Question

StreamGeometryContext中与省略号相关的唯一方法是ArcTo方法。不幸的是，它非常适合连接线而不是绘制椭圆。

特别是，弧的位置由起点和终点确定。对于一个完整的椭圆，两者显然重合，确切的方向变得不确定。

到目前为止，我发现以100,100大小10,10为中心绘制椭圆的最佳方法是这样的：

using (var ctx = geometry.Open())
{
    ctx.BeginFigure(new Point(100+5, 100), isFilled: true, isClosed: true);
    ctx.ArcTo(
        new Point(100 + 5*Math.Cos(0.01), 100 + 5*Math.Sin(0.01)), // need a small angle but large enough that the ellipse is positioned accurately
        new Size(10/2, 10/2), // docs say it should be 10,10 but in practice it appears that this should be half the desired width/height...
        0, true, SweepDirection.Counterclockwise, true, true);
}

这是非常难看的，并留下一个小的“平坦”区域（虽然在正常的缩放级别不可见）。

我怎样才能使用StreamGeometryContext绘制完整的椭圆？

Answer 1

如您所述，ArcTo无法绘制完整的椭圆。事实上，当你试图减少“平坦”区域时，它会在数值上变得不稳定。另一个考虑因素是弧形绘制比现代硬件上的Bezier绘图要慢。这种最现代的系统使用四条贝塞尔曲线来近似椭圆，而不是绘制一个真正的椭圆。

你可以看到WPF的EllipseGeometry通过执行以下代码，打破DrawBezierFigure方法调用，并检查调试器中的PathFigure来实现这一点：

using(var ctx = geometry.Open())
{
  var ellipse = new EllipseGeometry(new Point(100,100), 10, 10);
  var figure = PathGeometry.CreateFromGeometry(ellipse).Figures[0];
  DrawBezierFigure(ctx, figure);
}

void DrawBezierFigure(StreamGeometryContext ctx, PathFigure figure)
{
  ctx.BeginFigure(figure.StartPoint, figure.IsFilled, figure.IsClosed);
  foreach(var segment in figure.Segments.OfType<BezierSegment>())
    ctx.BezierTo(segment.Point1, segment.Point2, segment.Point3, segment.IsStroked, segment.IsSmoothJoin);
}

上面的代码是一种将有效椭圆绘制到StreamGeometry中的简单方法，但它是一种非常特殊的代码。在实际应用中，我使用了几个通用的扩展方法，用于将任意几何图形绘制到StreamGeometryContext中，所以我可以简单地写一下：

using(var ctx = geometry.Open())
{
  ctx.DrawGeometry(new EllipseGeometry(new Point(100,100), 10, 10));
}

这是DrawGeometry扩展方法的实现：

public static class GeometryExtensions
{
  public static void DrawGeometry(this StreamGeometryContext ctx, Geometry geo)
  {
    var pathGeometry = geo as PathGeometry ?? PathGeometry.CreateFromGeometry(geo);
    foreach(var figure in pathGeometry.Figures)
      ctx.DrawFigure(figure);
  }

  public static void DrawFigure(this StreamGeometryContext ctx, PathFigure figure)
  {
    ctx.BeginFigure(figure.StartPoint, figure.IsFilled, figure.IsClosed);
    foreach(var segment in figure.Segments)
    {
      var lineSegment = segment as LineSegment;
      if(lineSegment!=null) { ctx.LineTo(lineSegment.Point, lineSegment.IsStroked, lineSegment.IsSmoothJoin); continue; }

      var bezierSegment = segment as BezierSegment;
      if(bezierSegment!=null) { ctx.BezierTo(bezierSegment.Point1, bezierSegment.Point2, bezierSegment.Point3, bezierSegment.IsStroked, bezierSegment.IsSmoothJoin); continue; }

      var quadraticSegment = segment as QuadraticBezierSegment;
      if(quadraticSegment!=null) { ctx.QuadraticBezierTo(quadraticSegment.Point1, quadraticSegment.Point2, quadraticSegment.IsStroked, quadraticSegment.IsSmoothJoin); continue; }

      var polyLineSegment = segment as PolyLineSegment;
      if(polyLineSegment!=null) { ctx.PolyLineTo(polyLineSegment.Points, polyLineSegment.IsStroked, polyLineSegment.IsSmoothJoin); continue; }

      var polyBezierSegment = segment as PolyBezierSegment;
      if(polyBezierSegment!=null) { ctx.PolyBezierTo(polyBezierSegment.Points, polyBezierSegment.IsStroked, polyBezierSegment.IsSmoothJoin); continue; }

      var polyQuadraticSegment = segment as PolyQuadraticBezierSegment;
      if(polyQuadraticSegment!=null) { ctx.PolyQuadraticBezierTo(polyQuadraticSegment.Points, polyQuadraticSegment.IsStroked, polyQuadraticSegment.IsSmoothJoin); continue; }

      var arcSegment = segment as ArcSegment;
      if(arcSegment!=null) { ctx.ArcTo(arcSegment.Point, arcSegment.Size, arcSegment.RotationAngle, arcSegment.IsLargeArc, arcSegment.SweepDirection, arcSegment.IsStroked, arcSegment.IsSmoothJoin); continue; }
    }
  }
}

另一种选择是自己计算积分。通过将控制点设置为半径的（Math.Sqrt（2）-1）* 4/3，可以找到椭圆的最佳近似值。因此，您可以显式计算点并绘制Bezier，如下所示：

const double ControlPointRatio = (Math.Sqrt(2)-1)*4/3;

var x0 = centerX - radiusX;
var x1 = centerX - radiusX * ControlPointRatio;
var x2 = centerX;
var x3 = centerX + radiusX * ControlPointRatio;
var x4 = centerX + radiusX;

var y0 = centerY - radiusY;
var y1 = centerY - radiusY * ControlPointRatio;
var y2 = centerY;
var y3 = centerY + radiusY * ControlPointRatio;
var y4 = centerY + radiusY;

ctx.BeginFigure(new Point(x2,y0), true, true);
ctx.BezierTo(new Point(x3, y0), new Point(x4, y1), new Point(x4,y2), true, true);
ctx.BezierTo(new Point(x4, y3), new Point(x3, y4), new Point(x2,y4), true, true);
ctx.BezierTo(new Point(x1, y4), new Point(x0, y3), new Point(x0,y2), true, true);
ctx.BezierTo(new Point(x0, y1), new Point(x1, y0), new Point(x2,y0), true, true);

另一个选择是使用两个ArcTo调用，但正如我之前提到的那样效率较低。如果你想这样做，我相信你可以弄清楚两个ArcTo调用的细节。

如何在WPF中的StreamGeometry中绘制完整的椭圆？

1 个答案: