C++ Vector_3::x方法代码示例

/**
 * True if u is steeper than v. Uses the square of slope to avoid sqrt.
 */
bool is_steeper(Vector_3 u, Vector_3 v)
{
    Vector_2 u_2 = Vector_2(u.x(), u.y());
    Vector_2 v_2 = Vector_2(v.x(), v.y());
    return ((u.z() * u.z() / u_2.squared_length()) > 
            (v.z() * v.z() / v_2.squared_length())); 
}

// Computes the intersection C+uV of the planes M*x+D=0 and N*x+E=0.
// Returns -1 if there are no intersections (parallel), 0 for a line
// intersection and 1 for co-planarity.
// precondition: A, B are normalized (hessian form)
int plane_plane_intersection(const Vector_3& M, const double D,
                             const Vector_3& N, const double E,
                             Point_3& C, Vector_3& V)
{
  typedef CGAL::Cartesian<double> K;
  typedef CGAL::Plane_3<K> Plane_3;
  typedef CGAL::Line_3<K> Line_3;

  Plane_3 P1(M.x(), M.y(), M.z(), D);
  Plane_3 P2(N.x(), N.y(), N.z(), E);
  CGAL::Object result = CGAL::intersection(P1, P2);
  if (const Line_3 *iline = CGAL::object_cast<Line_3>(&result)) {
    CGAL::Point_3<K> p = iline->point(0);
    CGAL::Vector_3<K> v = iline->to_vector();
    C = Point_3(p.x(), p.y(), p.z());
    V = Vector_3(v.x(), v.y(), v.z());
    return 0;
  } 
  else if (const Plane_3 *iplane = CGAL::object_cast<Plane_3>(&result)) {
    return 1;
  } 
  else {
    return -1;
  }
}

int line_plane_intersection(const Point_3& B, const Vector_3& M,
                            const Vector_3& N, const double D,
                            Point_3& p)
{
  typedef CGAL::Cartesian<double> K;
  typedef CGAL::Plane_3<K> Plane_3;
  typedef CGAL::Line_3<K> Line_3;

  CGAL::Point_3<K> CB(B.x(), B.y(), B.z());
  CGAL::Vector_3<K> CM(M.x(), M.y(), M.z());

  Line_3 L(CB, CM);
  Plane_3 P(N.x(), N.y(), N.z(), D);
  CGAL::Object result = CGAL::intersection(L, P);
  if (const CGAL::Point_3<K> *ipoint = CGAL::object_cast<CGAL::Point_3<K> >(&result)) {
    p = Point_3(ipoint->x(), ipoint->y(), ipoint->z());
    return 0;
  } 
  else if (const Line_3 *iline = CGAL::object_cast<Line_3>(&result)) {
    return 1;
  } 
  else {
    return -1;
  }
}

static std::vector<Point_3> mapPointsFromOXYplane(std::vector<Point_2> points,
		Vector_3 nu)
{
	DEBUG_START;

	ASSERT(!!Vector3d(nu.x(), nu.y(), nu.z()) && "nu is null vector");

	Vector_3 ez(0., 0, 1.);
	double length = sqrt(nu.squared_length());
	ASSERT(std::fpclassify(length) != FP_ZERO);
	nu = nu * 1. / length; /* Normalize std::vector \nu. */
	ASSERT(std::isfinite(nu.x()));
	ASSERT(std::isfinite(nu.y()));
	ASSERT(std::isfinite(nu.z()));
	Vector_3 tau = cross_product(nu, ez);

	std::vector<Point_3> pointsMapped;
	CGAL::Origin o;
	for (auto &point : points)
	{
		pointsMapped.push_back(o + tau * point.x() + ez * point.y());
	}
	DEBUG_END;
	return pointsMapped;
}

void Viewer::alphaChanged()
{

    normals.resize(0);
    pos_poly.resize(0);

    std::list<Facet> facets;
    scene->alpha_shape.get_alpha_shape_facets(std::back_inserter(facets), Alpha_shape_3::REGULAR);

    for(std::list<Facet>::iterator fit = facets.begin();
        fit != facets.end();
        ++fit) {
      const Cell_handle& ch = fit->first;
      const int index = fit->second;

      //const Vector_3& n = ch->normal(index); // must be unit vector

      const Point_3& a = ch->vertex((index+1)&3)->point();
      const Point_3& b = ch->vertex((index+2)&3)->point();
      const Point_3& c = ch->vertex((index+3)&3)->point();

      Vector_3 v = CGAL::unit_normal(a,b,c);

      normals.push_back(v.x()); normals.push_back(v.y()); normals.push_back(v.z());
      normals.push_back(v.x()); normals.push_back(v.y()); normals.push_back(v.z());
      normals.push_back(v.x()); normals.push_back(v.y()); normals.push_back(v.z());
      pos_poly.push_back(a.x()); pos_poly.push_back(a.y()); pos_poly.push_back(a.z());
      pos_poly.push_back(b.x()); pos_poly.push_back(b.y()); pos_poly.push_back(b.z());
      pos_poly.push_back(c.x()); pos_poly.push_back(c.y()); pos_poly.push_back(c.z());

    }

    initialize_buffers();

}

//compute the cross point
Point_3 compute_cross_point(Plane_3 plane, Point_3 start, Point_3 end)
{
	Vector_3 normal = plane.orthogonal_vector();
	Vector_3 line_direction = end - start;
	Point_3  p= plane.point();
	double t;
	double a = (start.x() - p.x()) * normal.x() + (start.y() - p.y()) * normal.y() + (start.z() - p.z()) * normal.z();
	double b = line_direction.x() * normal.x() + line_direction.y() * normal.y() + line_direction.z() * normal.z();

	assert(b != 0);
	t = -a / b;

	return start + t * line_direction;
}

void rotate_points3d(const Eigen::MatrixXd& ptsin, const Point_3& center, const Vector_3& direction, double angle, Eigen::MatrixXd& ptsout)
{
	Eigen::Vector3d c(center.x(), center.y(), center.z());
    Eigen::Vector3d dir(direction.x(), direction.y(), direction.z());
    Eigen::Matrix4d rotMat = create_rotation3d_line_angle(center, direction, angle);

	ptsout.resize(ptsin.rows(), ptsin.cols() );
    ptsout = transform_point3d(ptsin, rotMat);
}

// Réalise un impact sur la face fs à partir d'une liste de points à déplacer, répartis par couronne (pts[0] = première couronne intérieure, pts[0][0] = premier point de la première couronne)
void DegradeAnObject::impactTheFacetArea(std::vector< std::vector<Point_3> > pts, Facet fs, double ray, int index) {
	double str = 0.02;
	Vector_3 normal = normalizeVector(getNormalOfFacet(fs));
	Kernel::Plane_3 pl(fs.halfedge()->vertex()->point(), normal);
	for(int i = 0 ; i < pts.size() ; i++) {
		for(int j = 0 ; j < pts[i].size() ; j++) {
			bool chk = false;
			Point_iterator pi = polys[index].points_begin();
			while(!chk) {
				++pi;
				if(*pi == pts[i][j]) {
					*pi = Point_3(pi->x() - (impactStrengh(str, i))*normal.x(), pi->y() - (impactStrengh(str, i))*normal.y(), pi->z() - (impactStrengh(str, i))*normal.z());
					chk = true;
				}
			}
		}
	}
}

// Génère le vecteur qui a subi une rotation d'angle teta
Vector_3 DegradeAnObject::rotationVector(Vector_3 v, Vector_3 normal, double teta) {
	double c = cos(teta);
	double s = sin(teta);
	Kernel::RT m00 = normal.x() * normal.x() * (1-c) + c;
	Kernel::RT m01 = normal.x() * normal.y() * (1-c) - normal.z() * s;
	Kernel::RT m02 = normal.x() * normal.z() * (1-c) + normal.y() * s;
	Kernel::RT m10 = normal.x() * normal.y() * (1-c) + normal.z() * s;
	Kernel::RT m11 = normal.y() * normal.y() * (1-c) + c;
	Kernel::RT m12 = normal.z() * normal.y() * (1-c) - normal.x() * s;
	Kernel::RT m20 = normal.x() * normal.z() * (1-c) - normal.y() * s;
	Kernel::RT m21 = normal.z() * normal.y() * (1-c) + normal.x() * s;
	Kernel::RT m22 = normal.z() * normal.z() * (1-c) + c;
	CGAL::Aff_transformation_3<Kernel> rotate(m00, m01, m02, m10, m11, m12, m20, m21, m22);
	return rotate.transform(v);
}

Polyhedron_3 obtainPolyhedron(Polyhedron_3 initialP, std::map<int, int> map,
		IpoptTopologicalCorrector *FTNLP)
{
	DEBUG_START;
	std::vector<Vector_3> directions = FTNLP->getDirections();
	std::vector<double> values = FTNLP->getValues();
	std::vector<Plane_3> planes(initialP.size_of_facets());
	unsigned iFacet = 0;
	for (auto I = initialP.facets_begin(), E = initialP.facets_end();
			I != E; ++I)
	{
		auto it = map.find(iFacet);
		if (it != map.end())
		{
			int i = it->second;
			Vector_3 u = directions[i];
			double h = values[i];
			ASSERT(h > 0);
			planes[iFacet] = Plane_3(-u.x(), -u.y(), -u.z(), h);
			std::cout << "Changing plane #" << iFacet << ": "
				<< I->plane() << " |--> " << planes[iFacet]
				<< std::endl;
		}
		else
		{
			planes[iFacet] = I->plane();
		}
		++iFacet;
	}

	Polyhedron_3 intersection(planes);
	std::cout << "Change in facets number: " << initialP.size_of_facets()
		<< " -> " << intersection.size_of_facets() << std::endl;
	ASSERT(initialP.size_of_facets() - intersection.size_of_facets()
			< map.size() &&
			"It seems that all extracted facets have gone");
	DEBUG_END;
	return intersection;
}

void Viewer::drawEdge(const Point_3& from, const Point_3& to, const QColor& clr, float r)
{
  /* Draw regular lines */
  if( m_isFlat ) {
    // disable lighting
    ::glDisable( GL_LIGHTING );

    ::glLineWidth(1.0);
  	qglColor( clr );

    ::glBegin(GL_LINES);
    ::glVertex3f( from.x(), from.y(), from.z() );
    ::glVertex3f( to.x(), to.y(), to.z() );
    ::glEnd();

    // resume lighting
    ::glEnable( GL_LIGHTING );

    return;
  }

  /* Draw edges as 3D cylinders */
  GLboolean lighting, colorMaterial;
  ::glGetBooleanv( GL_LIGHTING, &lighting );
  ::glGetBooleanv( GL_COLOR_MATERIAL, &colorMaterial );
  ::glEnable( GL_LIGHTING );
  ::glDisable(GL_COLOR_MATERIAL);

  float color[4];
  color[0] = clr.redF();
  color[1] = clr.greenF();
  color[2] = clr.blueF();
  color[3] = clr.alphaF();

  Vector_3 v = to - from;

  // compute the length of the edge
  // method 1:
//  float length = sqrt( CGAL::squared_distance( from, to ) );
  // method 2:
  float length = sqrt( v.squared_length() );

  // normalize
  v = v / length;
  // compute the angle: cos theta = v.z/1.0
  GLfloat angle = acos( v.z() ) / 3.1415927 * 180;

  ::glPushMatrix();

  // move to "from" point
  ::glTranslatef( from.x(), from.y(), from.z() );
  // rotate from z-axis to from-->to
  //  axis: cross product of z-axis and from-->to
  ::glRotatef( angle, -v.y(), v.x(), 0.0f );
  // draw
  GLUquadricObj* quadratic = ::gluNewQuadric();	// Create A Pointer To The Quadric Object
  ::gluQuadricNormals( quadratic, GLU_SMOOTH );	// Create Smooth Normals
  ::glMaterialfv( GL_FRONT_AND_BACK, GL_AMBIENT_AND_DIFFUSE, color );
  // gluCylinder draws a cylinder oriented along the z-axis
  ::gluCylinder( quadratic, r, r, length, 16, 4 );

  // move back to origin
  ::glPopMatrix();

  if ( colorMaterial )
    ::glEnable( GL_COLOR_MATERIAL );
  if ( !lighting )
    ::glDisable( GL_LIGHTING );
}

// Normalise un vecteur
Vector_3 DegradeAnObject::normalizeVector(Vector_3 v) {
	double norm = sqrt(to_double(v.x() * v.x() + v.y() * v.y() + v.z() * v.z()));
	return v/norm;
}

Point_3 vec_to_point(const Vector_3& v)
{
    return Point_3(v.x(),v.y(),v.z());
}

std::array<double,3> convert_to_array(const Vector_3& p)
{
    return std::array<double,3>({p.x(),p.y(),p.z()});
}