DTM Products

The 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.

See also:
SPRING reference information
How to generate a Rectangular Grid
How to generate a triangular grid
About Grids and Interpolators


Image Generation

Learn more about generation of Gray Level and Shaded Images in SPRING

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.

  • Gray Level Image

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.

mnt_imaNC.gif - 26652 Bytes


  • Shaded Image

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:

mnt_20.gif - 1220 Bytes

where:

q is the surface inclination angle.
zi is the value of the elevation for the i-th point on the grid.
f is the value of the exaggeration factor.
R is the value of the grid resolution element.

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.


mnt_imaSOM.gif - 28206 Bytes


DTM Products


Generation of Slopes or Aspect Maps

Learn more about the Generation of Slopes or Aspect Maps in SPRING

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:

mnt_21.gif - 1508 Bytes

The gradient is given by equation:

mnt_22.gif - 1467 Bytes

Where z is the altitude and x, and y are the axial coordinates.

The exposition is given by equation:

mnt_23.gif - 1430 Bytes

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):


  1. generate a rectangular altimetry grid from samples or from a triangular grid that was obtained from samples, or simply an altimetry triangular grid;
  2. generate a declivity or exposition grid from the altimetry grid ( check the procedure);
  3. slice one of the grids above in intervals of declivity or exposition ( check how to proceed with DTM Slicing), generating a map of the thematic model (in raster presentation). The classes of declivity or exposition and their corresponding categories should be previously defined in the database.


DTM Products



DTM Slicing

Learn more about DTM slicing in SPRING

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.

mnt_fat.gif - 13752 Bytes

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.

DTM Products



Generation of Contour Lines

Learn more about how to generate contour lines in SPRING

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...


mnt_5.gif - 18411 Bytes
- 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).


mnt_5a.gif - 6787 Bytes
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).


mnt_5b.gif - 4149 Bytes
Contour lines generated from a rectangular grid.




DTM Products



3D Visualization

Learn more about 3D Visualization in SPRING

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.


mnt_3d.gif - 19214 Bytes

The following prerequisites are needed for a 3D visualization:

a) Availability of an (texture) image generated from a digital terrain model to provide the relief information;
b) Availability of an (relief) image that you wish to superimpose on the digital terrain model;
c) Activate and present a visualization display.


DTM Products



Executing a Profile

Learn more about executing a Profile in SPRING

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" unix.gif - 943 Bytes our ALT+PrintScreen windows.gif - 1353 Bytes , to save the graph in a file.


DTM Products



Volume Calculation

Learn more about Volume Calculation in SPRING

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
Vt = total volume of the area;
Ac = constant, is the value of the area corresponding to each cell;

Zi = the value of the elevation of each cell, calculated accordingly to the used interpolator (see chapter 2, volume 3).

n = cell number

thus we have,

mnt_perfil_eq1.gif - 1079 Bytes

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:


mnt_perfil_eq2.gif - 1073 Bytes

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.


DTM Products


See also:
How to edit a DTM IL
How to generate a Rectangular Grid
How to generate a Triangular Grid

Grid Generation