/// <summary>
/// Split a bezier curve into 2 bezier curves, at tau.
/// </summary>
/// <param name="bezierCurve">The original bezier curve.</param>
/// <param name="tau">The t value were to split the curve, usually between 0 and 1, but not necessary.</param>
public static (PdfPath.BezierCurve, PdfPath.BezierCurve) Split(this PdfPath.BezierCurve bezierCurve, double tau)
{
// De Casteljau Algorithm
PdfPoint[][] points = new PdfPoint[4][];
points[0] = new[]
{
bezierCurve.StartPoint,
bezierCurve.FirstControlPoint,
bezierCurve.SecondControlPoint,
bezierCurve.EndPoint
};
points[1] = new PdfPoint[3];
points[2] = new PdfPoint[2];
points[3] = new PdfPoint[1];
for (int j = 1; j <= 3; j++)
{
for (int i = 0; i <= 3 - j; i++)
{
var x = (1 - tau) * points[j - 1][i].X + tau * points[j - 1][i + 1].X;
var y = (1 - tau) * points[j - 1][i].Y + tau * points[j - 1][i + 1].Y;
points[j][i] = new PdfPoint(x, y);
}
}
return(new PdfPath.BezierCurve(points[0][0], points[1][0], points[2][0], points[3][0]),
new PdfPath.BezierCurve(points[3][0], points[2][1], points[1][2], points[0][3]));
}
private static PdfPoint[] Intersect(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
var ts = IntersectT(bezierCurve, p1, p2);
if (ts == null || ts.Length == 0)
{
return(EmptyArray <PdfPoint> .Instance);
}
List <PdfPoint> points = new List <PdfPoint>();
foreach (var t in ts)
{
PdfPoint point = new PdfPoint(
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.X,
bezierCurve.FirstControlPoint.X,
bezierCurve.SecondControlPoint.X,
bezierCurve.EndPoint.X,
t),
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.Y,
bezierCurve.FirstControlPoint.Y,
bezierCurve.SecondControlPoint.Y,
bezierCurve.EndPoint.Y,
t));
if (Contains(p1, p2, point))
{
points.Add(point);
}
}
return(points.ToArray());
}
/// <summary>
/// Get the t values that are the intersections of the line and the curve.
/// </summary>
/// <returns>List of t values where the <see cref="PdfPath.BezierCurve"/> and the <see cref="PdfPath.Line"/> intersect.</returns>
public static double[] FindIntersectionT(this PdfPath.BezierCurve bezierCurve, PdfPath.Line line)
{
// if the bounding boxes do not intersect, they cannot intersect
var bezierBbox = bezierCurve.GetBoundingRectangle();
if (!bezierBbox.HasValue)
{
return(null);
}
var lineBbox = line.GetBoundingRectangle();
if (!lineBbox.HasValue)
{
return(null);
}
if (!bezierBbox.Value.IntersectsWith(lineBbox.Value))
{
return(null);
}
double x1 = line.From.X;
double y1 = line.From.Y;
double x2 = line.To.X;
double y2 = line.To.Y;
return(FindIntersectionT(bezierCurve, x1, y1, x2, y2));
}
/// <summary>
/// Get the <see cref="PdfPoint"/>s that are the intersections of the line and the curve.
/// </summary>
/// <returns></returns>
public static PdfPoint[] Intersect(this PdfPath.BezierCurve bezierCurve, PdfPath.Line line)
{
var ts = FindIntersectionT(bezierCurve, line);
if (ts.Count() == 0)
{
return(null);
}
List <PdfPoint> points = new List <PdfPoint>();
foreach (var t in ts)
{
PdfPoint point = new PdfPoint(
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.X,
bezierCurve.FirstControlPoint.X,
bezierCurve.SecondControlPoint.X,
bezierCurve.EndPoint.X,
t),
PdfPath.BezierCurve.ValueWithT(bezierCurve.StartPoint.Y,
bezierCurve.FirstControlPoint.Y,
bezierCurve.SecondControlPoint.Y,
bezierCurve.EndPoint.Y,
t)
);
points.Add(point);
}
return(points.ToArray());
}
private static double[] FindIntersectionT(PdfPath.BezierCurve bezierCurve, double x1, double y1, double x2, double y2)
{
double A = (y2 - y1);
double B = (x1 - x2);
double C = x1 * (y1 - y2) + y1 * (x2 - x1);
double alpha = bezierCurve.StartPoint.X * A + bezierCurve.StartPoint.Y * B;
double beta = 3.0 * (bezierCurve.FirstControlPoint.X * A + bezierCurve.FirstControlPoint.Y * B);
double gamma = 3.0 * (bezierCurve.SecondControlPoint.X * A + bezierCurve.SecondControlPoint.Y * B);
double delta = bezierCurve.EndPoint.X * A + bezierCurve.EndPoint.Y * B;
double a = (-alpha + beta - gamma + delta);
double b = (3 * alpha - 2 * beta + gamma);
double c = -3 * alpha + beta;
double d = alpha + C;
var solution = SolveCubicEquation(a, b, c, d);
return(solution.Where(s => !double.IsNaN(s)).Where(s => s >= -double.Epsilon && s <= 1.0).OrderBy(s => s).ToArray());
}
private static double[] IntersectT(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
// if the bounding boxes do not intersect, they cannot intersect
var bezierBbox = bezierCurve.GetBoundingRectangle();
if (!bezierBbox.HasValue)
{
return(null);
}
if (bezierBbox.Value.Left > Math.Max(p1.X, p2.X) || Math.Min(p1.X, p2.X) > bezierBbox.Value.Right)
{
return(null);
}
if (bezierBbox.Value.Top < Math.Min(p1.Y, p2.Y) || Math.Max(p1.Y, p2.Y) < bezierBbox.Value.Bottom)
{
return(null);
}
double A = (p2.Y - p1.Y);
double B = (p1.X - p2.X);
double C = p1.X * (p1.Y - p2.Y) + p1.Y * (p2.X - p1.X);
double alpha = bezierCurve.StartPoint.X * A + bezierCurve.StartPoint.Y * B;
double beta = 3.0 * (bezierCurve.FirstControlPoint.X * A + bezierCurve.FirstControlPoint.Y * B);
double gamma = 3.0 * (bezierCurve.SecondControlPoint.X * A + bezierCurve.SecondControlPoint.Y * B);
double delta = bezierCurve.EndPoint.X * A + bezierCurve.EndPoint.Y * B;
double a = -alpha + beta - gamma + delta;
double b = 3 * alpha - 2 * beta + gamma;
double c = -3 * alpha + beta;
double d = alpha + C;
var solution = SolveCubicEquation(a, b, c, d);
return(solution.Where(s => !double.IsNaN(s)).Where(s => s >= -epsilon && (s - 1) <= epsilon).OrderBy(s => s).ToArray());
}
/// <summary>
/// Get the t values that are the intersections of the line and the curve.
/// </summary>
/// <returns>List of t values where the <see cref="PdfPath.BezierCurve"/> and the <see cref="PdfPath.Line"/> intersect.</returns>
public static double[] IntersectT(this PdfPath.BezierCurve bezierCurve, PdfPath.Line line)
{
return(IntersectT(bezierCurve, line.From, line.To));
}
/// <summary>
/// Get the t values that are the intersections of the line and the curve.
/// </summary>
/// <returns>List of t values where the <see cref="PdfPath.BezierCurve"/> and the <see cref="PdfLine"/> intersect.</returns>
public static double[] IntersectT(this PdfPath.BezierCurve bezierCurve, PdfLine line)
{
return(IntersectT(bezierCurve, line.Point1, line.Point2));
}
/// <summary>
/// Get the <see cref="PdfPoint"/>s that are the intersections of the line and the curve.
/// </summary>
public static PdfPoint[] Intersect(this PdfPath.BezierCurve bezierCurve, PdfPath.Line line)
{
return(Intersect(bezierCurve, line.From, line.To));
}
private static bool IntersectsWith(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
return(Intersect(bezierCurve, p1, p2).Length > 0);
}
/// <summary>
/// Checks if the curve and the line are intersecting.
/// <para>Avoid using this method as it is not optimised. Use <see cref="Intersect(PdfPath.BezierCurve, PdfPath.Line)"/> instead.</para>
/// </summary>
public static bool IntersectsWith(this PdfPath.BezierCurve bezierCurve, PdfPath.Line line)
{
return(IntersectsWith(bezierCurve, line.From, line.To));
}
/// <summary>
/// Checks if the curve and the line are intersecting.
/// <para>Avoid using this method as it is not optimised. Use <see cref="Intersect(PdfPath.BezierCurve, PdfLine)"/> instead.</para>
/// </summary>
public static bool IntersectsWith(this PdfPath.BezierCurve bezierCurve, PdfLine line)
{
return(IntersectsWith(bezierCurve, line.Point1, line.Point2));
}
