1v.vol.rst(1) Grass User's Manual v.vol.rst(1)
2
6 v.vol.rst - Interpolates point data to a G3D grid volume using regu‐
7 larized spline with tension (RST) algorithm.
8
10 vector
11
13 v.vol.rst
14 v.vol.rst help
15 v.vol.rst [-c] input=string [cellinp=string] [wcolumn=string]
16 [tension=float] [smooth=float] [scolumn=string] [where=sql_query]
17 [devi=string] [cvdev=string] [maskmap=string] [segmax=integer]
18 [npmin=integer] [dmin=float] [wmult=float] [zmult=float] [cell‐
19 out=string] [elev=string] [gradient=string] [aspect1=string]
20 [aspect2=string] [ncurv=string] [gcurv=string] [mcurv=string]
21 [--overwrite] [--verbose] [--quiet]
22 Flags:
24 -c
25 Perform a cross-validation procedure without volume interpolation
26 --overwrite
28 Allow output files to overwrite existing files
29 --verbose
31 Verbose module output
32 --quiet
34 Quiet module output
35 Parameters:
37 input=string
38 Name of the vector map with input x,y,z,w
39 cellinp=string
41 Name of the surface raster map for cross-section
42 wcolumn=string
44 Name of the column containing w attribute to interpolate
45 Default: flt1
46 tension=float
48 Tension parameter
49 Default: 40.
50 smooth=float
52 Smoothing parameter
53 Default: 0.1
54 scolumn=string
56 Name of the column with smoothing parameters
57 where=sql_query
59 WHERE conditions of SQL statement without 'where' keyword
60 Example: income = 10000
61 devi=string
63 Output deviations vector point file
64 cvdev=string
66 Output cross-validation vector map
67 maskmap=string
69 Name of the raster map used as mask
70 segmax=integer
72 Maximum number of points in a segment
73 Default: 50
74 npmin=integer
76 Minimum number of points for approximation in a segment (>segmax)
77 Default: 200
78 dmin=float
80 Minimum distance between points (to remove almost identical points)
81 Default: 0.500000
82 wmult=float
84 Conversion factor for w-values used for interpolation
85 Default: 1.0
86 zmult=float
88 Conversion factor for z-values
89 Default: 1.0
90 cellout=string
92 Output cross-section raster map
93 elev=string
95 Output elevation g3d-file
96 gradient=string
98 Output gradient magnitude g3d-file
99 aspect1=string
101 Output gradient horizontal angle g3d-file
102 aspect2=string
104 Output gradient vertical angle g3d-file
105 ncurv=string
107 Output change of gradient g3d-file
108 gcurv=string
110 Output gaussian curvature g3d-file
111 mcurv=string
113 Output mean curvature g3d-file
114
116 v.vol.rst interpolates values to a 3-dimensional raster map from
117 3-dimensional point data (e.g. temperature, rainfall data from climatic
118 stations, concentrations from drill holes etc.) given in a 3-D vector
119 point file named input. The size of the output 3d raster map elev is
120 given by the current 3D region. Sometimes, the user may want to get a
121 2-D map showing a modelled phenomenon at a crossection surface. In that
122 case, cellinp and cellout options must be specified and then the output
123 2D raster map cellout contains crossection of the interpolated volume
124 with a surface defined by cellinp 2D raster map. As an option, simulta‐
125 neously with interpolation, geometric parameters of the interpolated
126 phenomenon can be computed (magnitude of gradient, direction of gradi‐
127 ent defined by horizontal and vertical angles), change of gradient,
128 Gauss-Kronecker curvature, or mean curvature). These geometric parame‐
129 teres are saved as 3d raster maps gradient, aspect1, aspect2, ncurv,
130 gcurv, mcurv, respectively.
131 At first, data points are checked for identical points and points that
133 are closer to each other than given dmin are removed. Parameters wmult
134 and zmult allow user to re-scale the w-values and z-coordinates of the
135 point data (useful e.g. for transformation of elevations given in feet
136 to meters, so that the proper values of gradient and curvatures can be
137 computed). Rescaling of z-coordinates is also needed when the dis‐
138 tances in vertical direction are much smaller than the horizontal dis‐
139 tances, if that is the case, the value of zmult should be selected so
140 that the vertical and horizontal distances have about the same magni‐
141 tude.
142 Regularized spline with tension method is used in the interpolation.
144 The tension parameter controls the distance over which each given point
145 influences the resulting volume (with very high tension, each point
146 influences only its close neighborhood and the volume goes rapidly to
147 trend between the points). Higher values of tension parameter reduce
148 the overshoots that can appear in volumes with rapid change of gradi‐
149 ent. For noisy data, it is possible to define a global smoothing param‐
150 eter, smooth. With the smoothing parameter set to zero (smooth=0) the
151 resulting volume passes exactly through the data points. When smooth‐
152 ing is used, it is possible to output a vector map devi containing
153 deviations of the resulting volume from the given data.
154 User can define a 2D raster map named maskmap, which will be used as a
156 mask. The interpolation is skipped for 3-dimensional cells whose
157 2-dimensional projection has zero value in mask. Zero values will be
158 assigned to these cells in all output 3d raster maps.
159 If the number of given points is greater than 700, segmented processing
161 is used. The region is split into 3-dimensional "box" segments, each
162 having less than segmax points and interpolation is performed on each
163 segment of the region. To ensure the smooth connection of segments the
164 interpolation function for each segment is computed using the points in
165 given segment and the points in its neighborhood. The minimum number of
166 points taken for interpolation is controlled by npmin , the value of
167 which must be larger than segmax and less than 700. This limit of 700
168 was selected to ensure the numerical stability and efficiency of the
169 algorithm.
170 EXAMPLE
172 Spearfish example (we simulate 3D soil range data):
173 g.region -dp
174 # define volume
175 g.region res=50 tbres=50 b=0 t=1500 -ap3
176 # random elevation extraction (2D)
177 r.random elevation.10m vector_output=elevrand n=200
178 # conversion to 3D
179 v.db.addcol elevrand col="x double precision, y double precision"
180 v.to.db elevrand option=coor col=x,y
181 v.db.select elevrand
182 # create new 3D map
183 v.in.db elevrand out=elevrand_3d x=x y=y z=value key=cat
184 v.info -c elevrand_3d
185 v.info -t elevrand_3d
186 # remove the now superfluous 'x', 'y' and 'value' (z) columns
187 v.db.dropcol elevrand_3d col=x
188 v.db.dropcol elevrand_3d col=y
189 v.db.dropcol elevrand_3d col=value
190 # add attribute to interpolate
191 # (Soil range types taken from the USDA Soil Survey)
192 d.rast soils.range
193 d.vect elevrand_3d
194 v.db.addcol elevrand_3d col="soilrange integer"
195 v.what.rast elevrand_3d col=soilrange rast=soils.range
196 # fix 0 (no data in raster map) to NULL:
197 v.db.update elevrand_3d col=soilrange value=NULL where="soilrange=0"
198 v.db.select elevrand_3d
199 # interpolate volume
200 v.vol.rst elevrand_3d wcol=soilrange elev=soilrange zmult=100
201 # visualize
202 nviz elevation.10m vol=soilrange
203 # export to Paraview
204 r.out.vtk elevation.10m out=elev.vtk
205 r3.out.vtk elevrand_3d out=volume.vtk
206 paraview
207 SQL support
210 Using the where parameter, the interpolation can be limited to use only
211 a subset of the input vectors.
212 # preparation as in above example
213 v.vol.rst elevrand_3d wcol=soilrange elev=soilrange zmult=100
214 where="soilrange > 3"
215 Cross validation procedure
218 Sometimes it can be difficult to figure out the proper values of inter‐
219 polation parameters. In this case, the user can use a crossvalidation
220 procedure using -c flag (a.k.a. "jack-knife" method) to find optimal
221 parameters for given data. In this method, every point in the input
222 point file is temporarily excluded from the computation and interpola‐
223 tion error for this point location is computed. During this procedure
224 no output grid files can be simultanuously computed. The procedure for
225 larger datasets may take a very long time, so it might be worth to use
226 just a sample data representing the whole dataset.
227 Example (<based on Slovakia3d dataset):
229 v.info -c precip3d
232 v.vol.rst -c input=precip3d wcolumn=precip zmult=50 segmax=700
233 cvdev=cvdevmap tension=10
234 v.db.select cvdevmap
235 v.univar cvdevmap col=flt1 type=point
236 From the results, parameters have to be optimized. It is recommended
237 to plot the CV error as curve while modifying the parameters.
238 The best approach is to start with tension, smooth and zmult with rough
240 steps, or to set zmult to a constant somewhere between 30-60. This
241 helps to find minimal RMSE values while then finer steps can be used in
242 all parameters. The reasonable range is tension=10...100,
243 smooth=0.1...1.0, zmult=10...100.
244 In v.vol.rst the tension parameter is much more sensitive to changes
246 than in v.surf.rst, therefore the user should always check the result
247 by visual inspection. Minimizing CV does not always provide the best
248 result, especially when the density of data are insufficient. Then the
249 optimal result found by CV is an oversmoothed surface.
250 Further notes
252 v.vol.rst uses regularized spline with tension for interpolation from
253 point data (as described in Mitasova and Mitas, 1993). The implementa‐
254 tion has an improved segmentation procedure based on Oct-trees which
255 enhances the efficiency for large data sets.
256 Geometric parameters - magnitude of gradient (gradient), horizontal
258 (aspect1) and vertical (aspect2) aspects, change of gradient (ncurv),
259 Gauss-Kronecker (gcurv) and mean curvatures (mcurv) are computed
260 directly from the interpolation function so that the important rela‐
261 tionships between these parameters are preserved. More information on
262 these parameters can be found in Mitasova et al., 1995 or Thorpe, 1979.
263 The program gives warning when significant overshoots appear and higher
265 tension should be used. However, with tension too high the resulting
266 volume will have local maximum in each given point and everywhere else
267 the volume goes rapidly to trend. With smoothing parameter greater than
268 zero the volume will not pass through the data points and the higher
269 the parameter the closer the volume will be to the trend. For theory on
270 smoothing with splines see Talmi and Gilat, 1977 or Wahba, 1990.
271 If a visible connection of segments appears, the program should be
273 rerun with higher npmin to get more points from the neighborhood of
274 given segment.
275 If the number of points in a vector map is less then 400, segmax should
277 be set to 400 so that segmentation is not performed when it is not nec‐
278 essary.
279 The program gives warning when user wants to interpolate outside the
281 "box" given by minimum and maximum coordinates in vector map, zoom into
282 the area where the points are is suggested in this case.
283 For large data sets (thousands of data points) it is suggested to zoom
285 into a smaller representative area and test whether the parameters cho‐
286 sen (e.g. defaults) are appropriate.
287 The user must run g.region before the program to set the 3D region for
289 interpolation.
290
292 The vector points map must be a 3D vector map (x, y, z as geometry).
293 The module v.in.db can be used to generate a 3D vector map from a table
294 containing x,y,z columns.
295
297 devi file is written as 2D and deviations are not written as
298 attributes.
299
301 g.region, v.in.ascii, r3.mask, v.in.db, v.surf.rst, v.univar
302
304 Original version of program (in FORTRAN) and GRASS enhancements:
305 Lubos Mitas, NCSA, University of Illinois at Urbana-Champaign, Illi‐
306 nois, USA, since 2000 at Department of Physics, North Carolina State
307 University, Raleigh, USA lubos_mitas@ncsu.edu
308 Helena Mitasova, Department of Marine, Earth and Atmospheric Sciences,
309 North Carolina State University, Raleigh, USA, <a href="mailto:hmi‐
310 taso@unity.ncsu.edu">hmitaso@unity.ncsu.edu
311 Modified program (translated to C, adapted for GRASS, new segmentation
313 procedure):
314 Irina Kosinovsky, US Army CERL, Champaign, Illinois, USA
315 Dave Gerdes, US Army CERL, Champaign, Illinois, USA
316 Modifications for g3d library, geometric parameters, cross-validation,
318 deviations:
319 Jaro Hofierka, Department of Geography and Regional Development, Uni‐
320 versity of Presov, Presov, Slovakia, <a
321 href="MAILTO:hofierka@fhpv.unipo.sk">hofierka@fhpv.unipo.sk, <a
322 href="http://www.geomodel.sk">http://www.geomodel.sk
323
325 Hofierka J., Parajka J., Mitasova H., Mitas L., 2002, Multivariate
326 Interpolation of Precipitation Using Regularized Spline with Tension.
327 Transactions in GIS 6, pp. 135-150.
328 Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley,
330 M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Informa‐
331 tion Systems: Principles, Techniques, Management and Applications,
332 Wiley, pp.481-492
333 Mitas L., Brown W. M., Mitasova H., 1997, <a
335 href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/lcgfin/cg-
336 mitas.html">Role of dynamic cartography in simulations of landscape
337 processes based on multi-variate fields. Computers and Geosciences,
338 Vol. 23, No. 4, pp. 437-446 (includes CDROM and WWW: www.else‐
339 vier.nl/locate/cgvis)
340 Mitasova H., Mitas L., Brown W.M., D.P. Gerdes, I. Kosinovsky,
342 Baker, T.1995, Modeling spatially and temporally distributed phenomena:
343 New methods and tools for GRASS GIS. International Journal of GIS, 9
344 (4), special issue on Integrating GIS and Environmental modeling,
345 433-446.
346 Mitasova, H., Mitas, L., Brown, B., Kosinovsky, I., Baker, T., Gerdes,
348 D. (1994): <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
349 lena/gmslab/viz/ches.html">Multidimensional interpolation and visual‐
350 ization in GRASS GIS
351 <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
353 lena/gmslab/papers/lmg.rev1.ps">Mitasova H. and Mitas L. 1993: Interpo‐
354 lation by Regularized Spline with Tension: I. Theory and Implementa‐
355 tion, Mathematical Geology 25, 641-655.
356 <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
358 lena/gmslab/papers/hmg.rev1.ps">Mitasova H. and Hofierka J. 1993:
359 Interpolation by Regularized Spline with Tension: II. Application to
360 Terrain Modeling and Surface Geometry Analysis, Mathematical Geology
361 25, 657-667.
362 Mitasova, H., 1992 : New capabilities for interpolation and topographic
364 analysis in GRASS, GRASSclippings 6, No.2 (summer), p.13.
365 Wahba, G., 1990 : Spline Models for Observational Data, CNMS-NSF
367 Regional Conference series in applied mathematics, 59, SIAM, Philadel‐
368 phia, Pennsylvania.
369 Mitas, L., Mitasova H., 1988 : General variational approach to the
371 interpolation problem, Computers and Mathematics with Applications 16,
372 p. 983
373 Talmi, A. and Gilat, G., 1977 : Method for Smooth Approximation of
375 Data, Journal of Computational Physics, 23, p.93-123.
376 Thorpe, J. A. (1979): Elementary Topics in Differential Geometry.
378 Springer-Verlag, New York, pp. 6-94.
379 Last changed: $Date: 2008-02-19 20:39:46 +0100 (Tue, 19 Feb 2008) $
381 Full index
383 © 2003-2008 GRASS Development Team
385GRASS 6.3.0 v.vol.rst(1)