/// <summary>
/// Generates an approximation of a circular arc.
/// </summary>
/// <param name="tol">The maximum chord-to-circumference distance.</param>
/// <returns></returns>
public static IPointGeometry[] GetApproximation(ICircularArcGeometry g, ILength tol)
{
// Get info about the circle the curve lies on.
IPosition center = g.Circle.Center;
double radius = g.Circle.Radius;
// Determine the change in bearing which will satisfy the specified tolerance
// (if no tolerance has been specified, arbitrarily use a tolerance of 1mm on the ground).
double tolm = (tol.Meters > Double.Epsilon ? tol.Meters : 0.001);
double dbear = Math.Acos((radius - tolm) / radius);
IPointGeometry start = g.BC;
IPointGeometry end = g.EC;
bool iscw = g.IsClockwise;
// Get the total angle subtended by the curve.
Turn reft = new Turn(center, start);
double totang = reft.GetAngleInRadians(end); // clockwise
if (!iscw)
{
totang = MathConstants.PIMUL2 - totang;
}
// Figure out how many positions we'll generate
int nv = (int)(totang / dbear); // truncate
Debug.Assert(nv >= 0);
// Handle special case of very short arc.
if (nv == 0)
{
return new IPointGeometry[] { start, end }
}
;
// Sign the delta-bearing the right way.
if (!iscw)
{
dbear = -dbear;
}
// Get the initial bearing to the first position along the curve.
double curbear = reft.BearingInRadians + dbear;
// Append positions along the length of the curve.
List <IPointGeometry> result = new List <IPointGeometry>(nv);
result.Add(start);
for (int i = 0; i < nv; i++, curbear += dbear)
{
IPosition p = BasicGeom.Polar(center, curbear, radius);
result.Add(PositionGeometry.Create(p));
}
result.Add(end);
return(result.ToArray());
}
/// <summary>
/// Gets the position that is a specific distance from the start of a circular arc.
/// </summary>
/// <param name="g">The geometry for the circular arc</param>
/// <param name="distance">The distance from the start of the arc.</param>
/// <param name="result">The position found</param>
/// <returns>True if the distance is somewhere ON the arc. False if the distance
/// was less than zero, or more than the arc length (in that case, the position
/// found corresponds to the corresponding terminal point).</returns>
public static bool GetPosition(ICircularArcGeometry g, ILength distance, out IPosition result)
{
// Allow 1 micron tolerance
const double TOL = 0.000001;
// Check for invalid distances.
double d = distance.Meters;
if (d < 0.0)
{
result = g.BC;
return(false);
}
double clen = g.Length.Meters; // Arc length
if (d > (clen + TOL))
{
result = g.EC;
return(false);
}
// Check for limiting values (if you don't do this, minute
// roundoff at the BC & EC can lead to spurious locations).
// (although it's possible to use TINY here, use 1 micron
// instead, since we can't represent position any better
// than that).
if (d < TOL)
{
result = g.BC;
return(true);
}
if (Math.Abs(d - clen) < TOL)
{
result = g.EC;
return(true);
}
// Get the bearing of the BC
ICircleGeometry circle = g.Circle;
IPosition c = circle.Center;
double radius = circle.Radius;
double bearing = BasicGeom.BearingInRadians(c, g.BC);
// Add the angle that subtends the required distance (or
// subtract if the curve goes anti-clockwise).
if (g.IsClockwise)
{
bearing += (d / radius);
}
else
{
bearing -= (d / radius);
}
// Figure out the required point from the new bearing.
result = BasicGeom.Polar(c, bearing, radius);
return(true);
}