計算機圖形學直線演算法（DDA,中點畫線 ，Bresenham.VS2019 ）

功能：由滑鼠單擊給定初末點位置作出相應直線，

1，打開VS2019 選擇新建專案 Windows 表單應用（.NET framework）

2，此處專案名稱命名為“Computer_Graphics”，專案建立后出現如下視圖
3，在左側工具箱選中“MenuStrip”將其拖入“Form1”表單中

鍵入想要設計的功能，這里設計了如圖所示三種畫直線的演算法

表單設計完成，開始寫代碼，現在代碼區插入如下代碼

        Color BackColor1 = Color.White;              //指定表單背景色
        Color ForeColor1 = Color.Black;              //指定線的顏色
        public int MenuID = 0, PressNum = 0;         //pressnum = 1時畫直線
        public Point Firstpoint = new Point(0, 0);   //定義第一個點
        public Point Secondpoint = new Point(0, 0);  //定義第二個點
        public int Ways = 1;                         //記錄在表單中的操作

由于直線初末位置由滑鼠單擊表單給出，所以要先定義表單的滑鼠單擊回應函式，先單擊選中表單，在界面右下角找到屬性框，點擊“事件”（小閃電圖示）在下面給出的事件中找到“MouseClick”,雙擊進入代碼視窗進入代碼區后，鍵入如下代碼

            Graphics g = CreateGraphics();
            Pen Mypen = new Pen(Color.Red, 1);
            if (MenuID == 1)
            {
                if (PressNum == 0)
                {
                    Firstpoint.X = e.X; Firstpoint.Y = e.Y;
                    Secondpoint.X = e.X; Secondpoint.Y = e.Y;
                }
                else
                {
                    if (Ways == 1)
                    {
                        DDLline(Firstpoint.X, Firstpoint.Y, Secondpoint.X, Secondpoint.Y);//------呼叫DDA畫直線
                    }
                    if (Ways == 2)
                    {
                        Midpoint(Firstpoint.X, Firstpoint.Y, Secondpoint.X, Secondpoint.Y);//------呼叫中點畫線法
                    }
                    if (Ways == 3)
                    {
                        Bresenham(Firstpoint.X, Firstpoint.Y, Secondpoint.X, Secondpoint.Y);//-----呼叫bresenham演算法
                    }
                }
                PressNum++;
                if (PressNum >= 2)
                    PressNum = 0;
            }

此時還需要一個滑鼠移動函式記錄滑鼠在表單中的移動位置，同樣選中表單，在界面右下角找到屬性框，點擊“事件”（小閃電圖示）在下面給出的事件中找到“MouseMove”,雙擊進入代碼視窗

進入代碼區后鍵入如下代碼

            Graphics g = CreateGraphics();
            Pen Backpen = new Pen(BackColor1, 1);
            Pen Mypen = new Pen(ForeColor1, 1);
            if (MenuID == 1 && PressNum == 1)
            {
                if (!(e.X == Secondpoint.X && e.Y == Secondpoint.Y))
                {
                    g.DrawLine(Backpen, Firstpoint.X, Firstpoint.Y, Secondpoint.X, Secondpoint.Y);//底層白線，可不要
                    g.DrawLine(Mypen, Firstpoint.X, Firstpoint.Y, e.X, e.Y);//中間線黑線，可不要
                    Secondpoint.X = e.X;
                    Secondpoint.Y = e.Y;
                }
            }

接下來完善功能代碼，回到“Form1” 視窗，找到之前設計的“DDA畫線法”，雙擊進入代碼區域，鍵入如下代碼

            Ways = 1;
            MenuID = 1;插入代碼片

同樣的方式創立“中點畫線法”，“Bresenham畫線法”單擊回應函式

劃重點：三種直線演算法函式的設計
1.DDA畫線法
代碼區鍵入如下代碼

private void DDLline(int x0, int y0, int x1, int y1)//------------DDA畫直線
        {
            Graphics g = CreateGraphics();
            Pen b = new Pen(Color.Red, 1);
            if (x0 == x1 && y0 == y1)
                return;
            double x = x0, y = y0;
            double dx, dy, k;
            dx = x1 - x0;
            dy = y1 - y0;
            k = dy / dx;
            if (k <= 1 && k > 0)
            {
                if (x1 < x0)
                {
                    x = x0;
                    x0 = x1;
                    x1 = (int)x;
                    y = y1;
                }
                for (x = x0; x <= x1; x++)
                {
                    g.DrawRectangle(b, (int)x, (int)(y + 0.5), 1, 1);
                    y = y + k;
                }
            }
            if (k > 0 && k > 1)
            {
                if (y1 < y0)
                {
                    y = y0;
                    y0 = y1;
                    y1 = (int)y;
                    x = x1;
                }
                for (y = y0; y <= y1; y++)
                {
                    g.DrawRectangle(b, (int)(x + 0.5), (int)y, 1, 1);
                    x = x + (1 / k);
                }
            }
            if (k == 0)
            {
                if (x1 < x0)
                {
                    x = x0;
                    x0 = x1;
                    x1 = (int)x;
                    y = y1;
                }
                for (x = x0; x < x1; x++)
                {
                    g.DrawRectangle(b, (int)x, (int)y, 1, 1);
                }
            }
            if (k < 0 && k <= -1)
            {
                if (y1 < y0)
                {
                    y = y0;
                    y0 = y1;
                    y1 = (int)y;
                    x = x1;
                }
                for (y = y0; y <= y1; y++)
                {
                    g.DrawRectangle(b, (int)(x + 0.5), (int)y, 1, 1);
                    x = x + (1 / k);
                }
            }
            if (k < 0 && k > -1)
            {
                if (x1 < x0)
                {
                    x = x0;
                    x0 = x1;
                    x1 = (int)x;
                    y = y1;
                }
                for (x = x0; x <= x1; x++)
                {
                    g.DrawRectangle(b, (int)x, (int)(y + 0.5), 1, 1);
                    y = y + k;
                }
            }
            if (x1 == x0)
            {
                if (y1 < y0)
                {
                    y = y0;
                    y0 = y1;
                    y1 = (int)y;
                    x = x1;
                }
                for (y = y0; y <= y1; y++)
                {
                    g.DrawRectangle(b, (int)x, (int)y, 1, 1);
                }
            }

        }

放個圖

2，中點畫線法
代碼區鍵入如下代碼

private void Midpoint(int x0, int y0, int x1, int y1)//------------中點畫線法
        {
            Graphics g = CreateGraphics();
            Pen p = new Pen(Color.Green, 1);
            if (x0 == x1 && y0 == y1)
                return;
            double a = y0 - y1;
            double b = x1 - x0;
            double c = x0 * y1 - x1 * y0;
            double x, y, k, d;
            k = -a / b;
            //--------------------------------------
            if (k > 0 && k < 1)
            {
                if (x1 > x0)
                {
                    y = y0;
                    for (x = x0; x < x1;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d < 0)
                        { x++; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { x++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
                if (x1 < x0)
                {
                    y = y1;
                    for (x = x1; x < x0;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d > 0)
                        { x++; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { x++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
            }
            //-------------------------
            if (k >= 1)
            {
                if (y1 > y0)
                {
                    x = x0;
                    for (y = y0; y < y1;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d > 0)
                        { x++; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
                if (y1 < y0)
                {
                    x = x1;
                    for (y = y1; y < y0;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d < 0)
                        { x++; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
            }
            //------------------------------------
            if (k <= 0 && k > -1)
            {
                if (x1 > x0)
                {
                    y = y1;
                    for (x = x1; x > x0;)
                    {
                        d = a * (x - 1) + b * (y + 0.5) + c;
                        if (d < 0)
                        { x--; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { x--; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                    }
                }
                if (x0 > x1)
                {
                    y = y0;
                    for (x = x0; x > x1;)
                    {
                        d = a * (x - 1) + b * (y + 0.5) + c;
                        if (d > 0)
                        { x--; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { x--; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                    }
                }
            }
            //---------------------------------------
            if (k <= -1)
            {
                if (y1 > y0)
                {
                    x = x0;
                    for (y = y0; y < y1;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d < 0)
                        { x--; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
                if (y1 < y0)
                {
                    x = x1;
                    for (y = y1; y < y0;)
                    {
                        d = a * (x + 1) + b * (y + 0.5) + c;
                        if (d > 0)
                        { x--; y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }
                        else
                        { y++; g.DrawRectangle(p, (int)x, (int)y, 1, 1); }

                    }
                }
            }
            //---------------------------------------
            if (x1 == x0)
            {
                x = x0;
                if (y1 < y0)
                {
                    y = y0;
                    y0 = y1;
                    y1 = (int)y;
                    x = x1;
                }
                for (y = y0; y <= y1; y++)
                {
                    g.DrawRectangle(p, (int)x, (int)y, 1, 1);
                }
            }
        }

3，Bresenham畫線法
代碼區鍵入如下代碼

private void Bresenham(int x0, int y0, int x1, int y1)//--------------------------Bresenham演算法
        {
            Graphics g = CreateGraphics();
            Pen p = new Pen(Color.Blue, 1);
            if (x0 == x1 && y0 == y1)
                return;
            double dx = x1 - x0;
            double dy = y1 - y0;
            double k = dy / dx;
            double e = -0.5;
            int x = x0;
            int y = y0;
            int i;

            if (k > 0 && k <= 1)
            {
                if (x1 < x0)
                {
                    x = x1;
                    y = y1;
                    dx = x0 - x1;
                    dy = y0 - y1;
                }
                for (i = 0; i <= dx; i++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                    x = x + 1;
                    e = e + k;
                    if (e >= 0)
                    {
                        y++;
                        e = e - 1;
                    }
                }
            }
            //-----------------------------------------
            if (k > 1)
            {
                if (y1 < y0)
                {
                    x = x1;
                    y = y1;
                    dx = x0 - x1;
                    dy = y0 - y1;
                }
                for (i = 0; i <= dy; i++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                    y = y + 1;
                    e = e + 1 / k;
                    if (e >= 0)
                    {
                        x++;
                        e = e - 1;
                    }
                }
            }
            //--------------------------------------------
            if (k <= -1)
            {
                if (y1 < y0)
                {
                    x = x1;
                    y = y1;
                    dx = x0 - x1;
                    dy = y0 - y1;
                }
                for (i = 0; i <= dy; i++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                    y = y + 1;
                    e = e - 1 / k;
                    if (e >= 0)
                    {
                        x--;
                        e = e - 1;
                    }
                }
            }
            //--------------------------------------
            if (k < 0 && k > -1)
            {
                if (x1 < x0)
                {
                    x = x1;
                    y = y1;
                    dx = x0 - x1;
                    dy = y0 - y1;
                }
                for (i = 0; i <= dx; i++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                    x = x + 1;
                    e = e - k;
                    if (e >= 0)
                    {
                        y--;
                        e = e - 1;
                    }
                }
            }
            //---------------------------------------
            if (x1 == x0)
            {
                if (y1 < y0)
                {
                    y = y0;
                    y0 = y1;
                    y1 = y;
                    x = x1;
                }
                for (y = y0; y <= y1; y++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                }
            }
            //--------------------------

            if (k == 0)
            {
                if (x1 < x0)
                {
                    x = x0;
                    x0 = x1;
                    x1 = x;
                    y = y1;
                }
                for (x = x0; x < x1; x++)
                {
                    g.DrawRectangle(p, x, y, 1, 1);
                }
            }
        }

畫直線功能大功告成
運行結果

設計一個清除畫線功能，點擊清除進入代碼區
鍵入如下代碼

            Graphics g = CreateGraphics();
            g.Clear(Color.White);
            MenuID = 0;