有没有人有一个很好的算法来计算ArcSegment的终点？这不是圆弧，而是椭圆弧。
例如，我有这些初始值：
起点X = 0.251
起点Y = 0.928
宽度半径= 0.436
高度半径= 0.593
起始角度= 169.51
扫描角= 123.78
我知道我的弧线应终止的位置在X = 0.92和Y = 0.33左右（通过另一个程序），但是我需要在ArcSegment中指定终点。我只需要知道如何计算终点就可以了：
<ArcSegment Size="0.436,0.593" Point="0.92,0.33" IsLargeArc="False" SweepDirection="Clockwise" />
有人知道计算这个的好方法吗？ （我不认为这是WPF还是其他语言，因为数学应该是相同的）。
这是一张图片。除终点（橙色点）外，其中所有值都是已知的。
编辑：
我发现有一个名为
DrawArc with an overload in .NET GDI+的例程，几乎可以满足我的需要（在几秒钟内就可以完成更多操作）。为了简化查看，请以以下示例为例：
Public Sub MyDrawArc(e As PaintEventArgs)
Dim blackPen As New Pen(Color.Black, 2)
Dim x As Single = 0.0F
Dim y As Single = 0.0F
Dim width As Single = 100.0F
Dim height As Single = 200.0F
Dim startAngle As Single = 180.0F
Dim sweepAngle As Single = 135.0F
e.Graphics.DrawArc(blackPen, x, y, width, height, startAngle, sweepAngle)
Dim redPen As New Pen(Color.Red, 2)
e.Graphics.DrawLine(redPen, New Point(0, 55), New Point(95, 55))
End Sub
Private Sub ImageBox_Paint(sender As Object, e As System.Windows.Forms.PaintEventArgs) Handles ImageBox.Paint
MyDrawArc(e)
End Sub
此例程将结束点直接放在
X=95, Y=55。提及的其他用于椭圆的例程将导致X=85, Y=29。如果有办法1）不必绘制任何东西，2）使e.Graphics.DrawArc返回终点坐标，这就是我所需要的。现在，问题变得更加清晰了-有人知道
e.Graphics.DrawArc是如何实现的吗？ 最佳答案
有谁知道e.Graphics.DrawArc是如何实现的？Graphics.DrawArc调用gdiplus.dll中的本机函数GdipDrawArcI。此函数在同一dll中调用arc2polybezier函数。似乎使用贝塞尔曲线来近似椭圆弧。为了获得与您正在寻找的终点完全相同的端点，我们必须对该功能进行反向工程，并弄清楚其工作原理。
幸运的是，Wine的好人有already done that for us。
这是arc2polybezier方法，大致从C转换为C＃（请注意，由于此方法是从Wine转换的，因此该代码已在LGPL下获得许可）：
internal class GdiPlus
{
public const int MAX_ARC_PTS = 13;
public static int arc2polybezier(Point[] points, double x1, double y1, double x2, double y2,
double startAngle, double sweepAngle)
{
int i;
double end_angle, start_angle, endAngle;
endAngle = startAngle + sweepAngle;
unstretch_angle(ref startAngle, x2/2.0, y2/2.0);
unstretch_angle(ref endAngle, x2/2.0, y2/2.0);
/* start_angle and end_angle are the iterative variables */
start_angle = startAngle;
for(i = 0; i < MAX_ARC_PTS - 1; i += 3)
{
/* check if we've overshot the end angle */
if(sweepAngle > 0.0)
{
if(start_angle >= endAngle) break;
end_angle = Math.Min(start_angle + Math.PI/2, endAngle);
}
else
{
if(start_angle <= endAngle) break;
end_angle = Math.Max(start_angle - Math.PI/2, endAngle);
}
if(points != null)
{
Point[] returnedPoints = add_arc_part(x1, y1, x2, y2, start_angle, end_angle, i == 0);
//add_arc_part returns a Point[] of size 4
for(int j = 0; j < 4; j++)
points[i + j] = returnedPoints[j];
}
start_angle += Math.PI/2*(sweepAngle < 0.0 ? -1.0 : 1.0);
}
if(i == 0)
return 0;
return i + 1;
}
public static void unstretch_angle(ref double angle, double rad_x, double rad_y)
{
angle = deg2rad(angle);
if(Math.Abs(Math.Cos(angle)) < 0.00001 || Math.Abs(Math.Sin(angle)) < 0.00001)
return;
double stretched = Math.Atan2(Math.Sin(angle)/Math.Abs(rad_y), Math.Cos(angle)/Math.Abs(rad_x));
int revs_off = (int)Math.Round(angle/(2.0*Math.PI), MidpointRounding.AwayFromZero) -
(int)Math.Round(stretched/(2.0*Math.PI), MidpointRounding.AwayFromZero);
stretched += revs_off*Math.PI*2.0;
angle = stretched;
}
public static double deg2rad(double degrees)
{
return Math.PI*degrees/180.0;
}
private static Point[] add_arc_part(double x1, double y1, double x2, double y2,
double start, double end, bool write_first)
{
double center_x,
center_y,
rad_x,
rad_y,
cos_start,
cos_end,
sin_start,
sin_end,
a,
half;
int i;
rad_x = x2/2.0;
rad_y = y2/2.0;
center_x = x1 + rad_x;
center_y = y1 + rad_y;
cos_start = Math.Cos(start);
cos_end = Math.Cos(end);
sin_start = Math.Sin(start);
sin_end = Math.Sin(end);
half = (end - start)/2.0;
a = 4.0/3.0*(1 - Math.Cos(half))/Math.Sin(half);
Point[] pt = new Point[4];
if(write_first)
{
pt[0].X = cos_start;
pt[0].Y = sin_start;
}
pt[1].X = cos_start - a*sin_start;
pt[1].Y = sin_start + a*cos_start;
pt[3].X = cos_end;
pt[3].Y = sin_end;
pt[2].X = cos_end + a*sin_end;
pt[2].Y = sin_end - a*cos_end;
/* expand the points back from the unit circle to the ellipse */
for(i = (write_first ? 0 : 1); i < 4; i ++)
{
pt[i].X = pt[i].X*rad_x + center_x;
pt[i].Y = pt[i].Y*rad_y + center_y;
}
return pt;
}
}
使用此代码作为指南，并结合了一些数学运算，我编写了以下端点计算器类（不是LGPL）：
using System;
using System.Windows;
internal class DrawArcEndPointCalculator
{
public Point GetFinalPoint(Point startPoint, double width, double height,
double startAngle, double sweepAngle)
{
Point radius = new Point(width / 2.0, height / 2.0);
double endAngle = startAngle + sweepAngle;
int sweepDirection = (sweepAngle < 0 ? -1 : 1);
//Adjust the angles for the radius width/height
startAngle = UnstretchAngle(startAngle, radius);
endAngle = UnstretchAngle(endAngle, radius);
//Determine how many times to add the sweep-angle to the start-angle
int angleMultiplier = (int)Math.Floor(2*sweepDirection*(endAngle - startAngle)/Math.PI) + 1;
angleMultiplier = Math.Min(angleMultiplier, 4);
//Calculate the final resulting angle after sweeping
double calculatedEndAngle = startAngle + angleMultiplier*Math.PI/2*sweepDirection;
calculatedEndAngle = sweepDirection*Math.Min(sweepDirection * calculatedEndAngle, sweepDirection * endAngle);
//Calculate the final point
return new Point
{
X = (Math.Cos(calculatedEndAngle) + 1)*radius.X + startPoint.X,
Y = (Math.Sin(calculatedEndAngle) + 1)*radius.Y + startPoint.Y,
};
}
private double UnstretchAngle(double angle, Point radius)
{
double radians = Math.PI * angle / 180.0;
if(Math.Abs(Math.Cos(radians)) < 0.00001 || Math.Abs(Math.Sin(radians)) < 0.00001)
return radians;
double stretchedAngle = Math.Atan2(Math.Sin(radians) / Math.Abs(radius.Y), Math.Cos(radians) / Math.Abs(radius.X));
int rotationOffset = (int)Math.Round(radians / (2.0 * Math.PI), MidpointRounding.AwayFromZero) -
(int)Math.Round(stretchedAngle / (2.0 * Math.PI), MidpointRounding.AwayFromZero);
return stretchedAngle + rotationOffset * Math.PI * 2.0;
}
}
这里有些例子。请注意，您给出的第一个示例是错误的-对于这些初始值，
DrawArc()的端点为（0.58，0.97），而不是（0.92，0.33）。Point startPoint = new Point(0, 0);
double width = 100;
double height = 200;
double startAngle = 180;
double sweepAngle = 135;
DrawArcEndPointCalculator _endPointCalculator = new DrawArcEndPointCalculator();
Point lastPoint = _endPointCalculator.GetFinalPoint(startPoint, width, height, startAngle, sweepAngle);
Console.WriteLine("X = {0}, Y = {1}", lastPoint.X, lastPoint.Y);
//Output: X = 94.7213595499958, Y = 55.2786404500042
startPoint = new Point(0.251, 0.928);
width = 0.436;
height = 0.593;
startAngle = 169.51;
sweepAngle = 123.78;
_endPointCalculator.GetFinalPoint(startPoint, width, height, startAngle, sweepAngle);
//Returns X = 0.579143189905416, Y = 0.968627455618129
Point startPoint = new Point(0, 0);
double width = 20;
double height = 30;
double startAngle = 90;
double sweepAngle = 90;
_endPointCalculator.GetFinalPoint(startPoint, width, height, startAngle, sweepAngle);
//Returns X = 0, Y = 15