Implementing data-dependent triangulations with higher order Delaunay triangulations

The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. It has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria to build TINs. Data-dependent triangulations were introduced decades ago to address this. However, they are rarely used in practice, mostly because the optimization of data- dependent criteria often results in triangulations with many thin and elongated triangles. Recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time-data-dependent criteria and good triangle shape. Nevertheless, most previous studies about them have been limited to theoretical aspects. In this work we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS terrains that show that HODTs can give significant improvements over the Delaunay triangulation for the criteria identified as most important for data-dependent triangulations. The resulting triangulations have data-dependent values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and are faster to compute.Peer ReviewedPostprint (published version

Implementing data-dependent triangulations with higher order delaunay triangulations

The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. This can affect the quality of the approximating surface. In fact, it has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria that take elevation into account to build TINs. Data-dependent triangulations were introduced decades ago to address this exact issue. However, data-dependent trianguations are rarely used in practice, mostly because the optimization of data-dependent criteria often results in triangulations with many slivers (i.e., thin and elongated triangles), which can cause several types of problems. More recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time—data-dependent criteria and good triangle shape—by combining data-dependent criteria with a relaxation of the Delaunay criterion. In this paper, we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS 30m digital elevation models that show that the use of HODTs can give significant improvements over the Delaunay triangulation for the criteria previously identified as most important for data-dependent triangulations, often with only a minor increase in running times. The triangulations produced have measure values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and can be computed much faster.Peer Reviewe

Implementing data-dependent triangulations with higher order Delaunay triangulations

The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. It has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria to build TINs. Data-dependent triangulations were introduced decades ago to address this. However, they are rarely used in practice, mostly because the optimization of data- dependent criteria often results in triangulations with many thin and elongated triangles. Recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time-data-dependent criteria and good triangle shape. Nevertheless, most previous studies about them have been limited to theoretical aspects. In this work we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS terrains that show that HODTs can give significant improvements over the Delaunay triangulation for the criteria identified as most important for data-dependent triangulations. The resulting triangulations have data-dependent values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and are faster to compute.Peer Reviewe

Strategies for Reducing Voluntary Employee Turnover in Small Business

Small business owners who lack strategies to reduce high rates of voluntary employee turnover experience decreased organizational performance. Grounded in the two-factor theory, the purpose of this qualitative multiple case study was to explore strategies that small business owners use to reduce high voluntary employee turnover to increase organizational performance. Participants were four small business owners from Midwestern Illinois who successfully used strategies to reduce high voluntary employee turnover. Data were collected from semistructured interviews and internal documents and analyzed using thematic analysis. Four themes emerged: (a) employee turnover, (b) job satisfaction, (c) employee engagement, and (d) monetary incentives. A key recommendation is small business owners should develop employee feedback mechanisms and instill employees with a sense of purpose and direction. The implications for positive social change include the opportunity to increase economic growth in local communities, lower poverty, and improve the quality of life for local residents

Strategies to Handle Complaints or Incidents of Suspected Workplace Misconduct

AbstractBusiness leaders often fail to investigate cases of workplace misconduct effectively, costing organizations millions of dollars in losses each year. Effective investigation of cases of workplace misconduct is essential to avoid costly lawsuits. Grounded in Adams’ equity theory, the purpose of this qualitative multiple case study was to explore strategies business leaders use to investigate complaints of workplace misconduct. The participants were three business leaders from three different organizations in Georgia, United States, with successful strategies to investigate complaints of workplace misconduct. Data were collected from semistructured interviews, organizational documents, and artifacts. Yin’s five-step process guided the data analysis. Two themes emerged from analyses: improved process for handling workplace misconduct investigations and decreased employee perceptions of favoritism. A key recommendation is to build relationships with employees to avoid employee perception of unfair treatment and favoritism and provide leaders with proper investigation training to reduce bias. The implications for positive social change include the potential for effective investigation of workplace misconduct that leads to a positive workplace, which is critical to the behaviors of the employees at work, at home, and in their communities

Generalized Delaunay triangulations : graph-theoretic properties and algorithms

This thesis studies different generalizations of Delaunay triangulations, both from a combinatorial and algorithmic point of view. The Delaunay triangulation of a point set S, denoted DT(S), has vertex set S. An edge uv is in DT(S) if it satisfies the empty circle property: there exists a circle with u and v on its boundary that does not enclose points of S. Due to different optimization criteria, many generalizations of the DT(S) have been proposed. Several properties are known for DT(S), yet, few are known for its generalizations. The main question we explore is: to what extent can properties of DT(S) be extended for generalized Delaunay graphs? First, we explore the connectivity of the flip graph of higher order Delaunay triangulations of a point set S in the plane. The order-k flip graph might be disconnected for k = 3, yet, we give upper and lower bounds on the flip distance from one order-k triangulation to another in certain settings. Later, we show that there exists a length-decreasing sequence of plane spanning trees of S that converges to the minimum spanning tree of S with respect to an arbitrary convex distance function. Each pair of consecutive trees in the sequence is contained in a constrained convex shape Delaunay graph. In addition, we give a linear upper bound and specific bounds when the convex shape is a square. With focus still on convex distance functions, we study Hamiltonicity in k-order convex shape Delaunay graphs. Depending on the convex shape, we provide several upper bounds for the minimum k for which the k-order convex shape Delaunay graph is always Hamiltonian. In addition, we provide lower bounds when the convex shape is in a set of certain regular polygons. Finally, we revisit an affine invariant triangulation, which is a special type of convex shape Delaunay triangulation. We show that many properties of the standard Delaunay triangulations carry over to these triangulations. Also, motivated by this affine invariant triangulation, we study different triangulation methods for producing other affine invariant geometric objects.Esta tesis estudia diferentes generalizaciones de la triangulación de Delaunay, tanto desde un punto de vista combinatorio como algorítmico. La triangulación de Delaunay de un conjunto de puntos S, denotada DT(S), tiene como conjunto de vértices a S. Una arista uv está en DT(S) si satisface la propiedad del círculo vacío: existe un círculo con u y v en su frontera que no contiene ningún punto de S en su interior. Debido a distintos criterios de optimización, se han propuesto varias generalizaciones de la DT (S). Hoy en día, se conocen bastantes propiedades de la DT(S), sin embargo, poco se sabe sobre sus generalizaciones. La pregunta principal que exploramos es: ¿Hasta qué punto las propiedades de la DT(S) se pueden extender para generalizaciones de gráficas de Delaunay? Primero, exploramos la conectividad de la gráfica de flips de las triangulaciones de Delaunay de orden alto de un conjunto de puntos S en el plano. La gráfica de flips de triangulaciones de orden k = 3 podría ser disconexa, sin embargo, nosotros damos una cota superior e inferior para la distancia en flips de una triangulación de orden k a alguna otra cuando S cumple con ciertas características. Luego, probamos que existe una secuencia de árboles generadores sin cruces tal que la suma total de la longitud de las aristas con respecto a una distancia convexa arbitraria es decreciente y converge al árbol generador mínimo con respecto a la distancia correspondiente. Cada par de árboles consecutivos en la secuencia se encuentran en una triangulación de Delaunay con restricciones. Adicionalmente, damos una cota superior lineal para la longitud de la secuencia y cotas específicas cuando el conjunto convexo es un cuadrado. Aún concentrados en distancias convexas, estudiamos hamiltonicidad en las gráficas de Delaunay de distancia convexa de k-orden. Dependiendo en la distancia convexa, exhibimos diversas cotas superiores para el mínimo valor de k que satisface que la gráfica de Delaunay de distancia convexa de orden-k es hamiltoniana. También damos cotas inferiores para k cuando el conjunto convexo pertenece a un conjunto de ciertos polígonos regulares. Finalmente, re-visitamos una triangulación afín invariante, la cual es un caso especial de triangulación de Delaunay de distancia convexa. Probamos que muchas propiedades de la triangulación de Delaunay estándar se preservan en estas triangulaciones. Además, motivados por esta triangulación afín invariante, estudiamos diferentes algoritmos que producen otros objetos geométricos afín invariantes

Cross-Cultural Communication Strategies That Engage Employees and Increase Productivity.

AbstractLow employee engagement can negatively impact productivity for small fast-food restaurants in the United States. Small fast-food restaurant managers who do not engage employees experience decreased employee productivity. Grounded in Hofstede\u27s cross-cultural dimensions theory, the purpose of this qualitative multiple case study was to explore strategies managers of small fast-food restaurants managers use to improve employee engagement. Participants were four small fast-food restaurants manager within the southern region of the United States who used cross-cultural strategies to successfully engage employees. Data were collected through semistructured interviews and internal company documents and were analyzed using thematic analysis. Four themes emerged: (a) developing relationships, (b) empathy, (c) mindfulness and respect for others, and (d) training and communicating. A key recommendation is for managers to implement cross-cultural communication training for employees. The implication for positive social change includes the potential to enhance economic growth that supports family well–being in local communities