计算给定水平线的形状宽度

Question

假设我有这样一个多边形

public partial class Window2 : Window
{
    public Window2()
    {
        InitializeComponent();

        var myPolygon = new Polygon();
        myPolygon.Stroke = Brushes.Black;
        myPolygon.Fill = Brushes.LightSeaGreen;
        myPolygon.StrokeThickness = 2;

        myPolygon.Points = new PointCollection(new Point[] {
            new Point(50,50),
            new Point(50,165),
            new Point(140,165),
            new Point(140,120),
            new Point(70,120),
            new Point(80,70),
            new Point(140,70),
            new Point(140,50)
        });

        this.Content = myPolygon;
    }
}

假设我想绘制从一边到另一边穿过多边形的红线，如下图所示：

我只知道线应该站立的垂直位置，但是我怎么知道我应该从哪个水平点开始线以及哪个水平点结束线？

我的主要目标是知道线从哪个水平点开始和在哪个点结束，以便在这条线上安排文本。

如果线在几个地方穿过形状（如下图所示），我想获得所有线的数组：

请注意，形状可以由直线和拱形组成。

以下是 Adob​​e Illustrator 以形状排列文本的方式：

我如何在 C# 中做到这一点？

谢谢！

注意：对于赏金，请附上 C# 中的示例。

Answer 1

WPF 内置了很多算法，可以避免为像我这样的懒人编写复杂的算法。如果使用得当，Geometry类可以做很多事情，而且性能很好。所以你真的想开始使用几何图形而不是点或形状的集合（它们是更多的 UI 实用程序）。

在这里，我简单地使用几何的组合特征，对于 4 行代码算法：

public static IEnumerable<Rect> ComputeIntersectingSegments(Geometry geometry, double y, double width)
{
    // Add a geometry line to compute intersections.
    // A geometry must not be 0 thickness for combination to be meaningful.
    // So we widen the line by a very small size
    var line = new LineGeometry(new Point(0, y), new Point(width, y)).GetWidenedPathGeometry(new Pen(null, 0.01));

    // Intersect the line with input geometry and compute intersections
    var combined = Geometry.Combine(line, geometry, GeometryCombineMode.Intersect, null);
    foreach (var figure in combined.Figures)
    {
        // the resulting figure can be a complex thing
        // we just want the bounding box
        yield return new PathGeometry(new PathFigure[] { figure }).Bounds;
    }
}

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();

        // use a canvas to display shape and intersections
        var canvas = new Canvas();
        Content = canvas;

        // your polygon can be built as a geometry for example like this:
        // var myPolygon = Geometry.Parse("M50,50 L50,165 L140,165 L140,120 L70,120 L80,70 L140,70 L140,50");

        // build a 'o' shape for testing, add it to the canvas
        var circle1 = new EllipseGeometry(new Point(100, 100), 70, 70);
        var circle2 = new EllipseGeometry(new Point(100, 100), 40, 40);

        // exclude mode will compute the 'o' shape ...
        var oGeometry = new CombinedGeometry(GeometryCombineMode.Exclude, circle1, circle2);

        var oPath = new Path();
        oPath.Stroke = Brushes.Black;
        oPath.Fill = Brushes.LightSeaGreen;
        oPath.StrokeThickness = 2;
        oPath.Data = oGeometry;

        canvas.Children.Add(oPath);

        // test many heights
        for (int y = 0; y < Height; y += 25)
        {
            foreach (var segment in ComputeIntersectingSegments(oGeometry, y, Width))
            {
                // for our sample, we add each segment to the canvas
                // Height is irrelevant, we use 2 for tests
                var line = new Rectangle();
                Canvas.SetLeft(line, segment.X);
                Canvas.SetTop(line, segment.Y);
                line.Width = segment.Width;
                line.Height = 2;
                line.Stroke = Brushes.Red;
                line.StrokeThickness = 1;
                canvas.Children.Add(line);
            }
        }
    }
}

这是结果：