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The software I am developing draws images based upon dimensional values drawn from a datbase. I am currently using the Wu-Line algorighm to antialaise straight lines with great results. However the curved lines of the image still display the jagged line which greatly detracts from the image quality. I have read that Wu also developed an antialiased curved line drawing algorithm but have been unable to locate any code showing the algorithm.

Does anyone have a reference to the algorithm or a similr algorithm that will draw antialiased ellipses, circles or arcs in 24 bit colors?

Any help will be sincerely appreciated.

Respectfully,

Tom Myers

Does anyone have a reference to the algorithm or a similr algorithm that will draw antialiased ellipses, circles or arcs in 24 bit colors?

Any help will be sincerely appreciated.

Respectfully,

Tom Myers

Thank you for your response. Although, the code and sample present a very clear and concise insight into the method of antiailiasing a circle and I may need to devise a method of using it, I really need to find Wu's circle antiailiasing algorighm to work in conjunction with my present line antiailiasing code.

I am going to be away from my computer for the next 3 days. If the Wu algorithm has not turned up by then, I'll re-evaluate my requirements.

Until then,

Respectfully,

Tom Myers

Here is a very good implementation of Wu Lang Algorithm for drawing circles in C++: http://www.codeproject.com/KB/GDI/antialias.aspx

Actually DrawWuCirlce uses DrawWuLine method for drawing a circle. The source of DrawWuLine is attached. As you told in the Question you have the source code for drawing a line using Wu Algorithm. So I think it's easy to use the algorithm for drawing a circle using Wu Line Drawing function.

```
void DrawWuCirlce (CDC * pDC, int x, int y, int r)
{
short x1, y1, x2, y2;
float dt = 5;
for ( float theta= 0; theta< 360; theta += dt )
{
x1 = (short)( r*cos(theta*3.141593/180.0)+x);
y1 = (short)(-r*sin(theta*3.141593/180.0)+y);
x2 = (short)( r*cos((theta+dt)*3.141593/180.0)+x);
y2 = (short)(-r*sin((theta+dt)*3.141593/180.0)+y);
DrawWuLine ( pDC, x1, y1, x2, y2, RGB(192,0,0));
}
}
```

It's very appreciated if you could share Wu Lang Antialias Line Drawing function with community :)

I beleive that both responses will be quite useful.

Thank you for your patience and efforts.

I will post the procedure that was derived from the Wu Line code that I use to draw antialiased lines.

Tom Myers

After I have used the common Delphi code to sketch and color the image, I call the Wu procedure to draw over the boundry lines to match the existing colors on each side of the line.

I works great for me. Now I just need to incorporate the Wu antialiased circle code to complete the process.

Tom Myers

```
Uses Math, Graphics;
procedure WuLine(ABitmap : TBitmap ; Point1, Point2 : TPoint ; AColor : TColor);
procedure AlphaBlendPixel(ABitmap : TBitmap ; X, Y : integer ; R, G, B : byte ; ARatio : Real);
Var
X1,X2,Y1,Y2 : Integer;
LineColor : TColor;
Point1, Point2 : TPoint;
DrawPlace : TBitmap;
begin
DrawPlace := TBitmap.Create;
DrawPlace := Image1.Picture.Bitmap;
Drawplace.PixelFormat := pf24Bit;
Drawplace.Height := Image1.Height;
DrawPlace.Width := Image1.Width;
X1 := 10, X2 := 100, Y1 := 10, Y2 := 50;
LineColor := clBlack
WuLine(Drawplace, Point(X1,Y1), Point(X2,Y1),SketchColor.Color);
procedure TFormDraw.WuLine(ABitmap : TBitmap ; Point1, Point2 : TPoint ; AColor : TColor);
var
deltax, deltay, loop, start, finish : integer;
dx, dy, dydx : single; // fractional parts
LR, LG, LB : byte;
x1, x2, y1, y2 : integer;
begin
x1 := Point1.X; y1 := Point1.Y;
x2 := Point2.X; y2 := Point2.Y;
deltax := abs(x2 - x1); // Calculate deltax and deltay for initialisation
deltay := abs(y2 - y1);
if (deltax = 0) or (deltay = 0) then begin // straight lines
ABitmap.Canvas.Pen.Color := AColor;
ABitmap.Canvas.MoveTo(x1, y1);
ABitmap.Canvas.LineTo(x2, y2);
exit;
end;
LR := (AColor and $000000FF);
LG := (AColor and $0000FF00) shr 8;
LB := (AColor and $00FF0000) shr 16;
if deltax > deltay then
begin // horizontal or vertical
if y2 > y1 then // determine rise and run
dydx := -(deltay / deltax)
else
dydx := deltay / deltax;
if x2 < x1 then
begin
start := x2; // right to left
finish := x1;
dy := y2;
end else
begin
start := x1; // left to right
finish := x2;
dy := y1;
dydx := -dydx; // inverse slope
end;
for loop := start to finish do
begin
AlphaBlendPixel(ABitmap, loop, trunc(dy), LR, LG, LB, 1 - frac(dy));
AlphaBlendPixel(ABitmap, loop, trunc(dy) + 1, LR, LG, LB, frac(dy));
dy := dy + dydx; // next point
end;
end else
begin
if x2 > x1 then // determine rise and run
dydx := -(deltax / deltay)
else
dydx := deltax / deltay;
if y2 < y1 then
begin
start := y2; // right to left
finish := y1;
dx := x2;
end else
begin
start := y1; // left to right
finish := y2;
dx := x1;
dydx := -dydx; // inverse slope
end;
for loop := start to finish do
begin
AlphaBlendPixel(ABitmap, trunc(dx), loop, LR, LG, LB, 1 - frac(dx));
AlphaBlendPixel(ABitmap, trunc(dx) + 1, loop, LR, LG, LB, frac(dx));
dx := dx + dydx; // next point
end;
end;
end;
// blend a pixel with the current colour
procedure TFormDraw.AlphaBlendPixel(ABitmap : TBitmap ; X, Y : integer ; R, G, B : byte ; ARatio : Real);
Var
LBack, LNew : TRGBTriple;
LMinusRatio : Real;
LScan : PRGBTripleArray;
begin
if (X < 0) or (X > ABitmap.Width - 1) or (Y < 0) or (Y > ABitmap.Height - 1) then
Exit; // clipping
LScan := ABitmap.Scanline[Y];
LMinusRatio := 1 - ARatio;
LBack := LScan[X];
LNew.rgbtBlue := round(B*ARatio + LBack.rgbtBlue*LMinusRatio);
LNew.rgbtGreen := round(G*ARatio + LBack.rgbtGreen*LMinusRatio);
LNew.rgbtRed := round(R*ARatio + LBack.rgbtRed*LMinusRatio);
LScan[X] := LNew;
end;
```

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It's free and works like a charm. But I'm not sure about the algorithm.