/// <summary>
///
/// </summary>
/// <param name="line1Start"></param>
/// <param name="line1End"></param>
/// <param name="line2Start"></param>
/// <param name="line2End"></param>
/// <returns></returns>
public static double AngleLineSegments(
Point2 line1Start, Point2 line1End,
Point2 line2Start, Point2 line2End)
{
double angle1 = Math.Atan2(line1Start.Y - line1End.Y, line1Start.X - line1End.X);
double angle2 = Math.Atan2(line2Start.Y - line2End.Y, line2Start.X - line2End.X);
double result = (angle2 - angle1) * 180.0 / Math.PI;
if (result < 0)
result += 360.0;
return result;
}
/// <summary>
///
/// </summary>
/// <param name="centerPoint"></param>
/// <param name="angleInDegrees"></param>
/// <returns></returns>
public Point2 RotateAt(
Point2 centerPoint,
double angleInDegrees)
{
double angleInRadians = angleInDegrees * (Math.PI / 180.0);
double cosTheta = Math.Cos(angleInRadians);
double sinTheta = Math.Sin(angleInRadians);
return new Point2
{
X = (cosTheta * (this.X - centerPoint.X) - sinTheta * (this.Y - centerPoint.Y) + centerPoint.X),
Y = (sinTheta * (this.X - centerPoint.X) + cosTheta * (this.Y - centerPoint.Y) + centerPoint.Y)
};
}
/// <summary>
///
/// </summary>
/// <param name="point"></param>
/// <returns></returns>
public double Distance(Point2 point)
{
double dx = this.X - point.X;
double dy = this.Y - point.Y;
return Math.Sqrt(dx * dx + dy * dy);
}
/// <summary>
///
/// </summary>
/// <param name="tl"></param>
/// <param name="br"></param>
/// <param name="dx"></param>
/// <param name="dy"></param>
/// <returns></returns>
public static Rect2 Create(
Point2 tl, Point2 br,
double dx = 0.0, double dy = 0.0)
{
return Rect2.Create(tl.X, tl.Y, br.X, br.Y, dx, dy);
}
/// <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>
/// Check if line intersects with rectangle using Liang-Barsky line clipping algorithm.
/// </summary>
/// <param name="rect"></param>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <returns>True if line intersects with rectangle.</returns>
public static bool LineIntersectsWithRect(Rect2 rect, Point2 p0, Point2 p1)
{
double left = rect.Left;
double right = rect.Right;
double bottom = rect.Bottom;
double top = rect.Top;
double x0 = p0.X;
double y0 = p0.Y;
double x1 = p1.X;
double y1 = p1.Y;
double t0 = 0.0;
double t1 = 1.0;
double dx = x1 - x0;
double dy = y1 - y0;
double p = 0.0, q = 0.0, r;
for (int edge = 0; edge < 4; edge++)
{
if (edge == 0)
{
p = -dx;
q = -(left - x0);
}
if (edge == 1)
{
p = dx;
q = (right - x0);
}
if (edge == 2)
{
p = dy;
q = (bottom - y0);
}
if (edge == 3)
{
p = -dy;
q = -(top - y0);
}
r = q / p;
if (p == 0.0 && q < 0.0)
{
return false;
}
if (p < 0.0)
{
if (r > t1)
{
return false;
}
else if (r > t0)
{
t0 = r;
}
}
else if (p > 0.0)
{
if (r < t0)
{
return false;
}
else if (r < t1)
{
t1 = r;
}
}
}
// to calulate clipped line position
// x0clip = x0 + t0 * dx;
// y0clip = y0 + t0 * dy;
// x1clip = x0 + t1 * dx;
// y1clip = y0 + t1 * dy;
return true;
}
/// <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>
/// Check if line intersects with rectangle using Liang-Barsky line clipping algorithm.
/// </summary>
/// <param name="rect"></param>
/// <param name="p0"></param>
/// <param name="p1"></param>
/// <returns>True if line intersects with rectangle.</returns>
public static bool LineIntersectsWithRect(Rect2 rect, Point2 p0, Point2 p1)
{
double left = rect.Left;
double right = rect.Right;
double bottom = rect.Bottom;
double top = rect.Top;
double x0 = p0.X;
double y0 = p0.Y;
double x1 = p1.X;
double y1 = p1.Y;
double t0 = 0.0;
double t1 = 1.0;
double dx = x1 - x0;
double dy = y1 - y0;
double p = 0.0, q = 0.0, r;
for (int edge = 0; edge < 4; edge++)
{
if (edge == 0)
{
p = -dx;
q = -(left - x0);
}
if (edge == 1)
{
p = dx;
q = (right - x0);
}
if (edge == 2)
{
p = dy;
q = (bottom - y0);
}
if (edge == 3)
{
p = -dy;
q = -(top - y0);
}
r = q / p;
if (p == 0.0 && q < 0.0)
{
return(false);
}
if (p < 0.0)
{
if (r > t1)
{
return(false);
}
else if (r > t0)
{
t0 = r;
}
}
else if (p > 0.0)
{
if (r < t0)
{
return(false);
}
else if (r < t1)
{
t1 = r;
}
}
}
// to calulate clipped line position
// x0clip = x0 + t0 * dx;
// y0clip = y0 + t0 * dy;
// x1clip = x0 + t1 * dx;
// y1clip = y0 + t1 * dy;
return(true);
}
/// <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
});
}
/// <summary>
///
/// </summary>
/// <param name="tl"></param>
/// <param name="br"></param>
/// <param name="dx"></param>
/// <param name="dy"></param>
/// <returns></returns>
public static Rect2 Create(
Point2 tl, Point2 br,
double dx = 0.0, double dy = 0.0)
{
return(Rect2.Create(tl.X, tl.Y, br.X, br.Y, dx, dy));
}