Knuthian Drawings of Series-Parallel Flowcharts

Inspired by a classic paper by Knuth, we revisit the problem of drawing flowcharts of loop-free algorithms, that is, degree-three series-parallel digraphs. Our drawing algorithms show that it is possible to produce Knuthian drawings of degree-three series-parallel digraphs with good aspect ratios and small numbers of edge bends.Comment: Full versio

Development of a CFD Procedure for the Axial Thrust Evaluation in Multistage Centrifugal Pumps

One of the most challenging aspects in horizontal pumps design is represented by the evaluation of the axial thrust acting on the rotating shaft. The thrust is affected by pump characteristics, working conditions and internal pressure fields. Solving this problem is simple for single stage pumps while several complications arise for multistage pumps even in partially self-balancing opposite impeller configuration. Therefore a systematic approach to the axial thrust evaluation for a multistage horizontal centrifugal pump has been assessed and validated. The method consists in CFD simulation of each single pump component to obtain correlations which express the axial thrust as a function of the working conditions. The global axial thrust is finally calculated as balance of the forces acting on each stage. The numerical procedure will be explained and its main results shown and discussed in the present paper

Comparison of mandibular arch expansion by the schwartz appliance using two activation protocols: A preliminary retrospective clinical study

Background and objectives: Dental crowding is more pronounced in the mandible than in the maxilla. When exceeding a significant amount, the creation of new space is required. The mandibular expansion devices prove to be useful even if the increase in the lower arch perimeter seems to be just ascribed to the vestibular inclination of teeth. The aim of the study was to compare two activation protocols of the Schwartz appliance in terms of effectiveness, particularly with regard to how quickly crowding is solved and how smaller is the increasing of vestibular inclination of the mandibular molars. Materials and methods: We compared two groups of patients treated with different activation's protocols of the lower Schwartz appliance (Group 1 protocol consisted in turning the expansion screw half a turn twice every two weeks and replacing the device every four months; Group 2 was treated by using the classic activation protocol-1/4 turn every week, never replacing the device). The measurements of parameters such as intercanine distance (IC), interpremolar distance (IPM), intermolar distance (IM), arch perimeter(AP), curve of Wilson (COW), and crowding (CR) were made on dental casts at the beginning and at the end of the treatment. Results: A significant difference between protocol groups was observed in the variation of COWL between time 0 and time 1 with protocol 1 with protocol 1 subjects showing a smaller increase in the parameter than protocol 2 subjects. The same trend was observed also for COWR, but the difference between protocol groups was slightly smaller and the interaction protocol-by-time did not reach the statistical significance. Finally, treatment duration in protocol 1 was significantly lower than in protocol 2. Conclusion: The results of our study suggest that the new activation protocol would seem more effective as it allows to achieve the objective of the therapy more quickly, and likely leading to greater bodily expansion

Upward Planar Morphs

We prove that, given two topologically-equivalent upward planar straight-line drawings of an $n$-vertex directed graph $G$, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of $O(1)$ morphing steps if $G$ is a reduced planar $st$-graph, $O(n)$ morphing steps if $G$ is a planar $st$-graph, $O(n)$ morphing steps if $G$ is a reduced upward planar graph, and $O(n^2)$ morphing steps if $G$ is a general upward planar graph. Further, we show that $\Omega(n)$ morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an $n$-vertex path.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) The current version is the extended on

Monte Carlo-based 3D surface point cloud volume estimation by exploding local cubes faces

This article proposes a state-of-the-art algorithm for estimating the 3D volume enclosed in a surface point cloud via a modified extension of the Monte Carlo integration approach. The algorithm consists of a pre-processing of the surface point cloud, a sequential generation of points managed by an affiliation criterion, and the final computation of the volume. The pre-processing phase allows a spatial reorientation of the original point cloud, the evaluation of the homogeneity of its points distribution, and its enclosure inside a rectangular parallelepiped of known volume. The affiliation criterion using the explosion of cube faces is the core of the algorithm, handles the sequential generation of points, and proposes the effective extension of the traditional Monte Carlo method by introducing its applicability to the discrete domains. Finally, the final computation estimates the volume as a function of the total amount of generated points, the portion enclosed within the surface point cloud, and the parallelepiped volume. The developed method proves to be accurate with surface point clouds of both convex and concave solids reporting an average percentage error of less than 7 %. It also shows considerable versatility in handling clouds with sparse, homogeneous, and sometimes even missing points distributions. A performance analysis is presented by testing the algorithm on both surface point clouds obtained from meshes of virtual objects as well as from real objects reconstructed using reverse engineering techniques

Finite volume scheme based on cell-vertex reconstructions for anisotropic diffusion problems with discontinuous coefficients

We propose a new second-order finite volume scheme for non-homogeneous and anisotropic diffusion problems based on cell to vertex reconstructions involving minimization of functionals to provide the coefficients of the cell to vertex mapping. The method handles complex situations such as large preconditioning number diffusion matrices and very distorted meshes. Numerical examples are provided to show the effectiveness of the method

Extending Upward Planar Graph Drawings

In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $\Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $\Gamma_H$ can be extended to an upward planar drawing of $G$. Our study fits into the line of research on the extensibility of partial representations, which has recently become a mainstream in Graph Drawing. We show the following results. First, we prove that the Upward Planarity Extension problem is NP-complete, even if $G$ has a prescribed upward embedding, the vertex set of $H$ coincides with the one of $G$, and $H$ contains no edge. Second, we show that the Upward Planarity Extension problem can be solved in $O(n \log n)$ time if $G$ is an $n$-vertex upward planar $st$-graph. This result improves upon a known $O(n^2)$-time algorithm, which however applies to all $n$-vertex single-source upward planar graphs. Finally, we show how to solve in polynomial time a surprisingly difficult version of the Upward Planarity Extension problem, in which $G$ is a directed path or cycle with a prescribed upward embedding, $H$ contains no edges, and no two vertices share the same $y$-coordinate in $\Gamma_H$

Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017