ProjectParameters.EdgeLengthMax Property
Gets or sets the maximum length of an edge in a line or polygon Feature.
Syntax
public AttributeVariable< System.Double > EdgeLengthMax { get; set; }Property Value
Default: 500000.0
The maximum length, in nominal meters, of an edge in a line or polygon feature.
Remarks
After extra points have been inserted, no edge is longer than edgeLengthMax. Its unit is nominal meters; that is, ordinary meters, but assuming that the nominal scale of the Crs is valid everywhere.
Using nominal meters means that the ProjectOperator can avoid computing the local scale for every edge. Fortunately, nominal meters are usually shorter than true meters, so that you get higher accuracy. Indeed, the nominal meters are usually shorter where the Projection of the Crs is more distorted, so that the extra points become denser just where needed. This is not true for all map projections, but it is true for conformal projections and for the LongLat projection. And geographic data is usually stored in either a national grid, which would be based on a conformal projection, or in LongLat.
Suppose that you want to allow at most d meters deviation between a reprojected line and the original line. You can compute a value of EdgeLengthMax that ensures such a limit, in the following way:
In the region you work in, find the shortest line segment which is straight in the original Crs, but deviates by d/2 meters at its midpoint from a great circle route. Let us say that the shortest such line segment is s meters.
Do the same thing for the new Crs; this time, the shortest segment is t meters.
Use the minimum of s and t as the value of EdgeLengthMax.
You can find the midpoint of the great circle route from p1 to p2 by first using the Crs.Length, then generating the great circle route from p1 to p2 with half the distance as the step with the Crs.Route method. The route will then have three points, so take the middle one. Then compute its distance to the midpoint on the straight line, which simply has its x = (p1.x + p2.x)/2, and its y = (p1.y + p2.y)/2.
Of course, it would be tedious to find the line segments without some knowledge of map projection errors, so remember:
In a conformal projection, a straight line deviates most from a great-circle route if it is parallel to the central line of the projection, and the deviation increases with the distance from the central line.
For MercatorProjection, the central line is the equator;
for TransverseMercatorProjection, it is the central meridian;
for LambertConformalConicProjection, it is a parallel circle that is about halfway between the two standard parallels.
The LongLat projection, although not conformal, has the same properties if you regard the equator as the central line.
For a StereographicProjection, the central line has degenerated to a point, the center point, and the worst position for the line segment is to start and end at the same distance from the center point.
Armed with this knowledge, you can test only line segments that are parallel with the central line, and as far from it as possible, within the region you work in. Then, you should know that the deviation from a great circle route is roughly proportional to the square of the length of the line segment, other things being equal. So, if you are looking for a line segment with deviation u, and you find another line segment with length h and deviation w, then you should try a line segment with length h * sqrt(u/w).
Platforms
Windows, Linux, Android