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




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.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);



#if AREA



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




        protected override void OnMouseMove(MouseEventArgs e)


            if (m_MouseDown)





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

                    m_Offset.Height + ptcell.Y * 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,





                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,


            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;











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.BackColor = Color.White



    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)


#If AREA Then


            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


        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, _


            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



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 (