// Gmsh - Copyright (C) 1997-2013 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.

#include "GmshConfig.h"
#include "MQuadrangle.h"
#include "GaussLegendre1D.h"
#include "Context.h"
#include "qualityMeasures.h"
#include "Numeric.h"
#include "BasisFactory.h"

#if defined(HAVE_MESH)
#include "qualityMeasures.h"
#endif

#define SQU(a)      ((a)*(a))

const nodalBasis* MQuadrangle::getFunctionSpace(int o) const
{
  int order = (o == -1) ? getPolynomialOrder() : o;

  int nf = getNumFaceVertices();

  if ((nf == 0) && (o == -1)) {
    switch (order) {
      case 0: return BasisFactory::getNodalBasis(MSH_QUA_1);
      case 1: return BasisFactory::getNodalBasis(MSH_QUA_4);
      case 2: return BasisFactory::getNodalBasis(MSH_QUA_8);
      case 3: return BasisFactory::getNodalBasis(MSH_QUA_12);
      case 4: return BasisFactory::getNodalBasis(MSH_QUA_16I);
      case 5: return BasisFactory::getNodalBasis(MSH_QUA_20);
      case 6: return BasisFactory::getNodalBasis(MSH_QUA_24);
      case 7: return BasisFactory::getNodalBasis(MSH_QUA_28);
      case 8: return BasisFactory::getNodalBasis(MSH_QUA_32);
      case 9: return BasisFactory::getNodalBasis(MSH_QUA_36I);
      case 10: return BasisFactory::getNodalBasis(MSH_QUA_40);
    }
  }
  switch (order) {
    case 0: return BasisFactory::getNodalBasis(MSH_QUA_1);
    case 1: return BasisFactory::getNodalBasis(MSH_QUA_4);
    case 2: return BasisFactory::getNodalBasis(MSH_QUA_9);
    case 3: return BasisFactory::getNodalBasis(MSH_QUA_16);
    case 4: return BasisFactory::getNodalBasis(MSH_QUA_25);
    case 5: return BasisFactory::getNodalBasis(MSH_QUA_36);
    case 6: return BasisFactory::getNodalBasis(MSH_QUA_49);
    case 7: return BasisFactory::getNodalBasis(MSH_QUA_64);
    case 8: return BasisFactory::getNodalBasis(MSH_QUA_81);
    case 9: return BasisFactory::getNodalBasis(MSH_QUA_100);
    case 10: return BasisFactory::getNodalBasis(MSH_QUA_121);
    default: Msg::Error("Order %d quadrangle function space not implemented", order);
  }
  return 0;
}

const JacobianBasis* MQuadrangle::getJacobianFuncSpace(int o) const
{
  int order = (o == -1) ? getPolynomialOrder() : o;

  int nf = getNumFaceVertices();

  if ((nf == 0) && (o == -1)) {
    switch (order) {
      case 1: return BasisFactory::getJacobianBasis(MSH_QUA_4);
      case 2: return BasisFactory::getJacobianBasis(MSH_QUA_8);
      case 3: return BasisFactory::getJacobianBasis(MSH_QUA_12);
      case 4: return BasisFactory::getJacobianBasis(MSH_QUA_16I);
      case 5: return BasisFactory::getJacobianBasis(MSH_QUA_20);
      case 6: return BasisFactory::getJacobianBasis(MSH_QUA_24);
      case 7: return BasisFactory::getJacobianBasis(MSH_QUA_28);
      case 8: return BasisFactory::getJacobianBasis(MSH_QUA_32);
      case 9: return BasisFactory::getJacobianBasis(MSH_QUA_36I);
      case 10: return BasisFactory::getJacobianBasis(MSH_QUA_40);
    }
  }
  switch (order) {
    case 1: return BasisFactory::getJacobianBasis(MSH_QUA_4);
    case 2: return BasisFactory::getJacobianBasis(MSH_QUA_9);
    case 3: return BasisFactory::getJacobianBasis(MSH_QUA_16);
    case 4: return BasisFactory::getJacobianBasis(MSH_QUA_25);
    case 5: return BasisFactory::getJacobianBasis(MSH_QUA_36);
    case 6: return BasisFactory::getJacobianBasis(MSH_QUA_49);
    case 7: return BasisFactory::getJacobianBasis(MSH_QUA_64);
    case 8: return BasisFactory::getJacobianBasis(MSH_QUA_81);
    case 9: return BasisFactory::getJacobianBasis(MSH_QUA_100);
    case 10: return BasisFactory::getJacobianBasis(MSH_QUA_121);
    default: Msg::Error("Order %d quadrangle function space not implemented", order);
  }
  return 0;
}

int MQuadrangleN::getNumEdgesRep(){ return 4 * CTX::instance()->mesh.numSubEdges; }
int MQuadrangle8::getNumEdgesRep(){ return 4 * CTX::instance()->mesh.numSubEdges; }
int MQuadrangle9::getNumEdgesRep(){ return 4 * CTX::instance()->mesh.numSubEdges; }

double MQuadrangle::getVolume()
{
  if(getNumVertices() > 4)
    return MElement::getVolume();
  double a = _v[0]->distance(_v[1]);
  double b = _v[1]->distance(_v[2]);
  double c = _v[2]->distance(_v[3]);
  double d = _v[3]->distance(_v[0]);
  double m = _v[0]->distance(_v[2]);
  double n = _v[1]->distance(_v[3]);
  double mn = 2. * m * n;
  double abcd = a*a - b*b + c*c - d*d;
  return sqrt( mn*mn - abcd*abcd ) / 4.;
}

static void _myGetEdgeRep(MQuadrangle *q, int num, double *x, double *y, double *z,
                          SVector3 *n, int numSubEdges)
{
  n[0] = n[1] = q->getFace(0).normal();
  int ie = num/numSubEdges;
  int isub = num%numSubEdges;
  double xi1 = -1. + (2.*isub)/numSubEdges;
  double xi2 = -1. + (2.*(isub+1))/numSubEdges;
  SPoint3 pnt1, pnt2;
  switch(ie){
    case 0:
      q->pnt( xi1, -1., 0., pnt1);
      q->pnt( xi2, -1., 0., pnt2);
      break;
    case 1:
      q->pnt( 1., xi1, 0., pnt1);
      q->pnt( 1., xi2, 0., pnt2);
      break;
    case 2:
      q->pnt( xi1, 1., 0., pnt1);
      q->pnt( xi2, 1., 0., pnt2);
      break;
    case 3:
      q->pnt(-1., xi1, 0., pnt1);
      q->pnt(-1., xi2, 0., pnt2);
      break;
  }
  x[0] = pnt1.x(); x[1] = pnt2.x();
  y[0] = pnt1.y(); y[1] = pnt2.y();
  z[0] = pnt1.z(); z[1] = pnt2.z();
}

void MQuadrangleN::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetEdgeRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MQuadrangle8::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetEdgeRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MQuadrangle9::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetEdgeRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}


int MQuadrangleN::getNumFacesRep(){ return 2*SQU(CTX::instance()->mesh.numSubEdges); }
int MQuadrangle8::getNumFacesRep(){ return 2*SQU(CTX::instance()->mesh.numSubEdges); }
int MQuadrangle9::getNumFacesRep(){ return 2*SQU(CTX::instance()->mesh.numSubEdges); }

static void _myGetFaceRep(MQuadrangle *t, int num, double *x, double *y, double *z,
                          SVector3 *n, int numSubEdges)
{
  int io = num%2;
  int ix = (num/2)/numSubEdges;
  int iy = (num/2)%numSubEdges;

  const double d = 2. / numSubEdges;
  const double ox = -1. + d*ix;
  const double oy = -1. + d*iy;

  SPoint3 pnt1, pnt2, pnt3;
  double J1[3][3], J2[3][3], J3[3][3];
  if (io == 0){
    t->pnt(ox, oy, 0, pnt1);
    t->pnt(ox + d, oy, 0, pnt2);
    t->pnt(ox + d, oy + d, 0, pnt3);
    t->getJacobian(ox, oy, 0, J1);
    t->getJacobian(ox + d, oy, 0, J2);
    t->getJacobian(ox + d, oy + d, 0, J3);
  } else{
    t->pnt(ox, oy, 0, pnt1);
    t->pnt(ox + d, oy + d, 0, pnt2);
    t->pnt(ox, oy + d, 0, pnt3);
    t->getJacobian(ox, oy, 0, J1);
    t->getJacobian(ox + d, oy + d, 0, J2);
    t->getJacobian(ox, oy + d, 0, J3);
  }
  {
    SVector3 d1(J1[0][0], J1[0][1], J1[0][2]);
    SVector3 d2(J1[1][0], J1[1][1], J1[1][2]);
    n[0] = crossprod(d1, d2);
    n[0].normalize();
  }
  {
    SVector3 d1(J2[0][0], J2[0][1], J2[0][2]);
    SVector3 d2(J2[1][0], J2[1][1], J2[1][2]);
    n[1] = crossprod(d1, d2);
    n[1].normalize();
  }
  {
    SVector3 d1(J3[0][0], J3[0][1], J3[0][2]);
    SVector3 d2(J3[1][0], J3[1][1], J3[1][2]);
    n[2] = crossprod(d1, d2);
    n[2].normalize();
  }

  x[0] = pnt1.x(); x[1] = pnt2.x(); x[2] = pnt3.x();
  y[0] = pnt1.y(); y[1] = pnt2.y(); y[2] = pnt3.y();
  z[0] = pnt1.z(); z[1] = pnt2.z(); z[2] = pnt3.z();
}

void MQuadrangleN::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetFaceRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MQuadrangle8::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetFaceRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}
void MQuadrangle9::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetFaceRep(this, num, x, y, z, n, CTX::instance()->mesh.numSubEdges);
}

void MQuadrangle::getIntegrationPoints(int pOrder, int *npts, IntPt **pts)
{
  *npts = getNGQQPts(pOrder);
  *pts = getGQQPts(pOrder);
}

double  MQuadrangle::etaShapeMeasure()
{
  double AR = 1;//(minEdge()/maxEdge());
  
  SVector3 v01 (_v[1]->x()-_v[0]->x(),_v[1]->y()-_v[0]->y(),_v[1]->z()-_v[0]->z());
  SVector3 v12 (_v[2]->x()-_v[1]->x(),_v[2]->y()-_v[1]->y(),_v[2]->z()-_v[1]->z());
  SVector3 v23 (_v[3]->x()-_v[2]->x(),_v[3]->y()-_v[2]->y(),_v[3]->z()-_v[2]->z());
  SVector3 v30 (_v[0]->x()-_v[3]->x(),_v[0]->y()-_v[3]->y(),_v[0]->z()-_v[3]->z());

  SVector3 a = crossprod(v01,v12);
  SVector3 b = crossprod(v12,v23);
  SVector3 c = crossprod(v23,v30);
  SVector3 d = crossprod(v30,v01);

  double sign = 1.0;
  if (dot(a,b) < 0 || dot(a,c) < 0 || dot(a,d) < 0 )sign = -1;
  // FIXME ...
  //  if (a.z() > 0 || b.z() > 0 || c.z() > 0 || d.z() > 0) sign = -1;

  double a1 = 180 * angle3Vertices(_v[0], _v[1], _v[2]) / M_PI;
  double a2 = 180 * angle3Vertices(_v[1], _v[2], _v[3]) / M_PI;
  double a3 = 180 * angle3Vertices(_v[2], _v[3], _v[0]) / M_PI;
  double a4 = 180 * angle3Vertices(_v[3], _v[0], _v[1]) / M_PI;

  a1 = std::min(180.,a1);
  a2 = std::min(180.,a2);
  a3 = std::min(180.,a3);
  a4 = std::min(180.,a4);
  double angle = fabs(90. - a1);
  angle = std::max(fabs(90. - a2),angle);
  angle = std::max(fabs(90. - a3),angle);
  angle = std::max(fabs(90. - a4),angle);

  return sign*(1.-angle/90) * AR;
}

/// a shape measure for quadrangles
/// assume (for now) 2D elements -- 
///  sf = (1 \pm xi) (1 \pm eta) / 4
///  dsf_xi  =  \pm (1 \pm  eta) / 4
///             1 + eta , -(1+eta) , -(1-eta), 1-eta  
///  dsf_eta =  \pm (1 \pm  xi)  / 4
///             1 + xi , 1 - xi ,  -(1-xi), -(1+xi)    
double MQuadrangle::gammaShapeMeasure(){
  return etaShapeMeasure();
}


double MQuadrangle::angleShapeMeasure()
{
#if defined(HAVE_MESH)
  return qmQuadrangleAngles(this);
#else
  return 1.;
#endif
}
double MQuadrangle::getOuterRadius()
{
  // TO DO!!!!!!!!!!!!! (BRUNO SENY)
  return 1.0;
}
double MQuadrangle::getInnerRadius()
{
#if defined(HAVE_LAPACK)
  // get the coordinates (x, y, z) of the 4 points defining the Quad
  double x[4] = {_v[0]->x(), _v[1]->x(), _v[2]->x(), _v[3]->x()};
  double y[4] = {_v[0]->y(), _v[1]->y(), _v[2]->y(), _v[3]->y()};
  double z[4] = {_v[0]->z(), _v[1]->z(), _v[2]->z(), _v[3]->z()};

  // get the coefficient (a,b,c,d) of the mean plane - least square!
  // the plane has for equation " a*x+b*y+c*z+d=0 "

  // compute the centroid of the 4 points
  double xm = (x[0] + x[1] + x[2] + x[3]) / 4;
  double ym = (y[0] + y[1] + y[2] + y[3]) / 4;
  double zm = (z[0] + z[1] + z[2] + z[3]) / 4;

  // using svd decomposition
  fullMatrix<double> U(4,3), V(3,3);
  fullVector<double> sigma(3);
  for (int i = 0; i < 4; i++) {
    U(i, 0) = x[i] - xm;
    U(i, 1) = y[i] - ym;
    U(i, 2) = z[i] - zm;
  }

  U.svd(V, sigma);
  double svd[3];
  svd[0] = sigma(0);
  svd[1] = sigma(1);
  svd[2] = sigma(2);
  int min;
  if(fabs(svd[0]) < fabs(svd[1]) && fabs(svd[0]) < fabs(svd[2]))
    min = 0;
  else if(fabs(svd[1]) < fabs(svd[0]) && fabs(svd[1]) < fabs(svd[2]))
    min = 1;
  else
    min = 2;
  double a = V(0, min);
  double b = V(1, min);
  double c = V(2, min);

  double d = -(xm * a + ym * b + zm * c);

  double norm = sqrt(a*a+b*b+c*c);

  // projection of the 4 original points on the mean_plane

  double xp[4], yp[4], zp[4];

  for (int i = 0; i < 4; i++) {
    xp[i] = ((b*b+c*c)*x[i]-a*b*y[i]-a*c*z[i]-d*a)/norm;
    yp[i] = (-a*b*x[i]+(a*a+c*c)*y[i]-b*c*z[i]-d*b)/norm;
    zp[i] = (-a*c*x[i]-b*c*y[i]+(a*a+b*b)*z[i]-d*c)/norm;
  }

  // go from XYZ-plane to XY-plane

  // 4 points, 4 edges => 4 inner radii of circles tangent to (at
  // least) 3 of the four edges!
  double xn[4], yn[4], r[4];

  planarQuad_xyz2xy(xp, yp, zp, xn, yn);

  // compute for each of the 4 possibilities the incircle radius,
  // keeping the minimum
  double R = 1.e22;
  for (int j = 0; j < 4; j++){
    r[j] = computeInnerRadiusForQuad(xn, yn, j);
    if(r[j] < R){
      R = r[j];
    }
  }
  return R;
#else // HAVE_LAPACK
  // Default implementation. Not sure that the following give exactly 
  // the same value as the HAVE_LAPACK case !
  // but same value for a square
  
  // Mid-point of each edge of the quadrangle
  SPoint3 A(_v[0]->x()+_v[1]->x(),_v[0]->y()+_v[1]->y(),_v[0]->z()+_v[1]->z());
  SPoint3 B(_v[1]->x()+_v[2]->x(),_v[1]->y()+_v[2]->y(),_v[1]->z()+_v[2]->z());
  SPoint3 C(_v[2]->x()+_v[3]->x(),_v[2]->y()+_v[3]->y(),_v[2]->z()+_v[3]->z());
  SPoint3 D(_v[3]->x()+_v[0]->x(),_v[3]->y()+_v[0]->y(),_v[3]->z()+_v[0]->z());
  A*=0.5; B*=0.5; C*=0.5; D*=0.5;

  // compute the length of the side
  double a = A.distance(B);
  double b = B.distance(C);
  double c = C.distance(D);
  double d = D.distance(A);

  // perimeter
  double s = a+b+c+d;
  double halfs = 0.5*s;

  return 0.25*sqrt( (a*c+b*d)*(a*d+b*c)*(a*b+c*d)/
                   ((halfs-a)*(halfs-b)*(halfs-c)*(halfs-d))
                  );
#endif // HAVE_LAPACK
}
