PC-Blue - MS DOS Public Domain Library/PC-Blue MS-DOS Public Domain Library - NYACC.iso/vol062/grid2con.doc

Text File | 1987-01-13 | 15.4 KB | 387 lines

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GRID2CON
(c) copyright 1983

Mark A. Herkommer
PETROSPEC
4005 Burning Tree Lane
Garland, Texas  75042



I.    ABSTRACT

    A. Program Title:    GRID2CON

    B. Programmer:        Mark A. Herkommer

    C. Date:        April 18, 1983  Rev. 2.0

    D. Language:        Advanced Basic 1.10

    E. Machine:        IBM PC, Epson MX printer, and
                one disk drive

    F. Field Length:    Approx. 55K bytes

    G. Description:        Gridding routine for randomly
                distributed data and line printer
                contour map generator.

    H. Input:        XYZ or LatLonZ data entered from the
                keyboard or a sequential disk file

    I. Output:        Files: Gridsave data file
                Printout: Contour map
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II.    INTRODUCTION

GRID2CON is a gridding and contouring program designed to run
on the IBM PC and an EPSON MX printer.  The program's operation
can be divided into two distinct parts that can be run indepen-
dently or successionally.  The first part reads X, Y, Z or Lat Lon,
Z data and generates a "gridsave" file that is read by the second.
The second half reads the gridsave file and generates a line printer
contour map.  Two map projections are currently available for
converting latitude and longitude into ground meters; Universal
Transverse Mercator and Polyconic.

GRID2CON has two gridding algorithms available to the user;
inverse-distance weighted and inverse-distance-squared weighted
moving averaging.  A "skip fator" speed enhancer can be used to
reduce the time required to grid a set of data.  As a third
"gridding" option, the user can input the coefficents of a polynomial
surface and have that surface contoured.

Randomly distributed (X, Y, Z or Lat, Lon, Z) data are input into the
program from a disk file.  The output contour map can be viewed on
the screen, printed on a line printer, or saved in a disk file.
If the map is printed, the width and height of the characters can be
varied to improve the resolution.  Also, maps that are wider than the
paper width are automatically printed in strips so that they can be
pieced together.

III.    METHOD OF SOLUTION

    A. Gridding

    Gridding is the operation that generates a Z-value at regular
    and predictable intervals (X,Y locations) given randomly
    distributed XYZ data points.  In version 1.0 of GRID2CON, only
    rectangular gridding is performed.

    One may think of the grid as a series of of reqularly spaced
    horizontal and vertical lines at the intersection of which is
    a Z-value calculated.  These intersections are called grid
    nodes and 4 of these define the smallest grid unit called a
    grid cell.

    When gridding, the distance from the grid node to each of the
    XYZ data points (hereafter called control points), is calcu-
    lated using the user's engineering units.  If the calculated
    distance between the control point and grid node is less than
    the "Search Radius", then the inverse-distance is used to weight
    that control point's contribution to the average at that
    grid node.  All the control points are tested against the search
    for each of the grid nodes.  This type of weighting is used
    because points further away are thought to influence the value
    at the node less.  The greater the distance, the less the
    weight.  The distance is calculated by:

        D^2 = ( X2 - X1 )^2 + ( Y2 - Y1)^2

    Where D is the distance between the node and the control point,
    X1 is the CP X-location, X2 is the grid node X-location, Y1 is
    the CP Y-location, and Y2 is the grid node Y-location.  The
    Z-value is computed by:

        Zsum = Z1/D1 + Z2/D2 + Z3/D3 + ... + Zn/Dn

    The sum of the weights is:

        Dsum = 1/D1 + 1/D2 + 1/D3 + ... + 1/Dn

    and the Z-value at the node is:

        Zvalue = Zsum/Dsum

    These calculations are performed at each node in the map area.
    The search radius is  calculated as 1/2 the diagonal distance
    of the map area, although this can be overridden. Nodes that
    have no control points close enough to pass the search radius
    test are assigned a value of 1E+32 (undefined).

    Traditionally when making line printer contour maps, each
    character of the printer is considered a node and a value is
    calculated for each.  Thus, a map that figures to be 20"x20"
    has 200 columns (at 10 cpi) and 160 rows (at 8 lpi) and
    would require 32,000 node calculations.  For most, the time
    required to calculate a grid of this size would be
    prohibative.  It is because of this time consideration that
    a skip factor is used.

    B. Trend Surface Coefficents

    The highest order polynomial that can be contoured is an
    8th.  In this case, 45 coefficents would be required.
    The number of ceofficents can be determined by:

        NCoefficents = (Order+1) * (Order+2)/2

    All required coefficents must be entered, although any can have
    the default value of 0.  The coefficents  correspond to the
    the polynomial thusly:

        Z-value = C1 + C2*X + C3*Y + C4*X^2 + C5*X*Y + C6*Y^2 +
              C7*X^3 + C8*X^2*Y + C9*X*Y^2 + C10*Y^3 + ...

    Coefficents must be entered in this order for the calculations
     to be performed correctly.

    C. Skip Factor

    The skip factor is nothing more than the number of columns
    that are skipped between grid nodes on each line (row) of the
    contour map.  The gridding time is reduced by a factor of the
    skip factor.  In the above example, a skip factor of 30 would
    mean that a total of 1280 nodes would be calculated.  Depending
    upon the curvature of the surface being calculated, skip
    factors as large as 1/4 the map width can produce satisfactory
    results.  Between the calculated nodes the Z-values are
    linearly interpolated.

    The skip factor is not used in the calculations of the
    vertical component of the line printer map.  Because of this,
    map resolution remains very high in the Y-direction.

IV.    PROGRAM OPTIONS AND RESTRICTIONS

    A. Options -- gridding

    Three surface generating algortihms are available, as discussed
    above.  A sutiable program for deriving the coefficents of a
    trend surface is CURVFIT-3D, available from PETROSPEC.

    The scale of the map per inch will determine the number of
    columns and rows in the map area.  The default character spacing
    is 10 characters per inch horizontally and 8 lines per inch ver-
    tically.  Thus a map 6 inches wide <the default>, will have
    60 columns and 48 rows.  GRID2CON will automatically panelize
    if it cannot plot the map within the width of the panel
    set by the user <80 is the default>.  It is worth noting that
    17 columns are used to draw the margins and axis labels on
    each panel.  Compressed and subscript characters are available
    to persons with EPSON MX printers.  These options improve the
    resolution of the map.  Vertical spacing greater than 10 cpi
    will put the printer input subscript mode.

    The Search radius is calculated as 1/2 the map diagonal,
    however, this can be input when the user is queried.  If
    a search radius is two small, many nodes will have 'undefined'
    values, shown by a '*' on the map.  A large Search radius will
    tend produce a map of moving averages for the whole map area--
    this is sometimes desirable.

    B. Options -- contouring

    Panel width can be set so the map will fit on the media it
    has been directed to.  The map will plot on the screen <SCRN:>
    unless the user specifies otherwise.  Other specifications might
    be LPT1: for the line printer, or B:MAP.FIL for a disk file.
    This option has been provided so the user can save her results
    in a file for future reference, or to make multiple copies
    without rerunning the job.

    C. Restrictions

    Only 1000 data points can be gridded.  Points numbering over
    1000 are ignored.

    Grid nodes are saved in the grid-save file of the user's
    specification.  If she is using a 320K drive, this would
    permit about 32K nodes to be saved without a disk full error
    (c. 10 bytes/node).

    Latitude and longitude input must be positive, in decimal
    degrees, and in the northern half of the western hemisphere.

V.    PROGRAM INPUT

    Keyboard input should always be in upper case letters.  There
    are three styles of prompts used in the program, each asks
    for a particular input data type.  They are

        "=" asks for numeric input
        ":" asks for an alpha-numeric string
        "?" asks for Y or N (Yes or No)

    The default value is shown between <>.

    XZY data must be in a sequential file arranged as X Y Z values.
    Latitude/longitude Z values must be in a sequential file
    arranged in that order.  No special characters can be present.
    Data may be separated by spaces or commas.  There can be no
    header cards, or any other superfluous information in the
    control point file.  When plotting a trend surface,
    at least 2 records must be present to define the limits
    of the map area.

VI.    PROGRAM OUTPUT

    A. Grid-save file

    The grid-save file is a sequential file in ASCII format and
    has the following structure:

    record 1: title
    record 2: Xmin,Xmax,Ymin,Ymax,Zmin,Zmax,MAPSCALE,ISTATE,CM,
          0,0,0,0,NROWS,NROWSKIP,NCOLS,NCOLSKIP,ALGORITHM#,
          SEARCHRADIUS,NORDER,CHRHOR,CHRVERT
    record 3-last: Zatthenode,NUMPOINTSusedtoestimateZ

    Z-values start in the upper left corner of the map area, and
    move left-to-right then down, and left-to-right again, etc.
    If no points passed the Search radius test, then Z=1E+32
    and NPTS=0.  If a trend surface was gridded, then Z=
    the calculated Z-value at the given X Y location. The
    number of points used to estimate Z will always equal 1.
    ISTATE is the map projection and CM is the central merridian.

    B. Contour maps

    Below is a sample contour map made from synthetic data.


 PANEL 1 OF 1           synthetic data--ncskip=1--npts=11

^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx+
y       55555  44   333333  22  1  $$ AA  BBB   CCC  DD  EEEEy= 5
y       55555  44  3333333  22 11 $$  AA  BBB  CCCC  DD  EEEEy
y 44           4   333333   2 11  $$ AA   BB   CCCC CDDD  EEEy
y4444         44   333333  22 11  $  AA  BBB   CCCC   DDD    y
y444444  444444   33333   22 11  $$  AA  BB   CCCCC    DDD   y
y  44444444444   3333    22  11 $$  AA   BB   CCCC      DDDDDy
y    4444       333    222  11  $$  AA   BB  CCCC          DDy
y33         333333   2222  11  $$  AAA  BBB  CCC             y
y333333  333333     222   11  $$   AA   BBB  CCC             y
y333333333        222   111  $$$  AAA    BBB  CCC    CCCCCCCCy
y              22222  111   $$$  AAAA    BBB   CCCCCCCCCCCCCCy
y        22222222    111   $$$   AAA     BBBB   CCCCCCCCCCCCCy
y2222222222222      1     $$$   AAAA      BBBB    CCCCCCC   Cy
y22222222        11111   $$$    AAAA       BBBBB             y
y222222      1111111   $$$$$    AAA         BBBBB            y
y         1111111      $$$$     AAA          BBBBBBB         y
y        111111      $$$$$      AAA            BBBBBBBBBBBBBBy
y  1111111         $$$$$$        AAA           BBBBBBBBBBBBBBy
y1111111111      $$$$$$$$        AAAA               B   BBBBBy
y1111111       $$$$$$$$$$$        AAAA                       y
y1111       $$$$$$$$$$$$$$$         AAAA                     y
y           $$$$$$$$     $$$$$$$     AAAAAAA             AAAAy
y         $$$$$$         $$$$$$$$$    AAAAAAAAA AAAAAAAAAAAAAy
y       $$$$$$           $$$$$$$$$     AAAAAAAAAAAAAAAAAAAAAAy
y     $$$$$$$             $$$$$$$$      AAAAAAAAAAAAAAAA     y
y   $$$$$$$$       A       $$$$$$$     AAAAAAAAAAAAAA        y
y  $$$$$$$$     AAAAAAA     $$$$$$      AAAAAAAAAAA          y
y $$$$$$$$     AAAAAAAAA                 AAAAAAA          $$$y
y $$$$$$$     AAAAA  AAAAA                  AA         $$$$$$y
y  $$$$$$     AAA      AAAA               AA         $$$$$$$$y
y$$$$$$$$     AAA       AAAA                       $$$$$$$$$$y
y$$$$$$$$     AAA        AAAA                     $$$$$$$$$$$y
y$$$$$$$      AAA        AAAAA                $$$$$$$$$$$$$$$y
y$$$$$$$$     AAA        AAAAAAA             $$$$$$$$$$$$$$$$y
y$$$$$$$       AAA       AAAAAAA            $$$$$$$$      $$$y
y$$$$$$$$$$     AAAA   AAAAAAAA             $$$$$$           y
y$$$$$$$$$$$$    AAAAAAAAAAAAAA            $$$$$$      111111y
y $$$$$$$$$$$$    AAAAAAAAAA              $$$$$$     11111   y
y  $$$$$$$$$$$$      AAAAAA               $$$$$$    1111     y
y   $$$$$$$$$$$$                        $$$$$$$     1111     y
y    $$$$$$$$$$$$                   $$$$$$$$$$$     111      y
y1    $$$$$$$$$$$                  $$$$$$$$$$       111      y
y111   $$$$$$$$$$$                 $$$$$$$$$$      11111     y
y1111    $$$$$$$$$$$              $$$$$$$$$$$      111111    y
y  1111   $$$$$$$$$$$$          $$$$$$$$$$$$$      11111111  y
y    111    $$$$$$$$$$$$$     $$$$$$$$$$$$$$$      11111111  y
y     111    $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$       111111111y
y     111     $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$        111111  y=-1
-xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
 !                                                          !
-1                                                           5

Contour interval            =  .3
Column skip factor          =  1
Gridded by inverse-distance-squared weighting

              *** KEY ***
 9.000E-01 <= value <  1.200E+00       ="E"
 1.200E+00 <= value <  1.500E+00       =" "
 1.500E+00 <= value <  1.800E+00       ="D"
 1.800E+00 <= value <  2.100E+00       =" "
 2.100E+00 <= value <  2.400E+00       ="C"
 2.400E+00 <= value <  2.700E+00       =" "
 2.700E+00 <= value <  3.000E+00       ="B"
 3.000E+00 <= value <  3.300E+00       =" "
 3.300E+00 <= value <  3.600E+00       ="A"
 3.600E+00 <= value <  3.900E+00       =" "
 3.900E+00 <= value <  4.200E+00       ="$"
 4.200E+00 <= value <  4.500E+00       =" "
 4.500E+00 <= value <  4.800E+00       ="1"
 4.800E+00 <= value <  5.100E+00       =" "
 5.100E+00 <= value <  5.400E+00       ="2"
 5.400E+00 <= value <  5.700E+00       =" "
 5.700E+00 <= value <  6.000E+00       ="3"
 6.000E+00 <= value <  6.300E+00       =" "
 6.300E+00 <= value <  6.600E+00       ="4"
 6.600E+00 <= value <  6.900E+00       =" "
 6.900E+00 <= value <  7.200E+00       ="5"
undefined                              ="*"
.D
VII.     LICENSE

    You may:

    A.    use this program on a single machine;

    B.    copy this program into any machine readable or printed
        form for backup in support of your use on a single
        machine;

    C.    copy this documentation for personal use or use within
        your organization;

    D.    terminate this license by destroying all machine
        readable and printed copies, including all modifica-
        tions and portions of this program contained or merged
        into other programs;

    E.     transfer this license to another party only if the
        other party accepts the terms and conditions of this
        license.  If you transfer this program, then you must
        at the same time either transfer all copies whether
        in machine readable or printed form to the same party
        or destroy all copies not transferred, including all
        modifications and portions of the program contained
        or merged into other programs.

    You may not:

    A.    transfer this license except as expressly provided
        for in this license.

    Term:

    This license is in effect until terminated.  If you transfer
    posession of any copy, modification or merged portion of this
    program to another party, your license is automatically
    terminated.
fafaifae+n un ohE,s hhatfaenalue <  5.100E+00       =" "
 5.100E+00 <= value <  5.400E+00       ="2"
 5.400E+00 <= value <  5.700E+00       =" "
 5.700E+00 <= value <  6