C++ SelfAdjointEigenSolver::computeDirect方法代码示例

  void DrawableTransformCovariance::updateCovarianceDrawList() {
    GLParameterTransformCovariance *covarianceParameter = dynamic_cast<GLParameterTransformCovariance*>(_parameter);
    glNewList(_covarianceDrawList, GL_COMPILE); 
    if(_covariance != Eigen::Matrix3f::Zero() && 
       covarianceParameter && 
       covarianceParameter->show() && 
       covarianceParameter->scale() > 0.0f) {
      float scale = covarianceParameter->scale();
      Eigen::Vector4f color = covarianceParameter->color();
      
      Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigenSolver;
      eigenSolver.computeDirect(_covariance, Eigen::ComputeEigenvectors);

      Eigen::Vector3f lambda = eigenSolver.eigenvalues();      
      Eigen::Isometry3f I = Eigen::Isometry3f::Identity();
      I.linear() = eigenSolver.eigenvectors();
      I.translation() = Eigen::Vector3f(_mean.x(), _mean.y(), _mean.z());
      
      float sx = sqrt(lambda[0]) * scale;
      float sy = sqrt(lambda[1]) * scale;
      float sz = sqrt(lambda[2]) * scale;
      
      glPushMatrix();
      glMultMatrixf(I.data());
      glColor4f(color[0], color[1], color[2], color[3]);
      glScalef(sx, sy, sz);
      glCallList(_sphereDrawList);
      glPopMatrix();	    
    }
    glEndList();
  }

  void DrawableUncertainty::updateCovarianceDrawList() {
    GLParameterUncertainty *uncertaintyParameter = dynamic_cast<GLParameterUncertainty*>(_parameter);
    glNewList(_covarianceDrawList, GL_COMPILE); 
    if(_covarianceDrawList &&
       _covariances && 
       uncertaintyParameter && 
       uncertaintyParameter->ellipsoidScale() > 0.0f) {
      uncertaintyParameter->applyGLParameter();
      Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> eigenSolver;
      float ellipsoidScale = uncertaintyParameter->ellipsoidScale();
      for(size_t i = 0; i < _covariances->size(); i += uncertaintyParameter->step()) {
	Gaussian3f &gaussian3f = _covariances->at(i);
	Eigen::Matrix3f covariance = gaussian3f.covarianceMatrix();
	Eigen::Vector3f mean = gaussian3f.mean();
	eigenSolver.computeDirect(covariance, Eigen::ComputeEigenvectors);
	Eigen::Vector3f eigenValues = eigenSolver.eigenvalues();      
	Eigen::Isometry3f I = Eigen::Isometry3f::Identity();
	I.linear() = eigenSolver.eigenvectors();
	I.translation() = mean;
	float sx = sqrt(eigenValues[0]) * ellipsoidScale;
	float sy = sqrt(eigenValues[1]) * ellipsoidScale;
	float sz = sqrt(eigenValues[2]) * ellipsoidScale;
	glPushMatrix();
	glMultMatrixf(I.data());	
	sx = sx;
	sy = sy;
	sz = sz;
	glScalef(sx, sy, sz);
	glCallList(_sphereDrawList);
	glPopMatrix();	    
      }   
    }
    glEndList();
  }

inline void calcNormalsEigen(Mat &depth_img, Mat &points, Mat &normals, int k=11, float max_dist=0.02, bool dist_rel_z=true) {

	if (normals.rows != depth_img.rows || normals.cols != depth_img.cols || normals.channels() != 3) {
		normals = cv::Mat::zeros(depth_img.rows, depth_img.cols, CV_32FC3);
	}
	Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> solver;
	const float bad_point = std::numeric_limits<float>::quiet_NaN ();

	for (int y = 0; y < depth_img.rows; ++y) {
		for (int x = 0; x < depth_img.cols; ++x) {

			Eigen::Vector3f p_q = points.at<Eigen::Vector3f>(y,x);
			// depth-nan handle: bad point
			if (depth_img.at<float>(y, x) == 0 || p_q(0) != p_q(0)){
				normals.at<Eigen::Vector3f>(y,x) = Eigen::Vector3f(bad_point, bad_point, bad_point);
				continue;
			}

			Eigen::Matrix3f A = Eigen::Matrix3f::Zero();
			std::vector<Eigen::Vector3f> p_j_list;
			Eigen::Vector3f _p = Eigen::Vector3f::Zero();
			float max_dist_rel = max_dist * ((dist_rel_z)? p_q[2]*1.5 : 1);
			
			for (int k_y = y-k/2; k_y <= y+k/2; ++k_y) {
				for (int k_x = x-k/2; k_x <= x+k/2; ++k_x) {

					if(k_y<0 || k_x<0 || k_y>=depth_img.rows || k_x >= depth_img.cols)
						continue;
					if (k_y == y && k_x == x)
						continue;
					if (depth_img.at<float>(k_y, k_x) == 0)
						continue;

					Eigen::Vector3f p_j = points.at<Eigen::Vector3f>(k_y,k_x);
					if( max_dist_rel <= 0 || ((p_q - p_j).norm() <= max_dist_rel) ) {
						p_j_list.push_back(p_j);
						_p += p_j;
					}
				}
			}


			_p /= p_j_list.size();
			double weight_sum = 0;
			for (int i = 0; i < p_j_list.size(); ++i) {
				double w = 1.0/(p_j_list[i] - _p).squaredNorm();
				A += w*((p_j_list[i] - _p)*((p_j_list[i] - _p).transpose()));
				weight_sum += w;
			}
			A /= weight_sum;
			solver.computeDirect(A);
			Eigen::Vector3f normal = solver.eigenvectors().col(0).normalized();
			// flip to viewpoint (0,0,0)
			if(normal(2) > 0)
				normal *= -1;
			normals.at<Eigen::Vector3f>(y,x) = normal;
		}
	}
}

IGL_INLINE void igl::polar_dec(
  const Eigen::PlainObjectBase<DerivedA> & A,
  Eigen::PlainObjectBase<DerivedR> & R,
  Eigen::PlainObjectBase<DerivedT> & T,
  Eigen::PlainObjectBase<DerivedU> & U,
  Eigen::PlainObjectBase<DerivedS> & S,
  Eigen::PlainObjectBase<DerivedV> & V)
{
  using namespace std;
  using namespace Eigen;
  typedef typename DerivedA::Scalar Scalar;

  const Scalar th = std::sqrt(Eigen::NumTraits<Scalar>::dummy_precision());

  Eigen::SelfAdjointEigenSolver<DerivedA> eig;
  feclearexcept(FE_UNDERFLOW);
  eig.computeDirect(A.transpose()*A);
  if(fetestexcept(FE_UNDERFLOW) || eig.eigenvalues()(0)/eig.eigenvalues()(2)<th)
  {
    cout<<"resorting to svd 1..."<<endl;
    return polar_svd(A,R,T,U,S,V);
  }

  S = eig.eigenvalues().cwiseSqrt();

  V = eig.eigenvectors();
  U = A * V;
  R = U * S.asDiagonal().inverse() * V.transpose();
  T = V * S.asDiagonal() * V.transpose();

  S = S.reverse().eval();
  V = V.rowwise().reverse().eval();
  U = U.rowwise().reverse().eval() * S.asDiagonal().inverse();

  if(R.determinant() < 0)
  {
    // Annoyingly the .eval() is necessary
    auto W = V.eval();
    const auto & SVT = S.asDiagonal() * V.adjoint();
    W.col(V.cols()-1) *= -1.;
    R = U*W.transpose();
    T = W*SVT;
  }

  if(std::fabs(R.squaredNorm()-3.) > th)
  {
    cout<<"resorting to svd 2..."<<endl;
    return polar_svd(A,R,T,U,S,V);
  }
}

OBB::OBB(Mesh::const_iterator begin, Mesh::const_iterator end)
{
	if (begin == end)
	{
		axes = -ZERO_SIZE * Matrix3f::Identity(); //make it inside out (i guess)
		origin = Vector3f::Zero();
		return;
	}

	Vector3f centerOfMass = centroid(begin, end);
	Matrix3f inertiaTensor = Matrix3f::Zero();

	auto addPt = [&](const Vector3f& pt, float mass)
	{
		Vector3f lpos = pt - centerOfMass;

		inertiaTensor(0, 0) += (lpos.y()*lpos.y() + lpos.z()*lpos.z()) * mass;
		inertiaTensor(1, 1) += (lpos.x()*lpos.x() + lpos.z()*lpos.z()) * mass;
		inertiaTensor(2, 2) += (lpos.x()*lpos.x() + lpos.y()*lpos.y()) * mass;
		inertiaTensor(1, 0) -= lpos.x()*lpos.y() * mass;
		inertiaTensor(2, 0) -= lpos.x()*lpos.z() * mass;
		inertiaTensor(2, 1) -= lpos.y()*lpos.z() * mass;
	};

	for (const auto& tri : make_range(begin, end))
	{
		float area = TriNormal(tri).norm() / 6.f;
		addPt(tri.col(0), area);
		addPt(tri.col(1), area);
		addPt(tri.col(2), area);
	}

	Eigen::SelfAdjointEigenSolver<Matrix3f> es;
	es.computeDirect(inertiaTensor);
	axes = es.eigenvectors();

	float maxflt = std::numeric_limits<float>::max();
	Eigen::Vector3f min{ maxflt, maxflt, maxflt };
	Eigen::Vector3f max = -min;

	for (const auto& tri : make_range(begin, end))
	{
		min = min.cwiseMin((axes.transpose() * tri).rowwise().minCoeff());
		max = max.cwiseMax((axes.transpose() * tri).rowwise().maxCoeff());
	}

    extent = (max - min).cwiseMax(ZERO_SIZE) / 2.f;
    origin = axes * (min + extent);
}

inline void calcPC(Mat &normals, Mat &points, Mat &depth_img, Mat &pc, int k=5, float max_dist=0.02, bool dist_rel_z=true) {

	if (pc.rows != depth_img.rows || pc.cols != depth_img.cols || pc.channels() != 5) {
		pc = Mat::zeros(depth_img.rows, depth_img.cols, CV_32FC(5));
	}
	Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> solver;
	Eigen::Matrix3f I = Eigen::Matrix3f::Identity();
	int failed = 0;

	for (int y = 0; y < depth_img.rows; ++y) {
		for (int x = 0; x < depth_img.cols; ++x) {

			Eigen::Matrix3f A = Eigen::Matrix3f::Zero();
			Eigen::Vector3f _m = Eigen::Vector3f::Zero();
			Eigen::Vector3f n_q = normals.at<Eigen::Vector3f>(y,x);
			Eigen::Vector3f p_q = points.at<Eigen::Vector3f>(y,x);
			std::vector<Eigen::Vector3f> m_j_list;
			Eigen::Matrix3f M = (I - n_q*(n_q.transpose()));
			float max_dist_rel = max_dist * ((dist_rel_z)? p_q[2]*1.5 : 1);


			for (int k_y = y-k/2; k_y <= y+k/2; ++k_y) {
				for (int k_x = x-k/2; k_x <= x+k/2; ++k_x) {

					if(k_y<0 || k_x<0 || k_y>=depth_img.rows || k_x >= depth_img.cols)
						continue;
					if(depth_img.at<float>(k_y,k_x) == 0)
						continue;

					Eigen::Vector3f p_j = points.at<Eigen::Vector3f>(k_y,k_x);

					if( max_dist_rel <= 0 || ((p_q - p_j).norm() < max_dist_rel) ) {
						Eigen::Vector3f n_j = normals.at<Eigen::Vector3f>(k_y,k_x);
						Eigen::Vector3f m_j = M * n_j;
						m_j_list.push_back(m_j);
						_m += m_j;
					}
					
				}
			}

			if(m_j_list.size() >= k) {
				_m /= m_j_list.size();
				for (int i = 0; i < m_j_list.size(); ++i) {
					A += (m_j_list[i] - _m)*((m_j_list[i] - _m).transpose());
				}
				A /= m_j_list.size();
				solver.computeDirect(A);
				float diff = solver.eigenvalues()(2) - solver.eigenvalues()(1);
				float mean = (solver.eigenvalues()(2) + solver.eigenvalues()(1)) / 2;
				float ratio = solver.eigenvalues()(1) / solver.eigenvalues()(2);
				Eigen::Vector3f evec = solver.eigenvectors().col(2);
				pc.at<Vector5f>(y,x) = Vector5f();
				pc.at<Vector5f>(y,x) << 
					solver.eigenvalues()(1),
					solver.eigenvalues()(2),
					evec;
			} else {
				failed++;
				pc.at<Vector5f>(y,x) = Vector5f::Zero();
				pc.at<Vector5f>(y,x) << std::numeric_limits<float>::quiet_NaN(),
										std::numeric_limits<float>::quiet_NaN(),
										std::numeric_limits<float>::quiet_NaN(),
										std::numeric_limits<float>::quiet_NaN(),
										std::numeric_limits<float>::quiet_NaN();
			}
		}
	}
}