Breaklines in surface modeling

Breaklines define and control surface behavior in terms of smoothness and continuity. As their name implies, breaklines are linear features. They have a significant effect in terms of describing surface behavior when incorporated in a surface model. Breaklines can describe and enforce a change in the behavior of the surface. Z-values along a breakline can be constant or can vary throughout its length.

Three types of breaklines can be employed to describe surface behavior:

• Soft breaklines
• Hard breaklines, and
• Faults

Soft breaklines

Soft breaklines are used to ensure that known z-values along a linear feature are maintained in a triangulated irregular network (TIN). Soft breaklines can also be used to ensure that linear features and polygon edges are maintained in a TIN surface model by enforcing the breakline as TIN edges. However, soft breaklines do not define interruptions in surface smoothness.

Here is an example of how the inclusion of a soft breakline can enforce a different surface behavior. Note how the TIN builder has added extra vertices along the breakline to ensure that the line is maintained in the TIN. The z-values for these new nodes have been derived by linear interpolation along the breakline.

The input data to build a TIN includes four points and one line with two nodes.

The TIN that results when the points and nodes are processed as mass points

When the line is enforced as a breakline, the line is maintained in the TIN. Note the z-values of the introduced nodes.

As with all breaklines, soft breaklines can have constant or varying z-values. For example, a section of pipe with a constant elevation can be defined as a soft breakline. In contrast, a highway with fluctuating elevation can be incorporated into a TIN surface model as a soft breakline.

Hard breaklines

Hard breaklines define interruptions in surface smoothness. They are probably the most common and easily understood type of a breakline. Hard breaklines are typically used to define streams, ridges, shorelines, building footprints, dams, and other locations of abrupt surface change.

Here, a smooth surface is interrupted as it encounters a lakeshore. The bold breakline is included in the surface model to define the boundary between two distinct types of surface behavior. The shoreline denotes the sharp transition between the planar surface behavior of the lake and the smooth surface of the surrounding terrain.

In the case of a hard breakline defining a stream, the breakline has varying z-values throughout its length. The surface exhibits smooth behavior on both sides of the stream, but the slope normals are radically different on opposite sides of the breakline.

Faults

Faults represent interruptions in surface continuity. Geologic faults are probably the most common type of fault, and their degree of surface continuity interruption is referred to as displacement. In the case below, the earth’s surface has been displaced vertically, causing a stair-step discontinuity in the surface. Vertical faults have more than one z-value for a given x,y location; an elevation exists at the same x,y location at both the top and bottom of the fault.

A vertical fault has more than one z-value at a given x,y location.

Faults aren't limited to the vertical plane but can be shifted, or transformed, in both the vertical and horizontal dimensions. Because functional surfaces are capable of storing only one z-value for a given x,y location, they are not capable of directly storing vertical faults. It is possible to represent a nearly vertical fault as two parallel breaklines: one containing surface z-values at the top of the fault, and a second with z-values at the bottom.

A transform fault, showing displacement in the vertical and horizontal planes. Offset upper and lower portions of a vertical fault to approximate it on a functional surface.

Using breaklines in surface modeling

The difference between hard and soft breaklines can only be noticed when using an interpolator with a TIN to produce a smooth surface (for example, the Natural Neighbors interpolator used in the geoprocessing TIN To Raster tool). Hard breaklines can be used to model an abrupt change in surface behavior caused by features, such as the boundary of a water body, a change in material, a building footprint, or a road. Hard breaklines can also be used to enhance the appearance of linear features in surface views and contour maps where sharp drainage or ridgelines are present. Soft breaklines are used to add information about the surface without implying a change in the surface behavior across the line. Examples include a survey line or study area boundary used to define the extent of a surface model.