Singularity-Free Frame Fields for Line Drawing Vectorization

State-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.     

Features of the exponential form of internal heat generation,Cattaneo–Christov heat theory on water-based graphene–CNT–titanium ternary hybrid nanofluid flow

To increase energy efficiency, the flow of fluids containing nanoparticles is crucial in industrial applications notably in nuclear reactors and nuclear system cooling. In light of this, this study examines the flow of a water-based ternary hybrid nanofluid (graphene, single-walled carbon nanotubes, and titanium dioxide) across a curved stretching sheet with suction. The non-Fourier heat flux model is also considered in the modeling. The existing partial differential equations are converted into ordinary differential equations through the use of similarity variables. These ordinary differential equations are then numerically solved using the Runge–Kutta–Fehlberg fourth- and fifth-order method along with a shooting approach. The collection of graphical findings for the key variables on the temperature and velocity profiles is investigated. Results reveal that the heat transport in ternary hybrid nanoliquid rises as the heat source/sink parameter rises. The Biot number influences the thermal profile positively, whereas the increasing curvature parameter values reduce heat transport. The curvature parameter has a positive impact on skin friction but the suction parameter has a negative impact on skin friction.