AtlasChart.h

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/* Author: Zachary Kingston, Caleb Voss */

#ifndef OMPL_BASE_SPACES_ATLAS_CHART_
#define OMPL_BASE_SPACES_ATLAS_CHART_

#include "ompl/base/spaces/constraint/AtlasStateSpace.h"
#include "ompl/datastructures/PDF.h"

#include <vector>
#include <eigen3/Eigen/Core>

namespace ompl
{
    namespace base
    {
        class AtlasChart
        {
        private:
            class Halfspace
            {
            public:
                // non-copyable
                Halfspace(const Halfspace &) = delete;
                Halfspace &operator=(const Halfspace &) = delete;

                Halfspace(const AtlasChart *owner, const AtlasChart *neighbor);

                bool contains(const Eigen::Ref<const Eigen::VectorXd> &v) const;

                void checkNear(const Eigen::Ref<const Eigen::VectorXd> &v) const;

                bool circleIntersect(double r, Eigen::Ref<Eigen::VectorXd> v1, Eigen::Ref<Eigen::VectorXd> v2) const;

                static void intersect(const Halfspace &l1, const Halfspace &l2, Eigen::Ref<Eigen::VectorXd> out);

                void setComplement(Halfspace *complement)
                {
                    complement_ = complement;
                }

                Halfspace *getComplement() const
                {
                    return complement_;
                }

                const AtlasChart *getOwner() const
                {
                    return owner_;
                }

            private:
                const AtlasChart *owner_;

                Halfspace *complement_{nullptr};

                Eigen::VectorXd u_;

                double usqnorm_;

                double rhs_;

                void setU(const Eigen::Ref<const Eigen::VectorXd> &u);

                double distanceToPoint(const Eigen::Ref<const Eigen::VectorXd> &v) const;

                void expandToInclude(const Eigen::Ref<const Eigen::VectorXd> &x);
            };

        public:
            // non-copyable
            AtlasChart(const AtlasChart &) = delete;
            AtlasChart &operator=(const AtlasChart &) = delete;

            AtlasChart(const AtlasStateSpace *atlas, const AtlasStateSpace::StateType *state);

            ~AtlasChart();

            void clear();

            const AtlasStateSpace::StateType *getOrigin() const
            {
                return state_;
            }

            unsigned int getAmbientDimension() const
            {
                return n_;
            }

            unsigned int getManifoldDimension() const
            {
                return k_;
            }

            void phi(const Eigen::Ref<const Eigen::VectorXd> &u, Eigen::Ref<Eigen::VectorXd> out) const;

            bool psi(const Eigen::Ref<const Eigen::VectorXd> &u, Eigen::Ref<Eigen::VectorXd> out) const;

            void psiInverse(const Eigen::Ref<const Eigen::VectorXd> &x, Eigen::Ref<Eigen::VectorXd> out) const;

            bool inPolytope(const Eigen::Ref<const Eigen::VectorXd> &u, const Halfspace *ignore1 = nullptr,
                            const Halfspace *ignore2 = nullptr) const;

            void borderCheck(const Eigen::Ref<const Eigen::VectorXd> &v) const;

            const AtlasChart *owningNeighbor(const Eigen::Ref<const Eigen::VectorXd> &x) const;

            bool toPolygon(std::vector<Eigen::VectorXd> &vertices) const;

            std::size_t getNeighborCount() const
            {
                return polytope_.size();
            }

            bool estimateIsFrontier() const;

            static void generateHalfspace(AtlasChart *c1, AtlasChart *c2);

        protected:
            const Constraint *constraint_;

            std::vector<Halfspace *> polytope_;

            void addBoundary(Halfspace *halfspace);

        private:
            const unsigned int n_;

            const unsigned int k_;

            const AtlasStateSpace::StateType *state_;

            const Eigen::MatrixXd bigPhi_;

            const double radius_;
        };
    }
}

#endif