/// <summary>
/// Gets the Y values for which the equation of the circle yields the given X.
/// </summary>
/// <param name="x">The X value.</param>
public decimal[] SolveForY(ref decimal x)
{
// Alternative calculations. May be faster/more accurate, but need to be tested.
//Dim absDiff = Math.Abs(x - _center.X)
//Select Case absDiff
// Case Is > _radius
// Return New Decimal() {}
// Case _radius
// Return New Decimal() {_center.Y}
// Case 0
// Return New Decimal() {_center.Y + _radius, _center.Y - _radius}
// Case Else
// Dim height = RightTriangle.GetSideFromSideHyp(absDiff, _radius)
// Return New Decimal() {_center.Y + height, _center.Y - height}
//End Select
decimal aCoeff = 0m;
decimal bCoeff = 0m;
decimal cCoeff = 0m;
// Solve for y
// (x - h)^2 + (y - k)^2 = r^2
// simplifies to
// y^2 - 2 * k * y + k^2 + (x - h)^2 - r^2 = 0
aCoeff = 1;
bCoeff = -2 * _center.Y;
cCoeff = _center.Y * _center.Y + (x - _center.X) * (x - _center.X) - _radius * _radius;
return(DecimalEx.SolveQuadratic(aCoeff, bCoeff, cCoeff));
}
/// <summary>
/// Gets the X values for which the equation of the circle yields the given Y.
/// </summary>
/// <param name="y">The Y value.</param>
public decimal[] SolveForX(decimal y)
{
decimal aCoeff = 0m;
decimal bCoeff = 0m;
decimal cCoeff = 0m;
// Solve for x
// (x - h)^2 + (y - k)^2 = r^2
// simplifies to
// x^2 - 2 * h * x + h^2 + (y - k)^2 - r^2 = 0
aCoeff = 1;
bCoeff = -2 * _center.X;
cCoeff = _center.X * _center.X + (y - _center.Y) * (y - _center.Y) - _radius * _radius;
return(DecimalEx.SolveQuadratic(aCoeff, bCoeff, cCoeff));
}
/// <summary>
/// Gets the points of intersection between this circle and the line which
/// contains the given line segment.
/// </summary>
/// <param name="l">Line segment used to determine line equation.</param>
public Point2D[] GetIntersectFast(ref LineSeg2D l)
{
decimal[] x = new decimal[2];
decimal m = 0m;
decimal b = 0m;
decimal aCoeff = 0m;
decimal bCoeff = 0m;
decimal cCoeff = 0m;
decimal lineX = 0m;
decimal t = 0m;
decimal p = 0m;
decimal q = 0m;
Point2D[] pts = null;
if (!l.IsVertical)
{
// Circle (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2
// Center: (h, k)
// Radius: r
// Line y = m * x + b
// (x - h) ^ 2 + (m * x + b - k) ^ 2 = r ^ 2
// (x - h) * (x - h) + (m * x + b - k) * (m * x + b - k) = r^2
// (x^2 - 2 * h * x + h^2) + (m^2 * x^2 + 2 * (b - k) * m * x + (b - k)^2 = r^2
// (m^2 + 1) * x^2 + (2 * (b - k) * m - 2 * h) * x + (h^2 + (b - k)^2 - r^2) = 0
m = l.Slope;
b = l.YIntersect;
aCoeff = DecimalEx.Pow(m, 2) + 1;
bCoeff = 2 * (b - _center.Y) * m - 2 * _center.X;
cCoeff = DecimalEx.Pow(_center.X, 2) + DecimalEx.Pow(b - _center.Y, 2) - DecimalEx.Pow(_radius, 2);
x = DecimalEx.SolveQuadratic(aCoeff, bCoeff, cCoeff);
if (x.Length == 0)
{
return new Point2D[] { }
}
;
pts = new Point2D[x.Length];
for (var i = 0; i <= x.Length - 1; i++)
{
pts[i] = new Point2D(x[i], m * x[i] + b);
}
}
else
{
// Circle (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2
// Center: (h, k)
// Radius: r
// Line x = lineX
// Got the following from
// http://www.sonoma.edu/users/w/wilsonst/Papers/Geometry/circles/T1--2/T1-3-2.html
// http://www.sonoma.edu/users/w/wilsonst/Papers/Geometry/circles/default.html
lineX = l.Pt1.X;
t = _radius * _radius - (lineX - _center.X) * (lineX - _center.X);
if (t < 0)
{
return(new Point2D[] { });
}
else
{
p = _center.Y + DecimalEx.Sqrt(t);
q = _center.Y - DecimalEx.Sqrt(t);
pts = new Point2D[1];
pts[0] = new Point2D(lineX, p);
// NOTE that P=Q when t=0
if (p != q)
{
Array.Resize(ref pts, 2);
pts[1] = new Point2D(lineX, q);
}
}
}
return(pts);
}
