Bindings for quadrature data and element Jacobian

bindings/Modules/CMakeLists.txt

@@ -6,6 +6,7 @@ set(MODULEBINDINGS_MODULE_LIST
     SofaLinearSolver
     SofaLinearSystem
     SofaConstraintSolver
+    SofaFEM
 )
 
 sofa_find_package(Sofa.GL QUIET)

bindings/Modules/src/SofaPython3/SofaFEM/Binding_Quadrature.cpp

@@ -0,0 +1,282 @@
+/******************************************************************************
+*                              SofaPython3 plugin                             *
+*                  (c) 2021 CNRS, University of Lille, INRIA                  *
+*                                                                             *
+* This program is free software; you can redistribute it and/or modify it     *
+* under the terms of the GNU Lesser General Public License as published by    *
+* the Free Software Foundation; either version 2.1 of the License, or (at     *
+* your option) any later version.                                             *
+*                                                                             *
+* This program is distributed in the hope that it will be useful, but WITHOUT *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or       *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
+* for more details.                                                           *
+*                                                                             *
+* You should have received a copy of the GNU Lesser General Public License    *
+* along with this program. If not, see <http://www.gnu.org/licenses/>.        *
+*******************************************************************************
+* Contact information: contact@sofa-framework.org                             *
+******************************************************************************/
+#include <SofaPython3/SofaFEM/Binding_Quadrature.h>
+
+#include <pybind11/numpy.h>
+
+#include <sofa/config.h>
+#include <sofa/fem/FiniteElement[all].h>
+#include <sofa/defaulttype/VecTypes.h>
+#include <sofa/type/Mat.h>
+
+#include <array>
+#include <string>
+#include <vector>
+
+// Bindings for sofa::fem::FiniteElement's reference-element functions.
+// Exposes the element kernel (quadrature rule, shape functions, reference gradients) so that an 
+// integration loop can be carried out using SofaPython3's API. 
+
+namespace sofapython3
+{
+namespace py = pybind11;
+
+using RealArray = py::array_t<SReal, py::array::c_style | py::array::forcecast>;
+// Topology connectivity arrives as whatever integer type the SOFA container uses; forcecast makes
+// the binding indifferent to it.
+using IndexArray = py::array_t<sofa::Index, py::array::c_style | py::array::forcecast>;
+
+// FiniteElement class dispatch: (element name, ambient dimension)
+template <class ElementType, class DataTypes>
+struct ElementTag { using FiniteElement = sofa::fem::FiniteElement<ElementType, DataTypes>; };
+
+template <class Function>
+static py::tuple withElement(const std::string& element, py::ssize_t dim, Function&& f)
+{
+    using namespace sofa::defaulttype;
+    namespace geo = sofa::geometry;
+
+    if (element == "Edge"        && dim == 1) return f(ElementTag<geo::Edge,        Vec1Types>{});
+    if (element == "Edge"        && dim == 2) return f(ElementTag<geo::Edge,        Vec2Types>{});
+    if (element == "Edge"        && dim == 3) return f(ElementTag<geo::Edge,        Vec3Types>{});
+    if (element == "Triangle"    && dim == 2) return f(ElementTag<geo::Triangle,    Vec2Types>{});
+    if (element == "Triangle"    && dim == 3) return f(ElementTag<geo::Triangle,    Vec3Types>{});
+    if (element == "Quad"        && dim == 2) return f(ElementTag<geo::Quad,        Vec2Types>{});
+    if (element == "Quad"        && dim == 3) return f(ElementTag<geo::Quad,        Vec3Types>{});
+    if (element == "Tetrahedron" && dim == 3) return f(ElementTag<geo::Tetrahedron, Vec3Types>{});
+    if (element == "Hexahedron"  && dim == 3) return f(ElementTag<geo::Hexahedron,  Vec3Types>{});
+
+    throw py::value_error("SofaFEM: unsupported element '" + element + "' for dimension " + std::to_string(dim));
+}
+
+// Reference-space quadrature points' data for one FiniteElement specialization:
+//  - weights
+//  - shape functions' values N_a
+//  - shape functions' gradients dN_a/dxi
+template <class FE>
+static py::tuple quadratureDataFor(sofa::Size degree)
+{
+    constexpr py::ssize_t nbNodes = FE::NumberOfNodesInElement;
+    constexpr py::ssize_t topoDim = FE::TopologicalDimension;
+
+    const auto rule = FE::quadratureRule(degree);
+    const py::ssize_t Q = static_cast<py::ssize_t>(rule.size());
+
+    using Real = typename FE::Real;
+
+    py::array_t<Real> weights({Q});
+    py::array_t<Real> shapeFunctions({Q, nbNodes});
+    py::array_t<Real> shapeFunctionGrads({Q, nbNodes, topoDim});
+    auto weightsView = weights.template mutable_unchecked<1>();
+    auto functionsView = shapeFunctions.template mutable_unchecked<2>();
+    auto gradientsView = shapeFunctionGrads.template mutable_unchecked<3>();
+
+    py::ssize_t q = 0;
+    for (const auto& [referencePoint, weight] : rule)
+    {
+        weightsView(q) = weight;
+
+        const auto N = FE::shapeFunctions(referencePoint);
+        for (auto a = 0; a < nbNodes; ++a)
+            functionsView(q, a) = N[a];
+
+        const auto gradient = FE::gradientShapeFunctions(referencePoint);   // Mat<nbNodes, topoDim>
+        for (auto a = 0; a < nbNodes; ++a)
+            for (auto j = 0; j < topoDim; ++j)
+                gradientsView(q, a, j) = gradient[a][j];
+
+        ++q;
+    }
+    return py::make_tuple(weights, shapeFunctions, shapeFunctionGrads);
+}
+
+static py::tuple quadratureData(const std::string& element, py::ssize_t dim, sofa::Size degree)
+{
+    return withElement(element, dim, [&](auto tag)
+    {
+        return quadratureDataFor<typename decltype(tag)::FiniteElement>(degree);
+    });
+}
+
+// Physical-space shape function gradients dN_a/dx and the integration measure per quadrature point
+//  - physical space gradients dN_a/dxi
+//  - measures
+template <class FE>
+static py::tuple elementMappingFor(const RealArray& nodeCoordinatesArray, const RealArray& referenceGradientsArray)
+{
+    using Real = typename FE::Real;
+    using Coord = typename FE::Coord;
+    using Helper = typename FE::Helper;
+    constexpr py::ssize_t nbNodes = FE::NumberOfNodesInElement;
+    constexpr py::ssize_t spatialDim = FE::spatial_dimensions;
+    constexpr py::ssize_t topoDim = FE::TopologicalDimension;
+
+    const auto nodeCoordinates = nodeCoordinatesArray.unchecked<2>();     // (nbNodes, spatialDim)
+    const auto referenceGrads = referenceGradientsArray.unchecked<3>();   // (Q, nbNodes, topoDim)
+    const py::ssize_t Q = referenceGrads.shape(0);
+
+    std::array<Coord, FE::NumberOfNodesInElement> elementNodes;
+    for (auto a = 0; a < nbNodes; ++a)
+        for (auto d = 0; d < spatialDim; ++d)
+            elementNodes[a][d] = nodeCoordinates(a, d);
+
+    py::array_t<Real> physicalGradients({Q, nbNodes, spatialDim});
+    py::array_t<Real> measures({Q});
+    auto gradientsView = physicalGradients.template mutable_unchecked<3>();
+    auto measuresView = measures.template mutable_unchecked<1>();
+
+    for (py::ssize_t q = 0; q < Q; ++q)
+    {
+        sofa::type::Mat<FE::NumberOfNodesInElement, FE::TopologicalDimension, Real> referenceGradient;
+        for (auto a = 0; a < nbNodes; ++a)
+            for (auto j = 0; j < topoDim; ++j)
+                referenceGradient[a][j] = referenceGrads(q, a, j);
+
+        const auto jacobian = Helper::jacobianFromReferenceToPhysical(elementNodes, referenceGradient);
+        measuresView(q) = sofa::type::absGeneralizedDeterminant(jacobian);   // |det J|, or sqrt(det(J^T J)) if embedded
+        const auto inverseJacobian = sofa::type::inverse(jacobian);          // inverse, or left pseudo-inverse if embedded
+
+        for (auto a = 0; a < nbNodes; ++a)
+        {
+            const auto physicalGradient = inverseJacobian.transposed() * referenceGradient[a];   // dN_a/dx
+            for (auto d = 0; d < spatialDim; ++d)
+                gradientsView(q, a, d) = physicalGradient[d];
+        }
+    }
+    return py::make_tuple(physicalGradients, measures);
+}
+
+static py::tuple elementMapping(const std::string& element, RealArray nodeCoordinates, RealArray referenceGradients)
+{
+    if (nodeCoordinates.ndim() != 2)
+        throw py::value_error("element_mapping: node_coordinates must be a 2D array (nodes_per_element, spatial_dimension)");
+
+    return withElement(element, nodeCoordinates.shape(1), [&](auto tag)
+    {
+        return elementMappingFor<typename decltype(tag)::FiniteElement>(nodeCoordinates, referenceGradients);
+    });
+}
+
+// Same mapping, but for every element of a mesh in one call. A Python integration loop that calls
+// element_mapping per element pays a pybind crossing and two array allocations per element, which
+// dominates the cost of walking a large mesh; here the whole sweep is one crossing and one pair of
+// allocations. The per-quadrature-point block is identical to elementMappingFor.
+template <class FE>
+static py::tuple elementMappingBatchFor(const RealArray& nodeCoordinatesArray,
+                                        const IndexArray& nodeIndicesArray,
+                                        const RealArray& referenceGradientsArray)
+{
+    using Real = typename FE::Real;
+    using Coord = typename FE::Coord;
+    using Helper = typename FE::Helper;
+    constexpr py::ssize_t nbNodes = FE::NumberOfNodesInElement;
+    constexpr py::ssize_t spatialDim = FE::spatial_dimensions;
+    constexpr py::ssize_t topoDim = FE::TopologicalDimension;
+
+    const auto nodeCoordinates = nodeCoordinatesArray.unchecked<2>();     // (nbMeshNodes, spatialDim)
+    const auto nodeIndices = nodeIndicesArray.unchecked<2>();             // (nbElements, nbNodes)
+    const auto referenceGrads = referenceGradientsArray.unchecked<3>();   // (Q, nbNodes, topoDim)
+
+    const py::ssize_t nbElements = nodeIndices.shape(0);
+    const py::ssize_t Q = referenceGrads.shape(0);
+    const py::ssize_t nbMeshNodes = nodeCoordinates.shape(0);
+
+    if (nodeIndices.shape(1) != nbNodes)
+        throw py::value_error("element_mapping_batch: node_indices has the wrong number of nodes per element");
+
+    // The reference gradients do not depend on the element, so lift them out of the element loop.
+    std::vector<sofa::type::Mat<FE::NumberOfNodesInElement, FE::TopologicalDimension, Real>> referenceGradient(Q);
+    for (py::ssize_t q = 0; q < Q; ++q)
+        for (auto a = 0; a < nbNodes; ++a)
+            for (auto j = 0; j < topoDim; ++j)
+                referenceGradient[q][a][j] = referenceGrads(q, a, j);
+
+    py::array_t<Real> physicalGradients({nbElements, Q, nbNodes, spatialDim});
+    py::array_t<Real> measures({nbElements, Q});
+    auto gradientsView = physicalGradients.template mutable_unchecked<4>();
+    auto measuresView = measures.template mutable_unchecked<2>();
+
+    std::array<Coord, FE::NumberOfNodesInElement> elementNodes;
+    for (py::ssize_t e = 0; e < nbElements; ++e)
+    {
+        for (auto a = 0; a < nbNodes; ++a)
+        {
+            const auto node = static_cast<py::ssize_t>(nodeIndices(e, a));
+            if (node < 0 || node >= nbMeshNodes)
+                throw py::value_error("element_mapping_batch: node index out of range");
+            for (auto d = 0; d < spatialDim; ++d)
+                elementNodes[a][d] = nodeCoordinates(node, d);
+        }
+
+        for (py::ssize_t q = 0; q < Q; ++q)
+        {
+            const auto jacobian = Helper::jacobianFromReferenceToPhysical(elementNodes, referenceGradient[q]);
+            measuresView(e, q) = sofa::type::absGeneralizedDeterminant(jacobian);
+            const auto inverseJacobian = sofa::type::inverse(jacobian);
+
+            for (auto a = 0; a < nbNodes; ++a)
+            {
+                const auto physicalGradient = inverseJacobian.transposed() * referenceGradient[q][a];
+                for (auto d = 0; d < spatialDim; ++d)
+                    gradientsView(e, q, a, d) = physicalGradient[d];
+            }
+        }
+    }
+    return py::make_tuple(physicalGradients, measures);
+}
+
+static py::tuple elementMappingBatch(const std::string& element, RealArray nodeCoordinates,
+                                     IndexArray nodeIndices, RealArray referenceGradients)
+{
+    if (nodeCoordinates.ndim() != 2)
+        throw py::value_error("element_mapping_batch: nodes must be a 2D array (nb_mesh_nodes, spatial_dimension)");
+    if (nodeIndices.ndim() != 2)
+        throw py::value_error("element_mapping_batch: node_indices must be a 2D array (nb_elements, nodes_per_element)");
+
+    return withElement(element, nodeCoordinates.shape(1), [&](auto tag)
+    {
+        return elementMappingBatchFor<typename decltype(tag)::FiniteElement>(
+            nodeCoordinates, nodeIndices, referenceGradients);
+    });
+}
+
+void moduleAddQuadrature(py::module& m)
+{
+    m.def("quadrature_data", &quadratureData,
+          py::arg("element"), py::arg("dim"), py::arg("degree"),
+          "Reference-space quadrature data for the element at the given degree: "
+          "returns (quadrature weights, shape functions, shape function gradients).");
+
+    m.def("element_mapping", &elementMapping,
+          py::arg("element"), py::arg("node_coordinates"), py::arg("reference_gradients"),
+          "Reference->physical mapping for one element (reuses SOFA's jacobianFromReferenceToPhysical, "
+          "inverse and absGeneralizedDeterminant): returns (physical shape-function gradients dN_a/dx, "
+          "integration measures) per quadrature point; handles square and embedded (rectangular Jacobian) elements.");
+
+    m.def("element_mapping_batch", &elementMappingBatch,
+          py::arg("element"), py::arg("nodes"), py::arg("node_indices"), py::arg("reference_gradients"),
+          "Reference->physical mapping for every element of a mesh in one call, so a Python "
+          "integration loop pays one pybind crossing instead of one per element: returns "
+          "(physical shape-function gradients dN_a/dx of shape (nb_elements, nb_quadrature_points, "
+          "nodes_per_element, spatial_dimension), integration measures of shape (nb_elements, "
+          "nb_quadrature_points)).");
+}
+
+} // namespace sofapython3

bindings/Modules/src/SofaPython3/SofaFEM/Binding_Quadrature.h

@@ -0,0 +1,27 @@
+/******************************************************************************
+*                              SofaPython3 plugin                             *
+*                  (c) 2021 CNRS, University of Lille, INRIA                  *
+*                                                                             *
+* This program is free software; you can redistribute it and/or modify it     *
+* under the terms of the GNU Lesser General Public License as published by    *
+* the Free Software Foundation; either version 2.1 of the License, or (at     *
+* your option) any later version.                                             *
+*                                                                             *
+* This program is distributed in the hope that it will be useful, but WITHOUT *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or       *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
+* for more details.                                                           *
+*                                                                             *
+* You should have received a copy of the GNU Lesser General Public License    *
+* along with this program. If not, see <http://www.gnu.org/licenses/>.        *
+*******************************************************************************
+* Contact information: contact@sofa-framework.org                             *
+******************************************************************************/
+#pragma once
+
+#include <pybind11/pybind11.h>
+
+namespace sofapython3
+{
+void moduleAddQuadrature(pybind11::module& m);
+}

bindings/Modules/src/SofaPython3/SofaFEM/CMakeLists.txt

@@ -0,0 +1,26 @@
+project(Bindings.Modules.SofaFEM)
+
+set(SOURCE_FILES
+    ${CMAKE_CURRENT_SOURCE_DIR}/Binding_Quadrature.cpp
+    ${CMAKE_CURRENT_SOURCE_DIR}/Module_SofaFEM.cpp
+)
+
+set(HEADER_FILES
+    ${CMAKE_CURRENT_SOURCE_DIR}/Binding_Quadrature.h
+)
+
+if (NOT TARGET SofaPython3::Plugin)
+    find_package(SofaPython3 REQUIRED COMPONENTS Plugin Bindings.Sofa)
+endif()
+
+sofa_find_package(Sofa.FEM REQUIRED)
+
+SP3_add_python_module(
+    TARGET       ${PROJECT_NAME}
+    PACKAGE      Bindings.Modules
+    MODULE       SofaFEM
+    DESTINATION  Sofa
+    SOURCES      ${SOURCE_FILES}
+    HEADERS      ${HEADER_FILES}
+    DEPENDS      Sofa.FEM SofaPython3::Plugin SofaPython3::Bindings.Sofa.Core
+)

bindings/Modules/src/SofaPython3/SofaFEM/Module_SofaFEM.cpp

@@ -0,0 +1,36 @@
+/******************************************************************************
+*                              SofaPython3 plugin                             *
+*                  (c) 2021 CNRS, University of Lille, INRIA                  *
+*                                                                             *
+* This program is free software; you can redistribute it and/or modify it     *
+* under the terms of the GNU Lesser General Public License as published by    *
+* the Free Software Foundation; either version 2.1 of the License, or (at     *
+* your option) any later version.                                             *
+*                                                                             *
+* This program is distributed in the hope that it will be useful, but WITHOUT *
+* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or       *
+* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
+* for more details.                                                           *
+*                                                                             *
+* You should have received a copy of the GNU Lesser General Public License    *
+* along with this program. If not, see <http://www.gnu.org/licenses/>.        *
+*******************************************************************************
+* Contact information: contact@sofa-framework.org                             *
+******************************************************************************/
+#include <pybind11/pybind11.h>
+
+#include <SofaPython3/SofaFEM/Binding_Quadrature.h>
+
+namespace py { using namespace pybind11; }
+
+namespace sofapython3
+{
+
+PYBIND11_MODULE(SofaFEM, m)
+{
+    m.doc() = "Bindings for the sofa::fem finite-element machinery";
+
+    moduleAddQuadrature(m);
+}
+
+} // namespace sofapython3