Quasi-Isometric Mesh Parameterization Using Heat-Based Geodesics and Poisson Surface Fills

In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e., isometries) are obviously attractive. However, geodesic-based isometries present limitations when the mesh has concave or disconnected boundary (i.e., holes). Recent advances in computing geodesic maps using the heat equation in 2-manifolds motivate us to revisit mesh parameterization with geodesic maps. We devise a Poisson surface underlying, extending, and filling the holes of the mesh M. We compute a near-isometric mapping for quasi-developable meshes by using geodesic maps based on heat propagation. Our method: (1) Precomputes a set of temperature maps (heat kernels) on the mesh; (2) estimates the geodesic distances along the piecewise linear surface by using the temperature maps; and (3) uses multidimensional scaling (MDS) to acquire the 2D coordinates that minimize the difference between geodesic distances on M and Euclidean distances on R 2 . This novel heat-geodesic parameterization is successfully tested with several concave and/or punctured surfaces, obtaining bijective low-distortion parameterizations. Failures are registered in nonsegmented, highly nondevelopable meshes (such as seam meshes). These cases are the goal of future endeavors.

Life prediction of slewing bearing based on isometric mapping and fuzzy support vector regression

The monitoring data of slewing bearing is massive. In order to establish accurate life prediction model from complex vibration signal of slewing bearing, a life prediction method based on manifold learning and fuzzy support vector regression (SVR) is proposed. Firstly, the multiple features are extracted from time domain and time-frequency domain. Then isometric mapping (ISOMAP) is used to reduce high-dimensional features to low-dimensional features that can reflect degeneration of slewing bearing well. Finally, the fuzzy SVR is used to predict the life degradation trend of slewing bearing. The results show that: (1) Multi-feature fusion after ISOMAP can obtain more comprehensive degradation indicator. (2) The complexity of the life prediction model is simplified and the real-time life degradation trend of slewing bearing can be well predicted by fuzzy SVR, so it is very suitable to predict life degradation trend of slewing bearing based on massive data well. The time of prediction on average is reduced by 72.7%. The mean absolute error (MAE) and root mean square error (RMSE) of prediction are reduced by 73% and 59% respectively compared with traditional methods. The accuracy of prediction is greatly improved.