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如何在WPF中绘制流几何图形中的完整椭圆?

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Roman Starkov · 技术社区 · 15 年前

唯一的方法 StreamGeometryContext 与椭圆有关的是 ArcTo 方法。不幸的是,它主要用于连接线条,而不是绘制椭圆。

特别是,弧的位置由起点和终点决定。对于一个完整的椭圆,两者显然重合,并且精确的方向变得不确定。

到目前为止,绘制一个以100100为中心的10.10号椭圆的最佳方法如下:

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);
}

这是非常丑陋的,也留下了一个小的“平坦”的区域(虽然在正常的缩放级别不可见)。

不然我怎么画一个完整的椭圆 流几何内容 ?

1 回复 | 直到 15 年前

Ray Burns 15 年前

如您所述,arcto不能绘制完整的椭圆。事实上,当你试图缩小“平面”区域时,它在数值上变得不稳定。另一个需要考虑的问题是,在现代硬件上,圆弧绘制比贝塞尔绘制慢。这个最现代的系统使用四个贝塞尔曲线来近似一个椭圆,而不是画一个真正的椭圆。

您可以看到,WPF的ellipseGeometry通过执行以下代码、中断DrawBezierFigure方法调用并在调试器中检查路径图来实现这一点:

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);
}

上面的代码是将有效椭圆绘制成流几何图形的简单方法,但它是非常特殊的案例代码。在实际操作中,我使用了几种通用的扩展方法,这些方法被定义为将任意几何图形绘制到streamgeometryContext中,因此我可以简单地编写:

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

以下是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点。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,可以显式计算点并绘制贝塞尔曲线,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);

另一种选择是使用两个arcto调用,但正如我前面提到的,这效率较低。如果你想这样做的话,我相信你可以弄清楚两个arcto调用的细节。