public static Point SplitByNextIntersection(Point startPoint, EllipticalArcSegment segment, out SegmentBase segment1, out SegmentBase segment2)
{
Func<Point, EllipticalArcSegment> create = p => new EllipticalArcSegment(segment.Radii, segment.XAxisRotation, segment.IsLargeArc, segment.IsSweep, p);
return SplitByNextIntersection(startPoint, segment, out segment1, out segment2,
new EllipticalArcEquation(startPoint, segment),
(t, p) => create(p),
t => create(segment.EndPoint));
}
public EllipticalArcEquation(Point startPoint, EllipticalArcSegment segment)
{
var phi = ToRadians(segment.XAxisRotation);
_cos = Cos(phi);
_sin = Sin(phi);
var mid = (startPoint - segment.EndPoint) / 2;
var x1 = _cos * mid.X + _sin * mid.Y;
var y1 = -_sin * mid.X + _cos * mid.Y;
_rx = segment.Radii.X;
_ry = segment.Radii.Y;
var lambda = Square(x1 / _rx) + Square(y1 / _ry);
if (lambda > 1)
{
lambda = Sqrt(lambda);
_rx *= lambda;
_ry *= lambda;
}
var sqrt = Sqrt(Square(_rx * _ry) / (Square(_rx * y1) + Square(x1 * _ry)) - 1);
var sign = segment.IsLargeArc != segment.IsSweep ? 1 : -1;
var cx1 = sign * sqrt * _rx * y1 / _ry;
var cy1 = -sign * sqrt * _ry * x1 / _rx;
var avg = (startPoint + segment.EndPoint) / 2;
_cx = _cos * cx1 - _sin * cy1 + avg.X;
_cy = _sin * cx1 + _cos * cy1 + avg.Y;
_theta1 = ToDegrees(Atan2((y1 - cy1) / _ry, (x1 - cx1) / _rx));
var theta2 = ToDegrees(Atan2((-y1 - cy1) / _ry, (-x1 - cx1) / _rx));
_deltaTheta = (theta2 - _theta1) % 360;
_isSweep = segment.IsSweep;
if (_isSweep)
{
if (_deltaTheta < 0)
{
_deltaTheta += 360;
}
}
else
{
if (_deltaTheta > 0)
{
_deltaTheta -= 360;
}
}
_theta1 = ToRadians(_theta1);
_deltaTheta = ToRadians(_deltaTheta);
}
public static List<Point> Approximate(Point startPoint, EllipticalArcSegment segment)
{
return Approximate(new EllipticalArcEquation(startPoint, segment).GetPoint, startPoint, segment.EndPoint);
}
