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3D Surface Modelling

ISOMAP is the module that is used to calculate and render surfaces through contour lines or coloured and shaded areas with a high degree of precision.

The program allows the representation of the surface both in topographic map and perspective view forms.
The calculation is performed in two stages.

The first stage consists of creating a regular grid from a collection of arbitrarily positioned points.

The second stage consists of drawing the surface using the previously created grid.
The first stage can be performed using three methods: the inverse distance method, the kriging method, and a new interpolation and extrapolation method based on a weighted average of polynomial surfaces.

The use of this polynomial algorithm makes it possible to generate points that are external to the area of the sampled locations in such a way as to maintain the trend of the surface, even when this surface cannot be approximated by a simple horizontal plane.
This feature is especially useful for those problems that deal with the surface gradient, such as flow line tracing or rockfall analysis. The commonly used extrapolation algorithms based on the weighted average (including kriging) can lead to large errors, for example to the inversion of the flow direction in the peripheral areas of the map.

The use of a polynomial algorithm to create a grid also yields a more realistic surface of the area where the sampled locations can be found, as the evaluation is less sensitive to the spatial distribution and point density.
The regular square grid is then interpolated with bi-cubic splines to obtain a continuous surface that is continuously differentiable and which passes through the grid nodes.

The ISOMAP module has the following basic operations:

  • Grid Generation
  • Slope Map
  • Exposure Map
  • Grid Difference
  • Linear Transformation
  • Filtering
  • Grid Duplication
  • DTM Import

There are commands to execute transformations and operations between models (conversion of measurement units, linear transformations, construction of contour lines related to thickness and depth) and specific commands for the treatment of gravimetric and magnetometric data, such as the separation, obtained through digital filtering, of the local and regional anomalies.

The user can structure equidistances and the graphic quality of the contour lines.

Flow lines or vectors can be inserted to represent gradients or the dip direction. The representation can be limited to certain intervals and/or areas.

The program enables the generation of Map, Wireframe View, or Solid View. The view point distance and light vector can be determined.



Here are some examples of program-generated graphic outputs:

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