Add triangle to convexity helper

[JacquesOlivierLachaud]

PR Description

Add specific methods in ConvexityHelper and DigitalConvexity to build lattice polytope from 2 or 3 points, even in degenerate cases. This speeds up their construction by a factor 3 to 5.

Checklist

• Unit-test of your feature with Catch.
• Doxygen documentation of the code completed (classes, methods, types, members...)
• Documentation module page added or updated.
• New entry in the ChangeLog.md added.
• No warning raised in Debug mode.
• All continuous integration tests pass (Github Actions)

[JacquesOlivierLachaud]

PythonTests fail but it seems unrelated to this PR.

[dcoeurjo]

Looks good to me, just a minor comment

[dcoeurjo]

It looks like "testConvexityHelper" fails in the CI bots.

[JacquesOlivierLachaud]

Curiously it is working on my Mac Debug/Release. Do you have an ubuntu to tell me what's happening ?

[dcoeurjo]

On a linux docker image:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
testConvexityHelper is a Catch v2.13.7 host application.
Run with -? for options

-------------------------------------------------------------------------------
Scenario: ConvexityHelper< 3 > triangle tests
      Given: Given non degenerated triplets of points
       When: Computing their tightiest polytope or triangle, dilated by a cube
       Then: They have the same number of interior points
-------------------------------------------------------------------------------
/DGtal/tests/geometry/volumes/testConvexityHelper.cpp:528
...............................................................................

/DGtal/tests/geometry/volumes/testConvexityHelper.cpp:529: FAILED:
  REQUIRE( nbi_ok == nb_total )
with expansion:
  18 == 19
with messages:
  a := (4, 3, 9)
  b := (6, 4, 6)
  c := (7, 4, 6)
  n := (0, -3, -1)
  P := [BoundedLatticePolytope<3> A.rows=12 valid_edge_constraints=1]
    [ 1 0 0 ] . x <= 8
    [ -1 0 0 ] . x <= -4
    [ 0 1 0 ] . x <= 5
    [ 0 -1 0 ] . x <= -3
    [ 0 0 1 ] . x <= 10
    [ 0 0 -1 ] . x <= -6
    [ 0 -3 -1 ] . x <= -18
    [ 0 3 1 ] . x <= 22
    [ -3 0 -2 ] . x <= -30
    [ -1 2 0 ] . x <= 4
    [ 3 0 3 ] . x <= 45
    [ 1 -3 0 ] . x <= -4
  T := [BoundedLatticePolytope<3> A.rows=14 valid_edge_constraints=1]
    [ 1 0 0 ] . x <= 8
    [ -1 0 0 ] . x <= -4
    [ 0 1 0 ] . x <= 5
    [ 0 -1 0 ] . x <= -3
    [ 0 0 1 ] . x <= 10
    [ 0 0 -1 ] . x <= -6
    [ 0 -3 -1 ] . x <= -18
    [ 0 3 1 ] . x <= 22
    [ -3 0 -2 ] . x <= -30
    [ 0 0 -1 ] . x <= -6
    [ 3 0 3 ] . x <= 45
    [ -1 2 0 ] . x <= 4
    [ 0 1 0 ] . x <= 5
    [ 1 -3 0 ] . x <= -4
  nb_P := 24
  nb_T := 24
  nbi_P := 8
  nbi_T := 6

===============================================================================
test cases:   4 |   3 passed | 1 failed
assertions: 103 | 102 passed | 1 failed

[dcoeurjo]

Hi @JacquesOlivierLachaud , were you able to reproduce the bug ?

[JacquesOlivierLachaud]

Sorry I haven't found any time to work on it (and I forgot at some point :) ) . I will come back to it soon.