Settings for TIN

This section explains the settings for creating a TIN surface using the ground surface tool.

Flat triangle removal options

When a TIN surface is created from contour lines, some resulting triangles have their three vertices on the same contour line or on lines with the same height are called flat triangles. These flat triangles have three vertices with exactly the same height. This is an undesirable defect it because does not represent the real surface (there are no real flat summits) and prevents the correct calculation of water drainage (when water reaches a flat triangle it has no direction to follow).

There are three methods to remove flat triangles:

• Control lines to swap edges

• Adding interpolated fictive points

• In valleys, create a continuous fall

Note: If no breaklines are selected, the resulting flat triangles cannot be removed, as the resulting TIN is created from a cloud of points without line information.

Defining control lines to swap edges

A control line is an enhanced breakline to prevent the appearance of flat triangles connected to it. If a flat triangle appears is removed swapping its edge.

Figure: An area of flat triangles and its removal swapping edges: the contour lines have been selected as 'Control Lines'.

• A - Contour lines, marked as breaklines.

• B - Flat triangles, as a result of connecting the same contour line (all points of every flat triangle have the same height).

• C - Contour lines, marked as control lines.

• D - Swapped edges to prevent flat triangles.

If after swapping the edges of the flat triangles the resulting triangles are still flat, no swap is applied. If the area of the flat triangles has a complex form, then the swapping is applied to all swappable edges in order to maintain the integrity of the TIN.

Figure: Area of flat triangles with 'swap edges' applied.

• A - Flat triangles.

• B - Swapped edges.

• C - Remaining flat triangles: no swap edge can be applied on this area to remove flat triangles.

If control lines are selected, the resulting TIN contains exactly the same number of vertex and triangles as the TIN without control lines, but minimizes the number of flat triangles. To remove more flat triangles, an additional flat triangle removal method must be selected, such as the add fictive points or add fictive points in descending order.

Example of flat triangles removed with 'swap edges', defining the contour lines as 'Control Lines'.

Adding interpolated fictive points

This method removes flat triangles by adding new points to some edges and splitting the triangles to obtain non-flat triangles. When an edge between two triangles is split, a new vertex is added to the middle of the segment with a new height to obtain four triangles that are non-flat.

The height of the new vertex is obtained, when possible, from the interpolation of the neighbor areas.

Figure: Flat triangles on a previously flat summit removed using 'Adding interpolated fictive points'.

As the new height is obtained through interpolation, valleys can appear as 'hollows' or 'lakes' not present in real surfaces. To prevent this the method 'In valleys, create a continuous fall' must be selected.

Figure: Profile of an area with and without flat triangles. The 'Adding interpolated fictive points' has been selected.

In valleys, create a continuous fall

This is a flat triangle removal method equivalent to the previous one, but in valleys, the obtained height of the new vertices is descendent to the valley, in order to let the water flow downside as a river. In the case of ridges or summits, the result is the same as the previous method.

Figure: Profile of an area previously with flat triangles, comparing the two flat triangle removal methods.

• A - Interpolated new points.

• B - Continuous fall in the valley.

Both methods remove flat edges adding a new vertex with a different height to the middle of the edge.

Figure: Flat triangles removed using the interpolation method.

• A - Central part of the valley.

• B - Border of the valley, with a higher height than A. This would produce a lake around A if water is present.

Figure: Flat triangles removed with the continuous fall method.

• A - Central part of the valley.

• B - Exit of the valley, with its height lower than the height in A. The running water will go from A to B and exit the valley to reach lower levels.

Next topic: Sub Surface