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24   typedef typename HyperplaneType::Scalar Scalar;
25 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
26 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
39 Scalar s0 = internal::random<Scalar>();
40 Scalar s1 = internal::random<Scalar>();
42 VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
44 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
46 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
47 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
50 if (!NumTraits<Scalar>::IsComplex)
53 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
54 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
57 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
59 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
61 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
64 .absDistance((rot*scaling*translation) * p1), Scalar(1) );
67 .absDistance((rot*translation) * p1), Scalar(1) );
72 typedef typename GetDifferentType<Scalar>::type OtherScalar;
74 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
75 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
76 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
79 template<typename Scalar> void lines()
82 typedef Hyperplane<Scalar, 2> HLine;
83 typedef ParametrizedLine<Scalar, 2> PLine;
84 typedef Matrix<Scalar,2,1> Vector;
85 typedef Matrix<Scalar,3,1> CoeffsType;
92 Scalar a = internal::random<Scalar>();
93 while (abs(a-1) < 1e-4) a = internal::random<Scalar>();
101 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
102 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
117 template<typename Scalar> void hyperplane_alignment()
119 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
120 typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
122 EIGEN_ALIGN16 Scalar array1[4];
123 EIGEN_ALIGN16 Scalar array2[4];
124 EIGEN_ALIGN16 Scalar array3[4+1];
125 Scalar* array3u = array3+1;
139 if(internal::packet_traits<Scalar>::Vectorizable)