Area fill algorithm: crayons and coloring book
Kids know how to use crayons and a coloring book. How do you write such a program?
In my last post (Which pixels do you turn on when you draw a line?) I showed how to draw a line. Now suppose you have some lines or shapes already drawn. How would you write code to fill in an area bounded by the drawn pixels?
IOW, imagine you’ve drawn a circle. You want to fill the circle with a color. Right click inside. What code should run? What if the figure were more complex, like a large block “W” or a curled up snake.
More formally: Given an array of pixels that represents the outline of a shape, and a point’s x,y coordinate within that shape, how would you area fill that shape?
Perhaps you could write some code that will check all pixels to the East, North, West, South until it reached a pixel that was already painted. Then what?
What sort of algorithm and data structure would you use?
Below are C# and VB versions of a simple implementation that isn’t very efficient, but is quite simple.
The code is identical to the last post (the drawing parts) except for the areas delimited by “AREA”. This makes it easier for you to cut/paste the code.
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. Draw a shape, right click to fill.
How would you improve it? Why isn’t it efficient?
Try making the form bigger and paint more pixels. What happens?
Clue: look at the source code for MineSweeper that I wrote to take advantage of the (then) new feature Collections. It’s part of the Task Pane for Visual Foxpro 9.0
See also:
Remove double spaces from pasted code samples in blog
<C# Sample>
#define AREA
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;
}
}
}
#if AREA
SolidBrush m_brushFill = new SolidBrush(Color.Blue);
Color m_oColor = Color.Black;
/*
/*/
void AreaFill(Point ptcell)
{
if (ptcell.X >= 0 && ptcell.X < m_numCells.Width)
{
if (ptcell.Y >= 0 && ptcell.Y < m_numCells.Height)
{
// System.Threading.Thread.Sleep(100);
if (DrawACell(ptcell, m_brushFill))
{
m_oColor = Color.FromArgb((int)(((((uint)m_oColor.ToArgb() & 0xffffff) + 140) & 0xffffff) | 0xff000000));
m_brushFill = new SolidBrush(m_oColor);
AreaFill(new Point(ptcell.X - 1, ptcell.Y));
AreaFill(new Point(ptcell.X + 1, ptcell.Y));
AreaFill(new Point(ptcell.X, ptcell.Y + 1));
AreaFill(new Point(ptcell.X, ptcell.Y - 1));
}
}
}
}
//*/
#endif
}
}
</C# Sample>
<VB Sample>
#Const AREA = True
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
#If AREA Then
Dim m_brushFill = New SolidBrush(Color.Blue)
Dim m_oColor = Color.Black
Sub AreaFill(ByVal ptcell As Point)
If (ptcell.X >= 0 And ptcell.X < m_numCells.Width) Then
If (ptcell.Y >= 0 And ptcell.Y < m_numCells.Height) Then
' System.Threading.Thread.Sleep(100);
If (DrawACell(ptcell, m_brushFill)) Then
Me.m_oColor = Color.FromArgb((((Me.m_oColor.ToArgb And &HFFFFFF) + 140) And &HFFFFFF) Or &HFF000000)
' m_oColor = Color.FromArgb((int)(((((uint)m_oColor.ToArgb() & 0xffffff) + 140) & 0xffffff) | 0xff000000));
m_brushFill = New SolidBrush(m_oColor)
AreaFill(New Point(ptcell.X - 1, ptcell.Y)) ' West
AreaFill(New Point(ptcell.X + 1, ptcell.Y)) ' East
AreaFill(New Point(ptcell.X, ptcell.Y + 1)) ' South
AreaFill(New Point(ptcell.X, ptcell.Y - 1)) ' North
End If
End If
End If
End Sub
#End If
End Class
</VB Sample>