GD and Image 函数
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imagearc

(PHP 4, PHP 5)

imagearc — 画椭圆弧

说明

bool imagearc ( resource $image , int $cx , int $cy , int $w , int $h , int $s , int $e , int $color )

imagearc() 以 cx，cy（图像左上角为 0, 0）为中心在 image 所代表的图像中画一个椭圆弧。w 和 h 分别指定了椭圆的宽度和高度，起始和结束点以 s 和 e 参数以角度指定。0°位于三点钟位置，以顺时针方向绘画。

Example #1 用 imagearc() 画一个圆

<?php
// 创建一个 200X200 的图像
$img = imagecreatetruecolor(200, 200);
// 分配颜色
$white = imagecolorallocate($img, 255, 255, 255);
$black = imagecolorallocate($img, 0, 0, 0);
// 画一个黑色的圆
imagearc($img, 100, 100, 150, 150, 0, 360, $black);
// 将图像输出到浏览器
header("Content-type: image/png");
imagepng($img);
// 释放内存
imagedestroy($img);
?>

参见 imageellipse()，imagefilledellipse() 和 imagefilledarc()。

GD and Image 函数
在线手册：中文 英文
PHP手册
PHP手册 - N: 画椭圆弧

用户评论:

chandlerklebs at gmail dot com (08-Jan-2012 06:24)

This is an example script I wrote for myself to help me learn how to used the imagearc functions. Maybe if will also help others.

<?php
//example PHP script of imagearc functions
$image_width=360;$image_height=360;
$img = imagecreatetruecolor($image_width,$image_height); //make image variable

//create a background color by making a filled rectangle
$color = imagecolorallocate($img,255,255,255);
imagefilledrectangle($img,0,0,$image_width,$image_height,$color);

$r=$image_width/2 - $image_width/32 ; //radius
$cx=$image_width/2;
$cy=$image_height/2;

$color = imagecolorallocate($img,0,0,0);
imagearc($img, $cx, $cy, $r*2, $r*2,  0, 360, $color); //regular outlines arc

imagefilledarc($img, $cx, $cy, $r*1, $r*1,  0, 90, $color,IMG_ARC_CHORD); //filled triangle with chord of circle
imagefilledarc($img, $cx, $cy, $r*1, $r*1,  180, 270, $color,IMG_ARC_PIE); //pie slice

$font_number=5; //can use built in fonts numbered 1 to 5
$string="Hello world!";
imagestring($img, $font_number, $cx-(imagefontwidth($font_number)*strlen($string))/2, $cy-120, $string, $color);

header("Content-type: image/png");
imagepng($img);// output image in the browser

$filename="imagearc";
imagepng($img,"./frames/$filename.png",9); //make highly compressed png

imagedestroy($img);
?>

Michael (04-Mar-2011 10:56)

Hi, this is a function that replaces "imagearc" to solve the thickness-problem. it does not use the global value set by imagesetthickness, so you have to pass it along.

"connecting" the arc to lines is still a problem, it sometimes shifts by 1px, but so does the original function.

Theres still alot to improve ...

<?php
function myimagearc($im,$mid_x,$mid_y,$rad,$w1,$w2,$col,$thickness){
        global $cols;
        $rad+=$thickness/2;    // to calculate outer edge
        $th_fact = 1-((($thickness-1)/$rad));       
       
        $pts = 36*$rad;    // adjust density
        $fact = $pts/360;
        $w1 = $w1*$fact;
        $w2 = $w2*$fact;
        if($thickness > 2)    // to make sure we have neither gaps nor ugly looking artefacts
            imagesetthickness($handle,2);
        else
            imagesetthickness($handle,1);   
        $winkel = (2*pi())/$pts;
        for($i=$w1+1;$i< $w2;$i++){
            $x = (cos($i*$winkel)*($rad));
            $y = (sin($i*$winkel)*($rad));
            $x1 = $x+$mid_x;
            $y1 = $y+$mid_y;
            $x2 = $th_fact*$x+$mid_x;
            $y2 = $th_fact*$y+$mid_y;
            imageline($im, $x1,$y1,$x2,$y2,$col);
        }
        imagesetthickness($handle,1); // just to reset
    }
?>

ajim1417 at gmail dot com (29-Jan-2010 03:42)

I wrote a simple function that can draws an arc counter-clockwisekly. Here it is :

<?php

function imagearcCC(&$im, $cx, $cy, $w, $h, $s, $e, $c) {
$start = 360 - $e;
$end = 360 - $s;
return imagearc($im, $cx, $cy, $w, $h, $start, $end, $c);
}

?>

The params of this function is exactly the same as the usual imagearc function.

anton dot vandeghinste at telenet dot be (13-Dec-2009 03:27)

I needed an arc with a thick border and i didn't like to use 359.9 as end angle so i made a function that works pretty well:

<?php
function imagearcthick($image, $x, $y, $w, $h, $s, $e, $color, $thick = 1)
{
    if($thick == 1)
    {
        return imagearc($image, $x, $y, $w, $h, $s, $e, $color);
    }
    for($i = 1;$i<($thick+1);$i++)
    {
        imagearc($image, $x, $y, $w-($i/5), $h-($i/5),$s,$e,$color);
        imagearc($image, $x, $y, $w+($i/5), $h+($i/5), $s, $e, $color);
    }
}
?>

mojiro at awmn dot net (13-Dec-2005 08:28)

A previous for the Rotated (Filled)Ellipse note from(nojer2 at yahoo dot com, 02-Apr-2001 12:06) has a mistake, at the second arc. Replace them with the following listing.

if ($filled) {
    triangle($im, $cx, $cy, $cx+$px, $cy+$py, $cx+$x, $cy+$y, $colour);
    triangle($im, $cx, $cy, $cx-$px, $cy-$py, $cx-$x, $cy-$y, $colour);
} else {
    imageline($im, $cx+$px, $cy+$py, $cx+$x, $cy+$y, $colour);
    imageline($im, $cx-$px, $cy-$py, $cx-$x, $cy-$y, $colour);
}

ruturaj_v at yahoo dot com (17-May-2004 02:32)

this is another piechart eg. very simple ...

<?php
global $deg;

function get_polar($xrel, $yrel, $ang, $radius) {
    $i = $ang;
    $ang = ($ang * pi())/ 180;
   
    $ix = abs($radius*cos($ang));
    $iy = abs($radius*sin($ang));
   
    if ($i>=0 && $i<=90) {
        $ix = $xrel + $ix;
        $iy = $yrel - $iy;
    }
    if ($i>90 && $i<=180) {
        $ix = $xrel - $ix;
        $iy = $yrel - $iy;
    }
    if ($i>180 && $i<=270) {
        $ix = $xrel - $ix;
        $iy = $yrel + $iy;
    }
    if ($i>270 && $i<=360) {
        $ix = $xrel + $ix;
        $iy = $yrel + $iy;
    }

    $ix = floor($ix);
    $iy = floor($iy);
    //echo ($ix . " $iy<br>");
    $returnvals = array (
                        'x1' => $xrel,
                        'y1' => $yrel,
                        'x2' => $ix,
                        'y2' => $iy
                        );
    return $returnvals;
}

function get_degtotal($degindex)
{
    global $deg;
    if ($degindex == 0 ) {
       return (  $deg[$degindex] );
    }
    else {       
        return ( $deg[$degindex] + get_degtotal($degindex-1) );
    }   
}

$im  = imagecreate (400, 400);
$w   = imagecolorallocate ($im, 255, 255, 255);
$black   = imagecolorallocate ($im, 0, 0, 0);
$red = imagecolorallocate ($im, 255, 0, 0);
$green = imagecolorallocate ($im, 0, 180, 0);

$randcolor[0] = imagecolorallocate($im, 243, 54, 163);
$randcolor[1] = imagecolorallocate($im, 179, 51, 247);
$randcolor[2] = imagecolorallocate($im, 103, 48, 250);
$randcolor[3] = imagecolorallocate($im, 53, 145, 244);
$randcolor[4] = imagecolorallocate($im, 54, 243, 243);
$randcolor[5] = imagecolorallocate($im, 107, 245, 180);
$randcolor[6] = imagecolorallocate($im, 203, 242, 111);
$randcolor[7] = imagecolorallocate($im, 248, 201, 105);

$data[0] = 30;
$data[1] = 20;
$data[2] = 15;
$data[3] = 10;
$data[4] = 8;
$data[5] = 7;
$data[6] = 5;
$data[7] = 5;

$datasum = array_sum($data);

$deg[0] = number_format((30 / $datasum * 360), 2, ".", "");
$deg[1] = number_format((20 / $datasum * 360), 2, ".", "");
$deg[2] = number_format((15 / $datasum * 360), 2, ".", "");
$deg[3] = number_format((10 / $datasum * 360), 2, ".", "");
$deg[4] = number_format((8 / $datasum * 360), 2, ".", "");
$deg[5] = number_format((7 / $datasum * 360), 2, ".", "");
$deg[6] = number_format((5 / $datasum * 360), 2, ".", "");
$deg[7] = number_format((5 / $datasum * 360), 2, ".", "");
echo ('<pre>');

//print_r($deg);

$datadeg = array();
$datapol = array();
$degbetween = array();
$databetweenpol = array();

for ($i=0; $i < count($deg) ; $i++) {
    $datadeg[$i] = get_degtotal($i);
    $datapol[$i] = get_polar(200, 200, $datadeg[$i], 100);
}

for ($i=0; $i < count($datadeg) ; $i++) {
    /*this is a trick where you take 2deg angle before
    and get the smaller radius so that you can have a pt to
    `imagefill` the chartboundary
    */
    $degbetween[$i] = ($datadeg[$i]-2);
    $databetweenpol[$i] = get_polar(200, 200, $degbetween[$i], 50);
}

print_r($datadeg);
print_r($degbetween);
print_r($databetweenpol);
//exit;

for ($i=0; $i<count($deg); $i++) {
    imageline ($im, 200, 200, $datapol[$i]['x2'], $datapol[$i]['y2'], $black);
}
imagearc($im, 200, 200, 200, 200, 0, 360, $black);

for ($i=0; $i<count($deg); $i++) {
    imagefill ($im, $databetweenpol[$i]['x2'], $databetweenpol[$i]['y2'], $randcolor[$i]);

}

//header ("Content-type: image/png");
imagepng($im, 'piechart.png');
?>
<img src='piechart.png'>

jerryscript at aol dot com (26-Dec-2003 10:05)

[note-Apache/1.3.29 (Win32) PHP/4.3.4]

The imagearc (and imageellipse) functions do not accept line thicknesses when drawn from 0 to 360 degrees.

Drawing from 0 to 359 and again from 359 to 360 does create an ellipse with the current line thickness.

Jerry

eamon at hostelworld dot com (17-Dec-2003 03:24)

Right...
possibly the easiest way of drawing a filled circle:
Loop through the imagearc function incrementing the diameter by one pixel:
<?
 // --- code fragment --- //

for($i=1; $i<$Diameter; $i++){
  imagearc($Image, $CenterX, $CenterY, $i, $i, $Start, $End, $Color);
}

// --------------------- //

?>

This works great for circles with diameters up to about 60 or 70 pixels wide. After that, you start to get pixle gaps.

logang at deltatee dot com (05-Aug-2003 04:19)

Heres a function to make a curve between two points... This will be a downward curve but it wouldn't be hard to make a similar function to make an upward curve. The first point has to be to the left of the second point ($x1 < $x2), and height is actually backwards. The larger height is the less of a crest the curve has. I imagine with a few modifications this functions could make upward curves as well.

function ImageCurveDown ($image, $x1, $y1, $x2, $y2, $height, $color) {
    $presicion = 1;

    for ($left = ($x1-$x2); $left < 0; $left++){
        if ($y1 < $y2) {
            $cy = $y2 + $height;
            $cx = $x1 - $left;
        } else {
            $cy = $y1 + $height;
            $cx = $x2 + $left;
        }
        $nx1 = abs($x1 - $cx);
        $ny1 = abs($y1 - $cy);
        $nx2 = abs($x2 - $cx);
        $ny2 = abs($y2 - $cy);

        if ($y1 < $y2) {
            if ($nx2 == 0 || $ny1 == 0) continue;
            $angle1 = atan($height/$nx2);
            $A1 = $nx2/cos ($angle1);
            $B1 = $ny2/sin ($angle1);
            $angle2 = pi()/2 +atan($left/$ny1);
            $A2 = $nx1/cos ($angle2);
            $B2 = $ny1/sin ($angle2);
        } else {
            if ($ny2 == 0 || $nx1 == 0) continue;
            $angle1 = atan($ny2/$nx2);
            $A1 = abs($nx2/cos ($angle1));
            $B1 = abs($ny2/sin ($angle1));
            $angle2 = atan($height/$nx1);
            $A2 = abs ($nx1/cos ($angle2));
            $B2 = abs($ny1/sin ($angle2));
        }

        if (abs($A1 - $A2) < $presicion && abs ($B1 - $B2) < $presicion) {
            ImageArc($image, $cx, $cy, $A1*2, $B1*2, 180+rad2deg($angle2), 360-rad2deg($angle1), $color);
        }
    }
}

(23-Jan-2003 04:55)

Please note that in order to draw a complete circle or ellipse (without using the imageellipse) you mustn't use 0 for both s and e. If you do this you will get, umm, nothing. Instead set s to 0 and e to 360 to get a complete circle or ellipse.

jinny at 263 dot net (14-May-2002 06:27)

imagesetstyle() sets the style to be used by all line drawing functions when drawing with the special color .

Here goes a example of drawing a dashed-line circle.enjoy!

<?php

header("Content-type: image/jpeg");
$im = imagecreate(100,100);

$b   = imagecolorallocate ($im, 0, 0, 0);
$w   = imagecolorallocate ($im, 255, 255, 255);

$style = array ($b,$b,$b,$b,$b,$w,$w,$w,$w,$w);

imagesetstyle ($im, $style);

imagearc($im,50,50,100,100,0,360,IMG_COLOR_STYLED);

imagejpeg($im);
imagedestroy($im);
?>

arve at skogvold dot as (30-Nov-2001 09:04)

I found a better way for drawing a pie chart:

header ("Content-type: image/png");
$diameter = 100;
$radius = $diameter / 2;
$centerX = $radius;
$centerY = $radius;

$im = @ImageCreate ($diameter, $diameter)
    or die ("Cannot Initialize new GD image stream");

$background = ImageColorAllocate ($im, 0, 0, 0);
$red = ImageColorAllocate ($im, 176, 0, 0);

function fill_arc($start, $end, $color) {
    global $diameter, $centerX, $centerY, $im, $radius;
    imagearc($im, $centerX, $centerY, $diameter, $diameter, $start, $end, $color);
    imageline($im, $centerX, $centerY, $centerX + cos(deg2rad($start)) * $radius, $centerY + sin(deg2rad($start)) * $radius, $color);
    imageline($im, $centerX, $centerY, $centerX + cos(deg2rad($end)) * $radius, $centerY + sin(deg2rad($end)) * $radius, $color);
    imagefill ($im,$centerX + $radius * 0.5 *cos(deg2rad($start+($end-$start)/2)), $centerY + $radius * 0.5 * sin(deg2rad($start+($end-$start)/2)), $color);
    }


fill_arc(0,30,$red);
// Will make a red filled arc, starting at 0 degrees, ending at 30 degrees

ImagePng ($im);

marc at resiteit dot com (08-Nov-2001 09:04)

Round cornered anti-aliased dynamically sized button.

$w=40;
$h=20;
$im = ImageCreate($w,$h);
$white=ImageColorAllocate($im,255,255,255);
ImageFilledRectangle($im,0,0,$w,$h,$white);
imagecolortransparent ($im, $white);
ImageTTFText ($im, $h+ceil($h/3)+1, 0, -1, $h-1, $col1, "arialbd.ttf", "O");
ImageTTFText ($im, $h+ceil($h/3)+1, 0, $w-$h, $h-1, $col1, "arialbd.ttf", "O");
ImageTTFText ($im, $h+ceil($h/3)+1, 0, 1, $h-1, $col1, "arialbd.ttf", "O");
ImageTTFText ($im, $h+ceil($h/3)+1, 0, $w-$h-2, $h-1, $col1, "arialbd.ttf", "O");
$points=array(
    1,round($h/2),
    round($h/4),$h-round($h/4),
    round($h/2),$h,
    $w-(round($h/2)),$h,
    $w-(round($h/4)),$h-round($h/4),
    $w-2,round($h/2),
    $w-round($h/4),round($h/4),
    $w-round($h/2),0,
    round($h/2),0,
    round($h/4),round($h/4)
);
imagefilledpolygon ($im, $points, 10, $col1);

header("content-type: image/gif");
header("Content-Disposition: filename=name.gif");
ImageGif($im);
ImageDestroy($im);

foripepe at yahoo dot com (02-Sep-2001 05:56)

To fill an arc (DiameterX != DiameterY):

<?
function imagefilledarc($Image, $CenterX, $CenterY, $DiameterX, $DiameterY, $Start, $End, $Color) {
    // To draw the arc
    imagearc($Image, $CenterX, $CenterY, $DiameterX, $DiameterY, $Start, $End, $Color);
    // To close the arc with 2 lines between the center and the 2 limits of the arc
    $x = $CenterX + (cos(deg2rad($Start))*($DiameterX/2));
    $y = $CenterY + (sin(deg2rad($Start))*($DiameterY/2));
    imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
    $x = $CenterX + (cos(deg2rad($End))*($DiameterX/2));
    $y = $CenterY + (sin(deg2rad($End))*($DiameterY/2));
    imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
    // To fill the arc, the starting point is a point in the middle of the closed space
    $x = $CenterX + (cos(deg2rad(($Start+$End)/2))*($DiameterX/4));
    $y = $CenterY + (sin(deg2rad(($Start+$End)/2))*($DiameterY/4));
    imagefilltoborder($Image, $x, $y, $Color, $Color);
}
?>

To close the arc with 2 lines (DiameterX != DiameterY):

<?
function imagenofilledarc($Image, $CenterX, $CenterY, $DiameterX, $DiameterY, $Start, $End, $Color) {
    // To draw the arc
    imagearc($Image, $CenterX, $CenterY, $DiameterX, $DiameterY, $Start, $End, $Color);
    // To close the arc with 2 lines between the center and the 2 limits of the arc
    $x = $CenterX + (cos(deg2rad($Start))*($DiameterX/2));
    $y = $CenterY + (sin(deg2rad($Start))*($DiameterY/2));
    imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
    $x = $CenterX + (cos(deg2rad($End))*($DiameterX/2));
    $y = $CenterY + (sin(deg2rad($End))*($DiameterY/2));
    imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
}
?>

An example:
<?
    $destImage = imagecreate( 216, 152 );
    $c0 = imagecolorallocate( $destImage, 0, 255, 255 );
    $c1 = imagecolorallocate( $destImage, 0, 0, 0 );
    $c2 = imagecolorallocate( $destImage, 255, 0, 0 );
    ImageFilledRectangle ( $destImage, 0, 0, 216, 152, $c0 );
    imagefilledarc( $destImage, 108, 76, 180, 80, 0, 130, $c1 );
    imagenofilledarc( $destImage, 108, 76, 180, 80, 0, 130, $c2 );
    header("content-type: image/PNG");
    ImagePNG( $destImage );
    ImageDestroy( $destImage );
?>

(09-Apr-2001 06:37)

The following site contains heaps of different functions to draw graphs with easy to follow code for newbies and heaps of examples with OVER 60 different predefined graphs
http://www.aditus.nu/jpgraph/index.php

nojer2 at yahoo dot com (01-Apr-2001 10:18)

Here's a dashed circle function:

<?php
function dashedcircle($im, $cx, $cy, $radius, $colour, $dashsize=5) {

   $dash=false;
   for ($angle=0; $angle<=(180+$dashsize); $angle+=$dashsize) {
      $x = ($radius * cos(deg2rad($angle)));
      $y = ($radius * sin(deg2rad($angle)));

      if ($dash) {
         imageline($im, $cx+$px, $cy+$py, $cx+$x, $cy+$y, $colour);
         imageline($im, $cx-$px, $cx-$py, $cx-$x, $cy-$y, $colour);
      }
      $dash=!$dash;
      $px=$x;
      $py=$y;
   }
}
?>

nojer2 at yahoo dot com (01-Apr-2001 10:06)

Here's the function to draw rotated ellipses again. This time I've optimised it a bit, fixed the no-fill bug, and used a 'squishratio' rather than a 'radiusmodifier', to make the curves perfect, so ignore my previous version.

<?php
function rotatedellipse($im, $cx, $cy, $width, $height, $rotateangle, $colour, $filled=true) {
   $step=2;
   $cosangle=cos(deg2rad($rotateangle));
   $sinangle=sin(deg2rad($rotateangle));

   $squishratio = $height/$width;
   $nopreviouspoint = true;
   for ($angle=0; $angle<=(180+$step); $angle+=$step) {
      
      $ox = ($width * cos(deg2rad($angle)));
      $oy = ($width * sin(deg2rad($angle))) * $squishratio;

      $x =  + (($ox * $cosangle) - ($oy * $sinangle));
      $y = $centrey + (($ox * $sinangle) + ($oy * $cosangle));
 
      if ($nopreviouspoint) {
        $px=$x;
        $py=$y;
        $nopreviouspoint=false;
      }

      if ($filled) {
         triangle($im, $cx, $cy, $cx+$px, $cy+$py, $cx+$x, $cy+$y, $colour);
         triangle($im, $cx, $cy, $cx-$px, $cx-$py, $cx-$x, $cy-$y, $colour);
      } else {
         imageline($im, $cx+$px, $cy+$py, $cx+$x, $cy+$y, $colour);
         imageline($im, $cx-$px, $cx-$py, $cx-$x, $cy-$y, $colour);
      }
      $px=$x;
      $py=$y;
   }
}

function triangle($im, $x1,$y1, $x2,$y2, $x3,$y3, $colour) {
   $coords = array($x1,$y1, $x2,$y2, $x3,$y3);
   imagefilledpolygon($im, $coords, 3, $colour);
}
?>

ericquil at yahoo dot com (29-Sep-2000 12:30)

If circles overlap, a temporary border is needed when filling:
<?php
ImageArc ($im,$x,$y,$w,$h,0,360,$temp_color);
ImageFillToBorder($im,$x,$y,$temp_color,$fill_color);
ImageArc ($im,$x,$y,$w,$h,0,360,$fill_color);
?>

cbriou at orange-art dot fr (18-Sep-2000 03:03)

There is another way to fill an arc :

<?php
// To draw the arc
$Color = imagecolorallocate($Image, $Red, $Green, $Blue);
imagearc($Image, $CenterX, $CenterY, $Diameter, $Diameter, $Start, $End, $Color);
// To close the arc with 2 lines between the center and the 2 limits of the arc
$x = $CenterX + (cos(deg2rad($Start))*($Diameter/2));
$y = $CenterY + (sin(deg2rad($Start))*($Diameter/2));
imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
$x = $CenterX + (cos(deg2rad($End))*($Diameter/2));
$y = $CenterY + (sin(deg2rad($End))*($Diameter/2));
imageline($Image, $x, $y, $CenterX, $CenterY, $Color);
// To fill the arc, the starting point is a point in the middle of the closed space
$x = $CenterX + (cos(deg2rad(($Start+$End)/2))*($Diameter/4));
$y = $CenterY + (sin(deg2rad(($Start+$End)/2))*($Diameter/4));
imagefilltoborder($Image, $x, $y, $Color, $Color);
?>

timothyhouck at yahoo dot com (16-Aug-2000 11:58)

To do filled arcs, try something like this:

<?php
$diameter = 50;
imagearc($image, 25, 25, $diameter, $diameter, $start, $end, $color);
while($diameter > 0) {
  imagearc($image, 25, 25, $diameter, $diameter, $start, $start + 1, $color);
  imagearc($image, 25, 25, $diameter, $diameter, $end - 1, $end, $color);
  $diameter--;
}
?>

...well you get the point.  It's a kludge, and *very* slow, but it's free.

travis at duluth dot com (23-Dec-1999 02:36)

The wierd thing is that the first two integers tell where to place the "circle".
So for example I first create the "pallet" to place the circle on.
$image = imagecreate(500, 500); 
(this makes a huge 500x500 gif :) )
$colorBody = imagecolorallocate($image, 0, 0, 0);
(make the default color of the "pallet" black
$circleColor = imagecolorallocate($image, 255, 0, 255);
(going to make the circle an ugly pink color)
imagearc($image, 250, 250, 300, 300, 0, 360, $circleColor);
Places the image in the center (250,250) and the circle is 300 pixels in diameter.

Hope this helps.
 
Travis Kent Beste