getfem_mesh_slicers.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2004-2020 Julien Pommier
 
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/**@file getfem_mesh_slicers.h
   @author  Julien Pommier <[email protected]>
   @date February 2004.
   @brief Define various mesh slicers.
   
   Mesh slices are analogous to a refined P1-discontinuous mesh_fem, a
   list of nodes/simplexes on which the interpolation is very fast.
 
   A slice is built from a mesh, by applying some slicing operations
   (cut the mesh with a plane, intersect with a sphere, take the
   boundary faces, etc..).
 
   They are used for post-treatment (exportation of results to VTK or OpenDX,
   etc.)
*/
 
#ifndef GETFEM_MESH_SLICERS_H
#define GETFEM_MESH_SLICERS_H
 
#include <bitset>
#include <memory>
#include "gmm/gmm_kernel.h"
#include "getfem_mesh_fem.h"
#include "bgeot_rtree.h"
 
namespace getfem {
  /** @internal @brief node data in a slice.
 
      Contains both real position, and position in the reference
      convex
   */
  struct slice_node {
    typedef std::bitset<32> faces_ct; /** broken for convexes with more
                                       * than 32 faces. */
    base_node pt, pt_ref;
    faces_ct faces; 
    slice_node() {}
    slice_node(const base_node& pt_, const base_node& pt_ref_)
      : pt(pt_), pt_ref(pt_ref_) {}
    void swap(slice_node &other) { 
      std::swap(faces,other.faces); pt.swap(other.pt);
      pt_ref.swap(other.pt_ref);
    }
  };
  
 
  /** @internal @brief simplex data in a slice.
      
      Just a list of slice_node ids.
  */
  struct slice_simplex {
    std::vector<size_type> inodes;
    size_type dim() const { return inodes.size()-1; }
    slice_simplex(size_type n) : inodes(n) {} 
    slice_simplex() : inodes(4) {}
    bool operator==(const slice_simplex& o) const
    { return inodes == o.inodes; }
    bool operator!=(const slice_simplex& o) const
    { return inodes != o.inodes; }
  };
 
  class slicer_action;
  class stored_mesh_slice;
  class mesh_level_set;
 
  /** @brief Apply a serie a slicing operations to a mesh.
      
      No output is produced by this object, the real output obtained
      with the side-effect of certain getfem::mesh_slicer objects
      (such as getfem::slicer_build_stored_mesh_slice).
  */
  class mesh_slicer {
    std::deque<slicer_action*> action; /* pointed actions are not deleted */
  public:
    typedef std::vector<slice_node> cs_nodes_ct;
    typedef std::vector<slice_simplex> cs_simplexes_ct;
    const mesh& m;
    const mesh_level_set *mls; // optional
    size_type cv;
    short_type face, cv_nbfaces;
    dim_type cv_dim;
    bgeot::pgeometric_trans pgt;
    /* list of nodes and simplexes for the current convex 
       (including those who are outside of the slice) */
    cs_nodes_ct nodes;    
    cs_simplexes_ct simplexes;
    /* indexes of used simplexes and nodes,
       and index of simplexes who are considered to be in
       the slice */
    dal::bit_vector simplex_index, nodes_index, splx_in;
    size_type fcnt;
    bgeot::pconvex_ref cvr, prev_cvr;
    bool discont; // true when mls->is_convex_cut(cv) == true
 
    mesh tmp_mesh; // used only when mls != 0
    bgeot::mesh_structure tmp_mesh_struct; // used only when mls != 0
                                           //  for faces structure.
 
    void pack(); /* not used, indeed */
    void update_nodes_index();
    /** mesh_slicer constructor. Use mesh_slicer::exec to build the slice.
        @param m_ the mesh that is going to be sliced.
    */
    mesh_slicer(const mesh& m_);
    mesh_slicer(const mesh_level_set &mls_);
    void using_mesh_level_set(const mesh_level_set &mls_);
    void push_back_action(slicer_action &a) { action.push_back(&a); }
    void push_front_action(slicer_action &a) { action.push_front(&a); }
 
    size_type add_simplex(const slice_simplex& s, bool isin) {
      size_type i = simplexes.size();
      simplexes.push_back(s); splx_in[i] = isin; simplex_index.add(i);
      return i;
    }
    void sup_simplex(size_type i) {
      splx_in.sup(i); simplex_index.sup(i);
    }
    size_type dim() { 
      if (nodes.size()) return nodes[0].pt.size(); 
      else GMM_ASSERT1(false, "internal_error");
    }
    void simplex_orientation(slice_simplex& s);
    /**@brief build a new mesh_slice.
       @param nrefine number of refinments for each convex of the original
        mesh (size_type or a vector indexed by the convex number)
       @param cvlst the list of convex numbers (or convex faces) of m that
       will be taken into account for the slice
    */
    void exec(size_type nrefine, const mesh_region& cvlst); 
    void exec(const std::vector<short_type> &nrefine,const mesh_region& cvlst);
    void exec(size_type nrefine = 1);
    /**
       @brief build a new mesh slice.
       @param sms an initial stored_mesh_slice
    */
    void exec(const stored_mesh_slice& sms);
    /**
       @brief build a new mesh_slice than can be used to interpolate a field
       on a fixed set of points.
       @param pts the list of points
     */
     void exec(const std::vector<base_node>& pts);
  private:
    void exec_(const short_type *pnrefine, 
               int nref_stride, 
               const mesh_region& cvlst);
    const mesh& refined_simplex_mesh_for_convex_cut_by_level_set
    (const mesh &cvm, unsigned nrefine);
    const bgeot::mesh_structure &
    refined_simplex_mesh_for_convex_faces_cut_by_level_set(short_type f);
 
    void update_cv_data(size_type cv_, short_type f_ = short_type(-1));
    void init_indexes();
    void apply_slicers();
  };
 
 
  /* stupid class in order to use any vector type for field data associated
     to mesh_fems in slices (used for slice deformation and isovalues) */
  class mesh_slice_cv_dof_data_base {
  public:
    const mesh_fem *pmf;    
    virtual void copy(size_type cv, base_vector& coeff) const = 0;
    virtual scalar_type maxval() const = 0;
    virtual ~mesh_slice_cv_dof_data_base() {}
    virtual std::unique_ptr<mesh_slice_cv_dof_data_base> clone() const = 0;
  };
 
  /**
     Use this structure to specify that the mesh must be deformed before
     the slicing operation (with a mesh_fem and an associated field).
  */
  template<typename VEC> class mesh_slice_cv_dof_data
    : public mesh_slice_cv_dof_data_base {
    typedef typename gmm::linalg_traits<VEC>::value_type T;
    std::vector<T> u;
  public:
    mesh_slice_cv_dof_data(const mesh_fem &mf_, const VEC &u_) {
      pmf=&mf_;
      gmm::resize(u, mf_.nb_basic_dof());
      if (mf_.is_reduced())
        gmm::mult(mf_.extension_matrix(), u_, u);
      else
        gmm::copy(u_, u);
    }
    virtual void copy(size_type cv, base_vector& coeff) const {
      coeff.resize(pmf->nb_basic_dof_of_element(cv));
      const mesh_fem::ind_dof_ct &dof = pmf->ind_basic_dof_of_element(cv);
      base_vector::iterator out = coeff.begin();
      for (mesh_fem::ind_dof_ct::iterator it=dof.begin(); it != dof.end();
           ++it, ++out)
        *out = u[*it];
    }
    scalar_type maxval() const { return gmm::vect_norminf(u); }
    virtual std::unique_ptr<mesh_slice_cv_dof_data_base> clone() const
    { return std::make_unique<mesh_slice_cv_dof_data<VEC>>(*this); }
  };
  
 
  /** @brief generic slicer class.
      
  Given a list of slice_simplex/slice_node, it build a news list of
  slice_simplex/slice_node, indicating which ones are in the slice
  with the bit_vector splx_in.
  */
  class slicer_action {
  public:
    static const float EPS;
    virtual void exec(mesh_slicer &ms) = 0;
    virtual ~slicer_action() {}
  };
 
  /** This slicer does nothing. */
  class slicer_none : public slicer_action {
  public:
    slicer_none() {}
    void exec(mesh_slicer &/*ms*/) {}
    static slicer_none& static_instance();
  };
 
  /** Extraction of the boundary of a slice. */
  class slicer_boundary : public slicer_action {
    slicer_action *A;
    std::vector<slice_node::faces_ct> convex_faces;
    bool test_bound(const slice_simplex& s, slice_node::faces_ct& fmask, 
                    const mesh_slicer::cs_nodes_ct& nodes) const;
    void build_from(const mesh& m, const mesh_region& cvflst);
  public:
    slicer_boundary(const mesh& m, slicer_action &sA,
                    const mesh_region& fbound);
    slicer_boundary(const mesh& m,
                    slicer_action &sA = slicer_none::static_instance());
    void exec(mesh_slicer &ms);
  };
 
  /* Apply a precomputed deformation to the slice nodes */
  class slicer_apply_deformation : public slicer_action {
    mesh_slice_cv_dof_data_base *defdata;
    pfem pf;
    fem_precomp_pool fprecomp;
    std::vector<base_node> ref_pts;
 public:
    slicer_apply_deformation(mesh_slice_cv_dof_data_base &defdata_) 
      : defdata(&defdata_), pf(0) {
      if (defdata &&
          defdata->pmf->get_qdim() != defdata->pmf->linked_mesh().dim()) 
        GMM_ASSERT1(false, "wrong Q(=" << int(defdata->pmf->get_qdim()) 
                    << ") dimension for slice deformation: should be equal to "
                    "the mesh dimension which is "
                    << int(defdata->pmf->linked_mesh().dim()));
    }
    void exec(mesh_slicer &ms);
  };
 
  /**
     Base class for general slices of a mesh (planar, sphere,
     cylinder,isosurface)
  */
  class slicer_volume : public slicer_action {
  public:
    enum {VOLIN=-1, VOLBOUND=0, VOLOUT=+1, VOLSPLIT=+2}; 
  protected:
    /**
      orient defines the kind of slicing :
        VOLIN -> keep the inside of the volume,
        VOLBOUND -> its boundary,
        VOLOUT -> its outside,
        VOLSPLIT -> keep everything but make split simplexes 
        untils no simplex crosses the boundary
    */
    int orient;
    dal::bit_vector pt_in, pt_bin;    
    
    /** Overload either 'prepare' or 'test_point'.
     */
    virtual void prepare(size_type /*cv*/,
                         const mesh_slicer::cs_nodes_ct& nodes,
                         const dal::bit_vector& nodes_index) {
      pt_in.clear(); pt_bin.clear();
      for (dal::bv_visitor i(nodes_index); !i.finished(); ++i) {
        bool in, bin; test_point(nodes[i].pt, in, bin);        
        if (bin || ((orient > 0) ? !in : in)) pt_in.add(i);
        if (bin) pt_bin.add(i);
      }
    }
    virtual void test_point(const base_node&, bool& in, bool& bound) const
    { in=true; bound=true; }
    /** edge_intersect should always be overloaded */
    virtual scalar_type
    edge_intersect(size_type /*i*/, size_type /*j*/, 
                   const mesh_slicer::cs_nodes_ct& /*nodes*/) const = 0;
 
    slicer_volume(int orient_) : orient(orient_) {}
 
    /** Utility function */
    static scalar_type trinom(scalar_type a, scalar_type b, scalar_type c) {
      scalar_type delta = b*b - 4*a*c;
      if (delta < 0.) return 1./EPS;
      delta = sqrt(delta);
      scalar_type s1 = (-b - delta) / (2*a);
      scalar_type s2 = (-b + delta) / (2*a);
      if (gmm::abs(s1-.5) < gmm::abs(s2-.5)) return s1; else return s2;
    }
    void split_simplex(mesh_slicer &ms,
                       slice_simplex s, /* s is NOT a reference, it is on
                                         * purpose(push_back in the function)*/
                       size_type sstart, std::bitset<32> spin,
                       std::bitset<32> spbin);
  public:
    void exec(mesh_slicer &ms);
  };
 
  /**
     Slice a mesh with a half-space (or its boundary).
  */
  class slicer_half_space : public slicer_volume {
    const base_node x0, n; /* normal directed from inside toward outside */
    void test_point(const base_node& P, bool& in, bool& bound) const {
      scalar_type s = gmm::vect_sp(P-x0,n);
      in = (s <= 0); bound = (s*s <= EPS); // gmm::vect_norm2_sqr(P-x0)); No!
      // do not try to be smart with the boundary check .. easily broken with
      // slicer_mesh_with_mesh
    }
    scalar_type edge_intersect(size_type iA, size_type iB,
                               const mesh_slicer::cs_nodes_ct& nodes) const {
      const base_node& A=nodes[iA].pt;
      const base_node& B=nodes[iB].pt;
      scalar_type s1 = 0., s2 = 0.;
      for (unsigned i=0; i < A.size(); ++i)
        { s1 += (A[i] - B[i])*n[i]; s2 += (A[i]-x0[i])*n[i]; }
      if (gmm::abs(s1) < EPS) return 1./EPS;
      else return s2/s1;
    }
  public:
    slicer_half_space(base_node x0_, base_node n_, int orient_) : 
      slicer_volume(orient_), x0(x0_), n(n_/gmm::vect_norm2(n_)) {
        //n *= (1./bgeot::vect_norm2(n));
    }
  };
 
  /**
     Slices a mesh with a sphere (or its boundary).
  */
  class slicer_sphere : public slicer_volume {
    base_node x0;
    scalar_type R;
    void test_point(const base_node& P, bool& in, bool& bound) const {
      scalar_type R2 = gmm::vect_dist2_sqr(P,x0);
      bound = (R2 >= (1-EPS)*R*R && R2 <= (1+EPS)*R*R);
      in = R2 <= R*R;
    }
    scalar_type edge_intersect(size_type iA, size_type iB,
                               const mesh_slicer::cs_nodes_ct& nodes) const {
      const base_node& A=nodes[iA].pt;
      const base_node& B=nodes[iB].pt;
      scalar_type a,b,c; // a*x^2 + b*x + c = 0
      a = gmm::vect_norm2_sqr(B-A);
      if (a < EPS) return pt_bin.is_in(iA) ? 0. : 1./EPS;
      b = 2*gmm::vect_sp(A-x0,B-A);
      c = gmm::vect_norm2_sqr(A-x0)-R*R;
      return slicer_volume::trinom(a,b,c);
    }
  public:
    /* orient = -1 => select interior, 
       orient = 0  => select boundary 
       orient = +1 => select exterior */
    slicer_sphere(base_node x0_, scalar_type R_, int orient_) : 
      slicer_volume(orient_), x0(x0_), R(R_) {}
    //cerr << "slicer_volume, x0=" << x0 << ", R=" << R << endl; }
  };
  
  /**
     Slices a mesh with a cylinder (or its boundary).
  */
  class slicer_cylinder : public slicer_volume {
    base_node x0, d;
    scalar_type R;
    void test_point(const base_node& P, bool& in, bool& bound) const {
      base_node N = P;
      if (2 == N.size()) { /* Add Z coorinate if mesh is 2D */
        N.push_back(0.0);
      }
      N = N-x0;
      scalar_type axpos = gmm::vect_sp(d, N);
      scalar_type dist2 = gmm::vect_norm2_sqr(N) - gmm::sqr(axpos);
      bound = gmm::abs(dist2-R*R) < EPS;
      in = dist2 < R*R;
    }
    scalar_type edge_intersect(size_type iA, size_type iB,
                               const mesh_slicer::cs_nodes_ct& nodes) const {
      base_node F=nodes[iA].pt;
      base_node D=nodes[iB].pt-nodes[iA].pt;
      if (2 == F.size()) {
        F.push_back(0.0);
        D.push_back(0.0);
      }
      F = F - x0;
      scalar_type Fd = gmm::vect_sp(F,d);
      scalar_type Dd = gmm::vect_sp(D,d);
      scalar_type a = gmm::vect_norm2_sqr(D) - gmm::sqr(Dd);
      if (a < EPS) return pt_bin.is_in(iA) ? 0. : 1./EPS;
      assert(a> -EPS);
      scalar_type b = 2*(gmm::vect_sp(F,D) - Fd*Dd);
      scalar_type c = gmm::vect_norm2_sqr(F) - gmm::sqr(Fd) - gmm::sqr(R);
      return slicer_volume::trinom(a,b,c);
    }
  public:
    slicer_cylinder(base_node x0_, base_node x1_,scalar_type R_,int orient_) : 
      slicer_volume(orient_), x0(x0_), d(x1_-x0_), R(R_) {
      d /= gmm::vect_norm2(d);
    }
  };
 
 
  /**
     Extract an isosurface.
  */
  class slicer_isovalues : public slicer_volume {
    std::unique_ptr<const mesh_slice_cv_dof_data_base> mfU;
    scalar_type val;
    scalar_type val_scaling; /* = max(abs(U)) */
    std::vector<scalar_type> Uval;
    void prepare(size_type cv, const mesh_slicer::cs_nodes_ct& nodes,
                 const dal::bit_vector& nodes_index);
    scalar_type edge_intersect(size_type iA, size_type iB,
                               const mesh_slicer::cs_nodes_ct&) const {
      assert(iA < Uval.size() && iB < Uval.size());
      if (((Uval[iA] < val) && (Uval[iB] > val)) ||
          ((Uval[iA] > val) && (Uval[iB] < val)))
        return (val-Uval[iA])/(Uval[iB]-Uval[iA]);
      else return 1./EPS;
    }
  public:
    /* orient = -1: u(x) <= val, 0: u(x) == val, +1: u(x) >= val */
    slicer_isovalues(const mesh_slice_cv_dof_data_base& mfU_,
                     scalar_type val_, int orient_) : 
      slicer_volume(orient_), mfU(mfU_.clone()), val(val_) {
      GMM_ASSERT1(mfU->pmf->get_qdim() == 1,
                  "can't compute isovalues of a vector field !");
        val_scaling = mfU->maxval();
    }
  };
  
  /** 
      Slices a mesh with another mesh. (of same dimension,
      and whose convex are preferably linear). Note that slicing
      a refined mesh with a rough mesh should be faster than slicing 
      a rough mesh with a refined mesh.
  */
  class slicer_mesh_with_mesh : public slicer_action {
    const mesh& slm;
    bgeot::rtree tree; /* tree of bounding boxes for slm */
  protected:
    virtual void intersection_callback(mesh_slicer &/*ms*/,
                                       size_type /*slmcv*/) {}
  public:
    slicer_mesh_with_mesh(const mesh&);
    void exec(mesh_slicer &ms);
  };
 
  /**
     union of two slices
  */
  class slicer_union : public slicer_action {
    slicer_action *A, *B;
  public:
    slicer_union(const slicer_action &sA, const slicer_action &sB) : 
      A(&const_cast<slicer_action&>(sA)), B(&const_cast<slicer_action&>(sB)) {}
    void exec(mesh_slicer &ms);
  };
 
  /**
     Build the intersection of two slices
  */
  class slicer_intersect : public slicer_action {
    slicer_action *A, *B;
  public:
    slicer_intersect(slicer_action &sA, slicer_action &sB) : A(&sA), B(&sB) {}
    void exec(mesh_slicer &ms);
  };
 
  /**
     Build the complementary of a slice
  */
  class slicer_complementary : public slicer_action {
    slicer_action *A;
  public:
    slicer_complementary(slicer_action &sA) : A(&sA) {}
    void exec(mesh_slicer &ms);
  };
  
  /**
     Slicer whose side-effect is to compute the area of the
     slice. Note that if the slice is composed of simplexes of many
     dimensions, the resulting area is nonsense.
  */
  class slicer_compute_area : public slicer_action {
    scalar_type a;
  public:
    slicer_compute_area() : a(0) {}
    void exec(mesh_slicer &ms);
    scalar_type area() const { return a; }
  };
 
  /**
     Slicer whose side-effect is to build the list of edges
     (i.e. segments) and store them in a mesh object. 
 
     Hence all common nodes/edges are eliminated.  (this slicer
     is not useful for anything but visualization of sliced meshes)
  */
  class slicer_build_edges_mesh : public slicer_action {
    mesh& edges_m;
    dal::bit_vector *pslice_edges;
  public:
    /**  @param edges_m_ the mesh that will be filled with edges. */
    slicer_build_edges_mesh(mesh& edges_m_)
      : edges_m(edges_m_), pslice_edges(0) {}
    /**  @param edges_m_ the mesh that will be filled with edges.
         @param bv will contain on output the list of edges numbers
     (as convex numbers in edges_m_) which where not part of the
     original mesh, but became apparent when some convex faces were
     sliced. 
    */
    slicer_build_edges_mesh(mesh& edges_m_, dal::bit_vector& bv)
      : edges_m(edges_m_), pslice_edges(&bv) {}
    void exec(mesh_slicer &ms);
  };
 
  /**
     Slicer whose side-effect is to build a mesh from the slice
     simplexes.  Hence using slices is a good way to simplexify a
     mesh, however keep in mind that high order geometric
     transformation will be simplexified with linear simplexes!
  */
  class slicer_build_mesh : public slicer_action {
    mesh& m;
  public:
    slicer_build_mesh(mesh& m_) : m(m_) {}
    void exec(mesh_slicer &ms);
  };    
 
  /**
     Contract or expand each convex with respect to its gravity center
  */
  class slicer_explode : public slicer_action {
    scalar_type coef;
  public:
    /**
       @param c < 1 => contraction, > 1 -> expansion.
    */
    slicer_explode(scalar_type c) : coef(c) {}
    void exec(mesh_slicer &ms);
  };
 
}
 
#endif /*GETFEM_MESH_SLICERS_H*/