在来自A的给定的距离计算沿着线AB的点在来自A的给定的距离计算沿着线AB的点(Calculate a

我会很疯狂特林计算点沿给定线AB处从给定的距离，让我可以在两个特定点之间“画”的路线。 这听起来在一开始很简单，但我似乎无法得到它的权利。 更糟糕的是，我不明白的地方我已经错了。 几何（和一般的数学运算）是不是我的套件。

我看过类似的问题，并因此有回答了。 其实我抬起当前实现CalculatePoint功能的直接的Mads Elvheim的答案： 给定一个起点和终点，和距离，计算沿着一条线的一个点 （加上后来评论的修正-如果我正确地理解他），因为我上独立尝试解决的问题是让我无处，除了一流的特快票frusterpationland。

这是我更新的代码（请参阅编辑笔记后的底部）：

using System;
using System.Drawing;
using System.Windows.Forms;

namespace DrawLines
{
    public class MainForm : Form
    {
        // =====================================================================
        // Here's the part I'm having trouble with. I don't really understand
        // how this is suposed to work, so I can't seem to get it right!
        // ---------------------------------------------------------------------

        // A "local indirector" - Just so I don't have go down and edit the 
        // actual call everytime this bluddy thing changes names.
        private Point CalculatePoint(Point a, Point b, int distance) {
            return CalculatePoint_ByAgentFire(a, b, distance);
        }

        #region CalculatePoint_ByAgentFire
        //AgentFire: Better approach (you can rename the struct if you need):
        struct Vector2
        {
            public readonly double X;
            public readonly double Y;
            public Vector2(double x, double y) {
                this.X = x;
                this.Y = y;
            }
            public static Vector2 operator -(Vector2 a, Vector2 b) {
                return new Vector2(b.X - a.X, b.Y - a.Y);
            }
            public static Vector2 operator *(Vector2 a, double d) {
                return new Vector2(a.X * d, a.Y * d);
            }
            public override string ToString() {
                return string.Format("[{0}, {1}]", X, Y);
            }
        }
        // For getting the midpoint you just need to do the (a - b) * d action:
        //static void Main(string[] args)
        //{
        //    Vector2 a = new Vector2(1, 1);
        //    Vector2 b = new Vector2(3, 1);
        //    float distance = 0.5f; // From 0.0 to 1.0.
        //    Vector2 c = (a - b) * distance;
        //    Console.WriteLine(c);
        //}
        private Point CalculatePoint_ByAgentFire(Point a, Point b, int distance) {
            var vA = new Vector2(a.X, a.Y);
            var vB = new Vector2(b.X, b.Y);
            double lengthOfHypotenuse = LengthOfHypotenuseAsDouble(a,b);
            double portionOfDistanceFromAtoB = distance / lengthOfHypotenuse;
            var vC = (vA - vB) * portionOfDistanceFromAtoB;
            Console.WriteLine("vC="+vC);
            return new Point((int)(vC.X+0.5), (int)(vC.Y+0.5));
        }
        // Returns the length of the hypotenuse rounded to an integer, using
        // Pythagoras' Theorem for right angle triangles: The length of the
        // hypotenuse equals the sum of the square of the other two sides.
        // Ergo: h = Sqrt(a*a + b*b)
        private double LengthOfHypotenuseAsDouble(Point a, Point b) {
            double aSq = Math.Pow(Math.Abs(a.X - b.X), 2); // horizontal length squared
            double bSq = Math.Pow(Math.Abs(b.Y - b.Y), 2); // vertical length  squared
            return Math.Sqrt(aSq + bSq); // length of the hypotenuse
        }

        #endregion

        //dbaseman: I thought something looked strange about the formula ... the question 
        //you linked was how to get the point at a distance after B, whereas you want the
        //distance after A. This should give you the right answer, the start point plus 
        //distance in the vector direction.
        //
        // Didn't work as per: http://s1264.photobucket.com/albums/jj496/corlettk/?action=view&current=DrawLinesAB-broken_zps069161e9.jpg
        //
        private Point CalculatePoint_ByDbaseman(Point a, Point b, int distance) {
            // a. calculate the vector from a to b:
            double vectorX = b.X - a.X;
            double vectorY = b.Y - a.Y;
            // b. calculate the length:
            double magnitude = Math.Sqrt(vectorX * vectorX + vectorY * vectorY);
            // c. normalize the vector to unit length:
            vectorX /= magnitude;
            vectorY /= magnitude;
            // d. calculate and Draw the new vector, which is x1y1 + vxvy * (mag + distance).
            return new Point(
                (int)((double)a.X + vectorX * distance)     // x = col
              , (int)((double)a.Y + vectorY * distance)     // y = row
            );
        }

        // MBo: Try to remove 'magnitude' term in the parentheses both for X and for Y expressions.
        //
        // Didn't work as per: http://s1264.photobucket.com/albums/jj496/corlettk/?action=view&current=DrawLinesAB-broken_zps069161e9.jpg
        //
        //private Point CalculatePoint_ByMBo(Point a, Point b, int distance) {
        //    // a. calculate the vector from a to b:
        //    double vectorX = b.X - a.X;
        //    double vectorY = b.Y - a.Y;
        //    // b. calculate the length:
        //    double magnitude = Math.Sqrt(vectorX * vectorX + vectorY * vectorY);
        //    // c. normalize the vector to unit length:
        //    vectorX /= magnitude;
        //    vectorY /= magnitude;
        //    // d. calculate and Draw the new vector, which is x1y1 + vxvy * (mag + distance).
        //    return new Point(
        //        (int)(  ((double)a.X + vectorX * distance)  +  0.5  )
        //      , (int)(  ((double)a.X + vectorX * distance)  +  0.5  )
        //    );
        //}

        // Didn't work
        //private Point CalculatePoint_ByUser1556110(Point a, Point b, int distance) {
        //    Double magnitude = Math.Sqrt(Math.Pow(b.Y - a.Y, 2) + Math.Pow(b.X - a.X, 2));
        //    return new Point(
        //        (int)(a.X + distance * (b.X - a.X) / magnitude + 0.5)
        //      , (int)(a.Y + distance * (b.Y - a.Y) / magnitude + 0.5)
        //    );
        //}

        // didn't work
        //private static Point CalculatePoint_ByCadairIdris(Point a, Point b, int distance) {
        //    // a. calculate the vector from a to b:
        //    double vectorX = b.X - a.X;
        //    double vectorY = b.Y - a.Y;
        //    // b. calculate the proportion of hypotenuse
        //    double factor = distance / Math.Sqrt(vectorX*vectorX + vectorY*vectorY);
        //    // c. factor the lengths
        //    vectorX *= factor;
        //    vectorY *= factor;
        //    // d. calculate and Draw the new vector,
        //    return new Point((int)(a.X + vectorX), (int)(a.Y + vectorY));
        //}

        // Returns a point along the line A-B at the given distance from A
        // based on Mads Elvheim's answer to:
        // https://stackoverflow.com/questions/1800138/given-a-start-and-end-point-and-a-distance-calculate-a-point-along-a-line
        private Point MyCalculatePoint(Point a, Point b, int distance) {
            // a. calculate the vector from o to g:
            double vectorX = b.X - a.X;
            double vectorY = b.Y - a.Y;
            // b. calculate the length:
            double magnitude = Math.Sqrt(vectorX * vectorX + vectorY * vectorY);
            // c. normalize the vector to unit length:
            vectorX /= magnitude;
            vectorY /= magnitude;
            // d. calculate and Draw the new vector, which is x1y1 + vxvy * (mag + distance).
            return new Point(
                (int)(((double)a.X + vectorX * (magnitude + distance)) + 0.5) // x = col
              , (int)(((double)a.Y + vectorY * (magnitude + distance)) + 0.5) // y = row
            );
        }

        // =====================================================================

        private const int CELL_SIZE = 4; // width and height of each "cell" in the bitmap.

        private readonly Bitmap _bitmap; // to draw on (displayed in picBox1).
        private readonly Graphics _graphics; // to draw with.

        // actual points on _theLineString are painted red.
        private static readonly SolidBrush _thePointBrush = new SolidBrush(Color.Red);
        // ... and are labeled in Red, Courier New, 12 point, Bold
        private static readonly SolidBrush _theLabelBrush = new SolidBrush(Color.Red);
        private static readonly Font _theLabelFont = new Font("Courier New", 12, FontStyle.Bold);

        // the interveening calculated cells on the lines between actaul points are painted Black.
        private static readonly SolidBrush _theLineBrush = new SolidBrush(Color.Black);

        // the points in my line-string.
        private static readonly Point[] _theLineString = new Point[] {
            //          x,   y
            new Point(170,  85), // A
            new Point( 85,  70), // B
            //new Point(209,  66), // C
            //new Point( 98, 120), // D
            //new Point(158,  19), // E
            //new Point(  2,  61), // F
            //new Point( 42, 177), // G
            //new Point(191, 146), // H
            //new Point( 25, 128), // I
            //new Point( 95,  24)  // J
        };

        public MainForm() {
            InitializeComponent();
            // initialise "the graphics system".
            _bitmap = new Bitmap(picBox1.Width, picBox1.Height);
            _graphics = Graphics.FromImage(_bitmap);
            picBox1.Image = _bitmap;
        }

        #region actual drawing on the Grpahics

        private void DrawCell(int x, int y, Brush brush) {
            _graphics.FillRectangle(
                brush
              , x * CELL_SIZE, y * CELL_SIZE    // x, y
              , CELL_SIZE, CELL_SIZE        // width, heigth
            );
        }

        private void DrawLabel(int x, int y, char c) {
            string s = c.ToString();
            _graphics.DrawString(
                s, _theLabelFont, _theLabelBrush
              , x * CELL_SIZE + 5   // x
              , y * CELL_SIZE - 8   // y
            );
        }

        // ... there should be no mention of _graphics or CELL_SIZE below here ...

        #endregion

        #region draw points on form load

        private void MainForm_Load(object sender, EventArgs e) {
            DrawPoints();
        }

        // draws and labels each point in _theLineString
        private void DrawPoints() {
            char c = 'A'; // label text, as a char so we can increment it for each point.
            foreach ( Point p in _theLineString ) {
                DrawCell(p.X, p.Y, _thePointBrush);
                DrawLabel(p.X, p.Y, c++);
            }
        }

        #endregion

        #region DrawLines on button click

        private void btnDrawLines_Click(object sender, EventArgs e) {
            DrawLinesBetweenPointsInTheString();
        }

        // Draws "the lines" between the points in _theLineString.
        private void DrawLinesBetweenPointsInTheString() {
            int n = _theLineString.Length - 1; // one less line-segment than points
            for ( int i = 0; i < n; ++i )
                Draw(_theLineString[i], _theLineString[i + 1]);
            picBox1.Invalidate(); // tell the graphics system that the picture box needs to be repainted.
        }

        // Draws all the cells along the line from Point "a" to Point "b".
        private void Draw(Point a, Point b) {
            int maxDistance = LengthOfHypotenuse(a, b);
            for ( int distance = 1; distance < maxDistance; ++distance ) {
                var point = CalculatePoint(a, b, distance);
                DrawCell(point.X, point.X, _theLineBrush);
            }
        }

        // Returns the length of the hypotenuse rounded to an integer, using
        // Pythagoras' Theorem for right angle triangles: The length of the
        // hypotenuse equals the sum of the square of the other two sides.
        // Ergo: h = Sqrt(a*a + b*b)
        private int LengthOfHypotenuse(Point a, Point b) {
            double aSq = Math.Pow(Math.Abs(a.X - b.X), 2); // horizontal length squared
            double bSq = Math.Pow(Math.Abs(b.Y - b.Y), 2); // vertical length  squared
            return (int)(Math.Sqrt(aSq + bSq) + 0.5); // length of the hypotenuse
        }

        #endregion

        #region Windows Form Designer generated code
        /// <summary>
        /// Required method for Designer support - do not modify
        /// the contents of this method with the code editor.
        /// </summary>
        private void InitializeComponent() {
            this.picBox1 = new System.Windows.Forms.PictureBox();
            this.btnDrawLines = new System.Windows.Forms.Button();
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).BeginInit();
            this.SuspendLayout();
            // 
            // picBox1
            // 
            this.picBox1.Dock = System.Windows.Forms.DockStyle.Fill;
            this.picBox1.Location = new System.Drawing.Point(0, 0);
            this.picBox1.Name = "picBox1";
            this.picBox1.Size = new System.Drawing.Size(1000, 719);
            this.picBox1.TabIndex = 0;
            this.picBox1.TabStop = false;
            // 
            // btnDrawLines
            // 
            this.btnDrawLines.Location = new System.Drawing.Point(23, 24);
            this.btnDrawLines.Name = "btnDrawLines";
            this.btnDrawLines.Size = new System.Drawing.Size(77, 23);
            this.btnDrawLines.TabIndex = 1;
            this.btnDrawLines.Text = "Draw Lines";
            this.btnDrawLines.UseVisualStyleBackColor = true;
            this.btnDrawLines.Click += new System.EventHandler(this.btnDrawLines_Click);
            // 
            // MainForm
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(1000, 719);
            this.Controls.Add(this.btnDrawLines);
            this.Controls.Add(this.picBox1);
            this.Location = new System.Drawing.Point(10, 10);
            this.MinimumSize = new System.Drawing.Size(1016, 755);
            this.Name = "MainForm";
            this.SizeGripStyle = System.Windows.Forms.SizeGripStyle.Hide;
            this.StartPosition = System.Windows.Forms.FormStartPosition.Manual;
            this.Text = "Draw Lines on a Matrix.";
            this.Load += new System.EventHandler(this.MainForm_Load);
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).EndInit();
            this.ResumeLayout(false);
        }

        private System.Windows.Forms.PictureBox picBox1;
        private System.Windows.Forms.Button btnDrawLines;
        #endregion
    }

}

很抱歉，如果这是一个有点长，但这是一个SSCCE从我真正的项目，这是一个实现挖出A *最短路径算法运行MazeOfBolton ...即一个迷宫亚军。

我真正想要做的是预先计算出一个“篱笆”（即一个缓冲MBR迷宫（矩阵），使得“围墙”内的所有点都在一个特定的围绕两个给分（来源和目标））从“两点之间的直线”，以距离快速消除数百-的，成千上万的可能的路径，其正朝着偏离目标。

请注意，这种编程挑战年前关闭，因此没有与“竞争plagerism”这里没有问题。 不，这不是功课，其实我是一个专业的程序员......我只是WAAAAY在这里我的安乐窝，甚至相对简单的几何形状。 叹。

所以......请任何人都可以给我任何指针帮我把CalculatePoint功能正确 ：计算从A给定距离沿线AB点？

在此先感谢您的慷慨...即使在远阅读本。

干杯。 基思。

---

编辑：我刚刚更新了发布的源代码监守：

（1）我才意识到，这不是自包含的。 我忘了单独的MainForm。 设计师 cs文件，我已经追加到发布代码的底部。

（2）的最新版本包含了我到目前为止已经试过，用的photobucket链接什么每个故障看起来像一个图片...他们都是一样的。 伊？ WTF？

我想我的问题可能是在其他地方，像以前由其他人错过了，因为我忘了发布设计器生成的代码中的一些时髦的Windows窗体设置......除了everythingelse（在我的实际项目）正是描绘，我希望它，所以为什么要计算点有什么不同。 我不知道！？！？！？ 我很沮丧，我越来越胡思乱想，所以我想我会离开这个另一天;-)

正好说明我们有多么经常低估要花多少精力才能使一台计算机做任何事......即使只是画一个简单的线条......它甚至不是一个曲线，更何况是一个大圆或横轴墨卡托或任何幻想......只是一个简单的bluddy线！？！？！？ ;-)

非常感谢大家谁贴！

再次干杯。 基思。

Answer 1:

计算矢量AB

首先定义从点A处的向量（1，-1），以从B.点B（2,4）减去一个的载体将是VAB（1,5）。

计算AB的长度

使用勾股定理来计算矢量AB的长度。

|Vab| = SQRT(1²+5²)

长度为（四舍五入）5.1

计算单位矢量

通过其长度除以矢量得到的单位矢量（长度为1的向量）。

V1(1/5.1,5/5.1) = V1(0.2, 0.98)

计算矢量与长度4

现在乘V1与你想要的长度，例如4，得到的Vt。

Vt(0.2*4,0.98*4) = Vt(0.8,3.92)

计算目标点

添加矢量的Vt到A地去点T（目标）。

T = A + Vt = T(1.8,2.92)

编辑：回答您的编辑

该方法LengthOfHypotenuse看起来应该

• 固定在计算BSQ错误
• 并删除冗余Math.Abs​​打电话，因为2战俘始终为正
• 除去加入0.5，不知道你为什么会需要一个

• 你至少应该使用持股量返回值（双精度或十进制也将工作）

   //You should work with Vector2 class instead of Point and use their Length property private double LengthOfHypotenuse(Point a, Point b) { double aSq = Math.Pow(aX - bX, 2); // horizontal length squared double bSq = Math.Pow(aY - bY, 2); // vertical length squared return Math.Sqrt(aSq + bSq); // length of the hypotenuse } 

该方法绘制（A点，B点）看起来应该：

• 更正DrawCell（）调用

   private void Draw(Point a, Point b) { double maxDistance = LengthOfHypotenuse(a, b); for (int distance = 0; distance < maxDistance; ++distance) { var point = CalculatePoint(new Vector2(a), new Vector2(b), distance); DrawCell(point.X, point.Y, _theLineBrush); } } 

你CalculatePoint（A点，B点，INT距离）方法：

• 有些感动计算到Vector2类

   private Point CalculatePoint(Vector2 a, Vector2 b, int distance) { Vector2 vectorAB = a - b; return a + vectorAB.UnitVector * distance; } 

我已经扩展了Vector类为您丢失的运营商（学分AgentFire）添加

    //AgentFire: Better approach (you can rename the struct if you need):
    struct Vector2 {
        public readonly double X;
        public readonly double Y;
        public Vector2(Point p) : this(p.X,p.Y) { 
        }

        public Vector2(double x, double y) {
            this.X = x;
            this.Y = y;
        }
        public static Vector2 operator -(Vector2 a, Vector2 b) {
            return new Vector2(b.X - a.X, b.Y - a.Y);
        }
        public static Vector2 operator +(Vector2 a, Vector2 b) {
            return new Vector2(b.X + a.X, b.Y + a.Y);
        }
        public static Vector2 operator *(Vector2 a, double d) {
            return new Vector2(a.X * d, a.Y * d);
        }
        public static Vector2 operator /(Vector2 a, double d) {
            return new Vector2(a.X / d, a.Y / d);
        }

        public static implicit operator Point(Vector2 a) {
            return new Point((int)a.X, (int)a.Y);
        }

        public Vector2 UnitVector {
            get { return this / Length; }
        }

        public double Length {
            get {
                double aSq = Math.Pow(X, 2);
                double bSq = Math.Pow(Y, 2);
                return Math.Sqrt(aSq + bSq);
            }
        }

        public override string ToString() {
            return string.Format("[{0}, {1}]", X, Y);
        }
    }

Answer 2:

更好的方法（如果需要你可以重命名结构）：

struct Vector2
{
    public readonly float X;
    public readonly float Y;

    public Vector2(float x, float y)
    {
        this.X = x;
        this.Y = y;
    }

    public static Vector2 operator -(Vector2 a, Vector2 b)
    {
        return new Vector2(b.X - a.X, b.Y - a.Y);
    }
    public static Vector2 operator +(Vector2 a, Vector2 b)
    {
        return new Vector2(a.X + b.X, a.Y + b.Y);
    }
    public static Vector2 operator *(Vector2 a, float d)
    {
        return new Vector2(a.X * d, a.Y * d);
    }

    public override string ToString()
    {
        return string.Format("[{0}, {1}]", X, Y);
    }
}

为了得到中点你只需要做的(a - b) * d + a动作：

class Program
{
    static void Main(string[] args)
    {
        Vector2 a = new Vector2(1, 1);
        Vector2 b = new Vector2(3, 1);
        float distance = 0.5f; // From 0.0 to 1.0.
        Vector2 c = (a - b) * distance + a;
        Console.WriteLine(c);
    }
}

这会给你点：

output:\> [2, 1]

所有之后你需要的是for(the distance; up to one ; d += step)从0.0到1.0和绘制您的像素。

Answer 3:

    private static Point CalculatePoint(Point a, Point b, int distance)
    {

        // a. calculate the vector from o to g:
        double vectorX = b.X - a.X;
        double vectorY = b.Y - a.Y;

        // b. calculate the proportion of hypotenuse
        double factor = distance / Math.Sqrt(vectorX * vectorX + vectorY * vectorY);

        // c. factor the lengths
        vectorX *= factor;
        vectorY *= factor;

        // d. calculate and Draw the new vector,
        return new Point((int)(a.X + vectorX), (int)(a.Y + vectorY));
    }

Answer 4:

尝试删除“幅度”一词在括号既为X和Y的表达式：

(int)(  ((double)a.X + vectorX * distance)  +  0.5  )

Answer 5:

private Point CalculatePoint(Point a, Point b, int distance) {
      Point newPoint = new Point(10,10);
      Double Magnitude = Math.Sqrt(Math.Pow((b.Y - a.Y),2) + Math.Pow((b.X - a.X),2));
      newPoint.X = (int)(a.X + (distance * ((b.X - a.X)/magnitude)));
      newPoint.Y = (int)(a.Y + (distance * ((b.Y - a.Y)/magnitude)));
      return newPoint;
}

Answer 6:

好球员，我发现我的主要错误。 这是一个经典的卫生署！ 我的绘制方法是画在像素，页。 X

于是，我终于得到了一些作品。 请注意，我并不是说这是一个“很好的解决”，或“唯一可行的解​​决方案：”我只是说，它做什么，我想要它做的;-)

这里是我更新的工作代码：（完整和自足这个时候;-)

using System;
using System.Drawing;
using System.Windows.Forms;
using System.Diagnostics;

namespace DrawLines
{
    public class MainForm : Form
    {
        #region constants and readonly attributes

        private const int CELL_SIZE = 4; // width and height of each "cell" in the bitmap.

        private readonly Bitmap _myBitmap; // to draw on (displayed in picBox1).
        private readonly Graphics _myGraphics; // to draw with.

        // actual points on _theLineString are painted red.
        private static readonly SolidBrush _thePointBrush = new SolidBrush(Color.Red);
        // ... and are labeled in /*Bold*/ Black, 16 point Courier New
        private static readonly SolidBrush _theLabelBrush = new SolidBrush(Color.Black);
        private static readonly Font _theLabelFont = new Font("Courier New", 16); //, FontStyle.Bold);

        // the interveening calculated cells on the lines between actaul points are painted Silver.
        private static readonly SolidBrush _theLineBrush = new SolidBrush(Color.Silver);

        // the points in my line-string.
        private static readonly Point[] _thePoints = new Point[] {
            //          x,   y      c i
            new Point(170,  85), // A 0 
            new Point( 85,  70), // B 1
            new Point(209,  66), // C 2
            new Point( 98, 120), // D 3
            new Point(158,  19), // E 4
            new Point(  2,  61), // F 5
            new Point( 42, 177), // G 6
            new Point(191, 146), // H 7
            new Point( 25, 128), // I 8
            new Point( 95,  24)  // J 9
        };

        #endregion

        public MainForm() {
            InitializeComponent();
            // initialise "the graphics system".
            _myBitmap = new Bitmap(picBox1.Width, picBox1.Height);
            _myGraphics = Graphics.FromImage(_myBitmap);
            picBox1.Image = _myBitmap;
        }

        #region DrawPoints upon MainForm_Load

        private void MainForm_Load(object sender, EventArgs e) {
            DrawPoints();
        }

        // draws and labels each point in _theLineString
        private void DrawPoints() {
            char c = 'A'; // label text, as a char so we can increment it for each point.
            foreach ( Point p in _thePoints ) {
                DrawCell(p.X, p.Y, _thePointBrush);
                DrawLabel(p.X, p.Y, c++);
            }
        }

        #endregion

        #region DrawLines on button click

        // =====================================================================
        // Here's the interesting bit. DrawLine was called Draw

        // Draws a line from A to B, by using X-values to calculate the Y values.
        private void DrawLine(Point a, Point b)
        {
            if ( a.Y > b.Y ) // A is below B
                Swap(ref a, ref b); // make A the topmost point (ergo sort by Y)
            Debug.Assert(a.Y < b.Y, "A is still below B!");

            var left = Math.Min(a.X, b.X);
            var right = Math.Max(a.X, b.X);
            int width = right - left;
            Debug.Assert(width >= 0, "width is negative!");

            var top = a.Y;
            var bottom = b.Y;
            int height = bottom - top;
            Debug.Assert(height >= 0, "height is negative!");

            if ( width > height ) {
                // use given X values to calculate the Y values, 
                // otherwise it "skips" some X's
                double slope = (double)height / (double)width; 
                Debug.Assert(slope >= 0, "slope is negative!");
                if (a.X <= b.X)     // a is left-of b, so draw left-to-right.
                    for ( int x=1; x<width; ++x ) // xOffset
                        DrawCell( (left+x), (a.Y + ((int)(slope*x + 0.5))), _theLineBrush);
                else                // a is right-of b, so draw right-to-left.
                    for ( int x=1; x<width; ++x ) // xOffset
                        DrawCell( (right-x), (a.Y + ((int)(slope*x + 0.5))), _theLineBrush);
            } else {
                // use given Y values to calculate the X values, 
                // otherwise it "skips" some Y's
                double slope = (double)width/ (double)height; 
                Debug.Assert(slope >= 0, "slope is negative!");
                if (a.X <= b.X) {     // a is left-of b, so draw left-to-right. (FG)
                    for ( int y=1; y<height; ++y ) // yOffset
                        DrawCell( (a.X + ((int)(slope*y + 0.5))), (top+y), _theLineBrush);
                } else {              // a is right-of b, so draw right-to-left. (DE,IJ)
                    for ( int y=1; y<height; ++y ) // yOffset
                        DrawCell( (b.X + ((int)(slope*y + 0.5))), (bottom-y), _theLineBrush);
                }
            }
        }

        private void btnDrawLines_Click(object sender, EventArgs e) {
            DrawLines();  // join the points
            DrawPoints(); // redraw the labels over the lines.
        }

        // Draws a line between each point in _theLineString.
        private void DrawLines() {
            int n = _thePoints.Length - 1; // one less line-segment than points
            for ( int i=0; i<n; ++i )
                DrawLine(_thePoints[i], _thePoints[i+1]);
            picBox1.Invalidate(); // tell the graphics system that the picture box needs to be repainted.
        }

        private void Swap(ref Point a, ref Point b) {
            Point tmp = a;
            a = b;
            b = tmp;
        }

        #endregion

        #region actual drawing on _myGraphics

        // there should be no calls to Draw or Fill outside of this region

        private void DrawCell(int x, int y, Brush brush) {
            _myGraphics.FillRectangle(
                brush
              , x*CELL_SIZE
              , y*CELL_SIZE 
              , CELL_SIZE   // width
              , CELL_SIZE   // heigth
            );
        }

        private void DrawLabel(int x, int y, char c) {
            string s = c.ToString();
            _myGraphics.DrawString(
                s, _theLabelFont, _theLabelBrush
              , x * CELL_SIZE + 5   // x
              , y * CELL_SIZE - 10  // y
            );
        }

        #endregion

        #region Windows Form Designer generated code
        /// <summary>
        /// Required method for Designer support - do not modify
        /// the contents of this method with the code editor.
        /// </summary>
        private void InitializeComponent() {
            this.picBox1 = new System.Windows.Forms.PictureBox();
            this.btnDrawLines = new System.Windows.Forms.Button();
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).BeginInit();
            this.SuspendLayout();
            // 
            // picBox1
            // 
            this.picBox1.Dock = System.Windows.Forms.DockStyle.Fill;
            this.picBox1.Location = new System.Drawing.Point(0, 0);
            this.picBox1.Name = "picBox1";
            this.picBox1.Size = new System.Drawing.Size(1000, 719);
            this.picBox1.TabIndex = 0;
            this.picBox1.TabStop = false;
            // 
            // btnDrawLines
            // 
            this.btnDrawLines.Location = new System.Drawing.Point(23, 24);
            this.btnDrawLines.Name = "btnDrawLines";
            this.btnDrawLines.Size = new System.Drawing.Size(77, 23);
            this.btnDrawLines.TabIndex = 1;
            this.btnDrawLines.Text = "Draw Lines";
            this.btnDrawLines.UseVisualStyleBackColor = true;
            this.btnDrawLines.Click += new System.EventHandler(this.btnDrawLines_Click);
            // 
            // MainForm
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(1000, 719);
            this.Controls.Add(this.btnDrawLines);
            this.Controls.Add(this.picBox1);
            this.Location = new System.Drawing.Point(10, 10);
            this.MinimumSize = new System.Drawing.Size(1016, 755);
            this.Name = "MainForm";
            this.SizeGripStyle = System.Windows.Forms.SizeGripStyle.Hide;
            this.StartPosition = System.Windows.Forms.FormStartPosition.Manual;
            this.Text = "Draw Lines on a Matrix.";
            this.Load += new System.EventHandler(this.MainForm_Load);
            ((System.ComponentModel.ISupportInitialize)(this.picBox1)).EndInit();
            this.ResumeLayout(false);
        }

        private System.Windows.Forms.PictureBox picBox1;
        private System.Windows.Forms.Button btnDrawLines;
        #endregion
    }

}

编辑-更新上面的代码：此版本绘制“实”线。 先前发布的版本跳过细胞几乎垂直的线，所以我倒算法计算出X值（而不是Y值），在这种情况下......现在我可以用它来设置（并绘制）“固体篱笆”围绕一个“导航区域” ;-)

下面是正确的结果的最新状况。

再次感谢大家谁帮助......你确实帮助;-)

干杯。 基思。

文章来源: Calculate a point along the line A-B at a given distance from A