Similar to the triangulation transform, the constrained triangulation transform creates a constrained Delaunay triangulation of a point set by treating the points as nodes in a network and drawing links between them that divides the region between the points into triangular tiles.
There are two differences between triangulation and constrained triangulation:
· Unlike the triangulation transform, the constrained triangulation transform will not draw links between pre-existent line segments.
· The triangulation transform operates only on point objects. The constrained triangulation transform can operate on any object, and will treat the coordinates of lines and areas (inflection points) as points for the triangulation.
There are three transform operators for constrained triangulation:
· The Constrained Triangulation Lines operator creates lines for the triangulation.
· The Constrained Triangulation Areas operator creates areas for the triangulation.
· The Constrained Triangulation operator creates both lines and areas for the triangulation.
See the Transform - Triangulation topic for a general discussion of triangulation.
Example
If we take a set of points as shown above and apply the Triangulation Lines transform operator...
...we can create a triangulation consisting of lines, shown in blue above.
Suppose, however, if we had started with both points and lines (shown in yellow) as seen above and applied the Triangulation Lines transform operator.
The result would be the same triangulation, with some of the lines created for the triangulation crossing the pre-existing yellow lines. There are many applications where we would not want a triangulation crossing pre-existing lines. For example, perhaps such lines mark the boundaries between contours or show highways or property boundaries which the triangulation should not cut. We can respect pre-existing lines by using constrained triangulation.
Suppose we start with a set of points and lines and then apply the Constrained Triangulation Lines transform operator.
The result shown in light violet color shows that none of the triangulation lines cross any of the pre-existing lines.
We can see the difference between the lines created by triangulation and those created by constrained triangulation by showing the two together as layers in a map with constrained triangulation lines shown in light violet color and triangulation lines shown in thinner blue lines.
The red lines above show lines created in triangulation that are not created in the constrained triangulation.
Constrained triangulation creates a new line, shown in red above, that is not created by regular triangulation.
Example
Unlike regular triangulation, which only works with points, constrained triangulation can work with points, lines and areas. The coordinates of lines and areas are taken as points for the purpose of constrained triangulation. This allows us to create constrained triangulations using lines or areas.
The classic example might be creating a triangulation on a set of contour lines. If we begin with the lines seen above and apply the Constrained Triangulation Areas operator...
...we create the triangulation seen above, where the triangulation areas are colored in gray. Note that because of the constrained nature of the triangulation no created area cuts across a pre-existing contour line.
See Also
Other types of networks easily created with transform operators: