MeanField_SERiF/docs/xml/geometry__step_8cpp.xml

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<codeline lineno="1"><highlight class="preprocessor">#include<sp/>&quot;<ref refid="backend_2mfem_2geometry_2deformation_2geometry__step_8hpp" kindref="compound">serif/backend/mfem/geometry/deformation/geometry_step.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="2"><highlight class="normal"></highlight></codeline>
<codeline lineno="3"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;algorithm&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="4"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;cmath&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="5"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;exception&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="6"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;limits&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="7"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;optional&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="8"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;utility&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="9"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&lt;vector&gt;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="10"><highlight class="normal"></highlight></codeline>
<codeline lineno="11"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;mfem/fem/gridfunc.hpp&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="12"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;mfem/fem/pfespace.hpp&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="13"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;<ref refid="determinant__polynomial_8hpp" kindref="compound">serif/geometry/deformation/detail/determinant_polynomial.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="14"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;<ref refid="backend_2mfem_2mapping_2domain__mapper_8hpp" kindref="compound">serif/backend/mfem/mapping/domain_mapper.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="15"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;<ref refid="backend_2mfem_2shared_2finite_8hpp" kindref="compound">serif/backend/mfem/shared/finite.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="16"><highlight class="normal"></highlight><highlight class="preprocessor">#include<sp/>&quot;<ref refid="parallel_8hpp" kindref="compound">serif/backend/mfem/shared/parallel.hpp</ref>&quot;</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="17"><highlight class="normal"></highlight></codeline>
<codeline lineno="18"><highlight class="normal"></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal"><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1backend_1_1mfem" kindref="compound">serif::geometry::deformation::backend::mfem</ref><sp/>{</highlight></codeline>
<codeline lineno="19"><highlight class="normal"><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">namespace<sp/></highlight><highlight class="normal">{</highlight></codeline>
<codeline lineno="21"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1a08306ee593c172f4877facc061e98f97" kindref="member">DeformationStatus</ref><sp/>validate_inputs(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DomainMapper&amp;<sp/>mapper,<sp/>const<sp/>::mfem::FiniteElementSpace&amp;<sp/>displacement_space,<sp/>const<sp/>::mfem::GridFunction&amp;<sp/>compactification_coordinate,<sp/>const<sp/>::mfem::Vector&amp;<sp/>accepted,<sp/>const<sp/>::mfem::Vector&amp;<sp/>direction,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>std::span&lt;const<sp/>GeometrySampleRule&gt;<sp/>rules,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>GeometryStepOptions&amp;<sp/>options)<sp/>{</highlight></codeline>
<codeline lineno="22"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(options.maximum_step)<sp/>||<sp/>options.maximum_step<sp/>&lt;=<sp/>0.0<sp/>||<sp/>!std::isfinite(options.determinant_floor)<sp/>||<sp/>options.determinant_floor<sp/>&lt;<sp/>0.0<sp/>||<sp/>!std::isfinite(options.fraction_to_boundary)<sp/>||<sp/>options.fraction_to_boundary<sp/>&lt;=<sp/>0.0<sp/>||<sp/>options.fraction_to_boundary<sp/>&gt;=<sp/>1.0)<sp/>{</highlight></codeline>
<codeline lineno="23"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a9cc57114b319994e90322314a00521d4" kindref="member">DeformationFailureReason::invalid_configuration</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>controls<sp/>require<sp/>a<sp/>finite<sp/>positive<sp/>maximum<sp/>step,<sp/>nonnegative<sp/>determinant<sp/>floor,<sp/>and<sp/>fraction<sp/>to<sp/>boundary<sp/>strictly<sp/>between<sp/>zero<sp/>and<sp/>one.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="24"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="25"><highlight class="normal"></highlight></codeline>
<codeline lineno="26"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::Mesh*<sp/>mesh<sp/>=<sp/>displacement_space.GetMesh();</highlight></codeline>
<codeline lineno="27"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::FiniteElementSpace*<sp/>compactification_space<sp/>=<sp/>compactification_coordinate.FESpace();</highlight></codeline>
<codeline lineno="28"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>dimension<sp/>=<sp/>mapper.get_dimension();</highlight></codeline>
<codeline lineno="29"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::Ordering::Type<sp/><ref refid="namespaceserif_1_1solver_1_1preconditioner_1_1computations_1a93a14d176124c789b6d75a9a3a4e4d5c" kindref="member">ordering</ref><sp/>=<sp/>displacement_space.GetOrdering();</highlight></codeline>
<codeline lineno="30"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(mesh<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/>compactification_space<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/>compactification_space-&gt;GetMesh()<sp/>!=<sp/>mesh<sp/>||<sp/>dimension<sp/>&lt;<sp/>1<sp/>||<sp/>dimension<sp/>&gt;<sp/>3<sp/>||<sp/>mesh-&gt;Dimension()<sp/>!=<sp/>dimension<sp/>||<sp/>mesh-&gt;SpaceDimension()<sp/>!=<sp/>dimension<sp/>||<sp/>displacement_space.GetVDim()<sp/>!=<sp/>dimension<sp/>||<sp/>compactification_space-&gt;GetVDim()<sp/>!=<sp/>1<sp/>||<sp/>compactification_coordinate.Size()<sp/>!=<sp/>compactification_space-&gt;GetVSize()<sp/>||<sp/>(ordering<sp/>!=<sp/>::mfem::Ordering::byNODES<sp/>&amp;&amp;<sp/>ordering<sp/>!=<sp/>::mfem::Ordering::byVDIM))<sp/>{</highlight></codeline>
<codeline lineno="31"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871ad73416fa06a45d748a7c8d4349054cbb" kindref="member">DeformationFailureReason::incompatible_discretization</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>estimation<sp/>requires<sp/>compatible<sp/>scalar<sp/>compactification<sp/>and<sp/>vector<sp/>displacement<sp/>spaces<sp/>on<sp/>one<sp/>mesh<sp/>in<sp/>one<sp/>to<sp/>three<sp/>dimensions.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="32"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="33"><highlight class="normal"></highlight><highlight class="preprocessor">#ifdef<sp/>MFEM_USE_MPI</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="34"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">dynamic_cast&lt;</highlight><highlight class="keyword">const<sp/></highlight><highlight class="normal">::mfem::ParFiniteElementSpace*</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(&amp;displacement_space)<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/></highlight><highlight class="keyword">dynamic_cast&lt;</highlight><highlight class="keyword">const<sp/></highlight><highlight class="normal">::mfem::ParFiniteElementSpace*</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(compactification_space)<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">)<sp/>{</highlight></codeline>
<codeline lineno="35"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871ad73416fa06a45d748a7c8d4349054cbb" kindref="member">DeformationFailureReason::incompatible_discretization</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>estimation<sp/>currently<sp/>requires<sp/>serial<sp/>finite-element<sp/>spaces.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="36"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="37"><highlight class="normal"></highlight><highlight class="preprocessor">#endif</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="38"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(<ref refid="namespaceserif_1_1solver_1a6fa8bbc306fbf990b16ade9fb7771464a3e4d891a5df3d6d0d7dd9432a1bc6470" kindref="member">accepted</ref>.Size()<sp/>!=<sp/>displacement_space.GetTrueVSize()<sp/>||<sp/>direction.Size()<sp/>!=<sp/>displacement_space.GetTrueVSize())<sp/>{</highlight></codeline>
<codeline lineno="39"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a0181b84c792eb178181854d09c8fe7b9" kindref="member">DeformationFailureReason::invalid_size</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>displacement<sp/>vectors<sp/>must<sp/>match<sp/>the<sp/>space&apos;s<sp/>true-DOF<sp/>count.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="40"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="41"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!<ref refid="namespaceserif_1_1utils_1_1checks_1a4eb8e1d2bdd4bdae0242814f9018537e" kindref="member">utils::checks::is_finite</ref>(accepted)<sp/>||<sp/>!<ref refid="namespaceserif_1_1utils_1_1checks_1a4eb8e1d2bdd4bdae0242814f9018537e" kindref="member">utils::checks::is_finite</ref>(direction)<sp/>||<sp/>!<ref refid="namespaceserif_1_1utils_1_1checks_1a4eb8e1d2bdd4bdae0242814f9018537e" kindref="member">utils::checks::is_finite</ref>(compactification_coordinate))<sp/>{</highlight></codeline>
<codeline lineno="42"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a4013d0a2d04acba5257678a15922a094" kindref="member">DeformationFailureReason::non_finite</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>displacement<sp/>and<sp/>compactification<sp/>coefficients<sp/>must<sp/>all<sp/>be<sp/>finite.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="43"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="44"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(rules.empty()<sp/>||<sp/>rules.size()<sp/>&gt;<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(std::numeric_limits&lt;int&gt;::max()))<sp/>{</highlight></codeline>
<codeline lineno="45"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a9cc57114b319994e90322314a00521d4" kindref="member">DeformationFailureReason::invalid_configuration</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>step<sp/>estimation<sp/>requires<sp/>a<sp/>nonempty<sp/>list<sp/>of<sp/>sampling<sp/>rules<sp/>representable<sp/>by<sp/>integer<sp/>rule<sp/>indices.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="46"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="47"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{};</highlight></codeline>
<codeline lineno="48"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="49"><highlight class="normal"></highlight></codeline>
<codeline lineno="51"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1a08306ee593c172f4877facc061e98f97" kindref="member">DeformationStatus</ref><sp/>validate_rule(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DomainMapper&amp;<sp/>mapper,<sp/>const<sp/>::mfem::FiniteElementSpace&amp;<sp/>displacement_space,<sp/>const<sp/>::mfem::FiniteElementSpace&amp;<sp/>compactification_space,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1geometry_1_1deformation_1_1backend_1_1mfem_1_1_geometry_sample_rule" kindref="compound">GeometrySampleRule</ref>&amp;<sp/>rule)<sp/>{</highlight></codeline>
<codeline lineno="52"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Mesh&amp;<sp/>mesh<sp/>=<sp/>*displacement_space.GetMesh();</highlight></codeline>
<codeline lineno="53"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(rule.element<sp/>&lt;<sp/>0<sp/>||<sp/>rule.element<sp/>&gt;=<sp/>mesh.GetNE()<sp/>||<sp/>rule.integration_rule<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/>rule.integration_rule-&gt;GetNPoints()<sp/>&lt;=<sp/>0)<sp/>{</highlight></codeline>
<codeline lineno="54"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a9cc57114b319994e90322314a00521d4" kindref="member">DeformationFailureReason::invalid_configuration</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;A<sp/>geometry<sp/>sample<sp/>rule<sp/>must<sp/>name<sp/>an<sp/>existing<sp/>element<sp/>and<sp/>contain<sp/>at<sp/>least<sp/>one<sp/>point.&quot;</highlight><highlight class="normal">,<sp/>.element<sp/>=<sp/>rule.element});</highlight></codeline>
<codeline lineno="55"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="56"><highlight class="normal"></highlight></codeline>
<codeline lineno="57"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::ElementTransformation*<sp/>transformation<sp/>=<sp/>mesh.GetElementTransformation(rule.element);</highlight></codeline>
<codeline lineno="58"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::FiniteElement*<sp/>displacement_element<sp/>=<sp/>displacement_space.GetFE(rule.element);</highlight></codeline>
<codeline lineno="59"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::FiniteElement*<sp/>compactification_element<sp/>=<sp/>compactification_space.GetFE(rule.element);</highlight></codeline>
<codeline lineno="60"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keyword">auto</highlight><highlight class="normal"><sp/>supports_mapping<sp/>=<sp/>[](const<sp/>::mfem::FiniteElement*<sp/>element)<sp/>{</highlight></codeline>
<codeline lineno="61"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>element<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>&amp;&amp;<sp/>element-&gt;GetDof()<sp/>&gt;<sp/>0<sp/>&amp;&amp;<sp/>element-&gt;GetRangeType()<sp/>==<sp/>::mfem::FiniteElement::SCALAR<sp/>&amp;&amp;<sp/>element-&gt;GetMapType()<sp/>==<sp/>::mfem::FiniteElement::VALUE<sp/>&amp;&amp;<sp/>element-&gt;GetDerivType()<sp/>==<sp/>::mfem::FiniteElement::GRAD;</highlight></codeline>
<codeline lineno="62"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="63"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(transformation<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/>!supports_mapping(displacement_element)<sp/>||<sp/>!supports_mapping(compactification_element)<sp/>||<sp/>transformation-&gt;GetSpaceDim()<sp/>!=<sp/>mapper.get_dimension()<sp/>||<sp/>displacement_element-&gt;GetDim()<sp/>!=<sp/>mapper.get_dimension()<sp/>||<sp/>compactification_element-&gt;GetDim()<sp/>!=<sp/>mapper.get_dimension()<sp/>||<sp/>displacement_element-&gt;GetGeomType()<sp/>!=<sp/>compactification_element-&gt;GetGeomType())<sp/>{</highlight></codeline>
<codeline lineno="64"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871ad73416fa06a45d748a7c8d4349054cbb" kindref="member">DeformationFailureReason::incompatible_discretization</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>samples<sp/>require<sp/>scalar<sp/>value-mapped<sp/>finite<sp/>elements<sp/>with<sp/>gradients<sp/>and<sp/>compatible<sp/>dimensions.&quot;</highlight><highlight class="normal">,<sp/>.element<sp/>=<sp/>rule.element});</highlight></codeline>
<codeline lineno="65"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="66"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(mapper.is_compactified_element(*transformation)<sp/>&amp;&amp;<sp/>!mapper.get_exterior_map().is_affine_in_displacement())<sp/>{</highlight></codeline>
<codeline lineno="67"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a9cc57114b319994e90322314a00521d4" kindref="member">DeformationFailureReason::invalid_configuration</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;The<sp/>determinant<sp/>polynomial<sp/>requires<sp/>an<sp/>exterior<sp/>map<sp/>affine<sp/>in<sp/>displacement<sp/>at<sp/>fixed<sp/>compactification<sp/>coordinates.&quot;</highlight><highlight class="normal">,<sp/>.element<sp/>=<sp/>rule.element});</highlight></codeline>
<codeline lineno="68"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="69"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>{};</highlight></codeline>
<codeline lineno="70"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="71"><highlight class="normal"></highlight></codeline>
<codeline lineno="73"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/>::mfem::Vector<sp/>local_displacement(const<sp/>::mfem::FiniteElementSpace&amp;<sp/>space,<sp/>const<sp/>::mfem::Vector&amp;<sp/>true_values)<sp/>{</highlight></codeline>
<codeline lineno="74"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Vector<sp/>local(space.GetVSize());</highlight></codeline>
<codeline lineno="75"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::Operator*<sp/>prolongation<sp/>=<sp/>space.GetProlongationMatrix();</highlight></codeline>
<codeline lineno="76"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(prolongation<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">)<sp/>{</highlight></codeline>
<codeline lineno="77"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>prolongation-&gt;Mult(true_values,<sp/>local);</highlight></codeline>
<codeline lineno="78"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">else</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="79"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>local<sp/>=<sp/>true_values;</highlight></codeline>
<codeline lineno="80"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="81"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>local;</highlight></codeline>
<codeline lineno="82"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="83"><highlight class="normal"></highlight></codeline>
<codeline lineno="85"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">detail::JacobianEntries</ref><sp/>jacobian_entries(const<sp/>::mfem::DenseMatrix&amp;<sp/>matrix)<sp/>{</highlight></codeline>
<codeline lineno="86"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a757a7054052d6c66e85a186de62f6e37" kindref="member">detail::JacobianEntries</ref><sp/>entries{};</highlight></codeline>
<codeline lineno="87"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>row<sp/>=<sp/>0;<sp/>row<sp/>&lt;<sp/>matrix.Height();<sp/>++row)<sp/>{</highlight></codeline>
<codeline lineno="88"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>column<sp/>=<sp/>0;<sp/>column<sp/>&lt;<sp/>matrix.Width();<sp/>++column)<sp/>{</highlight></codeline>
<codeline lineno="89"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>entries[row][column]<sp/>=<sp/>matrix(row,<sp/>column);</highlight></codeline>
<codeline lineno="90"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="91"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="92"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>entries;</highlight></codeline>
<codeline lineno="93"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="94"><highlight class="normal"></highlight></codeline>
<codeline lineno="96"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>[[nodiscard]]<sp/>std::expected&lt;detail::DeterminantPolynomial,<sp/>DeformationFailure&gt;<sp/>sample_polynomial(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DomainMapper&amp;<sp/>mapper,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementMappingData&amp;<sp/>element_data,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementDisplacementData&amp;<sp/>direction_data,<sp/>::mfem::ElementTransformation&amp;<sp/>transformation,<sp/>const<sp/>::mfem::IntegrationPoint&amp;<sp/>point,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DMFixedMeshGeometry*<sp/>stored_geometry,<sp/>mapping::DMWorkspace&amp;<sp/>workspace,<sp/>mapping::MappingPointContext&amp;<sp/>context,<sp/>mapping::MappingPointVariation&amp;<sp/>variation,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>GeometryStepOptions&amp;<sp/>options)<sp/>{</highlight></codeline>
<codeline lineno="97"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(point.x)<sp/>||<sp/>(mapper.get_dimension()<sp/>&gt;<sp/>1<sp/>&amp;&amp;<sp/>!std::isfinite(point.y))<sp/>||<sp/>(mapper.get_dimension()<sp/>&gt;<sp/>2<sp/>&amp;&amp;<sp/>!std::isfinite(point.z)))<sp/>{</highlight></codeline>
<codeline lineno="98"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a4013d0a2d04acba5257678a15922a094" kindref="member">DeformationFailureReason::non_finite</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;Geometry<sp/>sample<sp/>coordinates<sp/>must<sp/>be<sp/>finite.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="99"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="100"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Both<sp/>maps<sp/>use<sp/>this<sp/>exact<sp/>point<sp/>and<sp/>reference<sp/>mesh.<sp/>Keep<sp/>the<sp/>checked<sp/>sample<sp/>local<sp/>so</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="101"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>resetting<sp/>MFEM&apos;s<sp/>integration<sp/>point<sp/>cannot<sp/>force<sp/>repeated<sp/>fixed-Jacobian<sp/>evaluation.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="102"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>A<sp/>stored<sp/>sample<sp/>is<sp/>the<sp/>same<sp/>sample_fixed_mesh_geometry<sp/>result<sp/>computed<sp/>once<sp/>for<sp/>the<sp/>unchanged</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="103"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>reference<sp/>mesh;<sp/>evaluating<sp/>the<sp/>high-order<sp/>mesh<sp/>Jacobian<sp/>here<sp/>dominated<sp/>every<sp/>Newton<sp/>preflight.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="104"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::expected&lt;mapping::DMFixedMeshGeometry,<sp/>mapping::MappingStatus&gt;<sp/>sampled_geometry<sp/>=<sp/>std::unexpected(<ref refid="namespaceserif_1_1mapping_1a4d8ed5ebf76c79667efd6777f3ee3b97ac9f1a6384b1c466d4612f513bd8e13ea" kindref="member">mapping::MappingStatus::VALID</ref>);</highlight></codeline>
<codeline lineno="105"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(stored_geometry<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">)<sp/>{</highlight></codeline>
<codeline lineno="106"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>sampled_geometry<sp/>=<sp/><ref refid="namespaceserif_1_1mapping_1a8935271a2117c2232be8306651d5ce9f" kindref="member">mapping::sample_fixed_mesh_geometry</ref>(transformation,<sp/>point);</highlight></codeline>
<codeline lineno="107"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="108"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DMFixedMeshGeometry*<sp/>fixed_geometry<sp/>=<sp/>stored_geometry<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>?<sp/>stored_geometry<sp/>:<sp/>(sampled_geometry<sp/>?<sp/>&amp;*sampled_geometry<sp/>:<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">);</highlight></codeline>
<codeline lineno="109"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(fixed_geometry<sp/>==<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>||<sp/>mapper.evaluate_point(element_data,<sp/>transformation,<sp/>point,<sp/>workspace,<sp/>context,<sp/>*fixed_geometry)<sp/>!=<sp/><ref refid="namespaceserif_1_1mapping_1a4d8ed5ebf76c79667efd6777f3ee3b97ac9f1a6384b1c466d4612f513bd8e13ea" kindref="member">mapping::MappingStatus::VALID</ref><sp/>||<sp/>!std::isfinite(context.mapping_determinate)<sp/>||<sp/>context.mapping_determinate<sp/>&lt;=<sp/>options.determinant_floor)<sp/>{</highlight></codeline>
<codeline lineno="110"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a146816aaee11d5a21b09baac60c9812e" kindref="member">DeformationFailureReason::invalid_geometry</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;The<sp/>accepted<sp/>displacement<sp/>must<sp/>have<sp/>a<sp/>valid<sp/>mapping<sp/>strictly<sp/>above<sp/>the<sp/>determinant<sp/>floor<sp/>at<sp/>every<sp/>sample.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="111"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="112"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(mapper.evaluate_point_variation(element_data,<sp/>direction_data,<sp/>transformation,<sp/>point,<sp/>context,<sp/>workspace,<sp/>variation,<sp/>fixed_geometry-&gt;inverse_jacobian)<sp/>!=<sp/><ref refid="namespaceserif_1_1mapping_1a4d8ed5ebf76c79667efd6777f3ee3b97ac9f1a6384b1c466d4612f513bd8e13ea" kindref="member">mapping::MappingStatus::VALID</ref><sp/>||<sp/>!<ref refid="namespaceserif_1_1utils_1_1checks_1a4eb8e1d2bdd4bdae0242814f9018537e" kindref="member">utils::checks::is_finite</ref>(context.mapping_jacobian)<sp/>||<sp/>!<ref refid="namespaceserif_1_1utils_1_1checks_1a4eb8e1d2bdd4bdae0242814f9018537e" kindref="member">utils::checks::is_finite</ref>(variation.mapping_jacobian_variation))<sp/>{</highlight></codeline>
<codeline lineno="113"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a146816aaee11d5a21b09baac60c9812e" kindref="member">DeformationFailureReason::invalid_geometry</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;The<sp/>mapping<sp/>variation<sp/>must<sp/>be<sp/>finite<sp/>at<sp/>every<sp/>geometry<sp/>sample.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="114"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="115"><highlight class="normal"></highlight></codeline>
<codeline lineno="116"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref><sp/>coefficients<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a49a9b973cf176686251d822aa17eed98" kindref="member">detail::determinant_polynomial</ref>(jacobian_entries(context.mapping_jacobian),<sp/>jacobian_entries(variation.mapping_jacobian_variation),<sp/>mapper.get_dimension(),<sp/>options.maximum_step,<sp/>options.determinant_floor);</highlight></codeline>
<codeline lineno="117"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Preserve<sp/>the<sp/>mapper&apos;s<sp/>determinant<sp/>rather<sp/>than<sp/>introducing<sp/>a<sp/>second<sp/>round-off<sp/>path<sp/>at<sp/>the<sp/>accepted<sp/>state.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="118"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>coefficients[0]<sp/>=<sp/>context.mapping_determinate<sp/>-<sp/>options.determinant_floor;</highlight></codeline>
<codeline lineno="119"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>coefficient<sp/>:<sp/>coefficients)<sp/>{</highlight></codeline>
<codeline lineno="120"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(coefficient))<sp/>{</highlight></codeline>
<codeline lineno="121"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a4013d0a2d04acba5257678a15922a094" kindref="member">DeformationFailureReason::non_finite</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;The<sp/>displacement<sp/>path<sp/>produced<sp/>a<sp/>non-finite<sp/>determinant<sp/>polynomial.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="122"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="123"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="124"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!std::isfinite(<ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">detail::evaluate_polynomial</ref>(coefficients,<sp/>1.0)<sp/>+<sp/>options.determinant_floor))<sp/>{</highlight></codeline>
<codeline lineno="125"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(DeformationFailure{.reason<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1abff36c0dd3d8b9c916a2e928ab69a871a4013d0a2d04acba5257678a15922a094" kindref="member">DeformationFailureReason::non_finite</ref>,<sp/>.message<sp/>=<sp/></highlight><highlight class="stringliteral">&quot;The<sp/>determinant<sp/>at<sp/>the<sp/>maximum<sp/>displacement<sp/>step<sp/>is<sp/>not<sp/>finite.&quot;</highlight><highlight class="normal">});</highlight></codeline>
<codeline lineno="126"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="127"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>coefficients;</highlight></codeline>
<codeline lineno="128"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="129"><highlight class="normal"></highlight></codeline>
<codeline lineno="131"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">void</highlight><highlight class="normal"><sp/>accumulate_sample(GeometryStepLimit&amp;<sp/>result,<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref>&amp;<sp/>limiting_coefficients,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref>&amp;<sp/>coefficients,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>GeometryStepOptions&amp;<sp/>options,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>element,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>rule,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>point)<sp/>{</highlight></codeline>
<codeline lineno="132"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>++result.sampled_point_count;</highlight></codeline>
<codeline lineno="133"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.minimum_determinant_at_accepted<sp/>=<sp/>std::min(result.minimum_determinant_at_accepted,<sp/>coefficients[0]<sp/>+<sp/>options.determinant_floor);</highlight></codeline>
<codeline lineno="134"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.minimum_determinant_at_maximum<sp/>=<sp/>std::min(result.minimum_determinant_at_maximum,<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">detail::evaluate_polynomial</ref>(coefficients,<sp/>1.0)<sp/>+<sp/>options.determinant_floor);</highlight></codeline>
<codeline lineno="135"><highlight class="normal"></highlight></codeline>
<codeline lineno="136"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>boundary_parameter<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a6d17541b413cd2f01996f32693c7396b" kindref="member">detail::first_boundary_parameter</ref>(coefficients);</highlight></codeline>
<codeline lineno="137"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">double</highlight><highlight class="normal"><sp/>boundary_step<sp/>=<sp/>options.maximum_step<sp/>*<sp/>boundary_parameter;</highlight></codeline>
<codeline lineno="138"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(std::isfinite(boundary_step)<sp/>&amp;&amp;<sp/>(!result.limited_by_geometry<sp/>||<sp/>boundary_step<sp/>&lt;<sp/>result.boundary_step))<sp/>{</highlight></codeline>
<codeline lineno="139"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limited_by_geometry<sp/>=<sp/></highlight><highlight class="keyword">true</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="140"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.boundary_step<sp/>=<sp/>boundary_step;</highlight></codeline>
<codeline lineno="141"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_element<sp/>=<sp/>element;</highlight></codeline>
<codeline lineno="142"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_rule<sp/>=<sp/>rule;</highlight></codeline>
<codeline lineno="143"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_point<sp/>=<sp/>point;</highlight></codeline>
<codeline lineno="144"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>limiting_coefficients<sp/>=<sp/>coefficients;</highlight></codeline>
<codeline lineno="145"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="146"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="147"><highlight class="normal"></highlight></codeline>
<codeline lineno="149"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">struct<sp/></highlight><highlight class="normal">RuleSamples<sp/>{</highlight></codeline>
<codeline lineno="150"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>GeometryStepLimit<sp/>limit{};</highlight></codeline>
<codeline lineno="151"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref><sp/>limiting_coefficients{};</highlight></codeline>
<codeline lineno="152"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::optional&lt;DeformationFailure&gt;<sp/>failure;</highlight></codeline>
<codeline lineno="153"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::exception_ptr<sp/>error;</highlight></codeline>
<codeline lineno="154"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="155"><highlight class="normal"></highlight></codeline>
<codeline lineno="162"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordtype">void</highlight><highlight class="normal"><sp/>merge_rule(GeometryStepLimit&amp;<sp/>result,<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref>&amp;<sp/>limiting_coefficients,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>RuleSamples&amp;<sp/>rule)<sp/>{</highlight></codeline>
<codeline lineno="163"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.sampled_point_count<sp/>+=<sp/>rule.limit.sampled_point_count;</highlight></codeline>
<codeline lineno="164"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.minimum_determinant_at_accepted<sp/>=<sp/>std::min(result.minimum_determinant_at_accepted,<sp/>rule.limit.minimum_determinant_at_accepted);</highlight></codeline>
<codeline lineno="165"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.minimum_determinant_at_maximum<sp/>=<sp/>std::min(result.minimum_determinant_at_maximum,<sp/>rule.limit.minimum_determinant_at_maximum);</highlight></codeline>
<codeline lineno="166"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(rule.limit.limited_by_geometry<sp/>&amp;&amp;<sp/>(!result.limited_by_geometry<sp/>||<sp/>rule.limit.boundary_step<sp/>&lt;<sp/>result.boundary_step))<sp/>{</highlight></codeline>
<codeline lineno="167"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limited_by_geometry<sp/>=<sp/></highlight><highlight class="keyword">true</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="168"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.boundary_step<sp/>=<sp/>rule.limit.boundary_step;</highlight></codeline>
<codeline lineno="169"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_element<sp/>=<sp/>rule.limit.limiting_element;</highlight></codeline>
<codeline lineno="170"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_rule<sp/>=<sp/>rule.limit.limiting_rule;</highlight></codeline>
<codeline lineno="171"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_point<sp/>=<sp/>rule.limit.limiting_point;</highlight></codeline>
<codeline lineno="172"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>limiting_coefficients<sp/>=<sp/>rule.limiting_coefficients;</highlight></codeline>
<codeline lineno="173"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="174"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="175"><highlight class="normal"></highlight></codeline>
<codeline lineno="177"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">struct<sp/></highlight><highlight class="normal">SampleWorkspace<sp/>{</highlight></codeline>
<codeline lineno="178"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">explicit</highlight><highlight class="normal"><sp/>SampleWorkspace(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>dimension)<sp/>:<sp/>mapping(dimension)<sp/>{}</highlight></codeline>
<codeline lineno="179"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>mapping::DMWorkspace<sp/>mapping;</highlight></codeline>
<codeline lineno="180"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>mapping::MappingPointContext<sp/>context;</highlight></codeline>
<codeline lineno="181"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>mapping::MappingPointVariation<sp/>variation;</highlight></codeline>
<codeline lineno="182"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>};</highlight></codeline>
<codeline lineno="183"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="184"><highlight class="normal"></highlight></codeline>
<codeline lineno="185"><highlight class="normal"><sp/><sp/><sp/><sp/>std::expected&lt;GeometryStepLimit,<sp/>DeformationFailure&gt;<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1backend_1_1mfem_1ac4ca6d2962b7c60c015fb04baf8cfc6a" kindref="member">estimate_geometry_step_limit</ref>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DomainMapper&amp;<sp/>mapper,<sp/>const<sp/>::mfem::FiniteElementSpace&amp;<sp/>displacement_space,<sp/>const<sp/>::mfem::GridFunction&amp;<sp/>compactification_coordinate,<sp/>const<sp/>::mfem::Vector&amp;<sp/>accepted_displacement,<sp/>const<sp/>::mfem::Vector&amp;<sp/>displacement_direction,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>std::span&lt;const<sp/>GeometrySampleRule&gt;<sp/>sample_rules,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>GeometryStepOptions<sp/>options)<sp/>{</highlight></codeline>
<codeline lineno="186"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1a08306ee593c172f4877facc061e98f97" kindref="member">DeformationStatus</ref><sp/>validation<sp/>=<sp/>validate_inputs(mapper,<sp/>displacement_space,<sp/>compactification_coordinate,<sp/>accepted_displacement,<sp/>displacement_direction,<sp/>sample_rules,<sp/>options);<sp/>!validation)<sp/>{</highlight></codeline>
<codeline lineno="187"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(validation.error());</highlight></codeline>
<codeline lineno="188"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="189"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::FiniteElementSpace&amp;<sp/>compactification_space<sp/>=<sp/>*compactification_coordinate.FESpace();</highlight></codeline>
<codeline lineno="190"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1geometry_1_1deformation_1_1backend_1_1mfem_1_1_geometry_sample_rule" kindref="compound">GeometrySampleRule</ref>&amp;<sp/>rule<sp/>:<sp/>sample_rules)<sp/>{</highlight></codeline>
<codeline lineno="191"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1a08306ee593c172f4877facc061e98f97" kindref="member">DeformationStatus</ref><sp/>validation<sp/>=<sp/>validate_rule(mapper,<sp/>displacement_space,<sp/>compactification_space,<sp/>rule);<sp/>!validation)<sp/>{</highlight></codeline>
<codeline lineno="192"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(validation.error());</highlight></codeline>
<codeline lineno="193"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="194"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="195"><highlight class="normal"></highlight></codeline>
<codeline lineno="196"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::Vector<sp/>accepted_local<sp/>=<sp/>local_displacement(displacement_space,<sp/>accepted_displacement);</highlight></codeline>
<codeline lineno="197"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>const<sp/>::mfem::Vector<sp/>direction_local<sp/>=<sp/>local_displacement(displacement_space,<sp/>displacement_direction);</highlight></codeline>
<codeline lineno="198"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>rule_count<sp/>=<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="keywordtype">int</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(sample_rules.size());</highlight></codeline>
<codeline lineno="199"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::vector&lt;RuleSamples&gt;<sp/>rules(sample_rules.size());</highlight></codeline>
<codeline lineno="200"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::vector&lt;SampleWorkspace&gt;<sp/>workspaces(</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(<ref refid="namespaceserif_1_1utils_1_1parallel_1a845c655da35a46d0be87880f0e4fa2d9" kindref="member">serif::utils::parallel::worker_count</ref>()),<sp/>SampleWorkspace(mapper.get_dimension()));</highlight></codeline>
<codeline lineno="201"><highlight class="normal"></highlight></codeline>
<codeline lineno="202"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Rules<sp/>are<sp/>independent:<sp/>each<sp/>one<sp/>is<sp/>sampled<sp/>into<sp/>its<sp/>own<sp/>slot,<sp/>then<sp/>folded<sp/>in<sp/>rule<sp/>order<sp/>below.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="203"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1utils_1_1parallel_1a453320d288c9e42300bdc59ee8dccd2d" kindref="member">serif::utils::parallel::for_each_index</ref>(rule_count,<sp/>[&amp;](</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>rule_index,<sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>worker)<sp/>{</highlight></codeline>
<codeline lineno="204"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/><ref refid="structserif_1_1geometry_1_1deformation_1_1backend_1_1mfem_1_1_geometry_sample_rule" kindref="compound">GeometrySampleRule</ref>&amp;<sp/>rule<sp/>=<sp/>sample_rules[</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(rule_index)];</highlight></codeline>
<codeline lineno="205"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>RuleSamples&amp;<sp/>samples<sp/>=<sp/>rules[</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(rule_index)];</highlight></codeline>
<codeline lineno="206"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>SampleWorkspace&amp;<sp/>workspace<sp/>=<sp/>workspaces[</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(worker)];</highlight></codeline>
<codeline lineno="207"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">try</highlight><highlight class="normal"><sp/>{</highlight></codeline>
<codeline lineno="208"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Local<sp/>MFEM<sp/>state:<sp/>the<sp/>space&apos;s<sp/>shared<sp/>DofTransformation<sp/>and<sp/>the<sp/>mesh&apos;s<sp/>shared<sp/>transformation<sp/>are<sp/>never<sp/>written.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="209"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::IsoparametricTransformation<sp/>transformation;</highlight></codeline>
<codeline lineno="210"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1utils_1_1parallel_1a8e0e78d02ab6c49ae588644e579bed79" kindref="member">serif::utils::parallel::element_transformation</ref>(*displacement_space.GetMesh(),<sp/>rule.element,<sp/>transformation);</highlight></codeline>
<codeline lineno="211"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Array&lt;int&gt;<sp/>displacement_dofs;</highlight></codeline>
<codeline lineno="212"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Array&lt;int&gt;<sp/>compactification_dofs;</highlight></codeline>
<codeline lineno="213"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::DofTransformation<sp/>displacement_transform;</highlight></codeline>
<codeline lineno="214"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::DofTransformation<sp/>compactification_transform;</highlight></codeline>
<codeline lineno="215"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>displacement_space.GetElementVDofs(rule.element,<sp/>displacement_dofs,<sp/>displacement_transform);</highlight></codeline>
<codeline lineno="216"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>compactification_space.GetElementDofs(rule.element,<sp/>compactification_dofs,<sp/>compactification_transform);</highlight></codeline>
<codeline lineno="217"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Vector<sp/>element_accepted;</highlight></codeline>
<codeline lineno="218"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Vector<sp/>element_direction;</highlight></codeline>
<codeline lineno="219"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>::mfem::Vector<sp/>element_compactification;</highlight></codeline>
<codeline lineno="220"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>accepted_local.GetSubVector(displacement_dofs,<sp/>element_accepted);</highlight></codeline>
<codeline lineno="221"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>direction_local.GetSubVector(displacement_dofs,<sp/>element_direction);</highlight></codeline>
<codeline lineno="222"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>compactification_coordinate.GetSubVector(compactification_dofs,<sp/>element_compactification);</highlight></codeline>
<codeline lineno="223"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(displacement_transform.GetDofTransformation()<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">)<sp/>{</highlight></codeline>
<codeline lineno="224"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>displacement_transform.InvTransformPrimal(element_accepted);</highlight></codeline>
<codeline lineno="225"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>displacement_transform.InvTransformPrimal(element_direction);</highlight></codeline>
<codeline lineno="226"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="227"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(compactification_transform.GetDofTransformation()<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">)<sp/>{</highlight></codeline>
<codeline lineno="228"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>compactification_transform.InvTransformPrimal(element_compactification);</highlight></codeline>
<codeline lineno="229"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="230"><highlight class="normal"></highlight></codeline>
<codeline lineno="231"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Element<sp/>VDofs<sp/>are<sp/>component-blocked<sp/>even<sp/>when<sp/>the<sp/>global<sp/>space<sp/>uses<sp/>byVDIM<sp/>ordering.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="232"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementDisplacementData<sp/>accepted_data<sp/>=<sp/><ref refid="namespaceserif_1_1mapping_1a89488756ce19ff5351dfbeb4235849c3" kindref="member">mapping::element_displacement_data_from_element_vdofs</ref>(*displacement_space.GetFE(rule.element),<sp/>element_accepted);</highlight></codeline>
<codeline lineno="233"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementDisplacementData<sp/>direction_data<sp/>=<sp/><ref refid="namespaceserif_1_1mapping_1a89488756ce19ff5351dfbeb4235849c3" kindref="member">mapping::element_displacement_data_from_element_vdofs</ref>(*displacement_space.GetFE(rule.element),<sp/>element_direction);</highlight></codeline>
<codeline lineno="234"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementCompactificationData<sp/>compactification_data(*compactification_space.GetFE(rule.element),<sp/>element_compactification);</highlight></codeline>
<codeline lineno="235"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::ElementMappingData<sp/>element_data{.displacement<sp/>=<sp/>accepted_data,<sp/>.compactification<sp/>=<sp/>compactification_data};</highlight></codeline>
<codeline lineno="236"><highlight class="normal"></highlight></codeline>
<codeline lineno="237"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="comment">//<sp/>Use<sp/>stored<sp/>reference<sp/>samples<sp/>only<sp/>when<sp/>they<sp/>cover<sp/>exactly<sp/>this<sp/>rule&apos;s<sp/>points.</highlight><highlight class="normal"></highlight></codeline>
<codeline lineno="238"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keywordtype">bool</highlight><highlight class="normal"><sp/>stored<sp/>=<sp/>rule.reference_geometry<sp/>!=<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal"><sp/>&amp;&amp;</highlight></codeline>
<codeline lineno="239"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>rule.reference_geometry-&gt;size()<sp/>==<sp/></highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(rule.integration_rule-&gt;GetNPoints());</highlight></codeline>
<codeline lineno="240"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keywordtype">int</highlight><highlight class="normal"><sp/>point<sp/>=<sp/>0;<sp/>point<sp/>&lt;<sp/>rule.integration_rule-&gt;GetNPoints();<sp/>++point)<sp/>{</highlight></codeline>
<codeline lineno="241"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>mapping::DMFixedMeshGeometry*<sp/>stored_geometry<sp/>=<sp/>stored<sp/>?<sp/>&amp;(*rule.reference_geometry)[</highlight><highlight class="keyword">static_cast&lt;</highlight><highlight class="normal">std::size_t</highlight><highlight class="keyword">&gt;</highlight><highlight class="normal">(point)]<sp/>:<sp/></highlight><highlight class="keyword">nullptr</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="242"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/></highlight><highlight class="keyword">auto</highlight><highlight class="normal"><sp/>coefficients<sp/>=<sp/>sample_polynomial(mapper,<sp/>element_data,<sp/>direction_data,<sp/>transformation,<sp/>rule.integration_rule-&gt;IntPoint(point),<sp/>stored_geometry,<sp/>workspace.mapping,<sp/>workspace.context,<sp/>workspace.variation,<sp/>options);</highlight></codeline>
<codeline lineno="243"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(!coefficients)<sp/>{</highlight></codeline>
<codeline lineno="244"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>DeformationFailure<sp/><ref refid="namespaceserif_1_1solver_1_1preconditioner_1_1backend_1_1mfem_1_1detail_1a707023cbec2faf9488d727eb98373bbe" kindref="member">failure</ref><sp/>=<sp/>coefficients.error();</highlight></codeline>
<codeline lineno="245"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1solver_1_1preconditioner_1_1backend_1_1mfem_1_1detail_1a707023cbec2faf9488d727eb98373bbe" kindref="member">failure</ref>.element<sp/>=<sp/>rule.element;</highlight></codeline>
<codeline lineno="246"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1solver_1_1preconditioner_1_1backend_1_1mfem_1_1detail_1a707023cbec2faf9488d727eb98373bbe" kindref="member">failure</ref>.point<sp/>=<sp/>point;</highlight></codeline>
<codeline lineno="247"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>samples.failure<sp/>=<sp/>std::move(failure);</highlight></codeline>
<codeline lineno="248"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal">;</highlight></codeline>
<codeline lineno="249"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="250"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>accumulate_sample(samples.limit,<sp/>samples.limiting_coefficients,<sp/>*coefficients,<sp/>options,<sp/>rule.element,<sp/>rule_index,<sp/>point);</highlight></codeline>
<codeline lineno="251"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="252"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}<sp/></highlight><highlight class="keywordflow">catch</highlight><highlight class="normal"><sp/>(...)<sp/>{</highlight></codeline>
<codeline lineno="253"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>samples.error<sp/>=<sp/>std::current_exception();</highlight></codeline>
<codeline lineno="254"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="255"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>});</highlight></codeline>
<codeline lineno="256"><highlight class="normal"></highlight></codeline>
<codeline lineno="257"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>GeometryStepLimit<sp/>result{.step<sp/>=<sp/>options.maximum_step,<sp/>.boundary_step<sp/>=<sp/>options.maximum_step};</highlight></codeline>
<codeline lineno="258"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a62740f4edaed2df52e6d246b78844c1b" kindref="member">detail::DeterminantPolynomial</ref><sp/>limiting_coefficients{};</highlight></codeline>
<codeline lineno="259"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">for</highlight><highlight class="normal"><sp/>(</highlight><highlight class="keyword">const</highlight><highlight class="normal"><sp/>RuleSamples&amp;<sp/>samples<sp/>:<sp/>rules)<sp/>{</highlight></codeline>
<codeline lineno="260"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(samples.error)<sp/>{</highlight></codeline>
<codeline lineno="261"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>std::rethrow_exception(samples.error);</highlight></codeline>
<codeline lineno="262"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="263"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(samples.failure)<sp/>{</highlight></codeline>
<codeline lineno="264"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>std::unexpected(*samples.failure);</highlight></codeline>
<codeline lineno="265"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="266"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>merge_rule(result,<sp/>limiting_coefficients,<sp/>samples);</highlight></codeline>
<codeline lineno="267"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="268"><highlight class="normal"></highlight></codeline>
<codeline lineno="269"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_point_determinant_at_step<sp/>=<sp/>result.minimum_determinant_at_maximum;</highlight></codeline>
<codeline lineno="270"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">if</highlight><highlight class="normal"><sp/>(result.limited_by_geometry)<sp/>{</highlight></codeline>
<codeline lineno="271"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.step<sp/>=<sp/>options.fraction_to_boundary<sp/>*<sp/>result.boundary_step;</highlight></codeline>
<codeline lineno="272"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>result.limiting_point_determinant_at_step<sp/>=<sp/><ref refid="namespaceserif_1_1geometry_1_1deformation_1_1detail_1a0bbe38cc124a51e394c9648d812e2ba4" kindref="member">detail::evaluate_polynomial</ref>(limiting_coefficients,<sp/>result.step<sp/>/<sp/>options.maximum_step)<sp/>+<sp/>options.determinant_floor;</highlight></codeline>
<codeline lineno="273"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="274"><highlight class="normal"><sp/><sp/><sp/><sp/><sp/><sp/><sp/><sp/></highlight><highlight class="keywordflow">return</highlight><highlight class="normal"><sp/>result;</highlight></codeline>
<codeline lineno="275"><highlight class="normal"><sp/><sp/><sp/><sp/>}</highlight></codeline>
<codeline lineno="276"><highlight class="normal">}</highlight></codeline>
    </programlisting>
    <location file="src/lib/serif/backend/mfem/geometry/deformation/geometry_step.cpp"/>
  </compounddef>
</doxygen>