88}, {1.58, 0.9}, {1.58, 0.92}, {1.58, 0.94}, {1.58, 1.04}, \
{1.58, 1.06}, {1.58, 1.08}, {1.58, 1.1}, {1.58, 1.12}, {1.58,
   1.14}, {1.58, 1.16}, {1.6, 0.76}, {1.6, 0.78}, {1.6, 
  0.8}, {1.6, 
    0.82}, {1.6, 0.84}, {1.6, 0.86}, {1.6, 0.88}, {1.6, 0.9}, {1.6, 0.92}, {
  1.6, 0.94}, {1.6, 1.04}, {
  1.6, 1.06}, {1.6, 1.08}, {1.6, 1.1}, {1.6, 1.12}, {1.6, 
  1.14}, {1.6, 1.16}, {1.62, 0.76}, {1.62, 0.78}, {1.62,
   0.8}, {1.62, 0.82}, {1.62, 0.84}, {1.62, 0.86}, {1.62, 
  0.88}, {1.62, 0.9}, {1.62, 0.96}, {1.62, 1.06}, {1.62,
   1.08}, {1.62, 1.1}, {1.62, 1.12}, {1.62, 1.14}, {1.62, 1.16}, {1.64, 
    0.78}, {1.64, 0.8}, {1.64, 0.82}, {
    1.64, 0.84}, {1.64, 0.86}, {1.64, 0.88}, {1.64, 0.9}, {
  1.64, 0.92}, {1.64, 0.98}, {1.64, 1.}, {1.64, 1.14}, {
  1.64, 1.16}, {1.64, 1.18}, {
  1.66, 0.78}, {
    1.66, 0.8}, {1.66, 0.82}, {1.66, 0.84}, {1.66, 0.86}, {1.66, 0.88}, \
{1.66, 0.9}, {1.66, 0.92}, {1.66, 0.98}, {1.66, 1.}, {
  1.66, 1.02}, {
    1.66, 1.04}, {1.66, 1.06}, {1.66, 1.16}, {1.66, 1.18}, {1.66, 1.52}, \
{1.66, 1.54}, {1.66, 1.56}, {1.68, 0.8}, {1.68, 0.82}, {1.68, 0.84}, {1.68, \
0.86}, {1.68, 0.88}, {1.68, 0.9}, {1.68, 0.92}, {1.68, 1.}, {
  1.68, 1.02}, {
    1.68, 1.04}, {1.68, 1.06}, {1.68, 1.16}, {1.68, 1.18}, {1.68, 1.2}, \
{1.68, 1.52}, {1.68, 1.54}, {1.68, 1.56}, {1.68, 1.58}, {1.68, 1.6}, {1.68, \
1.62}, {1.68, 1.64}, {1.68, 1.66}, {1.68, 1.68}, {1.68, 1.7}, {1.68, 1.72}, \
{1.7, 0.8}, {1.7, 0.82}, {1.7, 0.84}, {1.7, 0.86}, {
    1.7, 0.88}, {1.7, 0.9}, {1.7, 0.92}, {1.7,
   0.94}, {1.7, 1.}, {1.7, 1.02}, {1.7, 1.04}, {1.7, 1.06}, {1.7, 1.08}, {
    1.7, 1.18}, {1.7, 1.2}, {1.7, 1.52}, {1.7, 1.54}, {1.7, 1.56}, {1.7, \
1.58}, {1.7, 1.6}, {1.7, 1.62}, {1.7, 1.64}, {1.7, 1.66}, {1.7,
   1.68}, {1.7, 1.7}, {1.7, 1.72}, {1.7, 1.74}, {1.7, 1.76}, {1.7,
   1.78}, {1.7, 1.8}, {1.72, 0.82}, {1.72, 0.84}, {1.72,
   0.86}, {1.72, 0.88}, {1.72, 0.9}, {1.72, 0.92}, {1.72, 0.94}, {
    1.72, 1.}, {1.72, 1.02}, {1.72, 1.04}, {1.72, 1.06}, {1.72, 1.08}, {1.72, \
1.2}, {1.72, 1.22}, {1.72, 1.52}, {1.72, 1.54}, {1.72, 1.56}, {
    1.72, 1.58}, {1.72, 1.6}, {1.72, 1.62}, {1.72, 1.64}, {1.72, 1.66}, {
  1.72, 1.68}, {1.72, 1.7}, {1.72, 1.72}, {1.72, 1.74}, {1.72, 1.76}, {
    1.72, 1.78}, {1.72, 1.8}, {1.72, 1.82}, {1.72, 1.84}, {1.74, 0.82}, {
  1.74, 0.84}, {1.74, 0.86}, {
  1.74, 0.88}, {1.74, 0.9}, {1.74, 0.92}, {1.74, 0.94}, {1.74, 1.02}, {
    1.74, 1.04}, {1.74, 1.06}, {1.74, 1.08}, {1.74, 1.1}, {
    1.74, 1.2}, {1.74, 1.22}, {1.74, 1.52}, {1.74, 1.54}, {
    1.74, 1.56}, {1.74, 1.58}, {1.74, 1.6}, {1.74, 1.62}, {1.74, 1.64}, {
  1.74, 1.66}, {1.74, 1.68}, {1.74, 1.7}, {1.74, 1.72}, {1.74, 1.74}, {1.74, \
1.76}, {1.74, 1.78}, {1.74, 1.8}, {1.74, 1.82}, {1.74, 1.84}, {1.74, 1.86}, \
{1.74, 1.88}, {1.76, 0.84}, {1.76, 0.86}, {1.76, 0.88}, {1.76, 0.9}, {1.76, \
0.92}, {1.76, 0.94}, {1.76, 0.96}, {1.76, 1.02}, {1.76, 1.04}, {1.76, 1.06}, \
{1.76, 1.08}, {1.76, 1.1}, {1.76, 1.22}, {1.76, 1.24}, {
  1.76, 1.52}, {1.76, 1.54}, {
  1.76, 1.56}, {
    1.76, 1.58}, {1.76, 1.6}, {1.76, 1.62}, {1.76, 1.64}, {1.76, 1.66}, \
{1.76, 1.68}, {1.76, 1.7}, {1.76, 1.72}, {1.76, 1.74}, {
  1.76, 1.76}, {1.76, 1.78}, {
  1.76, 1.8}, {1.76, 1.82}, {1.76, 1.84}, {
    1.76, 1.86}, {1.76, 1.88}, {1.76, 1.9}, {1.78, 0.86}, {1.78, 0.88}, {
  1.78, 0.9}, {1.78, 0.92}, {1.78, 0.94}, {1.78, 0.96}, {1.78, 1.02}, {
    1.78, 1.04}, {1.78, 1.06}, {1.78, 1.08}, {1.78, 1.1}, {1.78, 1.12}, {
  1.78, 1.24}, {1.78, 1.52}, {1.78, 1.54}, {1.78, 1.56}, {
  1.78, 1.58}, {
    1.78, 1.6}, {1.78, 1.62}, {1.78, 1.64}, {1.78, 1.66}, {1.78, 1.68}, \
{1.78, 1.7}, {1.78, 1.72}, {1.78, 1.74}, {1.78, 1.76}, {1.78, 1.78}, {1.78, \
1.8}, {1.78, 1.82}, {1.78, 1.84}, {1.78, 1.86}, {1.78, 1.88}, {1.78, 1.9}, \
{1.78, 1.92}, {1.8, 0.86}, {1.8, 0.88}, {1.8, 0.9}, {1.8, 0.92}, {
    1.8, 0.94}, {1.8, 0.96}, {1.8, 1.04}, {1.8,
   1.06}, {1.8, 
    1.08}, {1.8, 1.1}, {1.8, 1.12}, {1.8, 1.24}, {1.8, 1.52}, {1.8, 1.54}, \
{1.8, 1.56}, {1.8, 1.58}, {1.8, 1.6}, {1.8, 1.62}, {1.8, 1.64}, {
  1.8, 1.66}, {1.8, 1.68}, {1.8, 1.7}, {1.8, 1.72}, {1.8, 1.74}, {1.8, 1.76}, \
{1.8, 1.78}, {1.8, 1.8}, {1.8, 1.82}, {1.8, 1.84}, {
  1.8, 1.86}, {1.8, 1.88}, {1.8, 1.9}, {1.8, 1.92}, {1.8, 1.94}, {1.82, \
0.88}, {1.82, 0.9}, {1.82, 0.92}, {1.82, 0.94}, {1.82, 0.96}, {1.82, 
    0.98}, {1.82,
   1.04}, {1.82, 1.06}, {1.82, 1.08}, {1.82, 1.1}, {1.82, 1.12}, {
    1.82, 1.14}, {
  1.82, 1.26}, {1.82, 1.52}, {1.82, 1.54}, {1.82, 1.56}, {1.82, 1.58}, {1.82, 
  1.6}, {1.82, 1.62}, {1.82, 1.64}, {1.82, 1.66}, {1.82,
   1.68}, {
    1.82, 1.7}, {1.82, 1.72}, {1.82, 1.74}, {1.82, 1.76}, {1.82, 1.78}, \
{1.82, 1.8}, {1.82, 1.82}, {1.82, 1.84}, {1.82, 1.86}, {1.82, 1.88}, {
    1.82, 1.9}, {1.82, 1.92}, {1.82, 1.94}, {1.82, 1.96}, {1.84, 0.88}, \
{1.84, 0.9}, {1.84, 0.92}, {1.84, 0.94}, {1.84, 0.96}, {1.84,
   0.98}, {1.84, 1.06}, {1.84, 1.08}, {
    1.84, 1.1}, {1.84, 1.12}, {1.84, 1.14}, {1.84, 1.52}, {1.84, 1.54}, \
{1.84, 1.56}, {1.84, 1.58}, {1.84, 1.6}, {1.84, 1.62}, {1.84,
   1.64}, {1.84, 1.66}, {1.84, 1.68}, {1.84, 1.7}, {1.84, 
  1.72}, {1.84, 1.74}, {1.84, 1.76}, {1.84, 1.78}, {1.84, 1.8}, {1.84,
     1.82}, {1.84, 1.84}, {1.84, 1.86}, {1.84, 1.88}, {1.84, 1.9}, {1.84, 
  1.92}, {1.84, 1.94}, {1.84, 1.96}, {1.86, 0.9}, {1.86,
   0.92}, {1.86, 0.94}, {1.86, 0.96}, {1.86, 0.98}, {1.86,
   1.06}, {1.86, 1.08}, {1.86,
   1.1}, {1.86, 
    1.12}, {1.86, 1.14}, {1.86, 1.16}, {1.86, 1.52}, {1.86, 1.54}, {1.86, \
1.56}, {1.86, 1.58}, {1.86, 1.6}, {1.86, 1.62}, {1.86, 1.64}, {
    1.86, 1.66}, {1.86, 1.68}, {1.86, 1.7}, {1.86, 1.72}, {1.86, 1.74}, {
  1.86, 1.76}, {1.86, 1.78}, {1.86, 1.8}, {1.86, 1.82}, {1.86, 
    1.84}, {1.86, 1.86}, {1.86, 1.88}, {1.86,
   1.9}, {1.86, 1.92}, {1.86, 1.94}, {1.88, 0.9}, {1.88, 0.92}, {
    1.88, 0.94}, {1.88, 0.96}, {1.88, 0.98}, {1.88, 1.}, {1.88, 1.08}, {1.88, 
    1.1}, {1.88, 1.12}, {1.88, 1.14}, {1.88, 1.16}, {1.88, 
    1.18}, {1.88, 1.52}, {1.88, 1.54}, {1.88, 1.56}, {1.88, 1.58}, {1.88, 
  1.6}, {1.88, 1.62}, {1.88, 1.64}, {1.88, 1.66}, {1.88,
   1.68}, {1.88, 1.7}, {1.88, 1.72}, {1.88, 1.74}, {1.88, 
  1.76}, {1.88, 1.78}, {1.88, 1.8}, {1.88, 1.82}, {1.88, 1.84}, {
    1.88, 1.86}, {1.88, 1.88}, {1.88, 1.9}, {1.88, 1.92}, {
    1.88, 1.94}, {1.9, 0.92}, {1.9, 0.94}, {1.9, 0.96}, {1.9, 0.98}, {1.9,
   1.}, {1.9, 
    1.08}, {1.9, 1.1}, {1.9, 1.12}, {1.9, 1.14}, {1.9, 1.16}, {1.9, 1.18}, \
{1.9, 1.52}, {1.9, 1.54}, {1.9, 1.56}, {1.9, 1.58}, {1.9, 1.6}, {1.9, 1.62}, \
{1.9, 1.64}, {1.9, 1.66}, {1.9, 1.68}, {1.9, 1.7}, {1.9, 1.72}, {1.9, 1.74}, {
    1.9, 1.76}, {1.9, 1.78}, {1.9, 1.8}, {1.9, 1.82}, {1.9, 1.84}, {1.9,
   1.86}, {1.9, 1.88}, {1.9, 1.9}, {1.9, 1.92}, {1.92, 0.92}, {1.92, 
    0.94}, {1.92, 0.96}, {1.92, 0.98}, {1.92, 1.}, {1.92, 1.02}, {1.92,
   1.1}, {1.92, 1.12}, {1.92, 1.14}, {1.92, 1.16}, {
  1.92, 1.18}, {1.92, 1.2}, {1.92, 1.32}, {1.92, 1.5}, {1.92, 1.52}, {1.92, \
1.54}, {1.92, 1.56}, {1.92, 1.58}, {1.92, 1.6}, {1.92,
   1.62}, {1.92, 1.64}, {1.92, 1.66}, {1.92, 1.68}, {1.92, 1.7}, {
    1.92, 1.72}, {
  1.92, 1.74}, {1.92, 1.76}, {1.92, 1.78}, {1.92, 1.8}, {1.92, 1.82}, {1.92,
   1.84}, {1.92, 1.86}, {1.92,
   1.88}, {1.92, 1.9}, {1.94, 0.94}, {1.94, 0.96}, {1.94, 0.98}, {1.94, 
  1.}, {1.94, 1.02}, {1.94, 1.1}, {1.94, 1.12}, {1.94,
   1.14}, {1.94, 1.16}, {1.94, 1.18}, {
    1.94, 1.2}, {1.94, 1.34}, {1.94, 1.5}, {1.94, 1.52}, {1.94, 1.54}, {1.94,
   1.56}, {1.94, 1.58}, {1.94,
   1.6}, {1.94, 1.62}, {1.94, 1.64}, {1.94, 1.66}, {1.94, 
    1.68}, {1.94, 1.7}, {1.94, 1.72}, {1.94, 1.74}, {1.94, 1.76}, {
    1.94, 1.78}, {1.94, 1.8}, {1.94, 1.82}, {1.94, 1.84}, {1.94, 1.86}, \
{1.94, 1.88}, {1.96, 0.94}, {1.96, 0.96}, {
    1.96, 0.98}, {1.96, 1.}, {1.96, 1.02}, {1.96, 1.14}, {1.96, 1.16}, {1.96, \
1.18}, {1.96, 1.2}, {1.96,
   1.22}, {1.96, 1.34}, {1.96, 1.36}, {
    1.96, 1.5}, {1.96, 1.52}, {1.96, 1.54}, {1.96, 1.56}, {1.96, 1.58}, \
{1.96, 1.6}, {1.96, 1.62}, {1.96,
   1.64}, {1.96, 1.66}, {1.96, 1.68}, {
    1.96, 1.7}, {1.96, 1.72}, {1.96, 1.74}, {1.96, 1.76}, {1.96, 1.78}, \
{1.96, 1.8}, {1.96, 1.82}, {1.96, 1.84}, {1.98, 0.96}, {1.98,
   0.98}, {1.98, 1.}, {1.98, 1.02}, {1.98, 1.04}, {1.98,
   1.12}, {1.98, 
    1.18}, {1.98, 1.2}, {1.98, 1.22}, {1.98, 1.36}, {1.98, 1.38}, {1.98, \
1.48}, {1.98, 1.5}, {1.98,
   1.52}, {1.98, 1.54}, {1.98, 1.56}, {1.98, 1.58}, {1.98, 1.6}, {
    1.98, 1.62}, {
  1.98, 1.64}, {
    1.98, 1.66}, {1.98, 1.68}, {1.98, 1.7}, {1.98, 1.72}, {1.98, 1.74}, \
{1.98, 1.76}, {1.98, 1.78}, {1.98, 1.8}, {2., 0.98}, {2., 1.}, {2., 
    1.02}, {2., 1.04}, {2., 1.14}, {2., 1.26}, {2., 1.28}, {2., 1.3}, {2.,
   1.32}, {2., 1.34}}
$\endgroup$
3
  • 1
    $\begingroup$ Please include the sample data that produced that plot. $\endgroup$
    – Mr.Wizard
    Oct 12, 2012 at 15:05
  • $\begingroup$ @Mr.Wizard: done $\endgroup$
    – enzotib
    Oct 12, 2012 at 15:53
  • 2
    $\begingroup$ This command downloads the sample data, for those who care NotebookPut@ImportString[Uncompress@FromCharacterCode@Flatten@ImageData[Import@ "http://i.stack.imgur.com/UbCUj.png","Byte"],"NB"] $\endgroup$ Oct 12, 2012 at 16:19

2 Answers 2

2
$\begingroup$

First try:

(* Closing the feedback loop with @Mr Wizard's answer *)   
dd1 = Dilation[Image@SparseArray[IntegerPart[list 100] -> 1], 1]

Show[ListCurvePathPlot@
    (Function[{x}, Position[x, #] & /@ Range@Max@x][
           MorphologicalComponents[MorphologicalPerimeter[dd1, CornerNeighbors -> False]]]
    )]

Mathematica graphics

$\endgroup$
5
  • $\begingroup$ I'm curious, why list 100 rather than list 50? $\endgroup$
    – Mr.Wizard
    Oct 12, 2012 at 20:06
  • 1
    $\begingroup$ @Mr.Wizard Interesting observation :) There are gaps in the image that I need to fill with dilation. Perhaps a Closing could work with 50, but for using dilation I need to stretch the image a bit $\endgroup$ Oct 12, 2012 at 20:09
  • 1
    $\begingroup$ @Mr.Wizard Like this !Mathematica graphics $\endgroup$ Oct 12, 2012 at 20:13
  • $\begingroup$ Well beyond my understanding, but thanks $\endgroup$
    – enzotib
    Oct 12, 2012 at 20:34
  • $\begingroup$ @enzotib Come to chat to ask for explanations, if you dare chat.stackexchange.com/rooms/2234/mathematica $\endgroup$ Oct 12, 2012 at 20:36
2
$\begingroup$

I ended up with something very similar to belisarius' answer, so rather than repeat that I'll focus on the parts that are different. Perhaps they will be of use.

With list = the data:

a = SparseArray[Round[50 * list] -> 1];
cor = ListCorrelate[BoxMatrix@1, a]*a[[2 ;; -2, 2 ;; -2]];
cor = Mod[cor, 9];

The ListCorrelate operation has lots of room for customization.

The result:

ArrayPlot[Reverse @ Transpose @ cor]

Mathematica graphics

Note that the output includes gray values which might be useful for tweaking the path you eventually generate.

From here you could use Image@cor and then MorphologicalComponents etc. as belisarius did, or you could convert it back to a form similar to your original list, for further manipulation, with:

SparseArray[Unitize@cor]["NonzeroPositions"]
$\endgroup$
2
  • $\begingroup$ Feedback loop closed. Prepare to takeoff. $\endgroup$ Oct 12, 2012 at 20:06
  • $\begingroup$ @belisarius you always make me smile :-) $\endgroup$
    – Mr.Wizard
    Oct 12, 2012 at 20:07

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