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fix Intersect(BezierCurve, Line) and add tests

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This commit is contained in:
BobLd
2020-02-18 12:05:08 +00:00
committed by Eliot Jones
parent 2878e74017
commit 67c5abf2b6
2 changed files with 508 additions and 131 deletions
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132
src/UglyToad.PdfPig/Geometry/GeometryExtensions.cs
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@@ -485,7 +485,6 @@
/// </summary>
public static PdfPoint? Intersect(this PdfLine line, PdfLine other)
{
if (!line.IntersectsWith(other)) return null;
return Intersect(line.Point1, line.Point2, other.Point1, other.Point2);
}
@@ -494,7 +493,6 @@
/// </summary>
public static PdfPoint? Intersect(this PdfLine line, PdfPath.Line other)
{
if (!line.IntersectsWith(other)) return null;
return Intersect(line.Point1, line.Point2, other.From, other.To);
}
@@ -547,7 +545,6 @@
/// </summary>
public static PdfPoint? Intersect(this PdfPath.Line line, PdfPath.Line other)
{
if (!line.IntersectsWith(other)) return null;
return Intersect(line.From, line.To, other.From, other.To);
}
@@ -556,7 +553,6 @@
/// </summary>
public static PdfPoint? Intersect(this PdfPath.Line line, PdfLine other)
{
if (!line.IntersectsWith(other)) return null;
return Intersect(line.From, line.To, other.Point1, other.Point2);
}
@@ -604,7 +600,7 @@
return tx >= 0 && (tx - 1) <= epsilon;
}
public static bool IntersectsWith(PdfPoint p11, PdfPoint p12, PdfPoint p21, PdfPoint p22)//this PdfPath.Line line, PdfPath.Line other)
public static bool IntersectsWith(PdfPoint p11, PdfPoint p12, PdfPoint p21, PdfPoint p22)
{
return (ccw(p11, p12, p21) != ccw(p11, p12, p22)) &&
(ccw(p21, p22, p11) != ccw(p21, p22, p12));
@@ -612,6 +608,8 @@
private static PdfPoint? Intersect(PdfPoint p11, PdfPoint p12, PdfPoint p21, PdfPoint p22)
{
if (!IntersectsWith(p11, p12, p21, p22)) return null;
var eq1 = GetSlopeIntercept(p11, p12);
var eq2 = GetSlopeIntercept(p21, p22);
@@ -659,6 +657,7 @@
bezierCurve.SecondControlPoint,
bezierCurve.EndPoint
};
points[1] = new PdfPoint[3];
points[2] = new PdfPoint[2];
points[3] = new PdfPoint[1];
@@ -677,14 +676,49 @@
new PdfPath.BezierCurve(points[3][0], points[2][1], points[1][2], points[0][3]));
}
/// <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);
}
/// <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);
}
private static bool IntersectsWith(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
return Intersect(bezierCurve, p1, p2).Length > 0;
}
/// <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, PdfLine line)
{
var ts = FindIntersectionT(bezierCurve, line);
if (ts == null || !ts.Any()) return null;
return Intersect(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 PdfPoint[] Intersect(PdfPath.BezierCurve bezierCurve, PdfPoint p1, PdfPoint p2)
{
var ts = FindIntersectionT(bezierCurve, p1, p2);
if (ts == null || !ts.Any()) return EmptyArray<PdfPoint>.Instance;
List<PdfPoint> points = new List<PdfPoint>();
foreach (var t in ts)
@@ -700,36 +734,7 @@
bezierCurve.SecondControlPoint.Y,
bezierCurve.EndPoint.Y,
t));
points.Add(point);
}
return points.ToArray();
}
/// <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 == null || !ts.Any()) 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);
if (Contains(p1, p2, point)) points.Add(point);
}
return points.ToArray();
}
@@ -740,21 +745,7 @@
/// <returns>List of t values where the <see cref="PdfPath.BezierCurve"/> and the <see cref="PdfLine"/> intersect.</returns>
public static double[] FindIntersectionT(this PdfPath.BezierCurve bezierCurve, PdfLine 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 (!bezierBbox.Value.IntersectsWith(lineBbox))
{
return null;
}
double x1 = line.Point1.X;
double y1 = line.Point1.Y;
double x2 = line.Point2.X;
double y2 = line.Point2.Y;
return FindIntersectionT(bezierCurve, x1, y1, x2, y2);
return FindIntersectionT(bezierCurve, line.Point1, line.Point2);
}
/// <summary>
@@ -762,30 +753,29 @@
/// </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)
{
return FindIntersectionT(bezierCurve, line.From, line.To);
}
private static double[] FindIntersectionT(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;
var lineBbox = line.GetBoundingRectangle();
if (!lineBbox.HasValue) return null;
if (!bezierBbox.Value.IntersectsWith(lineBbox.Value))
if (bezierBbox.Value.Left > Math.Max(p1.X, p2.X) || Math.Min(p1.X, p2.X) > bezierBbox.Value.Right)
{
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);
}
if (bezierBbox.Value.Top < Math.Min(p1.Y, p2.Y) || Math.Max(p1.Y, p2.Y) < bezierBbox.Value.Bottom)
{
return null;
}
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 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);
@@ -799,7 +789,7 @@
var solution = SolveCubicEquation(a, b, c, d);
return solution.Where(s => !double.IsNaN(s)).Where(s => s >= -epsilon && s <= 1.0).OrderBy(s => s).ToArray();
return solution.Where(s => !double.IsNaN(s)).Where(s => s >= -epsilon && (s - 1) <= epsilon).OrderBy(s => s).ToArray();
}
#endregion
@@ -836,7 +826,7 @@
/// <param name="d">d</param>
private static double[] SolveCubicEquation(double a, double b, double c, double d)
{
if (Math.Abs(a) <= double.Epsilon)
if (Math.Abs(a) <= epsilon)
{
// handle Quadratic equation (a=0)
double detQ = c * c - 4 * b * d;
@@ -846,7 +836,7 @@
double x0 = (-c - Math.Sqrt(detQ)) / (2.0 * b);
return new double[] { x, x0 };
}
return new double[0]; // no real roots
return EmptyArray<double>.Instance; // no real roots
}
double aSquared = a * a;
@@ -875,7 +865,7 @@
// Complex roots
double complexPart = Math.Sqrt(3) / 2.0 * (S - T); // complex part of complex root
if (Math.Abs(complexPart) <= double.Epsilon) // if complex part == 0
if (Math.Abs(complexPart) <= epsilon) // if complex part == 0
{
// complex roots only have real part
// the real part is the same for both roots