اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Weighted Gaussian Curvature Derivative of a Space-Filling Diagram
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The morphometric approach [HRC13,RHK06] writes the solvation free energy as a linear combination of weight
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Representing an atom by a solid sphere in $3$-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free ene
rgy. The morphometric approach [HRC13,RHK06] writes the latter as a linear combination of weight
Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second order differentiable. To tackle these three issues, we
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In this thesis we study one of the fundamental predicates required for the construction of the 3D Apollonius diagram (also known as the 3D Additively Weighted Voronoi diagram), namely the EDGECONFLICT predicate: given five sites $S_i, S_j,S_k,S_l,S_m
$ that define an edge $e_{ijklm}$ in the 3D Apollonius diagram, and a sixth query site $S_q$, the predicate determines the portion of $e_{ijklm}$ that will disappear in the Apollonius diagram of the six sites due to the insertion of $S_q$. Our focus is on the algorithmic analysis of the predicate with the aim to minimize its algebraic degree. We decompose the main predicate into sub-predicates, which are then evaluated with the aid of additional primitive operations. We show that the maximum algebraic degree required to answer any of the sub-predicates and primitives, and, thus, our main predicate is 10 in non-degenerate configurations when the trisector is of Hausdorff dimension 1. We also prove that all subpredicates developed can be evaluated using 10 or 8-degree demanding operations for degenerate input for these trisector types, depending on whether they require the evaluation of an intermediate INSPHERE predicate or not. Among the tools we use is the 3D inversion transformation and the so-called qualitative symbolic perturbation scheme. Most of our analysis is carried out in the inverted space, which is where our geometric observations and analysis is captured in algebraic terms.
Throughout this paper, a persistence diagram ${cal P}$ is composed of a set $P$ of planar points (each corresponding to a topological feature) above the line $Y=X$, as well as the line $Y=X$ itself, i.e., ${cal P}=Pcup{(x,y)|y=x}$. Given a set of per
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