/// <summary>
///
/// </summary>
/// <param name="rect"></param>
/// <param name="p1"></param>
/// <param name="p2"></param>
/// <param name="onlySegment"></param>
/// <returns></returns>
public static IList <Point2> FindEllipseSegmentIntersections(
Rect2 rect,
Point2 p1, Point2 p2,
bool onlySegment)
{
if ((rect.Width == 0) || (rect.Height == 0) || ((p1.X == p2.X) && (p1.Y == p2.Y)))
{
return new Point2[] { }
}
;
if (rect.Width < 0)
{
rect.X = rect.Right;
rect.Width = -rect.Width;
}
if (rect.Height < 0)
{
rect.Y = rect.Bottom;
rect.Height = -rect.Height;
}
double cx = rect.Left + rect.Width / 2.0;
double cy = rect.Top + rect.Height / 2.0;
rect.X -= cx;
rect.Y -= cy;
p1.X -= cx;
p1.Y -= cy;
p2.X -= cx;
p2.Y -= cy;
double a = rect.Width / 2.0;
double b = rect.Height / 2.0;
double A = (p2.X - p1.X) * (p2.X - p1.X) / a / a + (p2.Y - p1.Y) * (p2.Y - p1.Y) / b / b;
double B = 2 * p1.X * (p2.X - p1.X) / a / a + 2 * p1.Y * (p2.Y - p1.Y) / b / b;
double C = p1.X * p1.X / a / a + p1.Y * p1.Y / b / b - 1;
var solutions = new List <double>();
double discriminant = B * B - 4 * A * C;
if (discriminant == 0)
{
solutions.Add(-B / 2 / A);
}
else if (discriminant > 0)
{
solutions.Add((-B + Math.Sqrt(discriminant)) / 2 / A);
solutions.Add((-B - Math.Sqrt(discriminant)) / 2 / A);
}
var points = new List <Point2>();
foreach (var t in solutions)
{
if (!onlySegment || ((t >= 0f) && (t <= 1f)))
{
double x = p1.X + (p2.X - p1.X) * t + cx;
double y = p1.Y + (p2.Y - p1.Y) * t + cy;
points.Add(Point2.Create(x, y));
}
}
return(points);
}
/// <summary>
///
/// </summary>
/// <param name="arc"></param>
/// <param name="dx"></param>
/// <param name="dy"></param>
/// <returns></returns>
public static WpfArc FromXArc(XArc arc, double dx, double dy)
{
var p1 = Point2.Create(arc.Point1.X + dx, arc.Point1.Y + dy);
var p2 = Point2.Create(arc.Point2.X + dx, arc.Point2.Y + dy);
var p3 = Point2.Create(arc.Point3.X + dx, arc.Point3.Y + dy);
var p4 = Point2.Create(arc.Point4.X + dx, arc.Point4.Y + dy);
var rect = Rect2.Create(p1, p2);
var center = Point2.Create(rect.X + rect.Width / 2.0, rect.Y + rect.Height / 2.0);
double offsetX = center.X - rect.X;
double offsetY = center.Y - rect.Y;
double minLenght = Math.Max(offsetX, offsetY);
double length1 = center.Distance(p3);
double p3x = p3.X + (p3.X - center.X) / length1 * minLenght;
double p3y = p3.Y + (p3.Y - center.Y) / length1 * minLenght;
double length2 = center.Distance(p4);
double p4x = p4.X + (p4.X - center.X) / length2 * minLenght;
double p4y = p4.Y + (p4.Y - center.Y) / length2 * minLenght;
p3.X = p3x;
p3.Y = p3y;
p4.X = p4x;
p4.Y = p4y;
var p3i = MathHelpers.FindEllipseSegmentIntersections(rect, center, p3, true);
var p4i = MathHelpers.FindEllipseSegmentIntersections(rect, center, p4, true);
Point2 start;
Point2 end;
if (p3i.Count == 1)
{
start = p3i.FirstOrDefault();
}
else
{
start = Point2.Create(p3.X, p3.Y);
}
if (p4i.Count == 1)
{
end = p4i.FirstOrDefault();
}
else
{
end = Point2.Create(p4.X, p4.Y);
}
double angle = MathHelpers.AngleLineSegments(center, start, center, end);
bool isLargeArc = angle > 180.0;
double helperLenght = 60.0;
double lengthStart = center.Distance(start);
double p3hx = start.X + (start.X - center.X) / lengthStart * helperLenght;
double p3hy = start.Y + (start.Y - center.Y) / lengthStart * helperLenght;
double lengthEnd = center.Distance(end);
double p4hx = end.X + (end.X - center.X) / lengthEnd * helperLenght;
double p4hy = end.Y + (end.Y - center.Y) / lengthEnd * helperLenght;
p3.X = p3hx;
p3.Y = p3hy;
p4.X = p4hx;
p4.Y = p4hy;
return(new WpfArc()
{
P1 = p1,
P2 = p2,
P3 = p3,
P4 = p4,
Rect = rect,
Center = center,
Start = start,
End = end,
Radius = Size2.Create(offsetX, offsetY),
IsLargeArc = isLargeArc,
Angle = angle
});
}
