Which pixels do you turn on when you draw a line?


When I wrote my cartoon animation program almost 30 years ago (see Cartoon animation program) I needed to know how to draw a line.


 


Of course, nowadays, we just call a library function that will draw a line given two points.


 


If you think about it, the problem is quite complex. Imagine a rectangular array of pixels. Which ones do you paint in order to “see” a straight line?


 


If the desired line is horizontal, or vertical, the problem is simple. However, choosing which pixels to draw for an oblique line is an interesting mathematical problem: see Bresenham‘s line algorithm – Wikipedia, the free encyclopedia


 


Even back then, I found Bresenham’s algorithm in a book and implemented it for my cartoon program.


 


Suppose you want to create a simple drawing program. When you move the mouse, you can handle the MouseMove event, and light up the pixel at the position of the mouse.


 


However, this will only create a dotted line, with fewer dots if the mouse moved quickly.


 


Let’s see if we can use Bresenham’s algorithm to light up the pixels between successive mouse events.


 


This sample uses larger “pixels”, so you can actually see them as squares. In the code I called them cells (mainly because I stole a lot of the code from my game of Life (see Cellular Automata: The Game of Life )


 


The actual mouse down causes a red pixel to be drawn, and the generated ones are black.


 


Below are C# and VB versions.


 


Start Visual Studio 2008


Choose  File->New->Project->C# or VB->Windows Forms Application.


Choose View->Code


 


Paste in the VB or C# version of the code below, hit F5 to run it.


 


Move the mouse slowly and you’ll see more red pixels. Quickly, and you’ll see more black generated pixels.


Note how the code needs to distinguish between 2 sets of x-y coordinates: actual pixels, and cell coordinates.


Try adjusting the Cell size.


 


Think about what a right click would do.


 


See also:


Comment/Uncomment code to switch versions quickly without using macros


Remove double spaces from pasted code samples in blog


 


 


<C#Sample>


using System;


using System.Collections.Generic;


using System.ComponentModel;


using System.Data;


using System.Drawing;


using System.Linq;


using System.Text;


using System.Windows.Forms;


 


namespace WindowsFormsApplication1


{


    public partial class Form1 : System.Windows.Forms.Form


    {


        Size m_numCells = new Size(350, 200);// we’ll use an array of Cells


        Boolean[,] m_cells; // the array of cells: whether they’ve been drawn or not


        Size m_cellSize = new Size(8, 8);  // cell height & width


        Size m_Offset = new Size(0, 0);


        bool m_MouseDown = false;


        Button btnErase;


        Point? m_PtOld;


        SolidBrush m_brushMouse = new SolidBrush(Color.Red);


        SolidBrush m_brushGenerated = new SolidBrush(Color.Black);


        delegate bool DrawCellDelegate(Point ptcell, Brush br);


        Graphics m_oGraphics;


        public Form1()


        {


            this.Load += new EventHandler(this.Loaded);


        }


        void Loaded(Object o, EventArgs e)


        {


            this.Width = 600;


            this.Height = 400;


            this.btnErase = new Button();


            this.btnErase.Text = “&Erase”;


            this.btnErase.Click += new EventHandler(this.btnErase_Click);


            this.Controls.Add(this.btnErase);


            this.BackColor = Color.White;


            btnErase_Click(null, null);


        }


        void btnErase_Click(object sender, System.EventArgs e)


        {


            m_oGraphics = Graphics.FromHwnd(this.Handle);


            m_numCells.Width = this.Width / m_cellSize.Width;


            m_numCells.Height = this.Height / m_cellSize.Height;


            m_cells = new Boolean[m_numCells.Width, m_numCells.Height];


            m_oGraphics.FillRectangle(Brushes.White, new Rectangle(0, 0, this.Width, this.Height));


        }


        Point PointToCell(Point p1)


        {


            Point ptcell = new Point(


            (p1.X – m_Offset.Width) / m_cellSize.Width,


            (p1.Y – m_Offset.Height) / m_cellSize.Height);


            return ptcell;


        }


        protected override void OnMouseDown(MouseEventArgs e)


        {


            if (e.Button == MouseButtons.Left)


            {


                m_MouseDown = true;


                m_PtOld = new Point(e.X, e.Y);


                CheckMouseDown(e);


            }


#if AREA


            else


            {


                AreaFill(PointToCell(new Point(e.X, e.Y)));


            }


#endif


        }


        protected override void OnMouseMove(MouseEventArgs e)


        {


            if (m_MouseDown)


            {


                CheckMouseDown(e);


            }


        }


        protected override void OnMouseUp(MouseEventArgs e)


        {


            m_MouseDown = false;


        }


        void CheckMouseDown(MouseEventArgs e)


        {


            Point ptMouse = new Point(e.X, e.Y);


            Point ptcell = PointToCell(ptMouse);


            if (ptcell.X >= 0 && ptcell.X < m_numCells.Width &&


                ptcell.Y >= 0 && ptcell.Y < m_numCells.Height)


            {


                DrawLineOfCells(PointToCell(m_PtOld.Value), ptcell, new DrawCellDelegate(DrawACell));


                m_PtOld = ptMouse;


            }


        }


 


        bool DrawACell(Point ptcell, Brush br)


        {


            bool fDidDraw = false;


            if (!m_cells[ptcell.X, ptcell.Y]) // if not drawn already


            {


                m_cells[ptcell.X, ptcell.Y] = true;


                //*


                m_oGraphics.FillRectangle(br,


                    m_Offset.Width + ptcell.X * m_cellSize.Width,


                    m_Offset.Height + ptcell.Y * m_cellSize.Height,


                    m_cellSize.Width,


                    m_cellSize.Height);


                /*/


                 g.DrawRectangle(new Pen(Color.Blue,1),


                    m_Offset.Width + ptcell.X * m_cellSize.Width,


                    m_Offset.Height + ptcell.Y * m_cellSize.Height,


                    m_cellSize.Width,


                    m_cellSize.Height);


                


                  //*/


                fDidDraw = true;


            }


            return fDidDraw;


        }


        void DrawLineOfCells(Point p1, Point p2, DrawCellDelegate drawit)


        {


            // http://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm


            Brush br =  m_brushMouse;


            int x0 = p1.X;


            int y0 = p1.Y;


            int x1 = p2.X;


            int y1 = p2.Y;


            int x, cx, deltax, xstep,


                y, cy, deltay, ystep,


                 error;


            bool st;


 


            // find largest delta for pixel steps


            st = (Math.Abs(y1 – y0) > Math.Abs(x1 – x0));


 


            // if deltay > deltax then swap x,y


            if (st)


            {


                x0 ^= y0; y0 ^= x0; x0 ^= y0; // swap(x0, y0);


                x1 ^= y1; y1 ^= x1; x1 ^= y1; // swap(x1, y1);


            }


 


            deltax = Math.Abs(x1 – x0);


            deltay = Math.Abs(y1 – y0);


            error = (deltax / 2);


            y = y0;


 


            if (x0 > x1) { xstep = -1; }


            else { xstep = 1; }


 


            if (y0 > y1) { ystep = -1; }


            else { ystep = 1; }


 


            for (x = x0; (x != (x1 + xstep)); x += xstep)


            {


                cx = x; cy = y; // copy of x, copy of y


 


                // if x,y swapped above, swap them back now


                if (st)


                {


                    cx ^= cy; cy ^= cx; cx ^= cy;


                }


                if (drawit(new Point(cx, cy), br))


                {


                    br = m_brushGenerated;


                }


 


                error -= deltay; // converge toward end of line


                if (error < 0)


                { // not done yet


                    y += ystep;


                    error += deltax;


                }


            }


        }


    }


}


</C#Sample>


 


 


 


<VBSample>


Public Class Form1


    Dim m_numCells = New Size(350, 300) ‘ we’ll use an array of cells


    Dim m_cells(,) As Boolean   ‘ the array of cells: whether they’ve been drawn or not


    Dim m_cellSize = New Size(8, 8) ‘ cell size & width


    Dim m_Offset = New Size(0, 0)


    Dim m_MouseDown = False


    Dim WithEvents btnErase As Button


    Dim m_PtOld As Point?


    Dim m_brushGenerated = New SolidBrush(Color.Black)


    Dim m_brushMouse = New SolidBrush(Color.Red)


    Dim m_oGraphics As Graphics


    Delegate Function DrawCellDelegate(ByVal ptCell As Point, ByVal br As Brush) As Boolean


 


    Sub Form_Load() Handles Me.Load


        Me.Width = 600


        Me.Height = 400


        Me.btnErase = New Button()


        Me.btnErase.Text = “&Erase”


        Me.Controls.Add(Me.btnErase)


        Me.BackColor = Color.White


        btnErase_Click()


 


    End Sub


    Sub btnErase_Click() Handles btnErase.Click


        m_oGraphics = Graphics.FromHwnd(Me.Handle)


        m_numCells.Width = Me.Width / m_cellSize.Width


        m_numCells.Height = Me.Height / m_cellSize.Height


        ReDim m_cells(m_numCells.Width, m_numCells.Height)


        m_oGraphics.FillRectangle(Brushes.White, New Rectangle(0, 0, Me.Width, Me.Height))


 


    End Sub


    Function PointToCell(ByVal p1 As Point) As Point


        Dim ptcell = New Point( _


            (p1.X – m_Offset.Width) / m_cellSize.Width, _


            (p1.Y – m_Offset.Height) / m_cellSize.Height)


        Return ptcell


 


    End Function


    Protected Overrides Sub OnMouseDown(ByVal e As System.Windows.Forms.MouseEventArgs)


        If e.Button = Windows.Forms.MouseButtons.Left Then


            m_MouseDown = True


            m_PtOld = New Point(e.X, e.Y)


            CheckMouseDown(e)


#If AREA Then


        Else


            AreaFill(PointToCell(New Point(e.X, e.Y)))


#End If


        End If


    End Sub


    Protected Overrides Sub OnMouseMove(ByVal e As System.Windows.Forms.MouseEventArgs)


        If m_MouseDown Then


            CheckMouseDown(e)


        End If


    End Sub


    Protected Overrides Sub OnMouseUp(ByVal e As System.Windows.Forms.MouseEventArgs)


        m_MouseDown = False


    End Sub


    Sub CheckMouseDown(ByVal e As MouseEventArgs)


        Dim ptMouse = New Point(e.X, e.Y)


        Dim ptcell = PointToCell(ptMouse)


        If (ptcell.X >= 0 And ptcell.X < m_numCells.Width And _


            ptcell.Y >= 0 And ptcell.Y < m_numCells.Height) Then


 


            DrawLineOfCells(PointToCell(m_PtOld.Value), ptcell, New DrawCellDelegate(AddressOf DrawACell))


            m_PtOld = ptMouse


        End If


    End Sub


    Function DrawACell(ByVal ptCell As Point, ByVal br As Brush) As Boolean


        Dim fDidDraw = False


        If Not m_cells(ptCell.X, ptCell.Y) Then


            m_cells(ptCell.X, ptCell.Y) = True


            m_oGraphics.FillRectangle(br, _


                    m_Offset.Width + ptCell.X * m_cellSize.Width, _


                    m_Offset.Height + ptCell.Y * m_cellSize.Height, _


                    m_cellSize.Width, _


                    m_cellSize.Height)


            fDidDraw = True


        End If


        Return fDidDraw


    End Function


    Sub DrawLineOfCells(ByVal p0 As Point, ByVal p1 As Point, ByVal drawit As DrawCellDelegate)


        Dim br = m_brushMouse


        Dim x0 = p0.X


        Dim y0 = p0.Y


        Dim x1 = p1.X


        Dim y1 = p1.Y


        Dim fSwapped = False


        Dim dx = Math.Abs(x1 – x0)


        Dim dy = Math.Abs(y1 – y0)


        If dy > dx Then


            fSwapped = True ‘ swap x0<=>y0, x1<->y1


            x0 = p0.Y


            y0 = p0.X


            x1 = p1.Y


            y1 = p1.X


            dx = Math.Abs(x1 – x0)


            dy = Math.Abs(y1 – y0)


        End If


        Dim err = CInt(dx / 2)


        Dim y = y0


        Dim xstep = 1


        If x0 > x1 Then


            xstep = -1


        End If


        Dim ystep = 1


        If y0 > y1 Then


            ystep = -1


        End If


        Dim x = x0


        While x <> x1 + xstep


            Dim cx = x, cy = y ‘ copy of x,y


            If fSwapped Then


                cx = y


                cy = x


            End If


            If drawit(New Point(cx, cy), br) Then ‘ if it wasn’t already drawn


                br = m_brushGenerated


            End If


            err -= dy


            If err < 0 Then


                y += ystep


                err += dx


            End If


            x += xstep


        End While


    End Sub


 


 


End Class


 


</VBSample>

Comments (3)

  1. MikeS says:

    Like Steven B said in your original blog entry, it’s amazing to see how such a little bit of VFP code translates into so much more C# and VB lines. This is progress?

  2. Kids know how to use crayons and a coloring book. How do you write such a program? In my last post (