Provided by: grass-doc_6.4.3-3_all 
NAME
v.vol.rst - Interpolates point data to a 3D raster map using regularized spline with tension (RST)
algorithm.
KEYWORDS
vector, interpolation
SYNOPSIS
v.vol.rst
v.vol.rst help
v.vol.rst [-c] input=string [cellinp=string] [wcolumn=string] [tension=float] [smooth=float]
[scolumn=string] [where=sql_query] [devi=string] [cvdev=string] [maskmap=string]
[segmax=integer] [npmin=integer] [npmax=integer] [dmin=float] [wmult=float] [zmult=float]
[cellout=string] [elev=string] [gradient=string] [aspect1=string] [aspect2=string]
[ncurv=string] [gcurv=string] [mcurv=string] [--overwrite] [--verbose] [--quiet]
Flags:
-c
Perform a cross-validation procedure without volume interpolation
--overwrite
Allow output files to overwrite existing files
--verbose
Verbose module output
--quiet
Quiet module output
Parameters:
input=string
Name of the vector map with input x,y,z,w
cellinp=string
Name of the surface raster map for cross-section
wcolumn=string
Name of the column containing w attribute to interpolate
Default: flt1
tension=float
Tension parameter
Default: 40.
smooth=float
Smoothing parameter
Default: 0.1
scolumn=string
Name of the column with smoothing parameters
where=sql_query
WHERE conditions of SQL statement without 'where' keyword
Example: income = 10000
devi=string
Output deviations vector point file
cvdev=string
Output cross-validation vector map
maskmap=string
Name of the raster map used as mask
segmax=integer
Maximum number of points in a segment
Default: 50
npmin=integer
Minimum number of points for approximation in a segment (>segmax)
Default: 200
npmax=integer
Maximum number of points for approximation in a segment (>npmin)
Default: 700
dmin=float
Minimum distance between points (to remove almost identical points)
Default: 0.500000
wmult=float
Conversion factor for w-values used for interpolation
Default: 1.0
zmult=float
Conversion factor for z-values
Default: 1.0
cellout=string
Output cross-section raster map
elev=string
Output elevation g3d-file
gradient=string
Output gradient magnitude g3d-file
aspect1=string
Output gradient horizontal angle g3d-file
aspect2=string
Output gradient vertical angle g3d-file
ncurv=string
Output change of gradient g3d-file
gcurv=string
Output gaussian curvature g3d-file
mcurv=string
Output mean curvature g3d-file
DESCRIPTION
v.vol.rst interpolates values to a 3-dimensional raster map from 3-dimensional point data (e.g.
temperature, rainfall data from climatic stations, concentrations from drill holes etc.) given in a 3-D
vector point file named input. The size of the output 3d raster map elev is given by the current 3D
region. Sometimes, the user may want to get a 2-D map showing a modelled phenomenon at a crossection
surface. In that case, cellinp and cellout options must be specified, with the output 2D raster map
cellout containing the crossection of the interpolated volume with a surface defined by cellinp 2D raster
map. As an option, simultaneously with interpolation, geometric parameters of the interpolated phenomenon
can be computed (magnitude of gradient, direction of gradient defined by horizontal and vertical angles),
change of gradient, Gauss-Kronecker curvature, or mean curvature). These geometric parameteres are saved
as 3d raster maps gradient, aspect1, aspect2, ncurv, gcurv, mcurv, respectively.
At first, data points are checked for identical positions and points that are closer to each other than
given dmin are removed. Parameters wmult and zmult allow the user to re-scale the w-values and z-
coordinates of the point data (useful e.g. for transformation of elevations given in feet to meters, so
that the proper values of gradient and curvatures can be computed). Rescaling of z-coordinates (zmult)
is also needed when the distances in vertical direction are much smaller than the horizontal distances;
if that is the case, the value of zmult should be selected so that the vertical and horizontal distances
have about the same magnitude.
Regularized spline with tension method is used in the interpolation. The tension parameter controls the
distance over which each given point influences the resulting volume (with very high tension, each point
influences only its close neighborhood and the volume goes rapidly to trend between the points). Higher
values of tension parameter reduce the overshoots that can appear in volumes with rapid change of
gradient. For noisy data, it is possible to define a global smoothing parameter, smooth. With the
smoothing parameter set to zero (smooth=0) the resulting volume passes exactly through the data points.
When smoothing is used, it is possible to output a vector map devi containing deviations of the resulting
volume from the given data.
The user can define a 2D raster map named maskmap, which will be used as a mask. The interpolation is
skipped for 3-dimensional cells whose 2-dimensional projection has a zero value in the mask. Zero values
will be assigned to these cells in all output 3d raster maps.
If the number of given points is greater than 700, segmented processing is used. The region is split into
3-dimensional "box" segments, each having less than segmax points and interpolation is performed on each
segment of the region. To ensure the smooth connection of segments, the interpolation function for each
segment is computed using the points in the given segment and the points in its neighborhood. The minimum
number of points taken for interpolation is controlled by npmin , the value of which must be larger than
segmax and less than 700. This limit of 700 was selected to ensure the numerical stability and efficiency
of the algorithm.
EXAMPLES
Spearfish example (we simulate 3D soil range data):
g.region -dp
# define volume
g.region res=50 tbres=50 b=0 t=1500 -ap3
# random elevation extraction (2D)
r.random elevation.10m vector_output=elevrand n=200
# conversion to 3D
v.db.addcol elevrand col="x double precision, y double precision"
v.to.db elevrand option=coor col=x,y
v.db.select elevrand
# create new 3D map
v.in.db elevrand out=elevrand_3d x=x y=y z=value key=cat
v.info -c elevrand_3d
v.info -t elevrand_3d
# remove the now superfluous 'x', 'y' and 'value' (z) columns
v.db.dropcol elevrand_3d col=x
v.db.dropcol elevrand_3d col=y
v.db.dropcol elevrand_3d col=value
# add attribute to interpolate
# (Soil range types taken from the USDA Soil Survey)
d.rast soils.range
d.vect elevrand_3d
v.db.addcol elevrand_3d col="soilrange integer"
v.what.rast elevrand_3d col=soilrange rast=soils.range
# fix 0 (no data in raster map) to NULL:
v.db.update elevrand_3d col=soilrange value=NULL where="soilrange=0"
v.db.select elevrand_3d
# interpolate volume
v.vol.rst elevrand_3d wcol=soilrange elev=soilrange zmult=100
# visualize
nviz elevation.10m vol=soilrange
# export to Paraview
r.out.vtk elevation.10m out=elev.vtk
r3.out.vtk elevrand_3d out=volume.vtk
paraview
SQL support
Using the where parameter, the interpolation can be limited to use only a subset of the input vectors.
# preparation as in above example
v.vol.rst elevrand_3d wcol=soilrange elev=soilrange zmult=100 where="soilrange > 3"
Cross validation procedure
Sometimes it can be difficult to figure out the proper values of interpolation parameters. In this case,
the user can use a crossvalidation procedure using -c flag (a.k.a. "jack-knife" method) to find optimal
parameters for given data. In this method, every point in the input point file is temporarily excluded
from the computation and interpolation error for this point location is computed. During this procedure
no output grid files can be simultanuously computed. The procedure for larger datasets may take a very
long time, so it might be worth to use just a sample data representing the whole dataset.
Example (based on Slovakia3d dataset):
v.info -c precip3d
v.vol.rst -c input=precip3d wcolumn=precip zmult=50 segmax=700 cvdev=cvdevmap tension=10
v.db.select cvdevmap
v.univar cvdevmap col=flt1 type=point
Based on these results, the parameters will have to be optimized. It is recommended to plot the CV error
as curve while modifying the parameters.
The best approach is to start with tension, smooth and zmult with rough steps, or to set zmult to a
constant somewhere between 30-60. This helps to find minimal RMSE values while then finer steps can be
used in all parameters. The reasonable range is tension=10...100, smooth=0.1...1.0, zmult=10...100.
In v.vol.rst the tension parameter is much more sensitive to changes than in v.surf.rst, therefore the
user should always check the result by visual inspection. Minimizing CV does not always provide the best
result, especially when the density of data are insufficient. Then the optimal result found by CV is an
oversmoothed surface.
NOTES
The vector points map must be a 3D vector map (x, y, z as geometry). The module v.in.db can be used to
generate a 3D vector map from a table containing x,y,z columns. Also, the input data should be in a
projected coodinate system, such as Univeral Transverse Mercator. The module does not appear to have
support for geographic (Lat/Long) coordinates as of May 2009.
v.vol.rst uses regularized spline with tension for interpolation from point data (as described in
Mitasova and Mitas, 1993). The implementation has an improved segmentation procedure based on Oct-trees
which enhances the efficiency for large data sets.
Geometric parameters - magnitude of gradient (gradient), horizontal (aspect1) and vertical (aspect2)
aspects, change of gradient (ncurv), Gauss-Kronecker (gcurv) and mean curvatures (mcurv) are computed
directly from the interpolation function so that the important relationships between these parameters are
preserved. More information on these parameters can be found in Mitasova et al., 1995 or Thorpe, 1979.
The program gives warning when significant overshoots appear and higher tension should be used. However,
with tension too high the resulting volume will have local maximum in each given point and everywhere
else the volume goes rapidly to trend. With a smoothing parameter greater than zero, the volume will not
pass through the data points and the higher the parameter the closer the volume will be to the trend. For
theory on smoothing with splines see Talmi and Gilat, 1977 or Wahba, 1990.
If a visible connection of segments appears, the program should be rerun with higher npmin to get more
points from the neighborhood of given segment.
If the number of points in a vector map is less than 400, segmax should be set to 400 so that
segmentation is not performed when it is not necessary.
The program gives a warning when the user wants to interpolate outside the "box" given by minimum and
maximum coordinates in the input vector map. To remedy this, zoom into the area encompassing the input
vector data points.
For large data sets (thousands of data points), it is suggested to zoom into a smaller representative
area and test whether the parameters chosen (e.g. defaults) are appropriate.
The user must run g.region before the program to set the 3D region for interpolation.
BUGS
devi file is written as 2D and deviations are not written as attributes.
REFERENCES
Hofierka J., Parajka J., Mitasova H., Mitas L., 2002, Multivariate Interpolation of Precipitation Using
Regularized Spline with Tension. Transactions in GIS 6, pp. 135-150.
Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley, M.F. Goodchild, D.J. Maguire,
D.W.Rhind (Eds.), Geographical Information Systems: Principles, Techniques, Management and Applications,
Wiley, pp.481-492
Mitas L., Brown W. M., Mitasova H., 1997, <a
href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/lcgfin/cg-mitas.html">Role of dynamic cartography in
simulations of landscape processes based on multi-variate fields. Computers and Geosciences, Vol. 23, No.
4, pp. 437-446 (includes CDROM and WWW: www.elsevier.nl/locate/cgvis)
Mitasova H., Mitas L., Brown W.M., D.P. Gerdes, I. Kosinovsky, Baker, T.1995, Modeling spatially and
temporally distributed phenomena: New methods and tools for GRASS GIS. International Journal of GIS, 9
(4), special issue on Integrating GIS and Environmental modeling, 433-446.
Mitasova, H., Mitas, L., Brown, B., Kosinovsky, I., Baker, T., Gerdes, D. (1994): <a
href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/viz/ches.html">Multidimensional interpolation and
visualization in GRASS GIS
<a href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/papers/lmg.rev1.ps">Mitasova H. and Mitas L. 1993:
Interpolation by Regularized Spline with Tension: I. Theory and Implementation, Mathematical Geology 25,
641-655.
<a href="http://skagit.meas.ncsu.edu/%7Ehelena/gmslab/papers/hmg.rev1.ps">Mitasova H. and Hofierka J.
1993: Interpolation by Regularized Spline with Tension: II. Application to Terrain Modeling and Surface
Geometry Analysis, Mathematical Geology 25, 657-667.
Mitasova, H., 1992 : New capabilities for interpolation and topographic analysis in GRASS, GRASSclippings
6, No.2 (summer), p.13.
Wahba, G., 1990 : Spline Models for Observational Data, CNMS-NSF Regional Conference series in applied
mathematics, 59, SIAM, Philadelphia, Pennsylvania.
Mitas, L., Mitasova H., 1988 : General variational approach to the interpolation problem, Computers and
Mathematics with Applications 16, p. 983
Talmi, A. and Gilat, G., 1977 : Method for Smooth Approximation of Data, Journal of Computational
Physics, 23, p.93-123.
Thorpe, J. A. (1979): Elementary Topics in Differential Geometry. Springer-Verlag, New York, pp. 6-94.
SEE ALSO
g.region, v.in.ascii, r3.mask, v.in.db, v.surf.rst, v.univar
AUTHOR
Original version of program (in FORTRAN) and GRASS enhancements:
Lubos Mitas, NCSA, University of Illinois at Urbana-Champaign, Illinois, USA, since 2000 at Department of
Physics, North Carolina State University, Raleigh, USA lubos_mitas@ncsu.edu
Helena Mitasova, Department of Marine, Earth and Atmospheric Sciences, North Carolina State University,
Raleigh, USA, <a href="mailto:hmitaso@unity.ncsu.edu">hmitaso@unity.ncsu.edu
Modified program (translated to C, adapted for GRASS, new segmentation procedure):
Irina Kosinovsky, US Army CERL, Champaign, Illinois, USA
Dave Gerdes, US Army CERL, Champaign, Illinois, USA
Modifications for g3d library, geometric parameters, cross-validation, deviations:
Jaro Hofierka, Department of Geography and Regional Development, University of Presov, Presov, Slovakia,
<a href="MAILTO:hofierka@fhpv.unipo.sk">hofierka@fhpv.unipo.sk, <a
href="http://www.geomodel.sk">http://www.geomodel.sk
Last changed: $Date: 2011-11-08 03:29:50 -0800 (Tue, 08 Nov 2011) $
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