TargetForms.hpp

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#pragma once
 
#include <polyfem/Common.hpp>
#include <polyfem/optimization/DiffCache.hpp>
#include <polyfem/optimization/forms/SpatialIntegralForms.hpp>
#include <polyfem/utils/ExpressionValue.hpp>
#include <polyfem/utils/LazyCubicInterpolator.hpp>
 
#include <Eigen/Core>
#include <igl/AABB.h>
 
#include <memory>
#include <utility>
#include <cassert>
#include <map>
#include <set>
#include <string>
#include <vector>
 
namespace polyfem::solver
{
    class TargetForm : public SpatialIntegralForm
    {
    public:
        TargetForm(const VariableToSimulationGroup &variable_to_simulations, std::shared_ptr<const varform::DifferentiableVarForm> varform, std::shared_ptr<const DiffCache> diff_cache, const json &args)
            : SpatialIntegralForm(variable_to_simulations, std::move(varform), std::move(diff_cache), args)
        {
            set_integral_type(SpatialIntegralType::Surface);
 
            auto tmp_ids = args["surface_selection"].get<std::vector<int>>();
            ids_ = std::set(tmp_ids.begin(), tmp_ids.end());
        }
        ~TargetForm() = default;
 
        virtual std::string name() const override { return "target"; }
        // target is another simulation solution
        void set_reference(const std::shared_ptr<const varform::DifferentiableVarForm> &target_varform, std::shared_ptr<const DiffCache> target_diff_cache, const std::set<int> &reference_cached_body_ids);
        // target is a constant displacement
        void set_reference(const Eigen::VectorXd &disp) { target_disp = disp; }
        // target is a lambda function depending on deformed position
        void set_reference(const json &func, const json &grad_func);
        void set_active_dimension(const std::vector<bool> &mask) { active_dimension_mask = mask; }
 
    protected:
        IntegrableFunctional get_integral_functional() const override;
 
        std::shared_ptr<const varform::DifferentiableVarForm> target_varform_;
        std::shared_ptr<const DiffCache> target_diff_cache_;
        std::map<int, int> e_to_ref_e_;
 
        std::vector<bool> active_dimension_mask;
        Eigen::VectorXd target_disp;
 
        bool have_target_func = false;
        utils::ExpressionValue target_func;
        std::array<utils::ExpressionValue, 3> target_func_grad;
    };
 
    class SDFTargetForm : public SpatialIntegralForm
    {
    public:
        SDFTargetForm(const VariableToSimulationGroup &variable_to_simulations, std::shared_ptr<const varform::DifferentiableVarForm> varform, std::shared_ptr<const DiffCache> diff_cache, const json &args)
            : SpatialIntegralForm(variable_to_simulations, std::move(varform), std::move(diff_cache), args)
        {
            set_integral_type(SpatialIntegralType::Surface);
 
            auto tmp_ids = args["surface_selection"].get<std::vector<int>>();
            ids_ = std::set(tmp_ids.begin(), tmp_ids.end());
        }
 
        virtual std::string name() const override { return "sdf-target"; }
 
        void solution_changed_step(const int time_step, const Eigen::VectorXd &new_x) override;
        void set_bspline_target(const Eigen::MatrixXd &control_points, const Eigen::VectorXd &knots, const double delta);
        void set_bspline_target(const Eigen::MatrixXd &control_points, const Eigen::VectorXd &knots_u, const Eigen::VectorXd &knots_v, const double delta);
 
    protected:
        IntegrableFunctional get_integral_functional() const override;
 
    private:
        void compute_distance(const Eigen::MatrixXd &point, double &distance) const;
 
        int dim;
        double delta_;
 
        Eigen::MatrixXd t_or_uv_sampling;
        Eigen::MatrixXd point_sampling;
        int samples;
 
        std::unique_ptr<LazyCubicInterpolator> interpolation_fn;
    };
 
    class MeshTargetForm : public SpatialIntegralForm
    {
    public:
        MeshTargetForm(const VariableToSimulationGroup &variable_to_simulations, std::shared_ptr<const varform::DifferentiableVarForm> varform, std::shared_ptr<const DiffCache> diff_cache, const json &args)
            : SpatialIntegralForm(variable_to_simulations, std::move(varform), std::move(diff_cache), args)
        {
            set_integral_type(SpatialIntegralType::Surface);
 
            auto tmp_ids = args["surface_selection"].get<std::vector<int>>();
            ids_ = std::set(tmp_ids.begin(), tmp_ids.end());
        }
 
        virtual std::string name() const override { return "mesh-target"; }
 
        void solution_changed_step(const int time_step, const Eigen::VectorXd &new_x) override;
        void set_surface_mesh_target(const Eigen::MatrixXd &V, const Eigen::MatrixXi &F, const double delta);
 
    protected:
        IntegrableFunctional get_integral_functional() const override;
 
    private:
        int dim;
        double delta_;
 
        Eigen::MatrixXd V_;
        Eigen::MatrixXi F_;
        igl::AABB<Eigen::MatrixXd, 3> tree_;
 
        std::unique_ptr<LazyCubicInterpolator> interpolation_fn;
    };
 
    class NodeTargetForm : public StaticForm
    {
    public:
        NodeTargetForm(std::shared_ptr<const varform::DifferentiableVarForm> varform, std::shared_ptr<const DiffCache> diff_cache, const VariableToSimulationGroup &variable_to_simulations, const json &args);
        NodeTargetForm(std::shared_ptr<const varform::DifferentiableVarForm> varform, std::shared_ptr<const DiffCache> diff_cache, const VariableToSimulationGroup &variable_to_simulations, const std::vector<int> &active_nodes_, const Eigen::MatrixXd &target_vertex_positions_);
        ~NodeTargetForm() = default;
 
        std::string name() const override { return "node-target"; }
 
        Eigen::VectorXd compute_adjoint_rhs_step(const int time_step, const Eigen::VectorXd &x, const varform::DifferentiableVarForm &varform, const DiffCache &diff_cache) const override;
        double value_unweighted_step(const int time_step, const Eigen::VectorXd &x) const override;
        void compute_partial_gradient_step(const int time_step, const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const override;
 
    protected:
        std::shared_ptr<const varform::DifferentiableVarForm> varform_;
        std::shared_ptr<const DiffCache> diff_cache_;
 
        Eigen::MatrixXd target_vertex_positions;
        std::vector<int> active_nodes;
    };
 
    class BarycenterTargetForm : public StaticForm
    {
    public:
        BarycenterTargetForm(const VariableToSimulationGroup &variable_to_simulations, const json &args, const std::shared_ptr<varform::DifferentiableVarForm> &varform1, std::shared_ptr<const DiffCache> diff_cache1, const std::shared_ptr<varform::DifferentiableVarForm> &varform2, std::shared_ptr<const DiffCache> diff_cache2);
 
        Eigen::VectorXd compute_adjoint_rhs_step(const int time_step, const Eigen::VectorXd &x, const varform::DifferentiableVarForm &varform, const DiffCache &diff_cache) const override;
        void compute_partial_gradient_step(const int time_step, const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const override;
        double value_unweighted_step(const int time_step, const Eigen::VectorXd &x) const override;
 
    private:
        std::vector<std::unique_ptr<PositionForm>> center1, center2;
        int dim;
    };
 
    class MinTargetDistForm : public AdjointForm
    {
    public:
        MinTargetDistForm(const VariableToSimulationGroup &variable_to_simulations, const std::vector<int> &steps, const Eigen::VectorXd &target, const json &args, const std::shared_ptr<varform::DifferentiableVarForm> &varform, std::shared_ptr<const DiffCache> diff_cache);
        virtual ~MinTargetDistForm() = default;
 
        Eigen::MatrixXd compute_adjoint_rhs(const Eigen::VectorXd &x, const varform::DifferentiableVarForm &varform, const DiffCache &diff_cache) const override;
        void compute_partial_gradient(const Eigen::VectorXd &x, Eigen::VectorXd &gradv) const override;
 
    protected:
        double value_unweighted(const Eigen::VectorXd &x) const override;
 
    private:
        static double eval1(Eigen::VectorXd &x)
        {
            return 1. / x.array().inverse().sum();
        }
        static Eigen::VectorXd eval1_grad(Eigen::VectorXd &x)
        {
            return x.array().pow(-2.0) * pow(eval1(x), 2);
        }
 
        double eval2(Eigen::VectorXd &x) const
        {
            assert(x.size() == dim + 1);
            double out = 0;
            for (int d = 0; d < dim; d++)
                out += pow(x(d) / x(dim) - target_(d), 2);
            return out;
        }
        Eigen::VectorXd eval2_grad(Eigen::VectorXd &x) const
        {
            Eigen::VectorXd g = Eigen::VectorXd::Zero(dim + 1);
            for (int d = 0; d < dim; d++)
            {
                const double tmp = 2 * (x(d) / x(dim) - target_(d));
                g(d) += tmp / x(dim);
                g(dim) += tmp * (-x(d) / x(dim) / x(dim));
            }
            return g;
        }
 
        const std::vector<int> steps_;
        const Eigen::VectorXd target_;
 
        int dim;
        std::vector<std::unique_ptr<StaticForm>> objs;
    };
} // namespace polyfem::solver