… In Section 3, we introduce our proposed Parallel Field Embedding algorithm. The extensive
experimental results on both synthetic and real data sets are presented in Section 4. Finally, …

We propose a new technique for visual exploration of streamlines in 3D vector fields. We
construct a map from the space of all streamlines to points in IR n based on the preservation of …

… of semi-complete vector fields. In a parallel manner, we present certain quantitative
characteristics of boundary regular null points of semi-complete vector fields and corresponding …

… three types of velocity vector fields corresponding to typical cracks in this research are
summarized and named types Ⅰ, II, and III, respectively. Type Ⅰ represents a tensile crack while …

… vector field, of which we propose a new geometric definition, as conformally equivalent to the
previous class and such that the Killing vector field … a null parallel vector field. This class of …

… category, embed in flows or are generated by vector fields with … of these results concerning
flows generated by vector fields. … We perform a local perturbation of ƒ parallel to E to achieve …

… embedded in Rp, we prove the relation between VDM and the connection Laplacian operator
for vector fields … matrix Oij is an approximation to the parallel transport operator4 from Txj M …

… Learning an accurate low dimensional embedding for … We propose to learn the low dimensional
embedding with a manifold … M is the parallel transport of a scaled velocity vector field of α …

… by the existence of a parallel lightlike vector field.2. Bargmannian … vector field together
with a (possibly torsionful) connection preserving both the metric and the lightlike vector field. In …

… there are non-parallel unit vector fields which define isometric embeddings with respect to a
… embedding if and only if d = a and M is K-contact manifold. If ξ(x) is a unit vector field on M, …