/// <summary>
/// Find the closet point along this line from a_point
/// </summary>
/// <param name="a_point"></param>
/// <returns></returns>
public DVector2 ClosestPoint(DVector2 a_point)
{
DVector2 delta = v1 - v0;
double lengthSquared = delta.SqrMagnitude();
if (lengthSquared.Equals(0f))
{
return(v0);
}
double projection = DVector2.Dot(a_point - v0, delta);
double scale = projection / lengthSquared;
return(v0 + delta * scale);
}
/// <summary>
/// Calculates the center of a circle that intersects abc. Returns false if abc are colinear, or if the
/// arc is diverging. Divergence is determine by whether the points are ordered clockwise or ccw around
/// the center of the circle
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <param name="d"></param>
/// <returns></returns>
bool Circumcenter(DVector2 a, DVector2 b, DVector2 c, out DVector2 d)
{
DVector2 ba = b - a;
DVector2 ca = c - a;
double baLength = ba.SqrMagnitude();
double caLength = ca.SqrMagnitude();
double denominator = 2d * (ba.x * ca.y - ba.y * ca.x);
if (denominator <= 0d)
{
d = b;
return(false);
}
d.x = a.x + (ca.y * baLength - ba.y * caLength) / denominator;
d.y = a.y + (ba.x * caLength - ca.x * baLength) / denominator;
return(true);
}
