Thin profile portions after difference

[esuig]

Hello,
I think this topic has been discussed already in some way, but I also think it would be nice to create a discussion here to talk about it in a comprehensive way.
My question is: let's suppose I'm doing a boolean difference between two closed profiles; let's take the following picture as an example: here a boolean difference between the green rectangle (subject) and red rectangle (clipper) is perfomed (of course green and red rectangles are partially overlapped). I would expect ot obtain the first result drawn in the upper right (drawn in green), but I often obtain the second result (the lower right one), where a very thin stripe is present.

I usually scale the input coords (that are doubles) something like 1.0e6 and turn those into int before passing it to Clipper routines. Of course I understand that those thin portions could be casued by small fluctuations in the input data (because of numerical factors or something), but I would like to know the best strategy to reduce those thin portions.
Hope I've been clear, hope to start a discussion here

[AngusJohnson]

  PathsD sub, clp, sol;
  
  sub.push_back(MakePathD({ 50,50, 250,50, 250,250, 50,250 }));
  clp.push_back(MakePathD({ 150,50, 250,50, 250,250, 150,250 }));
  sol = Difference(sub, clp, FillRule::NonZero);
  std::cout << sol << std::endl;
  SvgWriter svg;
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddClip(svg, clp, FillRule::NonZero);
  SvgAddSolution(svg, sol, FillRule::NonZero, false);
  SvgSaveToFile(svg, "c:\\temp\\tmp1.svg", 400, 300);
  System("c:\\temp\\tmp1.svg");

  sub.clear(); clp.clear();

  sub.push_back(MakePathD({ 50,50, 250,50, 250,250, 50,250 }));
  clp.push_back(MakePathD({ 150.0,50.0, 250.0,50.0, 250.0,250.0, 150.0,249.98 }));
  sol = Difference(sub, clp, FillRule::NonZero);
  std::cout << sol << std::endl;
  svg.Clear();
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddClip(svg, clp, FillRule::NonZero);
  SvgAddSolution(svg, sol, FillRule::NonZero, false);
  SvgSaveToFile(svg, "c:\\temp\\tmp2.svg", 400, 300);
  System("c:\\temp\\tmp2.svg");

  sol = SimplifyPaths(sol, 0.05);
  std::cout << sol << std::endl;
  svg.Clear();
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddSubject(svg, sub, FillRule::NonZero);
  SvgAddClip(svg, clp, FillRule::NonZero);
  SvgAddSolution(svg, sol, FillRule::NonZero, false);
  SvgSaveToFile(svg, "c:\\temp\\tmp3.svg", 400, 300);
  System("c:\\temp\\tmp3.svg");

150,50 , 150,250 , 50,250 , 50,50

150,50 , 150,249.977 , 250,250 , 50,250 , 50,50

150,50 , 150,249.977 , 50,250 , 50,50

[esuig]

Thank you very much for the clear explanation.
I have some cases in which the polygon simplification is not working as expected, but I would like to be sure if I'm trying to use it in a wrong way or expecting something that the function is currenlty not able to solve, or even I'm giving wrong input data somehow. For example, I have the following (closed) profile (please consider the first point is repeated to indicate that it is closed, but it is not passed to SimplifyPaths):

43.108814135,25.611344650
42.673949882,25.611344270
42.029922731,25.611344941
41.509319633,25.611345068
40.978205323,25.611345246
40.454432748,25.611345090
40.000000000,25.611344770
10.364139542,25.611344770
-40.000000000,25.611344770
-40.393473603,25.611344844
-40.850529790,25.611344844
-41.295526542,25.611344382
-41.754001833,25.611344770
-42.417487599,25.611344777
-42.911636822,25.611344598
-43.866204605,25.611344926
-44.219939679,25.611344561
-45.543121256,25.611345403
-45.604061842,25.611345425
-45.831067413,25.611345343
-45.687823258,25.724552438
-46.084190987,25.411345102
-45.465883307,25.411345333
-45.299896047,25.411345258
-44.115889274,25.411344506
-43.669054896,25.411344968
-42.839844912,25.411344685
-42.269710675,25.411344886
-41.710753657,25.411344878
-41.197131664,25.411344454
-40.829558454,25.411344834
-40.322663248,25.411344826
-40.000000000,25.411344767
15.697472870,25.411344767
40.000000000,25.411344767
40.372652046,25.411345035
40.954085954,25.411345206
41.393762752,25.411345057
41.979871407,25.411344916
42.526374713,25.411344349
43.032160684,25.411344782
43.814533241,25.411344722
44.202059135,25.411344297
45.606356412,25.411344767

After calling SimplifyPaths I still see a very thin portion in the resulting profile. I'm using 0.003 as epsilon for SimplifyPaths. Is this result expected or I am missing something?

[AngusJohnson]

PathsD subject = { MakePathD({ 
43.108814135,25.611344650, 42.673949882,25.611344270, 42.029922731,25.611344941,
41.509319633,25.611345068, 40.978205323,25.611345246, 40.454432748,25.611345090,
40.000000000,25.611344770, 10.364139542,25.611344770, -40.000000000,25.611344770,
-40.393473603,25.611344844, -40.850529790,25.611344844, -41.295526542,25.611344382,
-41.754001833,25.611344770, -42.417487599,25.611344777, -42.911636822,25.611344598,
-43.866204605,25.611344926, -44.219939679,25.611344561, -45.543121256,25.611345403,
-45.604061842,25.611345425, -45.831067413,25.611345343, -45.687823258,25.724552438,
-46.084190987,25.411345102, -45.465883307,25.411345333, -45.299896047,25.411345258,
-44.115889274,25.411344506, -43.669054896,25.411344968, -42.839844912,25.411344685,
-42.269710675,25.411344886, -41.710753657,25.411344878, -41.197131664,25.411344454,
-40.829558454,25.411344834, -40.322663248,25.411344826, -40.000000000,25.411344767,
15.697472870,25.411344767, 40.000000000,25.411344767, 40.372652046,25.411345035,
40.954085954,25.411345206, 41.393762752,25.411345057, 41.979871407,25.411344916,
42.526374713,25.411344349, 43.032160684,25.411344782, 43.814533241,25.411344722,
44.202059135,25.411344297, 45.606356412,25.411344767    }) };

  subject = SimplifyPaths(subject, 0.003);
  std::cout << subject << std::endl;

  // now scale subject so we can also see what's happening
  int err;
  subject = ScalePaths<double, double>(subject, 1, 100, err);

  SvgWriter svg;
  SvgAddSubject(svg, subject, FillRule::NonZero);
  SvgSaveToFile(svg, "tmp.svg", 400,400, 50);
  System("tmp.svg");

Simplified path:
43.1088,25.6113 , -45.8311,25.6113 , -46.0842,25.4113 , 45.6064,25.4113