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       v.vol.rst   -  Interpolates  point  data  to a 3D raster map using regularized spline with
       tension (RST) algorithm.


       vector, interpolation


       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]

           Perform a cross-validation procedure without volume interpolation

           Allow output files to overwrite existing files

           Verbose module output

           Quiet module output

           Name of the vector map with input x,y,z,w

           Name of the surface raster map for cross-section

           Name of the column containing w attribute to interpolate
           Default: flt1

           Tension parameter
           Default: 40.

           Smoothing parameter
           Default: 0.1

           Name of the column with smoothing parameters

           WHERE conditions of SQL statement without 'where' keyword
           Example: income = 10000

           Output deviations vector point file

           Output cross-validation vector map

           Name of the raster map used as mask

           Maximum number of points in a segment
           Default: 50

           Minimum number of points for approximation in a segment (>segmax)
           Default: 200

           Maximum number of points for approximation in a segment (>npmin)
           Default: 700

           Minimum distance between points (to remove almost identical points)
           Default: 0.500000

           Conversion factor for w-values used for interpolation
           Default: 1.0

           Conversion factor for z-values
           Default: 1.0

           Output cross-section raster map

           Output elevation g3d-file

           Output gradient magnitude g3d-file

           Output gradient horizontal angle g3d-file

           Output gradient vertical angle g3d-file

           Output change of gradient g3d-file

           Output gaussian curvature g3d-file

           Output mean curvature g3d-file


       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

       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.


       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" elevrand option=coor col=x,y elevrand
       # create new 3D map elevrand out=elevrand_3d x=x y=y z=value key=cat -c elevrand_3d -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" 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

   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): -c precip3d
       v.vol.rst -c input=precip3d wcolumn=precip zmult=50 segmax=700 cvdev=cvdevmap tension=10 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,
       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.


       The  vector  points map must be a 3D vector map (x, y, z as geometry).  The module
       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

       The user must run g.region before the program to set the 3D region for interpolation.


       devi file is written as 2D and deviations are not written as attributes.


       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="">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:

       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
       interpolation and visualization in GRASS GIS

       <a href="">Mitasova H.  and
       Mitas   L.  1993:  Interpolation  by  Regularized  Spline  with  Tension:  I.  Theory  and
       Implementation, Mathematical Geology 25, 641-655.

       <a href="">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.


       g.region,, r3.mask,,, v.univar


       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
       Helena  Mitasova,  Department  of  Marine,  Earth and Atmospheric Sciences, North Carolina
       State               University,               Raleigh,               USA,               <a

       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="">,   <a

       Last changed: $Date: 2011-11-08 03:29:50 -0800 (Tue, 08 Nov 2011) $

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