///<summary>
/// Computes the incentre of a triangle.
///</summary>
/// <remarks>
/// The <c>InCentre</c> of a triangle is the point which is equidistant
/// from the sides of the triangle.
/// It is also the point at which the bisectors of the triangle's angles meet.
/// It is the centre of the triangle's <c>InCircle</c>, which is the unique circle
/// that is tangent to each of the triangle's three sides.
/// </remarks>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <returns>The point which is the incentre of the triangle</returns>
public static Coordinate InCentre(Coordinate a, Coordinate b, Coordinate c)
{
// the lengths of the sides, labelled by their opposite vertex
double len0 = b.Distance(c);
double len1 = a.Distance(c);
double len2 = a.Distance(b);
double circum = len0 + len1 + len2;
double inCentreX = (len0 * a.X + len1 * b.X + len2 * c.X) / circum;
double inCentreY = (len0 * a.Y + len1 * b.Y + len2 * c.Y) / circum;
return(new Coordinate(inCentreX, inCentreY));
}
///<summary>Computes the point at which the bisector of the angle ABC cuts the segment AC.</summary>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <returns>The angle bisector cut point</returns>
public static Coordinate AngleBisector(Coordinate a, Coordinate b, Coordinate c)
{
/*
* Uses the fact that the lengths of the parts of the split segment
* are proportional to the lengths of the adjacent triangle sides
*/
double len0 = b.Distance(a);
double len2 = b.Distance(c);
double frac = len0 / (len0 + len2);
double dx = c.X - a.X;
double dy = c.Y - a.Y;
Coordinate splitPt = new Coordinate(a.X + frac * dx,
a.Y + frac * dy);
return(splitPt);
}
/// <summary>
/// Computes the closest point on this line segment to another point.
/// </summary>
/// <param name="p">The point to find the closest point to.</param>
/// <returns>
/// A Coordinate which is the closest point on the line segment to the point p.
/// </returns>
public Coordinate ClosestPoint(Coordinate p)
{
var factor = ProjectionFactor(p);
if (factor > 0 && factor < 1)
{
return(Project(p));
}
var dist0 = _p0.Distance(p);
var dist1 = _p1.Distance(p);
return(dist0 < dist1 ? _p0 : _p1);
}
///<summary>Computes the length of the longest side of a triangle</summary>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <returns>The length of the longest side of the triangle</returns>
public static double LongestSideLength(Coordinate a, Coordinate b, Coordinate c)
{
// ReSharper disable InconsistentNaming
double lenAB = a.Distance(b);
double lenBC = b.Distance(c);
double lenCA = c.Distance(a);
// ReSharper restore InconsistentNaming
double maxLen = lenAB;
if (lenBC > maxLen)
{
maxLen = lenBC;
}
if (lenCA > maxLen)
{
maxLen = lenCA;
}
return(maxLen);
}