C# 从直线到用户输入图形路径的最长距离

Question

我有一个由 PointF 数组定义的 GraphicsPath（通过鼠标单击创建），它由 Graphics.DrawCurve 绘制。然后将路径转换为将起点和终点旋转到 0 度。变换和旋转的曲线（和原始曲线）PointF 数组仍然可用。

我需要找到从路径的直线端点到曲线本身的最长垂直距离。

transformed output example

因为我已经旋转了曲线，找到最长的距离应该与边界的高度相同......但我还需要知道沿着（现在是什么）0轴的距离是（如果我能找到曲线，这将很容易）。我进行了广泛的搜索-我尝试了自定义样条函数来尝试沿曲线获得更多固定点，但这最终以相同的结果结束-我不知道这些点之间的曲线是什么，那就是给定点之间的插值，90% 的可能性是这种情况。

现在它已经旋转了，我尝试了一个 for 循环来计算顶部，并且在每一列中，尝试查看每个点是否相对于转换后的路径可见，但它总是 returns 错误.

输入点数（供参考）：{X=499,Y=64} {X=305,Y=117} {X=149,Y=114}

（从左到右，我知道我需要做一些检查以查看将来它们的输入方式，但现在，只是试图让它工作）

    GraphicsPath gP = new GraphicsPath();
gP.AddCurve(lPoints.ToArray());

Graphics g = pbImage.CreateGraphics();
g.SmoothingMode = SmoothingMode.AntiAlias;

//draws original curve (hiding for now to validate and visualize rotation:
//g.DrawPath(new Pen(Color.Blue, 1.75f), gP);
//g.DrawLine(new Pen(Color.Red, 1.75f), lPoints[0], lPoints[lPoints.Count - 1]);

// get angle in radians
double theta2 = Math.Atan2(lPoints[0].Y - lPoints[lPoints.Count - 1].Y, lPoints[0].X - lPoints[lPoints.Count - 1].X);

// convert radians to degrees
double angle = -1 * (theta2 * (180.0 / Math.PI));

//set a new path to the old one, to keep both sets of data
GraphicsPath newPath = gP;

//create rotational matrix, and transform
Matrix m = new Matrix();
m.RotateAt(Convert.ToSingle(angle), lPoints[0]);
newPath.Transform(m);

//draw transformed path to picture box
g.DrawPath(new Pen(Color.Green, 1f), newPath);

//get new points from transformed curve (interestingly enough, it adds more points than the oringial input)
PointF[] tP = newPath.PathPoints;

//create some temp variables to make the next section easier
PointF pS = tP[0];
PointF pE = tP[tP.Length - 1];

//draw the straight line for visual validation
g.DrawLine(new Pen(Color.Red, 1f), pS, pE);

//get the bounds of the new path
RectangleF bRect = newPath.GetBounds();
a
// loop through x's
for (float i = pE.X; i < pS.X; i = i + 5)
{
    float h = pS.Y - bRect.Y;
    bool bFound = false;

    // loop through y's - do loop until found
    do
    {
        if (newPath.IsVisible(i, h, g))
        {
            // never found
            tbOutPt.Text = tbOutPt.Text + "found!!!!";
            bFound = true;
        }
        h++;
    } while (bFound = false && h < bRect.Height);

}

我唯一能想到的另一件事是基于边界创建一个新的位图，重新绘制曲线，然后逐列获取像素颜色，直到它与曲线的颜色相匹配绘制。

希望有人有比这更好的解决方案。

Answer 1

Flatten() GraphicsPath，然后遍历结果点并使用标准 "Point to Line Distance" 测量找到最大距离：

private float PointToLineDist(float Px, float Py, float Ax, float Ay, float Bx, float By)
{
    float q = 0;
    if ((Ax == Bx) & (Ay == By)) {
        // A and B passed in define a point, not a line.
        // Point to Point Distance
        return PointToPointDist(Px, Py, Ax, Ay);
    } else {
        // Distance is the length of the line needed to connect the point to
        // the(segment)such that the two lines would be perpendicular.

        // q is the parameterized value needed to get to the intersection
        q = ((Px - Ax) * (Bx - Ax) + (Py - Ay) * (By - Ay)) / ((Bx - Ax) * (Bx - Ax) + (By - Ay) * (By - Ay));

        // Limit q to 0 <= q <= 1
        // If q is outside this range then the Point is somewhere past the 
        // endpoints of our segment.  By setting q = 0 or q = 1 we are 
        // measuring the actual distacne from the point to one of the 
        // endpoints(instead)
        if (q < 0)
            q = 0;
        if (q > 1)
            q = 1;

        // Distance
        return PointToPointDist(Px, Py, (1 - q) * Ax + q * Bx, (1 - q) * Ay + q * By);
    }
}

private float PointToPointDist(float Ax, float Ay, float Bx, float By)
{
    // PointToPointDist = SquareRoot((Bx - Ax)^2 + (By - Ay)^2)
    return Math.Sqrt((Bx - Ax) * (Bx - Ax) + (By - Ay) * (By - Ay));
}

在PointToLineDist()中，(Px,Py)为问题点，(Ax,Ay),(Bx,By)为线段的端点。

Answer 2

这是为将来的人生成的代码：

private void processArray()
{

// this is for demo only - real points should come from mouse input, or otherwise
PointF[] inputArray = new PointF[2];

inputArray[0] = new PointF(537, 147);
inputArray[1] = new PointF(334, 180);
inputArray[2] = new PointF(150, 167);

GraphicsPath gP = new GraphicsPath();
gP.AddCurve(inputArray);

Graphics g = pbImage.CreateGraphics();
g.SmoothingMode = SmoothingMode.AntiAlias;

//draws original curve
g.DrawPath(new Pen(Color.Blue, 1.75f), gP);

// draw a straight line between the ends of the curve
//g.DrawLine(new Pen(Color.Red, 1.75f), lPoints[0], lPoints[lPoints.Count - 1]);

// create second path to flatten
GraphicsPath pathFlat = gP;
pathFlat.Flatten();

// get list of points to step through
PointF[] fP = pathFlat.PathPoints;

//variables to store max distance
float maxDistance = 0;
PointF maxDistP = new PointF(0, 0);

foreach (PointF p in fP)
{
    // get the distance from the point to the closet point on the line segment
    float curDist = PointToLineDist(p.X, p.Y, lPoints[0].X, lPoints[0].Y, lPoints[lPoints.Count - 1].X, lPoints[lPoints.Count - 1].Y);

    // check the value against and store the longest point
    if (curDist > maxDistance)
    {
        maxDistance = curDist;
        maxDistP = new PointF(p.X, p.Y);
    }
}

// mark a dot at the longest point
g.DrawRectangle(new Pen(Color.Red), new Rectangle(Convert.ToInt32(maxDistP.X), Convert.ToInt32(maxDistP.Y), 2, 2
}

此功能应全部包含在一个 class 中，以便您可以创建和编辑图形路径并根据需要获取它们的属性。

C# 从直线到用户输入图形路径的最长距离

C# longest distance from a straight line to a user input graphicpath

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