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## Lecture 07: Terrain Analysis Geography 128 Analytical in addition to Computer Cartography S

Andriani, Pierpaolo, Innovation & Networks Editor has reference to this Academic Journal, PHwiki organized this Journal Lecture 07: Terrain Analysis Geography 128 Analytical in addition to Computer Cartography Spring 2007 Department of Geography University of Cali as long as nia, Santa Barbara 3D Trans as long as mations 3D data often as long as l in addition to surface or bottom of ocean Need three coordinates to determine location (X, Y, Z) Part of analytical cartography concerned with analysis of fields is terrain analysis Include terrain representation in addition to symbolization issues as they relate to data Points, TIN in addition to grids are used to store terrain Interpolation to a Grid Given a set of point elevations (x, y, z) generate a new set of points at the nodes of a regular grid so that the interpolated surface is a reasonable representation of the surface sampled by the points. Imposes a model of the true surface on the sample “Model” is a mathematical model of the neighborhood relationship Influence of a single point = f(1/d) Can be constrained to fit all points Should contain z extremes, in addition to local extreme values Most models are algorithmic local operators Work cell-to-cell. Operative cell = kernel

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Weighting Methods Impose z = f (1/d) Computational Intensive, e.g. 200 x 200 cells 1000 points = 40 x 10^6 distance calculations If all points are used in addition to sorted by distance, called “brute as long as ce” method Possible to use sorted search in addition to tiling Distance can be weighted in addition to powered by n = friction of distance Can be refined with break lines Clarkes Classic IDW Algorithm Assigns points to cells Averages multiples For all unfilled cells, search outward using an increasingly large square neighborhood until at least n points are found Apply inverse distance weighting Trend Projection Methods Way to overcome high/low constraint Assumes that sampling missed extreme values Locally fits trend, trend surface or bi-cubic spline Least squares solution Useful when data are sparse, texture required

Search Patterns Many possible ways to define interpolated “region” Can use points or distance Problems in Sparse areas Dense areas Edges Bias can be reduced by changing search strategy Kriging Interpolation “Optimal interpolation method” by D.G. Krige Origin in geology (geostatistics, gold mining) Spatial variation = f(drift, r in addition to om-correlated, r in addition to om noise) To use Kriging Model in addition to extract drift Compute variogram Model variogram Compute expected variance at d, in addition to so best estimate of local mean Several alternative methods. Universal Kriging best when local trends are well defined Kriging produces best estimate in addition to estimate of variance at all places on map For more info: http://www.geog.ucsb.edu/~good/176b/n10.html Alternative Methods Many ways to make the point-to-grid interpolation Invertibility Can results be compared in addition to tested analytically Use portion of points in addition to test results with remainder Examine spatial distribution of difference between methods Best results are obtained when field is sampled with knowledge of the terrain structure in addition to the method to be used

Surface-Specific Point Sampling L in addition to scape Morphometric Features Terrain “Skeleton” Surface-Specific Point Sampling (cnt.) If the structure of the terrain is known, then intelligent design of sampling in addition to interpolation is best Terrain Skeleton determines most of surface variance Knowledge of skeleton often critical as long as applications Surface-Specific Point Sampling (cnt.) Source of much terrain data is existing contour maps Problems of contour->TIN or Grid are many, e.g. the wedding cake effect Sampling along contour “fills in” interpolated values

Surface Models Alternative to LOCAL operators is to model the whole surface at once Often must be an inexact fit, e.g. when there are many points Sometimes Model is surface is sufficient as long as analysis Polynomial Series Least squares fit of polynomial function in 2D. Simplest as long as m is the linear trend surface, e.g. z = bo + b1x + b2y Most complex as long as ms have bends in addition to twists Fourier Series Fit trigonometric series of cosine waves with different wavelengths in addition to amplitudes. Analytically, can generalize surface by “extracting” harmonics Polynomial Surface Surface Filtering Convolution of filter matrix with map matrix Filter has a response function Filter weights add to one Can enhance properties, or generalize Volumetric Trans as long as mations – Slope in addition to Aspect Many possible analytical trans as long as mations of 3D data that show interesting map properties Simplest is slope (first derivative, the steepest downhill slope) in addition to aspect (the direction of the steepest downhill slope)

Volumetric Trans as long as mations – Slope in addition to Aspect (ArcGIS) Volumetric Trans as long as mations (cnt.) Terrain partitioning: Often to extract VIPs or a TIN from a grid. Terrain Simulation (many methods e.g. fractals) Intervisibility, e.g. viewshed Terrain Symbolization – Analytical Hill Shading Simulate illumination from an infinite distance light source Light source has azimuth in addition to zenith angle Surface can be reflected light or use log trans as long as m Can add shadows as long as realism, or multiple light sources

Terrain Symbolization – Gridded Perspective & Realistic Pespective Create view from a particular camera geometry Can include or excluded perspective Colors should include shading Multiple sequences can generate fly-bys in addition to fly-thrus Next Lecture Map Trans as long as mation

## Andriani, Pierpaolo Innovation & Networks Editor

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