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User's Manual
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The program SurGe is intended for the approximation (interpolation) of points
XYZ into nodes of a square
grid. It contains a method named ABOS (Approximation Based
On Smoothing). ABOS is a method for
approximating (interpolating) z-coordinates of irregularly spaced points
(usually measured in the terrain) by using a continuous function with two
independent variables.
Description of the ABOS
method
Definition of the interpolation function and
notations
The interpolation function is defined by a matrix of real numbers P, which represents the surface at nodes of a square grid. The domain of the interpolation function is defined by the outer lines of the grid:
The value of the surface at any point
(x0,y0)
within the grid can be evaluated from the equation of the bilinear
polynomial
f(x,y) = axy + bx + cy + d,
which is defined by corner points of the grid square containing the point
(x0,y0).
The following notation is used in the next text:
| XYZ | sequence of irregularly spaced points {Xi,Yi,Zi} i=1,...,n |
| x1,x2 | minimum and maximum of x-coordinates of points XYZ |
| y1,y2 | minimum and maximum of y-coordinates of points XYZ |
| Zmin | minimum of z-coordinates of points XYZ |
| Zmax | maximum of z-coordinates of points XYZ |
| i1,j1 | size of the grid - number of columns and rows of the matrix P |
| Pi,j | elements of the matrix P, i=1,...,i1 j=1,...,j1 |
| DP | auxiliary matrix with the same size as the matrix P |
| Z | vector of z-coordinates of points XYZ |
| DZ | auxiliary vector with the same size as the vector Z |
| K | matrix of parameters for tensioning. It has the same size as the matrix P |
| Kmax | maximal element of the matrix K |
| NB | matrix of integer numbers, which has the same size as the matrix P and determines, for any node in the grid, the index of the nearest point XYZ (so called matrix of the nearest points) |
The algorithm of the ABOS method can be described by the following scheme:
1. Determination of grid size, computation of the matrix
NB,
Z
->
DZ
2. Per partes constant interpolation of
DZ values into the matrix
P
3. Tensioning and smoothing of the matrix
P
4. Determination of differences
Z
-
P
->
DZ
5. If the maximal difference (maximal value of elements from
the vector DZ) does not exceed defined
precision, algorithm is finished
6. P
->
DP, per partes constant interpolation
of DZ values into the matrix
P
7. Tensioning and smoothing of the matrix
P
8. P
+
DP
->
P
9. Continue from step 4 again (=
start the next iteration step)
Particular steps of the algorithm are explained in more detail:
Step 1. As soon as the input data are read (using menu item
File / Basic file), it is possible to perform the interpolation
/ approximation using menu item Interpolation / Calculate grid.
The interpolation (approximation) is performed using the stand alone FORTRAN
program SURGEF.EXE, which firstly suggests the size of the square grid -
a value of i1 (grid size in
x-direction) and a value of
j1 (grid size in y-direction).
These values can be changed by the user. However, it is recommended not to
change the value of j1. Despite the
fact that the grid is referenced as a "square", in general it is not really
possible to set a square grid - the grid is generally formed by
rectangles. The program SURGEF.EXE calculates (according to the value of
i1) the value of
j1 so that the difference between
sizes of rectangle sides is as small as possible. In the whole SurGe
documentation the grid size
means max{i1,j1}.
In this step, the matrix
NB is calculated and values
of the vector Z are copied
into the vector DZ.
Step 2. Interpolation of DZ values into the matrix P is performed such that the value Pi,j for every node of grid is equal to the value DZ of the nearest point XYZ. Such interpolation (per partes constant, see pic. 2) is very fast.
Pic.2: Per partes constant interpolation
Step 3. Repeated tensioning (see pic.3), linear tensioning (see pic.4) and smoothing (see pic.5) of the matrix P improves the shape of the resulting surface, but smoothing decreases the accuracy - surface does not pass through the points XYZ exactly.
Pic.3: Tensioning of the matrix P
Pic.4: Linear tensioning of the matrix
P
Pic.5: Smoothing of the matrix P
Tensioning modifies the matrix P according to the formula:
Pi,j = (Pi+k,j + Pi,j+k + Pi-k,j + Pi,j-k)/4, k = Ki,j
only if k > 0. Values of the matrix k = Ki,j are determined for each node of the grid during computation of the matrix NB. The following scheme shows the nodes (marked by gray circles) corresponding to the elements of the matrix P, which are involved in the tensioning.
Tensioning is repeatedly performed in the loop with this pattern:
DO N
=
MAX(4,Kmax/2+2),1,-1
···
ENDDO
If k is greater than decreasing
loop variable N, then
k
=
N.
Linear tensioning modifies the matrix P according to the formula:
Pi,j = (Q(Pi+u,j+v + Pi-u,j-v)+ Pi-v,j+u+ Pi+v,j-u)/(2Q+2), where
(u,v) is the vector from the node
i,j to the nearest grid node
of point
NBi,j and
Q
=
L·(Kmax-Ki,j)2.
The constant L
=
1/((0.107·Kmax-0.714)·Kmax)
is an empirical constant suppressing the influence of
Kmax . This formula is valid
for default degree of linear tensioning 1. Generalized formula for other
degrees is in section Degrees of linear
tensioning.
The following scheme shows the nodes (marked by gray circles) corresponding
to the elements of the matrix
P, which are involved in the linear tensioning.
Linear tensioning is repeatedly performed in the loop with this pattern:
DO N
=
MAX(4,Kmax/2+2),1,-1
···
ENDDO
If the
length |(u,v)| of the vector
(u,v) is greater than decreasing loop
variable N, then the vector
(u,v) is multiplied by constant
c so that
c
·|(u,v)|
=
N.
Smoothing replaces elements of the matrix P by value of weighted average:
Pi,j
=
(å
Pk,l +
Pi,j(q
ti,j-1))/(8
+
q
ti,j),
k=i-1,..,i+1,
l=j-1,..,j+1,
where q is the user-defined parameter controlling smoothness of the interpolation (its default value is 0.5) and ti,j are weights, which are zero before the first smoothing and afterwards they are computed according to the formula
ti,j
=
(å(Pi,j-Pk,l))2,
k=i-2...i+2, l=j-2...j+2,
and re-calculated into interval [0,100]. In brief it can be said, the values of ti,j are higher at nodes, where the surface has a local extreme and lower at nodes, where the surface is decreasing / increasing. The following scheme shows the nodes (marked by gray circles) corresponding to the elements of the matrix P, which are involved in the smoothing.
Smoothing is repeatedly performed in the loop with this pattern:
DO N
=
MAX(4,Kmax*Kmax/16)1,-1
···
ENDDO
The process of the interpolation (approximation) is affected by user specified
parameters in the dialog "Interpolation / Interpolation parameters".
The first one is Filter within the interval
<3,9999> with the following
meaning:
If the horizontal distance between two points
[Xi,Yi,Zi]
and
[Xj,Yj,Zj]
is greater than
max{(x2-x1),(y2-y1)}/Filter, then
these two points are replaced by one point
[Xk,Yk,Zk]
with average coordinates
Xk=(Xi+Xj)/2,
Yk=(Yi+Yj)/2
and
Zk=(Zi+Zj)/2.
If it occurs, the resulting surface will be generally approximative.
Default value of filter is 500. Special
value 0 means that only the points having
the same x and y coordinates will be filtered. The filter pre-processes the
resolution of resulting map, which is similar to the resolution of a digital
picture - if the distance of two points with different colors is smaller
than the pixel size of the digital picture, you can see only one point with
"average" color.
Parameter Smoothness is the constant q mentioned in the formula for smoothing. The default value is 0.5.
The last parameter Accuracy determines maximal allowable inaccuracy (percentage value from the difference z2-z1) of the resulting surface. The default value is 1 [%].
There is a possibility to achieve a more linear interpolation between close
points using linear tensioning. If such a feature is desired, select suitable
value of Linear tensioning:
0 ... no linear tensioning
1 ... medium linear tensioning
2 ... strong linear tensioning
3 ... full linear tensioning
In fact, the parameter Enlargement is not a parameter affecting interpolation / approximation method. The value specifies number of grid rows and columns, which has to overlap interpolation area. By this way, the shape of the surface near to the grid boundary is improved. The value of parameter Enlargement should be approximately set to (i1+j1)/10 (where i1 and j1 are grid sizes). If it is greater than 98, the program SURGEF estimates it internally.
Step 4. The tensioned and smoothed surface does not pass through the Z-coordinates of points XYZ exactly, so the differences DZi = Zi-f(Xi,Yi), i=1...n are calculated. The Z-value of the surface is computed at any point (x0,y0) from the bilinear polynomial equation:
f(x,y) = axy + bx + cy + d,
where a,
b,
c and
d are defined by corner points
of the grid square containing the point
(x0,y0).
At the beginning of this step, the algorithm offers option (see check box
"Faster convergence") to modify elements of the matrix
P by the transformation
Pi,j = A ·Pi,j + B,
where constants A and B minimize the term
å(A
·f(Xi,Yi)
+
B
-
DZi)2.
By this way, the number of iteration steps can be reduced by 20-50%.
Step 5. If the maximal difference (maximal value of elements of the
vector DZ) is less than the specified accuracy
of the interpolation / approximation, the algorithm of the ABOS method is
finished. In the opposite case the algorithm continues from the step
6.
The accuracy is specified as a percentage value from the difference
Zmax
-
Zmin.
Step 6. The matrix P is copied into the matrix DP (element by element) and the vector of differences DZ is interpolated into the matrix P, likewise as in step 2.
Step 7. The surface of differences represented by the matrix P is tensioned and smoothed, likewise as in step 3.
Step 8. The matrices P and DP are added element by element (sum of two smooth surfaces is a smooth surface) and the result is stored into the matrix P. The algorithm continues from step 4.
Example of whole interpolating process can be
viewed here as an animated GIF - to start the animation click on the
next picture or refresh your browser (shortcut key F5 in Microsoft
Internet Explorer).
.
Computation of matrices NB and
K
The matrices NB and
K are computed using the algorithm
based on the "circulation" around the points
XYZ as the following picture
indicates:
Pic. 6: Computation of the matrices
NB and
K
All elements of the matrices NB and K are initially set to zero and the process of circulation continues as long as there are zero values in the matrix NB. The Euclidean distance is compared only if the element Ki,j corresponding to the evaluated node is not zero and IC/SQRT(2)<= Ki,j, where IC is the number of the current circulation. By this way, the number of distance computations is significantly reduced.
The computation of matrix NB defines the natural division of the domain of the interpolation function into polygons (so called Voronoi or Thiessen polygons, see pic.7), inside which interpolation with constant values is performed.
Pic.7: Division of the domain of the interpolation function
There are four degrees of linear tensioning (0-3) implemented in the ABOS method. The formula for linear tensioning can be expressed in this generalized form:
Pi,j
=
(Q(Pi+u,j+v
+
Pi-u,j-v)+
R(Pi-v,j+u+
Pi+v,j-u))/(2Q+2R)
for all i=1,..,i1, j=1,..,j1;
Ki,j>0
where the weights Q and
R, depending on the degree of linear
tensioning, are calculated as follows:
| Degree | Q |
R | L |
0 |
L(Kmax-Ki,j)2 | 1 |
0.7/((0.107Kmax-0.714)Kmax) |
1 |
L(Kmax-Ki,j)2 | 1 |
1.0/((0.107Kmax-0.714)Kmax) |
2 |
L(Kmax-Ki,j) | 1 |
1.0/(0.0360625Kmax+0.192)) |
3 |
1 |
0 |
- |
Formulas for the computation of the constant L are empirical and their role is to suppress the influence of Kmax .The next figure contains a cross-section plot demonstrating the typical influence of the linear tensioning degree.
Transformation of
z-coordinates
Processing speed can be increased and computer memory can be saved by transforming the interval (Zmin,Zmax) into the subinterval of INTEGER numbers (-24000,24000) (see pic. 8), which are stored in two bytes of RAM.
Pic 8: Transformation of z-coordinates into subinterval (-24000,24000)
The elements of the matrix
P can also be of type INTEGER.
Contour maps prove that the resolution of the subinterval
(-24000,24000) of INTEGER numbers
is sufficient for qualitative contours.
Input files containing map
objects
Coordinates and labels of points XYZ are assumed to be stored in the file NAME.DTs (s is a one-character suffix, which enables to distinguish between multiple surfaces - see below). NAME is the basic name of the surface and must be specified along with the suffix in the initial dialog box as input information. NAME and the suffix s can be specified as arguments in the command line, for example:
D:\>SURGE D27 A
If there is a file NAME.DBs (containing additional points XYZ) in the working directory, points from this file will be added to the points from file NAME.DTs. Their usage for interpolation can be switched on/off - using the dialog box Interpolation / Objects for interpolation. File NAME.DBs has the same format as the file NAME.DTs, but labels of points must begin with characters ##.
The shape of the surface can be defined not only by points XYZ, but also by spatial polylines. They can be defined in the file NAME.LNs. Usage of the spatial polylines for interpolation can be switched on/off by the dialog box Interpolation / Objects for interpolation.
The process of interpolation can be affected by so called faults. A fault is a sequence of line segments where a discontinuity is to be generated in the resulting surface. If there is a file NAME.ZL in the working directory, faults are assumed to be used during interpolation. Usage of faults for interpolation can be switched on/off by the dialog box Interpolation / Objects for interpolation.
There is also the possibility to specify if a boundary is to be used. The boundary is assumed to be stored in the file NAME.HR. If such file exists in the working directory, it is automatically read. If usage of the boundary is switched on (by the dialog box Interpolation / Objects for interpolation), values of x1, x2, y1 and y2 are determined from the boundary points instead of points XYZ.
Interpolation and other
calculations
The interpolation (approximation) can be performed by the menu item Interpolation / Calculate grid. The selection of this item causes the execution of the stand-alone program SURGEF.EXE. This program firstly estimates the minimal grid size, which can be changed by the user. The user can also change the number of smoothing iterations, which is estimated according to grid size and spatial configuration of points XYZ. The interpolation (approximation) process is described in the Tutorial.
There is the possibility to double the grid (using the menu item Interpolation / Double grid). Z-values of newly created grid nodes are computed by means of spline interpolation. The doubled grid provides better isolines and can be used for the creation of an extra smooth surface.
The function Calculate isolines in the menu Interpolation enables to calculate isolines and save them to the file NAME.VRs. In the presented dialog box there is the possibility to change the first level of isolines, the last level and isolines level interval.
The function Blank grid outside boundary is intended for canceling values of the grid points located outside the boundary. The boundary is defined by the contents of the file NAME.HR. To obtain isolines only inside the boundary, the function Calculate isolines must be then performed.
The function Substitute below enables to substitute values of the grid nodes with a specified constant. For example, negative values of the grid nodes can be substituted with zero. A similar function has the menu item Substitute above.
Math calculation
with grids enables to perform some calculations with all nodes of grids.
It is assumed that the first operand is the actual surface and the second
one is the previously created surface defined by the suffix. If the second
operand is not defined (the suffix is empty), the second operand is assumed
to be a constant (specified in the following dialog box). The result of the
operation is indicated by one character with the following meaning:
| operand | result |
~ |
negation |
+ |
addition |
- |
subtraction |
* |
multiplication |
: |
division |
m |
minimum |
M |
maximum |
a |
average |
$ |
the first operand; if the second is greater than the first, then average |
% |
the second operand; if the second is greater than the first, then average |
w |
weighted average (the weights are specified in the following dialog box) |
d |
derivative computed as the size of gradient vector |
The resulting surface is specified by a new suffix entered in the dialog
box. After calculating the grid, new z-coordinates of
XYZ points and polylines are
computed. They can be saved using the menu item Digitization /
Save.
Data analysis runs only the first part of SURGEF.EXE to get essential information about filtering, grid sizes and expected maximal gradient. Then it displays the following dialog box:
The first and second items inform about the number of points before and after
the filtration process.
If the grid size is smaller than the Minimal grid size set by filter,
there is a high probability that the iteration process will not converge.
The Suggested grid size is a grid size suggested by
SURGEF.EXE.
The Comment contains a verbal description of data analysis results
and some suggestions.
Edit box Filter enables to change the actual setting of filter (and,
for example, to run Data analysis again to observe its influence).
The Target grid size has two purposes:
1. If the Interpolation with trend surface is performed, this grid
size will be used without respect to the state of Use check box.
2. If the check box Use is switched on, this grid size will be used
for the interpolation / approximation and for the next Data
analysis.
The items Normal, Linear, Convex and Auto in
the Trend surface group box are intended only for the Interpolation
with trend surface (see the next section).
Interpolation with trend surface runs
SURGEF.EXE two or three times.
The first run creates the trend surface with a small grid having the following
properties:
The second (third) run reads the created grid of trend surface, doubles it
n-times and then performs steps 4. - 9. of the
interpolating algorithm.
Using this procedure the trend surface is involved into the interpolation,
meaning that the resulting surface keeps a proper trend in areas without
points.
It is recommended to perform Data analysis before the Interpolation
with trend surface and to set desired Target grid size.
In the basic display there are points XYZ (blue dots). If a boundary and/or faults and/or polylines exist, they are displayed too. The boundary is displayed as thick red lines, faults as green thin lines and polylines as thin orange dotted lines. In the move/zoom mode, the display can be moved using cursor keys and zoomed by keys PgUp or PgDn. If you only want to move/zoom basic objects, use Ctrl with these keys. Step of moving and zoom can be changed with shortcut keys "1", "2", "3", "4" or "5". Additional displays can be performed using the items in the Display menu.
The isolines can be displayed (assuming that they were calculated) using the item Display / Isolines or by the shortcut key I. The surface can be also represented as a color raster map using Display / Color Map (shortcut key C). Labels and z-coordinates of XYZ points can be displayed using the menu item Display / Labels (shortcut key N) and Display / Z-coordinates (shortcut key K), respectively. The menu item Display / Color scale (Alt+S) is intended for the color scale used in the color maps and isolines. Display / Mesh scale (Ctrl+S) enables to display a square mesh showing distances (if the mesh has to be labeled, use Ctrl+E). The designed size of the mesh can be altered by the user. The color of the base objects (points XYZ, labels, z-coordinates, boundary, faults and polylines) can be switched using Display / Change color (Ctrl+A) in order to achieve better visibility of these objects on the color map. Display / Refresh (shortcut key R) is intended for restoring of the basic display. Objects of the background can be displayed using Display / Background (shortcut key O) menu item. Background color can be changed using Display / B/W background color (shortcut key Ctrl+R). If there are cross-sections saved in the file NAME.RZY, they can be displayed using Display / Saved cross-sections (shortcut key Ctrl+C).
There are three items related to the gradient display. The first one,
Display / Gradient in nodes, shows gradient as short oriented
line segments starting at the nodes of the grid. The second one,
Display / Gradient in isolines, shows similar line segments
starting along the isolines - only if isolines have been calculated.
In both cases the user can change (in the provided dialog box) the
multiplier constant (default 100) specifying the length of the line segments
and the frequency (default 2). For example, frequency=2 means, the
gradient line segments will start in every second node. When function
Display / Gradient lines is selected, the program enters
digitization mode. In this mode the cursor has the shape of a little cross
and the cursor keys move the cursor (and not the map). The gradient lines
(starting from the cursor position) can be displayed using the shortcut key
Alt+G.
3D display
The menu item Display / 3D view is intended for displaying
the created surface in 3D from different angles of view and
different elevations. In this case the surface is firstly stored to
the file NAMEF.GRs and then is read again.
Before surface reading there is a possibility of changing the step of reading
node values. The default step value is 1 which means that all grid nodes
will be displayed. Higher values enable to display a more sparse grid.
Cursor keys can be used for moving the 3D view around the screen, shortcut
keys PgDn and PgUp are intended for zooming.
In the 3D view mode there is a special menu. The surface can be displayed
without colors (3DVIEW / Display wiry surface, key S) or with
colors (3DVIEW / Display color surface, key C). The horizontal
angle of the view is changed by 3DVIEW / Rotate counterclockwise
(key A) or 3DVIEW / Rotate clockwise (key
Shift+A). The vertical angle can be changed by 3DVIEW / Rotate
up (key B) or 3DVIEW / Rotate down
(key Shift+B). The items 3DVIEW / Increase z-scale
(key Z) and 3DVIEW / Decrease z-scale (key
Shift+Z) are intended for increasing and decreasing the superelevation,
respectively. The item 3DVIEW / Display / hide labels (key
K) switches on/off the display of point labels.
Step of angles, moving and zoom can be changed with shortcut keys "1",
"2" and "3".
The horizontal and vertical angles of view can be also changed by mouse,
if the left button is pressed.
Transformation of map
objects
The coordinates x and y of the basic map objects (points, boundary,
faults and polylines) can be transformed. Transformation functions are contained
under the menu Transformation. The first one (Move to beginning
of coordinate system, key Alt+0 (zero)) moves coordinates of the
basic map objects into the beginning of the coordinate system - this means
that the minimal x-coordinate and the minimal y-coordinate
are zeroes. The next two, Transformation x[i]=MaxX-x[i] (key
Alt+Z) and Transformation y[i]=MaxY-y[i] (key
Alt+Y), mirrors map objects according to the x axis or the
y axis. Coordinates x and y can be interchanged using
the item Interchange x and y coordinates (key
Alt+Z). All objects can be rotated - counterclockwise using the menu
item Rotation counterclockwise (key Alt+U) or clockwise
using the menu item Rotation clockwise (key
Ctrl+U).
Display of alternative coordinates
There is a possibility to display alternative x and y coordinates using so called georeferencing technique.
If there is a file NAME.ARs (s is a suffix) or
NAME.AR containing three or six pairs of corresponding points in original cartesian
coordinates and in alternative coordinates (for example WGS84), the alternative coordinates of cursor are displayed
in square brackets in the program bar. There is also a possibility to save basic data with the alternative coordinates
in the file NAME.ACs using the menu item Output / Alternative coordinates.
The following list contains an example of georeferencing file - the first two columns are x and y coordinates of points in
Gauss-Kruger coordinate system, the second two columns are corresponding coordinates of WGS84 coordinate system.
3511078.77 5560593.11 15.153347261 50.176152875
3590986.91 5555350.91 16.270562075 50.122175817
3519454.31 5515257.34 15.268321319 49.768353636
3579975.16 5515141.73 16.108291028 49.762326103
3529027.56 5476784.13 15.398379111 49.422064694
3598566.69 5478933.50 16.357198764 49.434113817
If there is a linear transformation between the two coordinate systems, only three points are sufficient for
precise transformation of coordinates.
For common geodetic coordinate systems, six points ensure reasonable precision of transformation in the range up to
100 kilometres.
Digitization
Digitization is intended for manipulating basic map objects. After selecting any item in the menu Digitization, the program enters digitization mode with a special menu. In this mode the cursor has the shape of a little cross and cursor keys change the position of the cursor (and not the position of the map). The step of the cursor movement can be changed with shortcut keys "1", "2", "3", "4" or "5". Of course, the location of the cursor can be changed using the mouse too. While the cursor is being moved, the main window bar shows the coordinates of the cursor. Additional information about digitization can be found in the SurGe Tutorial.
The menu Points enables to add or delete points XYZ or change their z-coordinate. A new point is specified by the cross cursor position when key B is pressed (or left mouse button). The point next to the cursor position is deleted using key Ctrl+B (or right mouse button). Key Shift+B is intended for setting a new z-coordinate of the point, which is next to the cursor position.
The menu item Boundaries is intended for creating and correcting the boundary. The boundary is handled as a horizontal polyline. Key Ctrl+H (or right mouse button) ends the definition of one boundary and starts a new one. A new point of the boundary polyline (including the first one) is defined by the position of the cursor when shortcut key H (or left mouse button) is pressed. The last defined point can be deleted by shortcut key D. Shortcut key U is intended for closing the boundary (for creating a boundary as a closed curve). Any point of the boundary can be marked using shortcut key Shift+H and then moved to a new position by shortcut key M. The last item under menu Boundaries creates a boundary as a convex envelope (convex hull) of points XYZ. The number entered in the following dialog box enables to scale the convex envelope. Using this feature you can change size of interpolation area and to remove grid values outside of the convex envelope - see the section How to modify the size and the shape of the grid area in the SurGe Tutorial.
Spatial polylines can be digitized using the menu
Polylines. Shortcut key Ctrl+L (or right mouse button)
ends the creation of one polyline and starts another. A new point is defined
by shortcut key L (or left mouse button), the last point can be deleted
using shortcut key D. As in the case of the boundary, the polyline
can be closed by shortcut key U. When defining a new point, the
corresponding z-coordinate must be specified in the provided dialog
box. If the z-coordinates of the polyline are to be the same, there
is the possibility to predefine a constant z-coordinate by shortcut
key F. This function can be canceled by shortcut key Ctrl+F.
Any point of the boundary can be marked using shortcut key Shift+L
and then moved to a new position by shortcut key M.
If a polyline is created, it is necessary to set its number of internal points.
In fact, SURGEF does not work with polylines directly - it works
only with the points, which are evenly distributed along the polyline. To
specify the number of these points, move the cross cursor near the polyline
and press shortcut key P. Then in the provided dialog box enter
the number of internal points (typical values are 50 - 200).
The menu item Faults enables to edit sequences of line segments (in horizontal plain), at which the resulting surface has to be discontinuous. Each fault is defined by a pair of points. A new point of the fault is specified by the cursor position when shortcut key Z is pressed (or left mouse button). The fault can be deleted using shortcut key D (or right mouse button) - the one whose center is closest to the cursor position. The position of the fault end point can be changed by shortcut key Shift+Z.
In the digitization mode there is also the possibility to modify isolines. The first function, Mark isoline (shortcut key X), serves for selecting an isoline. After selection, the isoline is represented by a sequence of white points. If the display is (due to operations) damaged, it can be restored using the menu item Redraw modified isoline (shortcut key A). The selected isoline can be smoothed (Smooth isoline, shortcut key S) as a whole, or partially (Smooth between points, shortcut key V) between the points selected using the menu items Mark first point (shortcut key Alt+1) and Mark second point (shortcut key Alt+2). There is also the possibility to mark a single isoline point (Mark point, shortcut key Shift+I) and move it (Move point, shortcut key M). A certain number (the number can be changed using Change number n, shortcut key Ctrl+Q) of isoline points can be moved by Move n points (shortcut key Q). The modified isoline can be saved to the file NAME.VRz using the menu item Save modified isoline (shortcut key Ctrl+I). Write marked isoline (shortcut key W) enables to store the selected isoline as the ASCII file IZ.$$$.
The menu Cross-section enables
to specify a polyline in the plane (x,y), which defines the cross-section
through the created surface. The first or next point of the cross-section
can be specified using the menu item shortcut key G (or left
mouse button). Points are displayed in red. A polyline connecting the red
points is displayed using the menu item Display cross-section line
(shortcut key E). All specified cross-section points can be
deleted by Delete specified cross-section (shortcut key
Ctrl+G) and then a new cross-section can be defined. In the cross-section
mode (see below), there is a possibility to save the position of the
cross-section and name it with a single letter. The function Select
saved cross-section (shortcut key Shift+G) enables to select
one or more saved cross-sections. When the cross-section is defined, the
key Enter or right mouse button is used for creating the
cross-section through the surface(s) and entering cross-section mode.
Cross-sections
Cross-section mode is invoked by the menu item Cross-section / Display cross-section (shortcut key Enter) in the digitization mode. The following dialog box appears:
The suffix convention enables to create a cross-section through several surfaces
(layers). In the presented dialogue box, the suffix of the surface and a
short description can be specified. The cross-section is constructed through
all specified surfaces and displayed in a 2D plot. There is a special menu
in the cross-section mode. The title of the plot and description of axes
can be modified using menu items Graph title (shortcut
key N), Description of x axis (shortcut key
X) and Description of y axis (shortcut key
Y). The range of the y axis can be changed by Change
range of y axis (shortcut key Ctrl+Y). The last menu item,
Save cross-section (shortcut key U) enables to
save the position of the cross-section polyline to the file
NAME.RZY for later use in digitization
mode (see above). The name of the cross-section must be specified as
a single character A-I.
Background
In some cases it is useful to display texts and some characteristic terrain
lines and / or objects to improve orientation in the map. For this purpose,
there is a special digitization level named Background under
the menu Digitization. Objects of background are handled as
polylines and here are the following functions for creating, changing or
deleting objects from background:
| Start new object (Ctrl+B) | ends construction of the current object and starts construction of a new one |
| New point of object (B) | a new point of object polyline is specified at cursor position |
| Delete last point (D) | the last specified point is deleted |
| Close polygon (U) | the next point will be at the same position as the first point of the polyline |
| Mark point (Shift+B) | mark the nearest point of the polyline by white color |
| Move point (M) | move marked point to a new position |
| New text (T) | specify text string, font size, font thickness, font color and text orientation |
| Change text (Shift T) | change text string, font size, font thickness, font color and text orientation |
Three functions are intended for manipulation with whole objects:
| Select object/text (S) | select / unselect the object next to the cursor. Selected object is displayed by violet color |
| Move selected object/text (Ctrl+M) | move whole object; moving vector is given by marked point and the cursor position |
| Delete selected object/text (Ctrl+D) | delete selected object |
All background objects can be saved to file
NAME.BG by the last menu item
Save background (shortcut key W).
Detail of map
The shortcut key Ctrl D pressed in the move / zoom mode enables to
enter a special digitization mode, where using the mouse left button a
rectangular region can be selected to determine a detail of map. As soon
as the detail is selected, new instance of SurGe containing only the points
from the specified region is run (selected points are first saved in the
file MAPDET#.DTs, which can be renamed appropriately and then used
as a new data file). This function is helpful (especially when used with
the shortcut key Alt S) in cases when there are clusters containing
a great number of points in the map and the user wants to see the points
distribution only in a certain small region.
Model grid
The function Model grid in the menu
Digitization enables to create or to modify an irregular
rectangular grid for a mathematical finite difference model, for example
MODFLOW. The program switches into a special mode with its own menu. In the
menu there are shortcut keys which can be used for creating the irregular
rectangular grid. The model grid is stored in the ASCII file
NAME.XY.
Output
Under Output menu, the following items can be selected:
Grid as ASCII file
z-values of the surface are stored in ASCII format in the file
NAME.GRs. This format is compatible with
the grid file format of the program Surfer (Golden Software) - see the
next section.
Grid as GRASS file
z-values of the surface are stored in ASCII format in the file
NAMEs.TXT. This file, compatible with GRASS
GIS system, can be imported as a raster file into LandSerf, a
free application for the visualization and analysis of surfaces.
Grid as ArcGIS file
z-values of the surface are stored in ASCII format in the file
NAMEs.GRD. This file, compatible with ArcGIS
system, can be imported as a raster file into LandSerf, a free application
for the visualization and analysis of surfaces.
Z-values at points
This function reads X and Y coordinates from
the specified input ASCII file, computes corresponding Z
value at surface and writes the result (X,
Y and Z values) into specified output file.
The input file must contain X and Y
coordinates in the first two items of each row. The rest of row is copied
into output file.
The format of the input file rows must be:
X Y [any-text]
The format of the output file rows is:
X Y Z [any-text]
Such a type of output provides very important universal tool for transferring
of surface z-values into any set of points located in the interpolation /
approximation function domain. For example, if the x and y coordinates in
the input file are triangle vertexes of an unstructured grid (for example
the grid of finite element model), then this tool provides conversion between
structured and unstructured grids.
Grid as DAT file
The grid values are stored in the format of the basic data file (see the
next section) NAME.GDs. The file containing
grid values in this format is also referred as a generic ASCII grid file
and it is used in many GIS systems such as Global Mapper.
Isolines as ASCII file
The isolines are stored in the ASCII format file
NAMEa.VRs.
NPR file
Surface values are interpolated into block centers of the model grid and
stored in the ASCII file NAME.NPs. The model
grid NAME.XY (see above) must exist.
Remark:
A grid compatible with Surfer (stored in ASCII format) can be read using
the menu item File / Read grid from ASCII file.
Format of input / output
files
The name of input / output files is referred to as the name of project or basic name (in this documentation denoted as NAME). The first and second characters of the file name extension indicate the type of data and the third character (if any) has an arbitrary suffix, denoted in this documentation as s. The suffix enables to distinguish between several surfaces with the same boundary and / or with the same faults. It can be any character allowed in the extension of a file name. Recommended are letters A-Z or digits 0-9.
The basic input file is an ordinary ASCII file which has a name in the form NAME.DTs, where NAME is the name of the project, DT is the extension indicating the type of data (points XYZ) and s is the suffix. Each row of the file has this format:
X Y Z L
where X, Y and Z are x, y and z coordinates of the points XYZ and L is the label of the point (min. 1, max. 23 characters). Items in a row must be separated by at least one space. The number of XYZ points (non-comment rows in the file) is limited only by available computer memory. The basic input file is the only file, which can have comment rows starting with the character # in the first column. An example of an input file can be found in the SurGe Tutorial.
Other input / output files can be:
The program SURGEF, which implements the interpolation / approximation method ABOS, can be used as an external console program called from user application, for example:
If you want to use SURGEF by this way, your application must provide:
1. Input file(s) for SURGEF (at least the basic input file must exist in the working directory - see the previous section).
2. The application must create an ASCII file PAR.3D (parametric file for
SURGEF):
| Row | Value |
Example | Meaning |
1. |
string |
ex1 |
Name of basic input file |
2. |
character |
a |
One-character suffix |
3. |
Y / N / C [,scale] |
C,1.2 |
Boundary has / has not to be used. If C is used, the boundary will be created as a convex envelope of input points. The following optional number than can be used as a scale of boundary (default value is 1.1). |
4. |
Y / N |
N |
Faults has / has not to be used |
5. |
Y / N |
N |
Additional points has / has not to be used |
6. |
Y / N |
N |
Polylines has / has not to be used |
7. |
Y / N |
Y |
Basic points has / has not to be used |
8. |
0-9999 |
500 |
Value of filter |
9. |
5-99 [, 0 / 5-5555, 0 / 5-5555] |
99, 300, 200 |
Grid enlargement, gird dimension(s) |
10. |
0-4, 0 / 1 |
1, 1 |
Degree of linear tensioning, fast convergence off / on |
11. |
0-99, 0-999.99 [,0-9999] |
1, 0.5, 50 |
Precision, smoothing, number of smoothing cycles |
12. |
Y / N |
N |
Blank / do not blank grid outside the boundary |
13. |
Y / N |
N |
Create / do not create NP file |
14. |
Y / N |
Y |
Create / do not create ASCII grid file |
[file-name-xy] |
points.xy |
Input file containing x and y coordinates of points as first two items | |
[16.] |
[file-name-xyz] |
points.xyz |
Output file containing records from file-name-xy + surface values |
3. Now the SURGEF can be called from the application - for example by the following command in C language (do not forget N parameter, which means "normal" interpolation; for other interpolation modes you can use L (linear) or C (convex) - see How to use different modes of interpolation in the Surge Tutorial):
system("C:\SurGe\SURGEF.EXE N");
or
system("C:\SurGe\SURGEF.EXE N A");
The second command line parameter means, that SURGEF will run automatically without waiting
for answers to prompts and the following letters can be used:
A ... external grid will not be read - see How to utilize an existing
grid in the SurGe Tutorial.
Y ... external grid will be read - see How to utilize an existing
grid in the SurGe Tutorial. In this case the external grid must exist.
Q ... preview mode, very fast interpolation without smoothing - see How to use different modes of
interpolation in the SurGe Tutorial.
There are no differences between registered and unregistered version of SURGEF. Of course, SURGEF can be also run "manually" as a console application, for example using the command:
E:\SurGeData>c:\SurGe\surgef.exe N Y
The menu item Miscellaneous / Grid info displays the information about grid size and coordinate ranges; the menu item Miscellaneous / Objects info displays information about the number of the objects.
The following tables contain commonly used shortcut keys.
Display
| N | labels of points |
| K | z-coordinates of points |
| C | raster color map |
| I | isolines |
| Alt+Q | shadowed relief |
| Alt+S | color scale |
| Ctrl+S | mesh scale |
| Ctrl+E | mesh labels |
| R | refresh display |
| Ctrl+R | change background color |
| O | background |
| Ctrl+C | saved cross-section(s) |
| Alt+W | highlight specified label of point |
Move/zoom
| Ctrl+arrow keys | move map objects |
| Ctrl+PgUp | zoom in map objects |
| Ctrl+PgDn | zoom out map objects |
The shortcut key Ctrl+L pressed in the basic display enables to edit colors used in the raster map and 3D display:
There are three color areas - the two on the left side display a color cube and the one on the right side contains color strips of palette.
The color cube is a method how to generate all colors defined by three components of the so called RGB (red, green and blue) color model. The intensity of the red component can be selected in the x-direction of the square, the intensity of the green component can be selected in the y-direction. The intensity of the blue component (z-direction) can be selected in the narrow rectangle next to the square.
Colors in all directions can be changed by selecting a color in the z-direction - try shortcut keys R,G and B.
The actual color (marked by a small white rectangle) can be selected in the strips on the right side - using left mouse button or using shortcut keys Shift+arrow up or Shift+arrow down. There is also the possibility to interpolate between two colors marked as 1 and 2. The color 1 can be marked by Ctrl+1 and color 2 by Ctrl+2. The interpolation can be performed using Ctrl+I. Using the interpolation, gradual color shades can be obtained between color 1 and 2 - see the above example, where color 1 is blue and color 2 is white.
The modified color palette can be saved into a file with extension .pal using the shortcut key Ctrl+S and loaded using Ctrl+L.
In addition to the default color palette (file 256.pal) there are four other predefined color palettes: Globe.pal, Polar.pal, Steel.pal and Topo.pal.
If faults are used in the created map, SURGEF.EXE may end with the following message:
Error in faults definition.
Return to SurGe and press key U to see undefined nodes of grid.
The next picture illustrates such situation:
In this configuration of points and faults there is an area, from which no point can be "seen over" faults. This area is marked by white points in the next picture:
The white points are displayed by shortcut key U in move/zoom mode. It means, there are grid nodes, which have undefined values. In this case, the interpolation / approximation cannot be performed. The only solution of this situation is to add a point - for example like this:
