/// <summary>
/// Returns the closest point on the polyline to the given point.
/// </summary>
/// <param name="p">a point</param>
/// <returns>A point which is the closest to the given point but still on the line.</returns>
public Point2D ClosestPointTo(Point2D p)
{
var minError = double.MaxValue;
var closest = default(Point2D);
for (var i = 0; i < this.VertexCount - 1; i++)
{
var segment = new LineSegment2D(this.points[i], this.points[i + 1]);
var projected = segment.ClosestPointTo(p);
var error = p.DistanceTo(projected);
if (error < minError)
{
minError = error;
closest = projected;
}
}
return(closest);
}
/// <summary>
/// Creates a <see cref="Circle2D"/> circle from three points which lie along its circumference.
/// Points may not be collinear
/// </summary>
/// <param name="pointA">The first point on the circle.</param>
/// <param name="pointB">The second point on the circle.</param>
/// <param name="pointC">The third point on the circle.</param>
/// <returns>A Circle which is defined by the three specified points</returns>
/// <exception cref="ArgumentException">An exception is thrown if no possible circle can be formed from the points</exception>
public static Circle2D FromPoints(Point2D pointA, Point2D pointB, Point2D pointC)
{
// ReSharper disable InconsistentNaming
var midpointAB = Point2D.MidPoint(pointA, pointB);
var midpointBC = Point2D.MidPoint(pointB, pointC);
var gradientAB = (pointB.Y - pointA.Y) / (pointB.X - pointA.X);
var gradientBC = (pointC.Y - pointB.Y) / (pointC.X - pointB.X);
var gradientl1 = -1 / gradientAB;
var gradientl2 = -1 / gradientBC;
// ReSharper restore InconsistentNaming
var denominator = gradientl2 - gradientl1;
var nominator = midpointAB.Y - (gradientl1 * midpointAB.X) + (gradientl2 * midpointBC.X) - midpointBC.Y;
var centerX = nominator / denominator;
var centerY = (gradientl1 * (centerX - midpointAB.X)) + midpointAB.Y;
var center = new Point2D(centerX, centerY);
if (double.IsNaN(center.X) || double.IsNaN(center.Y) || double.IsInfinity(center.X) || double.IsInfinity(center.Y))
{
throw new ArgumentException("Points cannot form a circle, are they collinear?");
}
return(new Circle2D(center, center.DistanceTo(pointA)));
}