Unittest++: test for multiple possible values

i am currently implementing a simple ray tracer in c++. I have a class named OrthonormalBasis, which generates three orthogonal unit vectors from one or two specified vectors, for example:

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void
OrthonormalBasis::init_from_u ( const Vector& u )
{
    Vector n(1,0,0);
    Vector m(0,1,0);
    u_ = unify(u);
    v_ = cross(u_,n);
    if ( v_.length() < ONB_EPSILON )
        v_ = cross(u_,m);
    w_ = cross(u_,v_);
}

I am testing all my methods with the Unittest++ framework. The Problem is, that there is more than one possible solution for a valid orthonormal basis. For example this test:

TEST ( orthonormalbasis__should_init_from_u )
{
    Vector u(1,0,0);
    OrthonormalBasis onb;

    onb.init_from_u(u);

    CHECK_EQUAL( Vector( 1, 0, 0 ), onb.u() );
    CHECK_EQUAL( Vector( 0, 0, 1 ), onb.v() );
    CHECK_EQUAL( Vector( 0, 1, 0 ), onb.w() );
}

sometimes it succeeds, sometimes it fails, because the vectors v and w could also have a negative 1, and still represent a valid orthonormal basis. Is there a way to specify multiple expected values? Or do you know another way to do that?

It is important, that i get the actual and expected values printed to the stdout, in order to debug the methods so this solution won't do the job:

TEST ( orthonormalbasis__should_init_from_u )
{
    Vector u(1,0,0);
    OrthonormalBasis onb;

    onb.init_from_u(u);

    CHECK_EQUAL( Vector( 1, 0, 0 ), onb.u() );
    CHECK(
        Vector( 0, 0, 1 ) == onb.v() ||
        Vector( 0, 0,-1 ) == onb.v() );
    CHECK(
        Vector( 0, 1, 0 ) == onb.w() ||
        Vector( 0,-1, 0 ) == onb.w() );
}

---

Surely if all you are testing is whether your basis is orthonormal, then that's what you need to test?

// check orthogonality

CHECK_EQUAL( 0, dot(onb.u(), onb.v));
CHECK_EQUAL( 0, dot(onb.u(), onb.w));
CHECK_EQUAL( 0, dot(onb.v(), onb.w));

// check normality

CHECK_EQUAL( 1, dot(onb.u(), onb.u));
CHECK_EQUAL( 1, dot(onb.v(), onb.v));
CHECK_EQUAL( 1, dot(onb.w(), onb.w));

---

One possibility is to create your own CHECK_MULTI function:

void CHECK_MULTI(TYPE actual, vector<TYPE> expected, const char* message)
{
  for (element in expected) {
    if (element == actual) {
      // there's a test here so the test count is correct
      CHECK(actual, element);
      return;   
    }
  }
  CHECK(actual, expected);
}

---

I'd use a utility function or class so you can do something like this:

CHECK_EQUAL(VectorList(0,0,1)(0,0,-1), onb.v());

Given, that interpretation of equality is somewhat weird, but it should print you all values you want to see without the need to introduce a custom macro.
If you are worried about EQUAL in that context, a custom macro like CHECK_CONTAINS() shouldn't be too hard to do.

VectorList would be constructed as a temporary and operator() be used to insert values into the contained list of Vectors, similar to Boost.Assign.

Basic approach:

class VectorList {
    std::vector<Vector> data_;
public:
    VectorList(double a, double b, double c) {
        data_.push_back(Vector(a,b,c));
    }
    VectorList& operator()(double a, double b, double c) {
        data_.push_back(Vector(a,b,c));
        return *this;
    }
    bool operator==(const Vector& rhs) const {
        return std::find(data_.begin(), data_.end(), rhs) != data_.end();
    }
};