EllipseOperator.ArcAccuracy Property
Gets or sets a value specifying the accuracy of generated arcs, expressed as segments per revolution.
Syntax
public AttributeVariable< System.Int64 > ArcAccuracy { get; set; }Property Value
Default: 32
The number of segments used for a full 360 degree arc.
Remarks
When circles are generated, the nodes on the arcs are evenly distributed, but when ellipses are generated, using Ratio ≠ 1, the nodes are denser where the arc is more curved.
Accuracy at segment midpoints
The nodes along the arc are placed at the accurate distance from the center, but of course the midpoint of each segment is slightly nearer the center (assuming the radius is less than 10 000 km). If you need the midpoint displacement to be less than some tolerance, you need to make the ArcAccuracy large enough - how large it must be depends also on the radius. (To simplify the calculations here, we will measure the displacement as if each edge follows a great circle or shortest route. In reality, each edge will appear as a straight line in the View.Crs, and such a straight line may deviate more or less from a great-circle route, depending on the View.Crs properties, but that is too complicated to consider here.)
Let us assume that the tolerance is t meters and the radius is r meters, and that t is small compared to r, and that we are generating a circle (not an ellipse). If r < 1 000 000 meters, then it is enough to ensure that
ArcAccuracy ≥ 2.222 * sqrt( r / t )
This simple formula is derived assuming a flat Earth and is therefore an overestimate when the radius is longer than about 1 000 000 meters - the curvature of the Earth will then make the midsegment error smaller than the formula expects. For a radius up to 5 000 000 meters, there is a better formula; it is enough to ensure that
ArcAccuracy ≥ 2.222 * sqrt( r / t ) * ( 1 − r² / 125e12 )
where 125e12 is scientific notation for 125 trillions (using the US English definition of a trillion).
The table below has been calculated using slightly more accurate formulas.
radius | 1 m tol. | 10 m tol. | 100 m tol. |
|---|---|---|---|
10 000 m | 223 | 71 | 23 |
100 000 m | 703 | 223 | 71 |
1 000 000 m | 2 204 | 697 | 221 |
2 000 000 m | 3 040 | 962 | 304 |
3 000 000 m | 3 568 | 1 129 | 357 |
4 000 000 m | 3 870 | 1 224 | 387 |
5 000 000 m | 3 971 | 1 256 | 398 |
As it turns out, the worst radius is about 5 000 000 meters or 45 degrees of arc distance. If the radius increases further towards 10 000 000 meters, the required ArcAccuracy will start to decrease, and is in fact symmetric around 5 000 000 meters. That is, the required ArcAccuracy for a radius of 6 000 000 meters is about the same as for a radius of 4 000 000 meters, etc.
Platforms
Windows, Linux, Android