//port from https://github.com/mrdoob/three.js/blob/7e0a78beb9317e580d7fa4da9b5b12be051c6feb/examples/js/loaders/SVGLoader.js#L569
public static IList <Point> Flatten(this ArcSegment segment, Point startPoint)
{
var start = startPoint;
var end = segment.Point;
var rx = segment.Size.Width;
var ry = segment.Size.Height;
var x_axis_rotation = segment.RotationAngle;
var large_arc_flag = segment.IsLargeArc ? 1 : 0;
var sweep_flag = (int)segment.SweepDirection;
// Ensure radii are positive
rx = Math.Abs(rx);
ry = Math.Abs(ry);
// Compute (x1′, y1′)
var dx2 = (start.x - end.x) / 2.0;
var dy2 = (start.y - end.y) / 2.0;
var x1p = Math.Cos(x_axis_rotation) * dx2 + Math.Sin(x_axis_rotation) * dy2;
var y1p = -Math.Sin(x_axis_rotation) * dx2 + Math.Cos(x_axis_rotation) * dy2;
// Compute (cx′, cy′)
var rxs = rx * rx;
var rys = ry * ry;
var x1ps = x1p * x1p;
var y1ps = y1p * y1p;
// Ensure radii are large enough
var cr = x1ps / rxs + y1ps / rys;
if (cr > 1)
{
// scale up rx,ry equally so cr == 1
var s = Math.Sqrt(cr);
rx = s * rx;
ry = s * ry;
rxs = rx * rx;
rys = ry * ry;
}
var dq = (rxs * y1ps + rys * x1ps);
var pq = (rxs * rys - dq) / dq;
var q = Math.Sqrt(Math.Max(0, pq));
if (large_arc_flag == sweep_flag)
{
q = -q;
}
var cxp = q * rx * y1p / ry;
var cyp = -q * ry * x1p / rx;
// Step 3: Compute (cx, cy) from (cx′, cy′)
var cx = Math.Cos(x_axis_rotation) * cxp - Math.Sin(x_axis_rotation) * cyp + (start.x + end.x) / 2;
var cy = Math.Sin(x_axis_rotation) * cxp + Math.Cos(x_axis_rotation) * cyp + (start.y + end.y) / 2;
// Step 4: Compute θ1 and Δθ
var theta = svgAngle(1, 0, (x1p - cxp) / rx, (y1p - cyp) / ry);
var delta = svgAngle((x1p - cxp) / rx, (y1p - cyp) / ry, (-x1p - cxp) / rx, (-y1p - cyp) / ry) % (Math.PI * 2);
var curve = new EllipseCurve(cx, cy, rx, ry, theta, theta + delta, sweep_flag == 0, x_axis_rotation);
// Calculate number of points for polyline approximation
var max = (int)(Math.Abs(delta) / MathEx.Deg2Rad(3));
IList <Point> points = new List <Point>(max);
for (double i = 0; i <= max; i++)
{
var p = curve.getPoint(i / max);
points.Add(p);
}
return(points);
}
public void ArcTo(Point point, double radius, double rotationAngle, bool isLargeArc, SweepDirection sweepDirection, bool isStroked)
{
ArcSegment segment = new ArcSegment(point, new Size(radius, radius), rotationAngle, isLargeArc, sweepDirection, isStroked);
Figure.Segments.Add(segment);
}
public void EllipseArcTo(Point point, Size size, double rotationAngle, bool isLargeArc, SweepDirection sweepDirection, bool isStroked)
{
ArcSegment segment = new ArcSegment(point, size, rotationAngle, isLargeArc, sweepDirection, isStroked);
Figure.Segments.Add(segment);
}
/// <summary>
/// Flatten the ArcSegment into a List of Points
/// </summary>
/// <param name="segment">the arc segment</param>
/// <param name="startPoint">start point</param>
/// <param name="tolerance">tolerance</param>
/// <returns>flattened point list</returns>
/// <remarks>
/// ref: http://www.charlespetzold.com/blog/2008/01/Mathematics-of-ArcSegment.html
/// </remarks>
public static IList <Point> Flatten(this ArcSegment segment, Point startPoint /*start point*/,
double tolerance = 1)
{
var pt1 = startPoint;
var pt2 = segment.Point;
var radiusX = segment.Size.Width;
var radiusY = segment.Size.Height;
var angleRotation = segment.RotationAngle;
var isLargeArc = segment.IsLargeArc;
var isCounterclockwise = segment.SweepDirection == SweepDirection.Counterclockwise;
// Adjust for different radii and rotation angle
Matrix matx = new Matrix();
matx.Rotate(-angleRotation);
matx.Scale(radiusY / radiusX, 1);
pt1 = matx.Transform(pt1);
pt2 = matx.Transform(pt2);
// Get info about chord that connects both points
Point midPoint = new Point((pt1.X + pt2.X) / 2, (pt1.Y + pt2.Y) / 2);
Vector vect = pt2 - pt1;
double halfChord = vect.Length / 2;
// Get vector from chord to center
Vector vectRotated;
// (comparing two Booleans here!)
if (isLargeArc == isCounterclockwise)
{
vectRotated = new Vector(-vect.Y, vect.X);
}
else
{
vectRotated = new Vector(vect.Y, -vect.X);
}
vectRotated.Normalize();
// Distance from chord to center
double centerDistance = Math.Sqrt(radiusY * radiusY - halfChord * halfChord);
// Calculate center point
Point center = midPoint + centerDistance * vectRotated;
// Get angles from center to the two points
double angle1 = Math.Atan2(pt1.Y - center.Y, pt1.X - center.X);
double angle2 = Math.Atan2(pt2.Y - center.Y, pt2.X - center.X);
// (another comparison of two Booleans!)
if (isLargeArc == (Math.Abs(angle2 - angle1) < Math.PI))
{
if (angle1 < angle2)
{
angle1 += 2 * Math.PI;
}
else
{
angle2 += 2 * Math.PI;
}
}
// Invert matrix for final point calculation
matx.Invert();
// Calculate number of points for polyline approximation
int max = (int)((4 * (radiusX + radiusY) * Math.Abs(angle2 - angle1) / (2 * Math.PI)) / tolerance);
IList <Point> points = new List <Point>(max);
// Loop through the points
for (int i = 0; i <= max; i++)
{
double angle = ((max - i) * angle1 + i * angle2) / max;
double x = center.X + radiusY * Math.Cos(angle);
double y = center.Y + radiusY * Math.Sin(angle);
// Transform the point back
Point pt = matx.Transform(new Point(x, y));
points.Add(pt);
}
return(points);
}
