/// <summary>
/// Creates an arc with the given center, start, and end points. Performs a check
/// at the given precision to make sure that both the start and end points are
/// the same distance from the center, throwing an exception if they're not. Note
/// that because radius is generated from start point, the resultant arc's start
/// point will be more accurate than the end point.
/// </summary>
/// <param name="center">Center of the arc.</param>
/// <param name="startPoint">Start point of the arc.</param>
/// <param name="endPoint">Point that end angle is projected through.</param>
/// <param name="decimals">Precision at which to check the distance of the endpoints to the center.
/// A negative value will perform an exact check.</param>
public Arc2D(Point2D center, Point2D startPoint, Point2D endPoint, int decimals = 15)
: this(center, center.DistanceTo(startPoint), 0, 0)
{
if ((decimals < 0 && center.DistanceTo(endPoint) != Radius) || (decimals >= 0 && center.DistanceTo(endPoint).RoundFromZero(decimals) != Radius.RoundFromZero(decimals)))
{
throw new Exception("Can't create arc from center and endpoints because endpoints have different distances from the center!");
}
_startAngle = Circle.AngleThroughPoint(startPoint);
_endAngle = Circle.AngleThroughPoint(endPoint);
}
/// <summary>
/// Gets the two line segments that start at the given point and terminate
/// on the circle and are tangent to the circle.
/// </summary>
/// <param name="point">The point for the tangent segments to go through.</param>
/// <remarks>
/// Got strategy from Wikipedia's description involving Thale's theorem.
/// http://en.wikipedia.org/wiki/Tangent_lines_to_circles
/// </remarks>
public LineSeg2D[] TangentsThroughPoint(Point2D point)
{
Circle2D intersectingCircle = default(Circle2D);
Point2D[] intersects = null;
if (point.DistanceTo(this.Center) <= this.Radius)
{
return(null);
}
intersectingCircle = new Circle2D(this.Center, point);
intersects = this.GetIntersect(intersectingCircle);
if (intersects.Length != 2)
{
throw new Exception("Unexpected number of intersects when getting tangents through a point.");
}
return(new LineSeg2D[] {
new LineSeg2D(point, intersects[0]),
new LineSeg2D(point, intersects[1])
});
}
/// <summary>
/// Returns the point on the line segment closest to the given point. Can also
/// return the closest point on the line through the line segment.
/// </summary>
/// <param name="pt">A 2D point.</param>
/// <param name="treatLineSegmentAsLine">If True, will return closest point on
/// the line through the line segment even if it doesn't lie on the segment
/// itself. If False, will find the closest point on the segment itself.</param>
public Point2D ClosestPointTo(Point2D pt, bool treatLineSegmentAsLine = false)
{
_CheckIsValid();
LineSeg2D l = default(LineSeg2D);
Point2D ret = default(Point2D);
if (this.IsHorizontal)
{
ret = new Point2D(pt.X, this.Pt1.Y);
}
else
{
l = FromPointSlope(pt, this.PerpendicularSlope);
ret = this.GetIntersect(l, true).Value;
}
if (!treatLineSegmentAsLine && !this.IsInBounds(ret))
{
if (pt.DistanceTo(Pt1) < pt.DistanceTo(Pt2))
{
ret = Pt1;
}
else
{
ret = Pt2;
}
}
return(ret);
//' Alt method using vector project
//' http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
//Dim v As Vector2D
//Dim r As Vector2D
//Dim proj As Vector2D
//Dim ret As XYPoint
//v = New Vector2D(Pt2.Y - Pt1.Y, -(Pt2.X - Pt1.X))
//r = New Vector2D(Pt1.X - pt.X, Pt1.Y - pt.Y)
//proj = r.ProjectOnto(v)
//ret = pt + proj
//' End alt method
//' Alt method using vectors
//' http://www.gamedev.net/community/forums/topic.asp?topic_id=198199&whichpage=1�
//' Not used because of round off problems that affect precision.
//Dim d As Decimal
//Dim t As Decimal
//Dim aToB As Vector2D
//Dim aToPt As Vector2D
//aToB = (New Vector2D(Pt1, Pt2)).Normalize
//aToPt = New Vector2D(Pt1, pt)
//d = Me.Length
//t = aToB.Dot(aToPt)
//If Not treatLineSegmentAsLine Then
// If t < 0 Then
// ret = Pt1
// ElseIf t > d Then
// ret = Pt2
// Else
// ret = Pt1 + aToB * t
// End If
//Else
// If Not (Pt1 + aToB * t).Equals(ret, 23) Then Stop
// ret = Pt1 + aToB * t
//End If
//' End alt method
}
/// <summary>
/// Finds the closest distance between a point and this line segment or
/// the line through this line segment.
/// </summary>
/// <param name="pt">A 2D point.</param>
/// <param name="treatLineSegmentAsLine">If True, will return distance to closest
/// point on the line through the line segment. If False, will return distance to the
/// closest point on the segment itself.</param>
public decimal DistanceTo(Point2D pt, bool treatLineSegmentAsLine = false)
{
return(pt.DistanceTo(this.ClosestPointTo(pt, treatLineSegmentAsLine)));
}