Improvement of the initial placement of modifier meshes:
Sphere and Cylinder are scaled to the same volume as Box Newly entered modifier meshes are rotated parallell to the world coordinates. If the instance coordinate system is rotated and scaled, it is not possible to create an unskewed modifier to world transformation. In that case the best possible transformation is found to minimize least squares error of the 8 corners of the new modifier mesh bounding box using Levenberg-Marquardt algorithm. FIXME: 1) The Levenberg-Marquardt non-linear least squares does not converge nicely, it may require some tuning. 2) Above all, if 1) is called, then often the skew of the modifier mesh is so high, that it is likely more useful to display the modifier with zero rotation and inverse scaling, so that the modifier will be of correct size, but not parallel to the world coordinates.
This commit is contained in:
bubnikv
parent
3053010446
commit
dc0c58a9c5
2 changed files with 178 additions and 26 deletions
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@ -242,6 +242,7 @@ public:
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void set_scaling_factor(const Vec3d& scaling_factor);
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void set_scaling_factor(const Vec3d& scaling_factor);
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void set_scaling_factor(Axis axis, double scaling_factor);
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void set_scaling_factor(Axis axis, double scaling_factor);
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bool is_scaling_uniform() const { return std::abs(m_scaling_factor.x() - m_scaling_factor.y()) < 1e-8 && std::abs(m_scaling_factor.x() - m_scaling_factor.z()) < 1e-8; }
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const Vec3d& get_mirror() const { return m_mirror; }
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const Vec3d& get_mirror() const { return m_mirror; }
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double get_mirror(Axis axis) const { return m_mirror(axis); }
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double get_mirror(Axis axis) const { return m_mirror(axis); }
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@ -1173,10 +1173,161 @@ void ObjectList::load_part( ModelObject* model_object,
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}
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}
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// Find volume transformation, so that the chained (instance_trafo * volume_trafo) will be as close to identity
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// as possible in least squares norm in regard to the 8 corners of bbox.
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// Bounding box is expected to be centered around zero in all axes.
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Geometry::Transformation volume_to_bed_transformation(const Geometry::Transformation &instance_transformation, const BoundingBoxf3 &bbox)
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{
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Geometry::Transformation out;
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if (instance_transformation.is_scaling_uniform()) {
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// No need to run the non-linear least squares fitting for uniform scaling.
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// Just set the inverse.
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out.set_from_transform(instance_transformation.get_matrix(true).inverse());
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}
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else
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{
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Eigen::Matrix3d instance_rotation_trafo =
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(Eigen::AngleAxisd(instance_transformation.get_rotation().z(), Vec3d::UnitZ()) *
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Eigen::AngleAxisd(instance_transformation.get_rotation().y(), Vec3d::UnitY()) *
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Eigen::AngleAxisd(instance_transformation.get_rotation().x(), Vec3d::UnitX())).toRotationMatrix();
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Eigen::Matrix3d instance_rotation_trafo_inv =
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(Eigen::AngleAxisd(- instance_transformation.get_rotation().x(), Vec3d::UnitX()) *
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Eigen::AngleAxisd(- instance_transformation.get_rotation().y(), Vec3d::UnitY()) *
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Eigen::AngleAxisd(- instance_transformation.get_rotation().z(), Vec3d::UnitZ())).toRotationMatrix();
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Vec3d euler_angles_inv = Geometry::extract_euler_angles(instance_rotation_trafo_inv);
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Eigen::Matrix3d instance_trafo = instance_rotation_trafo *
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Eigen::Scaling(instance_transformation.get_scaling_factor().cwiseProduct(instance_transformation.get_mirror()));
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// 8 corners of the bounding box.
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auto pts = Eigen::MatrixXd(8, 3);
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pts(0, 0) = bbox.min.x(); pts(0, 1) = bbox.min.y(); pts(0, 2) = bbox.min.z();
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pts(1, 0) = bbox.min.x(); pts(1, 1) = bbox.min.y(); pts(1, 2) = bbox.max.z();
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pts(2, 0) = bbox.min.x(); pts(2, 1) = bbox.max.y(); pts(2, 2) = bbox.min.z();
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pts(3, 0) = bbox.min.x(); pts(3, 1) = bbox.max.y(); pts(3, 2) = bbox.max.z();
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pts(4, 0) = bbox.max.x(); pts(4, 1) = bbox.min.y(); pts(4, 2) = bbox.min.z();
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pts(5, 0) = bbox.max.x(); pts(5, 1) = bbox.min.y(); pts(5, 2) = bbox.max.z();
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pts(6, 0) = bbox.max.x(); pts(6, 1) = bbox.max.y(); pts(6, 2) = bbox.min.z();
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pts(7, 0) = bbox.max.x(); pts(7, 1) = bbox.max.y(); pts(7, 2) = bbox.max.z();
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// Current parameters: 3x scale, 3x rotation
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auto beta = Eigen::MatrixXd(3 + 3, 1);
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beta << 1., 1., 1., euler_angles_inv(0), euler_angles_inv(1), euler_angles_inv(2);
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{
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// Trafo from world to the coordinate system of the modifier mesh, with the inverse rotation applied to the modifier.
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Eigen::Matrix3d A_scaling = instance_trafo * instance_rotation_trafo_inv;
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// Corners of the bounding box transformed into the modifier mesh coordinate space, with inverse rotation applied to the modifier.
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auto qs = pts * A_scaling.inverse().transpose();
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// Fill in scaling based on least squares fitting of the bounding box corners.
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for (int i = 0; i < 3; ++i)
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beta(i) = pts.col(i).dot(qs.col(i)) / pts.col(i).dot(pts.col(i));
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}
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// Jacobian
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// rows: 8 corners of a cube times 3 dimensions,
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// cols: 3x scale, 3x rotation
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auto J = Eigen::MatrixXd(8 * 3, 3 + 3);
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// Until convergence:
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Eigen::Matrix3d s, dsx, dsy, dsz;
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Eigen::Matrix3d rx, drx, ry, dry, rz, drz;
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s.setIdentity();
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rx.setIdentity(); ry.setIdentity(); rz.setIdentity();
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dsx.setZero(); dsy.setZero(); dsz.setZero();
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drx.setZero(); dry.setZero(); drz.setZero();
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dsx(0, 0) = 1.; dsy(1, 1) = 1.; dsz(2, 2) = 1.;
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// Solve the non-linear Least Squares problem by Levenberg–Marquardt algorithm (modified Gauss–Newton iteration)
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const double eps = 1.e-7;
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auto beta_best = beta;
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double beta_best_error = 1e10;
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for (size_t iter = 0; iter < 200; ++ iter) {
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// Current rotation & scaling transformation.
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auto trafo = instance_trafo *
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Eigen::AngleAxisd(beta(5), Vec3d::UnitZ()) *
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Eigen::AngleAxisd(beta(4), Vec3d::UnitY()) *
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Eigen::AngleAxisd(beta(3), Vec3d::UnitX()) *
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Eigen::Scaling(Vec3d(beta(0), beta(1), beta(2)));
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// Current error after rotation & scaling.
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auto dy = (pts - pts * trafo.transpose()).eval();
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double err = 0;
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for (int i = 0; i < 8; ++i)
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err += dy.row(i).norm();
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if (err < beta_best_error) {
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beta_best = beta;
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beta_best_error = err;
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}
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// Fill in the Jacobian at current beta.
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double cos_rx = cos(beta(3));
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double sin_rx = sin(beta(3));
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double cos_ry = cos(beta(4));
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double sin_ry = sin(beta(4));
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double cos_rz = cos(beta(5));
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double sin_rz = sin(beta(5));
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rx << 1., 0., 0., 0., cos_rx, -sin_rx, 0., sin_rx, cos_rx;
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drx << 0., 0., 0., 0., -sin_rx, -cos_rx, 0., cos_rx, -sin_rx;
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ry << cos_ry, 0., sin_ry, 0., 1., 0., -sin_ry, 0., cos_ry;
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dry << -sin_ry, 0., cos_ry, 0., 0., 0., -cos_ry, 0., -sin_ry;
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rz << cos_rz, -sin_rz, 0., sin_rz, cos_rz, 0., 0., 0., 1.;
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drz << -sin_rz, -cos_rz, 0., cos_rz, -sin_rz, 0., 0., 0., 0.;
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s(0, 0) = beta(0);
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s(1, 1) = beta(1);
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s(2, 2) = beta(2);
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auto rot = (instance_trafo * rz * ry * rx).eval();
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auto jrx = pts * (instance_trafo * rz * ry * drx * s).transpose();
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auto jry = pts * (instance_trafo * rz * dry * rx * s).transpose();
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auto jrz = pts * (instance_trafo * drz * ry * rx * s).transpose();
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for (int r = 0; r < 8; ++ r) {
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for (int i = 0; i < 3; ++ i) {
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J(r * 3 + i, 0) = rot(i, 0) * pts(r, 0);
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J(r * 3 + i, 1) = rot(i, 1) * pts(r, 1);
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J(r * 3 + i, 2) = rot(i, 2) * pts(r, 2);
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J(r * 3 + i, 3) = jrx(r, i);
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J(r * 3 + i, 4) = jry(r, i);
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J(r * 3 + i, 5) = jrz(r, i);
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}
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}
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// Solving the normal equations for delta beta.
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auto rhs = (J.transpose() * Eigen::Map<Eigen::VectorXd>(dy.data(), dy.size())).eval();
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double lambda = 1.; // 0.01;
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auto A = (J.transpose() * J + Eigen::Matrix<double, 6, 6>::Identity() * lambda).eval();
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auto L = A.ldlt();
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auto delta_beta = L.solve(rhs).eval();
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// Check for convergence.
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auto delta_beta_max = delta_beta.cwiseAbs().maxCoeff();
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if (delta_beta_max < eps)
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break;
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beta = beta + delta_beta;
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}
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out.set_rotation(Vec3d(beta_best(3), beta_best(4), beta_best(5)));
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out.set_scaling_factor(Vec3d(std::abs(beta_best(0)), std::abs(beta_best(1)), std::abs(beta_best(2))));
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out.set_mirror(Vec3d(beta_best(0) > 0 ? 1. : -1, beta_best(1) > 0 ? 1. : -1, beta_best(2) > 0 ? 1. : -1));
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}
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return out;
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}
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void ObjectList::load_generic_subobject(const std::string& type_name, const ModelVolumeType type)
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void ObjectList::load_generic_subobject(const std::string& type_name, const ModelVolumeType type)
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{
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{
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const auto obj_idx = get_selected_obj_idx();
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const auto obj_idx = get_selected_obj_idx();
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if (obj_idx < 0) return;
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if (obj_idx < 0)
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return;
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const GLCanvas3D::Selection& selection = wxGetApp().plater()->canvas3D()->get_selection();
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assert(obj_idx == selection.get_object_idx());
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// Selected instance index in ModelObject. Only valid if there is only one instance selected in the selection.
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int instance_idx = selection.get_instance_idx();
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assert(instance_idx != -1);
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if (instance_idx == -1)
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return;
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// Selected object
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ModelObject &model_object = *(*m_objects)[obj_idx];
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// Bounding box of the selected instance in world coordinate system including the translation, without modifiers.
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BoundingBoxf3 instance_bb = model_object.instance_bounding_box(instance_idx);
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const wxString name = _(L("Generic")) + "-" + _(type_name);
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const wxString name = _(L("Generic")) + "-" + _(type_name);
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TriangleMesh mesh;
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TriangleMesh mesh;
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@ -1185,48 +1336,48 @@ void ObjectList::load_generic_subobject(const std::string& type_name, const Mode
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const auto& sz = BoundingBoxf(bed_shape).size();
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const auto& sz = BoundingBoxf(bed_shape).size();
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const auto side = 0.1 * std::max(sz(0), sz(1));
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const auto side = 0.1 * std::max(sz(0), sz(1));
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if (type_name == "Box") {
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if (type_name == "Box")
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// Sitting on the print bed, left front front corner at (0, 0).
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mesh = make_cube(side, side, side);
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mesh = make_cube(side, side, side);
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// box sets the base coordinate at 0, 0, move to center of plate
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mesh.translate(-side * 0.5, -side * 0.5, 0);
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}
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else if (type_name == "Cylinder")
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else if (type_name == "Cylinder")
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mesh = make_cylinder(0.5*side, side);
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// Centered around 0, sitting on the print bed.
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// The cylinder has the same volume as the box above.
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mesh = make_cylinder(0.564 * side, side);
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else if (type_name == "Sphere")
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else if (type_name == "Sphere")
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mesh = make_sphere(0.5*side, PI/18);
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// Centered around 0, half the sphere below the print bed, half above.
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else if (type_name == "Slab") {
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// The sphere has the same volume as the box above.
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const auto& size = (*m_objects)[obj_idx]->bounding_box().size();
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mesh = make_sphere(0.62 * side, PI / 18);
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mesh = make_cube(size(0)*1.5, size(1)*1.5, size(2)*0.5);
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else if (type_name == "Slab")
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// box sets the base coordinate at 0, 0, move to center of plate and move it up to initial_z
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// Sitting on the print bed, left front front corner at (0, 0).
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mesh.translate(-size(0)*1.5 / 2.0, -size(1)*1.5 / 2.0, 0);
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mesh = make_cube(instance_bb.size().x()*1.5, instance_bb.size().y()*1.5, instance_bb.size().z()*0.5);
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}
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mesh.repair();
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mesh.repair();
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auto new_volume = (*m_objects)[obj_idx]->add_volume(mesh);
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// Mesh will be centered when loading.
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ModelVolume *new_volume = model_object.add_volume(std::move(mesh));
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new_volume->set_type(type);
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new_volume->set_type(type);
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#if !ENABLE_GENERIC_SUBPARTS_PLACEMENT
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#if !ENABLE_GENERIC_SUBPARTS_PLACEMENT
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new_volume->set_offset(Vec3d(0.0, 0.0, (*m_objects)[obj_idx]->origin_translation(2) - mesh.stl.stats.min(2)));
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new_volume->set_offset(Vec3d(0.0, 0.0, model_object.origin_translation(2) - mesh.stl.stats.min(2)));
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#endif // !ENABLE_GENERIC_SUBPARTS_PLACEMENT
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#endif // !ENABLE_GENERIC_SUBPARTS_PLACEMENT
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#if !ENABLE_VOLUMES_CENTERING_FIXES
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#if !ENABLE_VOLUMES_CENTERING_FIXES
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new_volume->center_geometry();
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new_volume->center_geometry();
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#endif // !ENABLE_VOLUMES_CENTERING_FIXES
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#endif // !ENABLE_VOLUMES_CENTERING_FIXES
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#if ENABLE_GENERIC_SUBPARTS_PLACEMENT
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#if ENABLE_GENERIC_SUBPARTS_PLACEMENT
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const GLCanvas3D::Selection& selection = wxGetApp().plater()->canvas3D()->get_selection();
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int instance_idx = selection.get_instance_idx();
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if (instance_idx != -1)
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if (instance_idx != -1)
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{
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{
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// First (any) GLVolume of the selected instance. They all share the same instance matrix.
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const GLVolume* v = selection.get_volume(*selection.get_volume_idxs().begin());
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const GLVolume* v = selection.get_volume(*selection.get_volume_idxs().begin());
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const Transform3d& inst_m = v->get_instance_transformation().get_matrix(true);
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// Transform the new modifier to be aligned with the print bed.
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TriangleMesh vol_mesh(mesh);
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const BoundingBoxf3 mesh_bb = new_volume->mesh.bounding_box();
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vol_mesh.transform(inst_m);
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new_volume->set_transformation(volume_to_bed_transformation(v->get_instance_transformation(), mesh_bb));
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Vec3d vol_shift = -vol_mesh.bounding_box().center();
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// Set the modifier position.
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vol_mesh.translate((float)vol_shift(0), (float)vol_shift(1), (float)vol_shift(2));
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auto offset = (type_name == "Slab") ?
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Vec3d world_mesh_bb_size = vol_mesh.bounding_box().size();
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// Slab: Lift to print bed
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BoundingBoxf3 inst_bb = (*m_objects)[obj_idx]->instance_bounding_box(instance_idx);
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Vec3d(0., 0., 0.5 * mesh_bb.size().z() + instance_bb.min.z() - v->get_instance_offset().z()) :
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Vec3d world_target = Vec3d(inst_bb.max(0), inst_bb.min(1), inst_bb.min(2)) + 0.5 * world_mesh_bb_size;
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// Translate the new modifier to be pickable: move to the left front corner of the instance's bounding box, lift to print bed.
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new_volume->set_offset(inst_m.inverse() * (world_target - v->get_instance_offset()));
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Vec3d(instance_bb.max(0), instance_bb.min(1), instance_bb.min(2)) + 0.5 * mesh_bb.size() - v->get_instance_offset();
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new_volume->set_offset(v->get_instance_transformation().get_matrix(true).inverse() * offset);
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}
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}
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#endif // ENABLE_GENERIC_SUBPARTS_PLACEMENT
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#endif // ENABLE_GENERIC_SUBPARTS_PLACEMENT
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