When interpolating a network of curves to create a C surface from spline patches, the network has to satisfy an algebraic condition, called the vertex enclosure constraint. We show the existence of a similar, additional constraint that governs the admissibility of curve networks for G interpolation by smooth patches.

This paper describes a new class of surface patch for use in computational geometry, where fairness is built in at the design stage by using ideas from differential geometry. Principal patches are patches whose sides are lines of curvature, and can be created by making the boundary curves obey two conditions called the frame and position matching equations. lt is shown that surface continuity i...

plants change their environment characteristics and especially soil properties while their growth and adaptation, to develop plant communities. in this study effect of halophyte patches from urmia lack in a vegetation type of salsola nitraria and aeluropus littoralis on chemical and physical properties of soil was investigated. so 4 vegitation patches along 2 transect with the length of 150 met...

In this report, we have shown that the yeast amphiphysin-like protein Rvs167p was localized mainly in small cortical patches throughout the cell in unbudding cells. During budding, the patches were polarized at bud emergence site. During mating, Rvs167p was concentrated at the tip of the shmoo. Rvs167p colocalized with actin patches during yeast vegetative growth and mating. Complete disruption...

Recent years have numerous algorithms to learn a sparse synthesis or analysis model from data. Recently, a generalized analysis model called the ’transform model’ has been proposed. Data following the transform model is approximately sparsified when acted on by a linear operator called a sparsifying transform. While existing transform learning algorithms can learn a transform for any vectorized...

We propose a new theory of cell surface capping based on the principles of nucleation. When antibody interacts with cell surface molecules, the molecules initially form small aggregates called patches that later coalesce into a large aggregate called a cap. While a cap can form by patches being pulled together by action of the cell's cytoskeleton, in the case of some molecules, disruption of th...

We derive optimality conditions for the paths of a Dubins vehicle when the state space is partitioned into two patches with different vehicle’s forward velocity. We recast this problem as a hybrid optimal control problem and solve it using optimality principles for hybrid systems. Among the optimality conditions, we derive a “refraction” law at the boundary of the patches which generalizes the ...

We study Bézier-like formulas with weights in geometric algebra for parametrizing a special class of rational surfaces in isotropic 3-space. These formulas are useful for constructing isotropic-Möbius invariant surfaces that are dual to rational offset surfaces in euclidean 3-space. Our focus is on bilinear CliffordBézier patches. We derive their implicitization formula and characterize them as...

      The present study was performed to explore the matrix property of Ficus glomerata fruit mucilage for making transdermal patches. The mucilage was evaluated for its physicochemical properties. Various transdermal patches of indomethacin were prepared by solvent evaporation technique using different proportions of F. glomerata fruit mucilage. The compatib...