![]() DTM ProductsThe products obtained from the grids (triangular and rectangular) are classified by functions and available from the SPRING main menu. They require that the Infolayer contains the representations Grid and TIN on the “Control Panel”. Therefore, if you do not have an available grid, see here how to create it.
Image Generation
Just the analysis of a rectangular or triangular grid does not give us the idea of the parameters being modeled. It is recommended to transform the grid in a product that is easier to be analyzed. SPRING allows the generation of gray level images (GL) from a DTM considering the interval between 0 (black) and 255 (white). The real numbers of the grid are transformed into integer values, inside the gray level interval, or in a shaded image where the azimuth and elevation angles of a light source are considered.
The generation of an image for the digital terrain model, where the pixels will contain the gray levels, consists in distributing the minimum and maximum values for the contour lines heights (z value), obtained from the rectangular grid, over the gray levels (from 0 to 255) using the linear equation (y=ax+b). The output image resolution (in meters) is the same as the
rectangular grid that generated it. To generate an image with xy
resolution different from the original it is necessary to generate
another grid with the desired resolution and then generate the gray
level image. That is because each cell in the grid will correspond to
exactly one pixel in the output image where the minimum values of the
elevation are represented by dark pixels while the maximum are
represented as light pixels. The figure below shows some samples (contour lines + spot heights) and the image in gray levels obtained after generating a grid with these samples.
![]()
The shaded image generated from a digital terrain model in SPRING allows the visualization of differences in relief in a certain region. A shaded image is generated from regular grid over which a illumination model is applied. This illumination model determines the intensity of the reflected light in a point on the surface considering a certain light source. The model depends on the light source that can be natural light or other source, and the surface reflections. The natural light provides an intensity of illumination a from the surface and can be modeled by I =IaKa.., where Ia is the intensity of the natural light and Ka is the material reflection coefficient. The reflection depends on the surface material (Kd), light source intensity (Ip) and angle between the light source direction and the normal on the surface (cosq), described by the equation IpKdcosq. The illumination model composed by the natural light and reflection is described by the following equation, where Kd is considered equal for all surfaces: I =IaKa + IpKdcosq, The direction of the light source is defined by the azimuth, referenced to the North (Y axis), measured in the clockwise direction and by the elevation angle referenced to the XY plane. In SPRING the minimum intensity of the surface illumination is equal to IaKd, which is equivalent to gray level 30, that is, when the angle between the light and the surface normal is 90°. The maximum light intensity is equal to the gray level 230 and occurs when IpKdcosq corresponds to gray level 200, that is, when the angle between the light source and the surface normal is 0°. For the calculation of the cosine q, that is the angle between
the surface normal and the light source direction, the scalar product
cosq = N . L is calculated, where N is the surface normal vector,
calculated from the partial derivatives of the values of x, y, and z of
the rectangular grid, that are constant for each cell. And the vector L
is defined from the direction of the observer, that is, the q azimuth,
measured in clockwise direction from Y, and the elevation angle from
the XY plane. An exaggeration of the relief is employed to increase the
vertical scale in comparison to the horizontal scale in the shaded
image, that allows for a better visualization of the surface forms and
structures. Such exaggeration causes an increase in the value of the
original inclination angle of the surface and is calculated from the
factor obtained by the following equation: ![]()
where: q is the surface inclination angle. The figure below presents a SPRING window with a shaded image,
with the following illumination parameters: Azimuth (degrees) = 45,
Elevation (degrees) = 45 and Relief Exaggeration = 2.70. ![]() ![]() Generation of Slopes or Aspect Maps
Declivity is the terrain surface inclination relative
to the horizontal plane. Considering a digital terrain model (DTM) of
altimetry data extracted from a topographic map and the drawing of a
plane tangent to that surface in a certain point (P), the
declivity in P will correspond to the inclination of such plane,
relative to the horizontal plane. In some applications of interest to geologists,
geomorphologists, etc... it is sometimes necessary to find regions with
little geologic accidents and that are exposed to the sun during a
certain period of the day. To answer these questions the declivity
provides two components: the gradient and the exposition. The gradient is the maximum rate of variation of the elevation, can be measured in degrees (0 to 90°) or as a percentage (%), in SPRING it is referenced as declivity, while the exposition is the direction of such variation measured in degrees (0 to 360°). The two components of the declivity (gradient and aspect) are
calculated from partial derivatives of first and second order
calculated on a grid (rectangular or triangular) resulting from the
values of surface elevation. For every point on this grid the partial
derivatives are calculated, from the values of elevation in a 3 x 3
window of points that move over the grid. The result corresponds to two
new grids: one is the gradient and the other is the exposition. The declivity, or
gradient, is calculated by the following equation: ![]() The gradient is given
by equation: ![]() Where z is the altitude and x, and y are the axial coordinates. The exposition is
given by equation: ![]() These partial derivatives are calculated differently according
to the type of the original grid (rectangular or triangular). The following procedures are needed for a declivity or
exposition map (see the figure below):
![]() ![]() DTM Slicing Slicing consists in
generating a thematic image from a rectangular
grid. The themes in the resulting thematic image correspond to
intervals of elevation values, called slices in SPRING (see figure
below). This way, an Information Layer of the numeric category will
originate an Information Layer of the thematic category representing a
particular aspect of the digital terrain model, consequently every slice should be associated to a
thematic class previously defined in the conceptual scheme of the loaded
Database. ![]() The definition of the intervals of elevation or slices, will
depend upon the variation in the grid values that we want to enhance. A
thematic image resulting from the slicing of the grid will provide a
pictorial vision of the model, at the same time that, being a thematic
Information Layer, can be used in boolean operations of the thematic
data crossing type. Slicing can also be performed by the operations
defined by the user in the field algebra, using a program in LEGAL. For the definition of the elevation intervals there is a
certain feature in SPRING to edit it in two modes: fixed and variable.
In the fixed mode the user defines manually the elevation intervals he
desires, while in the variable mode these intervals are automatically
set to be evenly distributed, according to a step provided by the
user. ![]() Generation of Contour Lines Contour Lines are curves that join points on the surface that
have the same elevation value (see figure below). The meaning of the elevation value depends on the physical
magnitude of the surface you want to model. Thus, for a surface
representing temperatures we obtain the isotherm, for the weather
forecast, the isobars, for terrain altimetry, the contour lines, etc...
![]() - Contour Lines of terrain altimetry. Contour lines can be visualized as a projection on the (x,y)
plane of the intersections between the surface and a family of
equidistant horizontal planes (see the figure below). ![]() Contour Lines of elevation z obtained by the projection on the xy plane. The isovalue curves have some important properties: they are
all closed unless they intercept the defined boundaries of the map and
never cross each other. SPRING generates contour lines or isovalue curves from a
digital terrain model (DTM) of rectangular or triangular form by using
the cell method. In this method, for each cell are generated all the
isovalue curves that intercept that cell. The line segments are stored
so that, in a final phase, they can be connected to form a closed
isovalue curve (in case they do not reach the boundary of the region of
interest) (see the figure below). ![]() Contour lines generated from a rectangular grid.
![]() 3D Visualization This feature allows the three dimensional visualization of
data (monochromatic images or color composites), with the possibility
of modifying the position of the observer. The 3D visualization is made from the
selection of two images, the relief
image and the texture image.
The information layer containing the relief
image will provide the 3D visualization with the surface elevation effect, while the
information layer containing the texture
image will provide the surface
that will be presented in 3D. The figure below shows the result of a 3D view, in parallel
projection, of a shaded image, superimposed tot he altimetry grid. Only
ILs of the image model can be used for this function. ![]() The following prerequisites are needed for a 3D visualization:
![]() Executing a Profile Data like DTM, with a topographic surface, can be represented
through profiles that describe the elevation of points (values of z)
along a line. Such application is performed over data from the digital
model (grids or contour lines) in raster format, presenting in a graph
the values of z of the points that define the trajectory. The profile is drawn from a line trajectory defined by the
user or from lines that were previously digitized and that belong to
the thematic, cadastral, or network data model. To consider the lines on the Information Layers of the above
mentioned data models it is necessary that they are loaded and active
in the same visualization display. Up to 5 trajectories can be selected i a same IL and
their profiles presented in one same graph. The graphs as of now cannot
be printed directly from SPRING, but we suggest the use of any screen
capture software, like "xv"
![]() Volume Calculation The calculation of volumes in SPRING is made from areas, that
is, closed polygons of the thematic or cadastral models and rectangular
or triangular grids of the digital model. From a grid we calculate the
central value of each cell, corresponding to the elevation (Z axis),
and multiply by the value of the area of the cell. This way, the volume
is given by the following equation: Vt = Ac*Z1 + Ac*Z2 + Ac*Z3 + ...Ac*Zn thus we have,
![]() The volume of the cut
and the volume of the fill are
calculated considering a base elevation provided by the user. The parts
above the base elevation correspond to the cut volume while those below
it represent the fill volume. The ideal elevation represent the most adequate value for the
volume of excavation, performed in the cut area, to be deposited in the
fill area, so that a balance is kept between the masses and volume of
material removed and deposited. The ideal elevation (Ci) is
calculated from the following equation: ![]() Volumes can be calculated for every area in an IL (total
volume) or for cursor selected areas (partial volume). The results are presented in a table and can be saved on disk.
The volume calculations for Dams
and Reservoirs are not
available in the present version. ![]()
![]() ![]() |