Constructing and analyzing area-of-influence polygons by computer

Hayes, Willis B.; Koch, George S.

doi:10.1016/0098-3004(84)90042-6

Cited by 8 publications

(3 citation statements)

References 3 publications

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“…Better estimates of the actual sizes of diffusional domains can be obtained by addressing explicitly the effects of competition for nutrients. The most common method for evaluating these effects is the calculation of Voronoi polyhedra (Gilbert, i962;Boots and Murdoch, 1983;Hayes and Koch, 1984;Evans and Jones, 1987). Voronoi polygons were used, for example, in the analysis of natural textures in thin sections of metamorphic eclogites by Trevius and Kovnurko (1985); see also Kretz (1969, Fig.…”

Section: Estimates Of Crystal Isolation and Sizes Of Diffusional Domainsmentioning

confidence: 99%

Competitive diffusion-controlled growth of porphyroblasts

Carlson

1991

Mineral. mag.

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In a diffusion-controlled process of nucleation and growth, adjacent porphyroblasts compete with one another for nutrients. When the effects of this competition are evaluated quantitatively for garnet porphyroblasts in pelitic rocks from the Picuris Range of New Mexico (U.S.A.), significant correlations arise between crystal sizes and the volumes of the domains from which the crystals drew their nutrients. These correlations strengthen the conclusion drawn from earlier work on spatial dispositions, zoning patterns, and crystal size distributions that the kinetics of intergranular diffusion governed the crystallisation of these porphyroblasts.Computer simulations indicate that competition for nutrients during diffusion-controlled growth may have small but detectable effects on crystal size frequency distributions. Diffusional competition therefore introduces relatively minor inaccuracies into attempts to extract quantitative information on crystallisation processes from size distributions using models for the growth of isolated porphyroblasts. In contrast, the effects of diffusional competition on patterns of compositional zoning may be substantial, especially for porphyroblasts in rocks for which chemical inhomogeneity of the precursor leads to strongly clustered spatial dispositions. In such rocks, clustering may alter the patterns of compositional zoning in ways that obscure evidence for diffusion-controlled growth.

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Section: Estimates Of Crystal Isolation and Sizes Of Diffusional Domainsmentioning

confidence: 99%

Competitive diffusion-controlled growth of porphyroblasts

Carlson

1991

Mineral. mag.

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“…The depth of influence for each sensor was assumed to reflect the soil moisture content within genetic horizons. The boundaries of Thiessen polygons were mathematically defined by the perpendicular bisectors of the lines between all the points of interest and surrounding points (Hayes and Koch, 1984).…”

Section: Methodsmentioning

confidence: 99%

Catchment‐Scale Soil Water Dynamics in a Mediterranean‐Type Oak Woodland

Swarowsky

Dahlgren

Tate

et al. 2011

Vadose Zone Journal

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Water availability is one of the most serious natural resource issues facing California, especially given projections for future climate change. The 3 million ha of oak (Quercus spp.) woodlands play a critical role in California's water supply system, providing runoff primarily from winter rainfall events and hosting two‐thirds of the state's drinking water reservoirs. Thus, understanding water storage and streamflow regulation by soils in these watersheds is essential for water resource planning under future climate change scenarios. The primary objectives of this research were to identify the drivers of soil moisture dynamics and the hydrologic budget at the catchment scale and their relationships with streamflow generation. A 33‐ha headwater catchment in the Sierra Nevada foothills of northern California was instrumented to monitor climate, subsurface lateral flow, streamflow, and soil moisture within 100 pedons distributed throughout the catchment. A catchment‐scale water balance was used to examine factors regulating spatial and temporal soil water distribution within the catchment. Relationships between soil, topographic, and vegetation characteristics and soil water content at each pedon were analyzed using a linear mixed‐effects model with four fixed effects: vegetation type or cover, presence or absence of a claypan, compound topographic index, and solar radiation. Streamflow was limited to periods when lower soil horizons were at or near saturation. Following saturation, each rainfall event generated subsurface lateral flow above the clay‐rich argillic horizon, resulting in sharp hydrograph responses with little base flow between rainfall events. For the two water years examined, 9.6 and 11.5% of rainfall left the catchment as streamflow. Vegetation (tree vs. grassland), presence or absence of a claypan, aspect, and compound topographic index (index of wetness) were all significantly correlated to soil moisture status and thus streamflow generation at various times throughout the year. Findings indicated that watershed‐scale hydrologic models based solely on surface topography will not fully explain dynamic temporal and spatial variability in hydrologic flow paths and streamflow generation in these oak woodland catchments. In particular, watershed‐scale knowledge of soil stratigraphy (e.g., claypan distribution) was important for understanding catchment hydrology, especially the occurrence of subsurface lateral flow dynamics.

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“…(Note: The influence polygon described here is different from the area-of-influence polygon (Hayes and Koch 1984), i.e., the V'u'uronoi or Thiessen polygon of a point. )…”

Section: Incremental Insertion Of Constraint Segmentsmentioning

confidence: 98%

Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

Tsai

1993

International journal of geographical information systems

146

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The Delaunay triangulation is commonly used to generate triangulared irregular network (TIN) models for a best description of the surface morphology in a variety of applications in geographic information systems (GIs). This paper discusses the definitions and basic properties of the standard and constrained Delaunay triangulations. Several existing Delaunay algorithms are reviewed and classified into three categories according to their procedures: ( I ) divide-and-conquer methods, (2) incremental insertion methods, and (3) triangulation growth methods. Furthermore, a linear-time Convex Hull Insertion algorithm is presented to construct T l N s for a set of points as well as specific features such as constraint breaklines and exclusion boundaries. Empirical results over various sets of up to 50000 points on personal computers show that the proposed algorithm efficiently expedites the construction of TIN models in approximately O ( N ) for N randomly distributed points.

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Constructing and analyzing area-of-influence polygons by computer

Cited by 8 publications

References 3 publications

Competitive diffusion-controlled growth of porphyroblasts

Competitive diffusion-controlled growth of porphyroblasts

Catchment‐Scale Soil Water Dynamics in a Mediterranean‐Type Oak Woodland

Delaunay triangulations in TIN creation: an overview and a linear-time algorithm

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