/// <summary>
/// Coordinates of where a perpendicular projection intersects the provided coordinate.
/// The first coordinate is of the closer intersection.
/// Returns infinity if the point is coincident with the circular curve center.
/// </summary>
/// <param name="point">The point.</param>
/// <param name="referenceArc">The line to which a perpendicular projection is drawn.</param>
/// <returns>CartesianCoordinate.</returns>
/// <exception cref="NotImplementedException"></exception>
public static Tuple <CartesianCoordinate, CartesianCoordinate> CoordinatesOfPerpendicularProjection(CartesianCoordinate point, CircularCurve referenceArc)
{
if (point == referenceArc.Center)
{
return(new Tuple <CartesianCoordinate, CartesianCoordinate>(
new CartesianCoordinate(double.PositiveInfinity, double.PositiveInfinity),
new CartesianCoordinate(double.PositiveInfinity, double.PositiveInfinity)
));
}
LinearCurve ray = new LinearCurve(referenceArc.Center, point);
CartesianCoordinate[] intersectionCoordinates = referenceArc.IntersectionCoordinate(ray);
double distance1 = CartesianOffset.Separation(point, intersectionCoordinates[0]);
double distance2 = CartesianOffset.Separation(point, intersectionCoordinates[1]);
CartesianCoordinate intersectionClose = (distance1 < distance2) ? intersectionCoordinates[0] : intersectionCoordinates[1];
CartesianCoordinate intersectionFar = (distance1 < distance2) ? intersectionCoordinates[1] : intersectionCoordinates[0];
return(new Tuple <CartesianCoordinate, CartesianCoordinate>(intersectionClose, intersectionFar));
}
