Adding scalar-dependent tolerances to GJK solvers

[SeanCurtis-TRI]

1. Extends fcl::constants to have scalar-dependent tolerances
   a. Documentation
   b. Tests
2. Modify default constructors for solvers to use default values.

Fixes #278

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This change is 

[sherm1]

FYI -- CI failure looks real for test_fcl_geometric_shapes.

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Review status: 0 of 5 files reviewed at latest revision, all discussions resolved, some commit checks failed.

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Comments from Reviewable

[sherm1]

with a few minor BTWs.

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Reviewed 5 of 5 files at r1.
Review status: all files reviewed at latest revision, all discussions resolved, some commit checks failed.

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include/fcl/math/constants.h, line 76 at r1 (raw file):

}  // namespace detail

/// A collection of scalar-dependent constants. This provides the ability to

Awesome documentation -- thanks!

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include/fcl/math/constants.h, line 110 at r1 (raw file):

/// following contrast will make it clear.
/// ```
/// S local_eps = 10 * std::numeric_limit<S>::epsilon();

BTW just to be clear to people who might be skimming this comment, add a comment above this line, like:

// DON'T DO THIS!

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include/fcl/math/constants.h, line 112 at r1 (raw file):

/// S local_eps = 10 * std::numeric_limit<S>::epsilon();
/// ```
/// The above example shows a common basis for defining a local epsilon. It

BTW "common basis" -> "common but incorrect"

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include/fcl/math/constants.h, line 135 at r1 (raw file):

static constexpr S pi() { return S(3.141592653589793238462643383279502884197169399375105820974944592L); }

/// The golden ratio

BTW missing periods on this and previous sentence.

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include/fcl/math/constants.h, line 139 at r1 (raw file):

/// Defines the default accuracy for gjk and epa tolerance. It is defined as
/// pow(epsilon, 7/8) -- where epsilon is the machine precision epsilon. This

BTW would be worth saying that this is the machine epsilon for the in-use RealType, and that it is much tighter in double -- approx 2e-14 vs 9e-7 for IEEE floating point double vs float, resp. Consider including those numbers in the comment to make it clear what this means.

Also, below you used ε rather than epsilon. Consider ε^(7/8) in comments rather than the awkward C "pow" syntax.

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include/fcl/narrowphase/detail/gjk_solver_libccd-inl.h, line 906 at r1 (raw file):

  max_distance_iterations = 1000;
  collision_tolerance = constants<S>::gjk_default_tolerance();
  distance_tolerance = 1e-6;

BTW why is this one still hardcoded?

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test/test_fcl_constant_eps.cpp, line 67 at r1 (raw file):

            << "Failed for " << type_name;
  EXPECT_EQ(std::pow(expected_eps, S(0.875)), constants<S>::eps_78())
            << "Failed for " << type_name;

BTW consider allowing for a small numerical error here?

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test/test_fcl_constant_eps.cpp, line 118 at r1 (raw file):

  ::testing::InitGoogleTest(&argc, argv);
  return RUN_ALL_TESTS();
}

BTW missing newline at eof

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Comments from Reviewable

[SeanCurtis-TRI]

Review status: 3 of 6 files reviewed at latest revision, 7 unresolved discussions.

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include/fcl/math/constants.h, line 76 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

Awesome documentation -- thanks!

Thanks

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include/fcl/math/constants.h, line 110 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW just to be clear to people who might be skimming this comment, add a comment above this line, like:

// DON'T DO THIS!

Done

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include/fcl/math/constants.h, line 112 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW "common basis" -> "common but incorrect"

Done

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include/fcl/math/constants.h, line 135 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW missing periods on this and previous sentence.

Done

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include/fcl/math/constants.h, line 139 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW would be worth saying that this is the machine epsilon for the in-use RealType, and that it is much tighter in double -- approx 2e-14 vs 9e-7 for IEEE floating point double vs float, resp. Consider including those numbers in the comment to make it clear what this means.

Also, below you used ε rather than epsilon. Consider ε^(7/8) in comments rather than the awkward C "pow" syntax.

Done

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include/fcl/narrowphase/detail/gjk_solver_libccd-inl.h, line 906 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW why is this one still hardcoded?

Because I'm not addressing distance yet and didn't want to get into distance tests until I'm good and ready.

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test/test_fcl_constant_eps.cpp, line 67 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW consider allowing for a small numerical error here?

Done

Added document acknowledging the expectation that the two values should match down to the last bit.

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test/test_fcl_constant_eps.cpp, line 118 at r1 (raw file):

Previously, sherm1 (Michael Sherman) wrote…

BTW missing newline at eof

Done

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Comments from Reviewable

[sherm1]

Reviewed 2 of 3 files at r2, 1 of 1 files at r3.
Review status: all files reviewed at latest revision, all discussions resolved.

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Comments from Reviewable

[SeanCurtis-TRI]

@sherm1 CI failures on the "standard" failures. Merge?

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Review status: all files reviewed at latest revision, all discussions resolved, some commit checks failed.

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Comments from Reviewable

[SeanCurtis-TRI]

Ooops.. CI failures are the "standard" failures. Merge?

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Review status: all files reviewed at latest revision, all discussions resolved, some commit checks failed.

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Comments from Reviewable