/// <returns>Null (no intercepts), or array of length 1 or 2.</returns>
public WPoint[] GetIntersectionPoints(WLine line)
{
//line does not intersect if perpendicular line from circle-center to line is longer than circle-radius
WPoint perpendicularToCenter = line.GetPerpendicularIntersect(Center);
if (perpendicularToCenter.Distance(Center) > Radius)
{
return(null);
}
//equation of circle with radius r and center (h, k)
//is (x - h)^2 + (y - k)^2 = r^2
//line: y = mx + b
//circle: (x - h)^2 + (y - k)^2 = r^2
//substitute y: (x - h)^2 + (mx + b - k)^2 = r^2
//expand: x^2 - 2hx + h^2 + m^2x^2 + 2(b - k)mx + (b - k)^2 - r^2 = 0
//group: (1 + m^2)x^2 + (-2h + 2(b - k)m)x + (h^2 + (b - k)^2 - r^2) = 0
//quadratic equation: if 0 = Ax^2 + Bx + C, then x = (-B +- sqrt(B^2 - 4AC)) / 2A
double A = 1 + Math.Pow(line.Slope, 2);
double B = (-2 * Center.X) + (2 * (line.YIntercept - Center.Y) * line.Slope);
double C = Math.Pow(Center.X, 2) + Math.Pow(line.YIntercept - Center.Y, 2) - Math.Pow(Radius, 2);
double x1 = (-1 * B + Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double x2 = (-1 * B - Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double y1 = line.Slope * x1 + line.YIntercept;
double y2 = line.Slope * x2 + line.YIntercept;
if (line.IsVertical)
{
x1 = line.A.X;
x2 = line.A.X;
//must use circle equation instead of line equation to find y's
y1 = Center.Y + Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
y2 = Center.Y - Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
}
if (line.IsHorizontal)
{
y1 = line.A.Y;
y2 = line.A.Y;
}
WPoint point1 = new WPoint(x1, y1);
WPoint point2 = new WPoint(x2, y2);
List <WPoint> result = new List <WPoint>()
{
point1
};
if (point1 != point2)
{
result.Add(point2);
}
return(result.ToArray());
}
//todo: better names for PointOnLine and PointPastLine, they are misleading
/// <summary>
/// Calculates point along line AB, starting at A and moving towards B
/// </summary>
/// <exception cref='ArgumentException'>Point A and B cannot be the same.</exception>
public static WPoint PointOnLine(WPoint a, WPoint b, double distance)
{
double lineLength = a.Distance(b);
if (lineLength == 0)
{
throw new ArgumentException("Point A and B cannot be the same.");
}
double lengthRatio = distance / lineLength;
double x = ((1d - lengthRatio) * a.X) + (lengthRatio * b.X);
double y = ((1d - lengthRatio) * a.Y) + (lengthRatio * b.Y);
return(new WPoint(x, y));
}
/// <summary>
/// Calculates point along line AB, starting at B and moving away from A
/// </summary>
public static WPoint PointPastLine(WPoint a, WPoint b, double distance)
{
double lineLength = a.Distance(b);
return(PointOnLine(a, b, lineLength + distance));
}