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)
{
// https://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>