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 [scolumn=string] [tension=float] [smooth=float] [devi=string]
17 [cvdev=string] [maskmap=string] [segmax=integer] [dmin=float]
18 [npmin=integer] [wmult=float] [zmult=float] [cellout=string]
19 [elev=string] [gradient=string] [aspect1=string] [aspect2=string]
20 [ncurv=string] [gcurv=string] [mcurv=string] [--overwrite]
21 Flags:
23 -c Perform a cross-validation procedure without volume interpolation
24 --overwrite
26 Parameters:
28 input=string
29 Name of the vector file with input x,y,z,w
30 cellinp=string
32 Name of the surface cell file for cross-section
33 wcolumn=string
35 Name of the column containing w attribute to interpolate Default:
36 flt1
37 scolumn=string
39 Name of the column with smoothing parameters
40 tension=float
42 Tension parameter Default: 40.
43 smooth=float
45 Smoothing parameter Default: 0.1
46 devi=string
48 Output deviations vector point file
49 cvdev=string
51 Output cross-validation vector file
52 maskmap=string
54 Name of the raster file used as mask
55 segmax=integer
57 Maximum number of points in a segment Default: 50
58 dmin=float
60 Minimum distance between points (to remove almost identical points)
61 Default: 0.500000
62 npmin=integer
64 Minimum number of points for approximation in a segment (>segmax)
65 Default: 200
66 wmult=float
68 Conversion factor for w-values used for interpolation Default: 1.0
69 zmult=float
71 Conversion factor for z-values Default: 1.0
72 cellout=string
74 Output cross-section cell file
75 elev=string
77 Output elevation g3d-file
78 gradient=string
80 Output gradient magnitude g3d-file
81 aspect1=string
83 Output gradient horizontal angle g3d-file
84 aspect2=string
86 Output gradient vertical angle g3d-file
87 ncurv=string
89 Output change of gradient g3d-file
90 gcurv=string
92 Output gaussian curvature g3d-file
93 mcurv=string
95 Output mean curvature g3d-file
96
98 v.vol.rst interpolates values to a 3-dimensional grid from 3-dimen‐
99 sional point data (e.g. temperature, rainfall data from climatic sta‐
100 tions, concentrations from drill holes etc.) given in a 3-D vector
101 point file named input. The size of the output 3-D grid g3d file elev
102 is given by the current 3D region. Sometimes, the user may want to get
103 a 2-D map showing a modelled phenomenon at a crossection surface. In
104 that case, cellinp and cellout options must be specified and then the
105 output 2D grid file cellout contains crossection of interpolated volume
106 with surface defined by cellinp 2D grid input file. As an option,
107 simultaneously with interpolation, geometric parameters of the interpo‐
108 lated phenomenon can be computed (magnitude of gradient, direction of
109 gradient defined by horizontal and vertical angles), change of gradi‐
110 ent, Gauss-Kronecker curvature, or mean curvature). These geometric
111 parameteres are saved as g3d files gradient, aspect1, aspect2, ncurv,
112 gcurv, mcurv, respectively.
113 At first, data points are checked for identical points and points that
116 are closer to each other than given dmin are removed. Parameters wmult
117 and zmult allow user to re-scale the w-values and z-coordinates of the
118 point data (useful e.g. for transformation of elevations given in feet
119 to meters, so that the proper values of gradient and curvatures can be
120 computed).
121 Regularized spline with tension method is used in the interpolation.
124 The tension parameter tunes the character of the resulting volume from
125 thin plate to membrane. Higher values of tension parameter reduce the
126 overshoots that can appear in volumes with rapid change of gradient.
127 For noisy data, it is possible to define a global smoothing parameter,
128 smooth. With the smoothing parameter set to zero (smooth=0) the
129 resulting volume passes exactly through the data points. Also, the user
130 can use a spatially variable smoothing using smatt option by setting
131 the parameter smatt to the value j for the j-th floating point
132 attribute in the input vector point file, representing the smoothing
133 parameter for each point. When smoothing is used, it is possible to
134 output vector map devi containing deviations of the resulting volume
135 from the given data.
136 User can define a 2D raster file named maskmap, which will be used as a
138 mask. The interpolation is skipped for 3-dimensional cells whose
139 2-dimensional projection has zero value in mask. Zero values will be
140 assigned to these cells in all output g3d files.
141 If the number of given points is greater than 700, segmented processing
143 is used. The region is split into 3-dimensional "box" segments, each
144 having less than segmax points and interpolation is performed on each
145 segment of the region. To ensure the smooth connection of segments the
146 interpolation function for each segment is computed using the points in
147 given segment and the points in its neighborhood. The minimum number of
148 points taken for interpolation is controlled by npmin , the value of
149 which must be larger than segmax and less than 700. This limit of 700
150 was selected to ensure the numerical stability and efficiency of the
151 algorithm.
152 Cross validation procedure
155 Sometimes it can be difficult to figure out the proper values of inter‐
156 polation parameters. In this case, the user can use a crossvalidation
157 procedure using -c flag (a.k.a. "jack-knife" method) to find optimal
158 parameters for given data. In this method, every point in the input
159 point file is temporarily excluded from the computation and interpola‐
160 tion error for this point location is computed. During this procedure
161 no output grid files can be simultanuously computed. The procedure for
162 larger datasets may take a very long time, so it might be worth to use
163 just a sample data representing the whole dataset.
164 Example (<based on Slovakia3d dataset):
167 v.info -c precip3d
170 v.vol.rst -c input=precip3d wcolumn=precip segmax=700 cvdev=cvdevmap
171 tension=10
172 v.db.select cvdevmap
173 v.univar cvdevmap col=flt1 type=point
174 From the results, parameters have to be optimized. It is recommended to
177 plot the CV error as curve while modifying the parameters.
178 The best approach is to start with tension, smooth and zmult with rough
180 steps, or to set zmult to a constant somewhere between 30-60. This
181 helps to find minimal RMSE values while then finer steps can be used in
182 all parameters. The reasonable range is tension=10...100,
183 smooth=0.1...1.0, zmult=10...100.
184 In v.vol.rst the tension parameter is much more sensitive to changes
186 than in v.surf.rst. Usually tension=10...20 provide best results. But
187 the user should always check the result by visual inspection, sometimes
188 CV does not provide the best results, especially when the density of
189 data are insufficient. Then the optimal result found by CV is an over‐
190 smoothed surface.
191 Further notes
195 v.vol.rst uses regularized spline with tension for interpolation from
196 point data (as described in Mitasova and Mitas, 1993). The implementa‐
197 tion has an improved segmentation procedure based on Oct-trees which
198 enhances the efficiency for large data sets.
199 Geometric parameters - magnitude of gradient (gradient), horizontal
201 (aspect1) and vertical (aspect2) aspects, change of gradient (ncurv),
202 Gauss-Kronecker (gcurv) and mean curvatures (mcurv) are computed
203 directly from the interpolation function so that the important rela‐
204 tionships between these parameters are preserved. More information on
205 these parameters can be found in Mitasova et al., 1995 or Thorpe, 1979.
206 The program gives warning when significant overshoots appear and higher
208 tension should be used. However, with tension too high the resulting
209 volume changes its behavior to membrane( rubber sheet stretched over
210 the data points resulting in a peak in each given point and everywhere
211 else the volume goes rapidly to trend). With smoothing parameter
212 greater than zero the volume will not pass through the data points and
213 the higher the parameter the closer the volume will be to the trend.
214 For theory on smoothing with splines see Talmi and Gilat, 1977 or
215 Wahba, 1990.
216 If a visible connection of segments appears, the program should be
218 rerun with higher npmin to get more points from the neighborhood of
219 given segment.
220 If the number of points in a vector map is less then 400, segmax should
222 be set to 400 so that segmentation is not performed when it is not nec‐
223 essary.
224 The program gives warning when user wants to interpolate outside the
226 "box" given by minimum and maximum coordinates in vector map, zoom into
227 the area where the points are is suggested in this case.
228 For large data sets (thousands of data points) it is suggested to zoom
230 into a smaller representative area and test whether the parameters cho‐
231 sen (e.g. defaults) are appropriate.
232 The user must run g.region before the program to set the 3D region for
234 interpolation.
235
238 The vector points map must be a 3D vector map (x, y, z as geometry).
239 The module v.in.db can be used to generate a 3D vector map from a table
240 containing x,y,z columns.
241
244 devi file is written as 2D and deviations are not written as
245 attributes.
246
249 g.region, v.in.ascii, r3.mask, v.in.db, v.surf.rst, v.univar
250
253 Original version of program (in FORTRAN) and GRASS enhancements:
254 Lubos Mitas, NCSA, University of Illinois at Urbana-Champaign, Illi‐
256 nois, USA,lubos_mitas@ncsu.edu
257 Helena Mitasova, Department of Marine, Earth and Atmospheric Sciences,
259 North Carolina State University, Raleigh, USA, <a href="mailto:hmi‐
260 taso@unity.ncsu.edu">hmitaso@unity.ncsu.edu
261 Modified program (translated to C, adapted for GRASS, new segmentation
263 procedure):
264 Irina Kosinovsky, US Army CERL, Champaign, Illinois, USA
266 Dave Gerdes, US Army CERL, Champaign, Illinois, USA
268 Modifications for g3d library, geometric parameters, cross-validation,
270 deviations:
271 Jaro Hofierka, Department of Geography and Regional Development, Uni‐
273 versity of Presov, Presov, Slovakia, <a
274 href="MAILTO:hofierka@fhpv.unipo.sk">hofierka@fhpv.unipo.sk, <a
275 href="http://www.geomodel.sk">http://www.geomodel.sk
276
281 Hofierka J., Parajka J., Mitasova H., Mitas L., 2002, Multivariate
282 Interpolation of Precipitation Using Regularized Spline with Tension.
283 Transactions in GIS 6, pp. 135-150.
284 Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley,
286 M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Informa‐
287 tion Systems: Principles, Techniques, Management and Applications,
288 Wiley, pp.481-492
289 Mitas L., Brown W. M., Mitasova H., 1997, <a
291 href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/lcgfin/cg-
292 mitas.html">Role of dynamic cartography in simulations of landscape
293 processes based on multi-variate fields. Computers and Geosciences,
294 Vol. 23, No. 4, pp. 437-446 (includes CDROM and WWW: www.else‐
295 vier.nl/locate/cgvis)
296 Mitasova H., Mitas L., Brown W.M., D.P. Gerdes, I. Kosinovsky,
298 Baker, T.1995, Modeling spatially and temporally distributed phenomena:
299 New methods and tools for GRASS GIS. International Journal of GIS, 9
300 (4), special issue on Integrating GIS and Environmental modeling,
301 433-446.
302 Mitasova, H., Mitas, L., Brown, B., Kosinovsky, I., Baker, T., Gerdes,
304 D. (1994): <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
305 lena/gmslab/viz/ches.html">Multidimensional interpolation and visual‐
306 ization in GRASS GIS
307 <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
309 lena/gmslab/papers/lmg.rev1.ps">Mitasova H. and Mitas L. 1993: Interpo‐
310 lation by Regularized Spline with Tension: I. Theory and Implementa‐
311 tion, Mathematical Geology 25, 641-655.
312 <a href="http://skagit.meas.ncsu.edu/%7Ehe‐
314 lena/gmslab/papers/hmg.rev1.ps">Mitasova H. and Hofierka J. 1993:
315 Interpolation by Regularized Spline with Tension: II. Application to
316 Terrain Modeling and Surface Geometry Analysis, Mathematical Geology
317 25, 657-667.
318 Mitasova, H., 1992 : New capabilities for interpolation and topographic
320 analysis in GRASS, GRASSclippings 6, No.2 (summer), p.13.
321 Wahba, G., 1990 : Spline Models for Observational Data, CNMS-NSF
323 Regional Conference series in applied mathematics, 59, SIAM, Philadel‐
324 phia, Pennsylvania.
325 Mitas, L., Mitasova H., 1988 : General variational approach to the
327 interpolation problem, Computers and Mathematics with Applications 16,
328 p. 983
329 Talmi, A. and Gilat, G., 1977 : Method for Smooth Approximation of
331 Data, Journal of Computational Physics, 23, p.93-123.
332 Thorpe, J. A. (1979): Elementary Topics in Differential Geometry.
334 Springer-Verlag, New York, pp. 6-94.
335 Last changed: $Date: 2006/06/16 12:12:37 $
338 Full index
340GRASS 6.2.2 v.vol.rst(1)