/// <summary>
/// Gets a functional values in defined y position.
/// </summary>
/// <param name="start">The start point of the segment.</param>
/// <param name="y">The y position.</param>
/// <param name="global">True, if y and returned x value is are global space, false, if y and x are related to the start point.</param>
/// <param name="tolerance">Tolerance</param>
/// <returns>A values related to the y position.</returns>
public override double[] GetValueByY(ref Point start, double y, bool global, double tolerance = 0)
{
Refresh(ref start);
if (!global)
{
y += start.Y;
}
if (Comparators.InIntervalBoth(start.Y, EndPoint.Y, y, tolerance))
{
// y = ax^2 + bx + c
// ax^2 + bx + (c - y) = 0;
var cc = c - y;
var discr = (b * b) - 4 * a * cc;
if (discr.IsGreater(0, 1e-5) && !a.IsZero())
{
var x1 = (-b + Math.Sqrt(discr)) / (2 * a);
var x2 = (-b - Math.Sqrt(discr)) / (2 * a);
if (Comparators.InIntervalBoth(start.X, EndPoint.X, x1, tolerance) && Comparators.InIntervalBoth(start.X, EndPoint.X, x2, tolerance))
{
return(new double[]
{
global?x1 : x1 - start.X,
global ? x2 : x2 - start.X,
});
}
else if (Comparators.InIntervalBoth(start.X, EndPoint.X, x1, tolerance))
{
return(new double[]
{
global?x1 : x1 - start.X
});
}
else if (Comparators.InIntervalBoth(start.X, EndPoint.X, x2, tolerance))
{
return(new double[]
{
global?x2 : x2 - start.X
});
}
}
}
return(new double[0]);
}
/// <summary>
/// Gets a functional values in defined y position.
/// </summary>
/// <param name="start">The start point of the segment.</param>
/// <param name="y">The y position.</param>
/// <param name="global">True, if y and returned x value is are global space, false, if y and x are related to the start point.</param>
/// <param name="tolerance">Tolerance</param>
/// <returns>A values related to the y position.</returns>
public override double[] GetValueByY(ref Point start, double y, bool global, double tolerance = 0)
{
if (!global)
{
y += start.Y;
}
var bounds = GetBounds(ref start);
if (Comparators.InIntervalBoth(bounds.Top, bounds.Bottom, y, tolerance))
{
var radius = GetRadius(ref start);
var centre = GetCentre(ref start);
y -= centre.Y;
var x = Math.Sqrt(radius * radius - y * y);
var c1 = Comparators.InIntervalBoth(bounds.Left, bounds.Right, centre.X + x, tolerance);
var c2 = Comparators.InIntervalBoth(bounds.Left, bounds.Right, centre.X - x, tolerance);
if (c1 && c2)
{
return(new double[]
{
global?centre.X + x : centre.X + x - start.X,
global ? centre.X - x : centre.X - x - start.X,
});
}
else if (c1)
{
return(new double[]
{
global?centre.X + x : centre.X + x - start.X
});
}
else if (c2)
{
return(new double[]
{
global?centre.X - x : centre.X - x - start.X
});
}
}
return(new double[0]);
}
/// <summary>
/// Gets a functional values in defined x position of the CircularArcSegment.
/// </summary>
/// <param name="start">The start point of the circular arc segment.</param>
/// <param name="x">The x position.</param>
/// <param name="global">True, if x and returned y value is are global space, false, if x and y are related to the start point.</param>
/// <param name="tolerance">Tolerance</param>
/// <returns>A values related to the x position.</returns>
public override double[] GetValueByX(ref Point start, double x, bool global, double tolerance = 0)
{
if (!global)
{
x += start.X;
}
var bounds = GetBounds(ref start);
if (Comparators.InIntervalBoth(bounds.Left, bounds.Right, x, tolerance))
{
var radius = GetRadius(ref start);
var centre = GetCentre(ref start);
x -= centre.X;
var y = Math.Sqrt(radius * radius - x * x);
var c1 = Comparators.InIntervalBoth(bounds.Top, bounds.Bottom, centre.Y + y, tolerance);
var c2 = Comparators.InIntervalBoth(bounds.Top, bounds.Bottom, centre.Y - y, tolerance);
if (c1 && c2)
{
return(new double[]
{
global?centre.Y + y : centre.Y + y - start.Y,
global ? centre.Y - y : centre.Y - y - start.Y,
});
}
else if (c1)
{
return(new double[]
{
global?centre.Y + y : centre.Y + y - start.Y,
});
}
else if (c2)
{
return(new double[]
{
global?centre.Y - y : centre.Y - y - start.Y,
});
}
}
return(new double[0]);
}
/// <summary>
/// Gets a functional values in defined x position of the ParabolicArcSegment.
/// </summary>
/// <param name="start">The start point of the parabolic arc segment.</param>
/// <param name="x">The x position.</param>
/// <param name="global">True, if x and returned y value is are global space, false, if x and y are related to the start point.</param>
/// <param name="tolerance">Tolerance</param>
/// <returns>A values related to the x position.</returns>
public override double[] GetValueByX(ref Point start, double x, bool global, double tolerance = 0)
{
Refresh(ref start);
if (!global)
{
x += start.X;
}
if (Comparators.InIntervalBoth(start.X, EndPoint.X, x, tolerance))
{
// y = ax^2 + bx + c
var y = a * x * x + b * x + c;
if (!global)
{
y -= start.Y;
}
return(new double[] { y });
}
return(new double[0]);
}
/// <summary>
/// Calculates relative position on segment by given x position.
/// </summary>
/// <param name="start">The start point of the segment.</param>
/// <param name="x">The x position.</param>
/// <param name="global">True, if x and returned y value is are global space, false, if x and y are related to the start point.</param>
/// <returns>The relative position.</returns>
public override double[] GetRelativePosition(ref Point start, double x, bool global, double tolerance = 0)
{
if (!global)
{
x += start.X;
}
var radius = GetRadius(ref start);
var centre = GetCentre(ref start);
if (Comparators.InIntervalBoth(centre.X - radius, centre.X + radius, x, tolerance))
{
var xx = x - centre.X;
var y = (radius * radius - xx * xx).IsZero() ? 0 : Math.Sqrt(radius * radius - xx * xx);
var cc = IsCounterClockwise(ref start);
var angle = GetAngle(ref start);
Func <Point, Point, double> getAngle = (s, p) =>
{
var u1 = Point.Subtract(s, centre);
var u2 = Point.Subtract(p, centre);
var a = Vector.AngleBetween(u1, u2) * cc;
if (a.IsZero())
{
return(0);
}
return(a < 0 ? 360 + a : a);
};
var px = new Point(x, centre.Y + y);
var angle1 = getAngle(start, px);
px.Y = centre.Y - y;
var angle2 = getAngle(start, px);
return(new double[] { angle1 / angle, angle2 / angle });
}
return(new double[0]);
}