/// <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));
}
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());
}