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Posted 6 Dec 2002

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# Image Rotation in .NET

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Rotates an image without having to worry about cropping the edges.

## Introduction

A few days ago Tweety asked me how you would go about rotating an Image object.  The reply seemed simple enough, use the `Transform` property of your `Graphics` object with a `Matrix` object having the appropriate `Rotate` method called on it.  But I forgot about one aspect regarding the transforms, while it is easy to rotate the `Image`, you have to jump through hoops to get it to rotate correctly and still remain in somewhat the same location.

Since I was disgusted from looking at the same non-working code for the past two weeks this was a welcome vacation.

## My first attempt

I wanted to take what seemed the obvious way to do this, so I started messing around with the `Rotate`/`RotateAt` methods and trying to figure out what the equation to create the proper translation should be.  Unfortunately I could never figure out the proper formula.  Looking over my previous drawings something did occur to me, I could figure out the size of the smallest possible rectangle in which the rotated bitmap would fit, or the bounding box.

## My second attempt or Ah ha!

Given an angle of rotation, theta, and knowing the width and height of the original bitmap I can figure out the size of the triangles of 'empty space'.

Some basic trig identities are used to calculate the lengths of the sides of the triangles.  Assuming a right triangle, then:

sin(theta) = length(opposite)/length(hypotenuse)

Solving for the unknown you get:

length(opposite) = sin(theta) * length(hypotenuse)

Since we have a known theta and hypotenuse we can calculate the length of the other two sides of each triangle.  To make it clear, the length of the hypotenuse is either the width or the height of the original rectangle, r

Now looking at the diagram we can see that the width of the bounding box will be oh + aw and the height of the bounding box will be ah + ow.  I'll leave it as an exercise for the reader to come up with the proof that shows why there are only at most two different sized triangles for any rectangle r in the above diagram.

Also looking at the diagram it became obvious what the coordinates of each corner of the bitmap would be for the rotation, now if only I had a way to specify the coordinates of each corner when drawing an image...what do you know, I do!

C#
`Graphics.DrawImage(Image image, Point[] destPoints);`

`destPoints` is a 3 element array of Point objects, which defines a parallelogram. The three points you need to pass in define where the upper-left corner, the upper-right corner, and the lower-left corner of the original image should be drawn. With this one method you can perform scales and rotations easily.

The last part to take into consideration is that the above portions only work when the angle of rotation is between 0 and 90 degrees, or 0 and PI/2 radians.  But handling rotations greater than that is easy, by using the absolute value of the values of cos(theta) and sin(theta) the first rotation of 90 degrees will cause the return to go from 0 to 1 and the next rotation causes it to go from 1 to 0, repeating forever which is the behavior we desire.  The only tricky part is that each time you rotate 90 degrees the height and width need to switch, else you'll be calculating values based on the wrong hypotenuse.

While the bitmap is rotating, the points used differ for each quadrant theta is in, so when calculating the points I had to break it up based on that condition.

In the code snippet before 7 values are used, `nWidth` and

`nHeight`
are the width and height, respectively, of the bounding box/new bitmap.  `adjacentTop` and `oppositeTop` are the lengths of the adjacent and opposite sides of the triangle labeled top in the diagram.  The same is true for `adjacentBottom` and
`oppositeBottom`
except it uses the other triangle; the last value is of course 0.  Because the trig functions expect everything to be done in radians (and I prefer radians anyway), `theta` has been converted from degrees to radians.

C#
```const double pi2 = Math.PI / 2.0;

if( theta >= 0.0 && theta < pi2 )
{
points = new Point[] {
new Point( (int) oppositeBottom, 0 ),
new Point( nWidth, (int) oppositeTop ),
new Point( 0, (int) adjacentBottom )
};
}
else if( theta >= pi2 && theta < Math.PI )
{
points = new Point[] {
new Point( nWidth, (int) oppositeTop ),
new Point( (int) adjacentTop, nHeight ),
new Point( (int) oppositeBottom, 0 )
};
}
else if( theta >= Math.PI && theta < (Math.PI + pi2) )
{
points = new Point[] {
new Point( (int) adjacentTop, nHeight ),
new Point( 0, (int) adjacentBottom ),
new Point( nWidth, (int) oppositeTop )
};
}
else // theta >= (Math.PI + pi2)
{
points = new Point[] {
new Point( 0, (int) adjacentBottom ),
new Point( (int) oppositeBottom, 0 ),
new Point( (int) adjacentTop, nHeight )
};
}```

## Intended usage

Rather than use the same bitmap for the rotation, I always create a new bitmap to draw on.  This is done for a couple reasons:

1. Consistent behavior - since the point of this was to rotate a bitmap and have it not get cut off, I would have to create a new bitmap if the one passed in wasn't large enough.
2. Consistent quality - if the same bitmap is rotated over and over again, eventually all the extrapolating done would degrade the image quality.

So when you pass an Image in, you will get a new one out and it should be of comparable quality to the original image.

The demo program is extremely basic, the only interesting portion of it, is that I made the `NumericUpDown` control wrap around using the next bit of code.

C#
```if( angle.Value > 359.9m )
{
angle.Value = 0;
return ;
}

if( angle.Value < 0.0m )
{
angle.Value = 359.9m;
return ;
}

pictureBox.Image = Utilities.RotateImage(img,
(float) angle.Value );```

After setting the new value I return from the method so that it can run again because of the change I made.

## Acknowledgments

• Tweety for asking the question which got me into writing the code and the article
• Shog9 and PJ Arends for offering suggestions and pointing me in the right direction while I was stuck with the code not working for non-square images.

## History

• December 7, 2002 - Initial posting

## Share

 Software Developer (Senior) InfoPlanIT, LLC United States
James has been programming in C/C++ since 1998, and grew fond of databases in 1999. His latest interest has been in C# and .NET where he has been having fun writing code starting when .NET v1.0 was in its first beta.

He is currently a senior developer and consultant for InfoPlanIT, a small international consulting company that focuses on custom solutions and business intelligence applications.

He was previously employed by ComponentOne where he was a Product Manager for the ActiveReports, Data Dynamics Reports, and ActiveAnalysis products.

Code contained in articles where he is the sole author is licensed via the new BSD license.

 First PrevNext
 請問要如何把它轉換為mfc Member 118434541-Oct-15 23:03 Member 11843454 1-Oct-15 23:03
 thanks 2010sampel25-Nov-12 12:14 2010sampel 25-Nov-12 12:14
 My vote of 5 Manoj Kumar Choubey20-Feb-12 1:27 Manoj Kumar Choubey 20-Feb-12 1:27
 tanx message Member 84568809-Dec-11 22:18 Member 8456880 9-Dec-11 22:18
 My vote of 5 t1_t1_t117-Mar-11 5:51 t1_t1_t1 17-Mar-11 5:51
 Not fast... Demaker28-Jan-10 21:44 Demaker 28-Jan-10 21:44
 Change your code for testing for speed perfomance... Set rotate event on trackbar scrolling... Image was 1280x1024 resolution... work very slow! Is it real to make rotate more fast?
 Re: Not fast... Xmen Real 11-Aug-10 16:40 Xmen Real 11-Aug-10 16:40
 This also works and is much faster :) DragonSimon24-May-09 12:14 DragonSimon 24-May-09 12:14
 quality suffering during rotation rikki2337527-May-09 22:58 rikki233752 7-May-09 22:58
 RotateFlip tobias00426-Apr-09 8:12 tobias004 26-Apr-09 8:12
 saving the new image Slylandro20-Oct-08 19:30 Slylandro 20-Oct-08 19:30
 Thanks! HughJampton5-Oct-08 0:14 HughJampton 5-Oct-08 0:14
 How to rotate 3 or more words in a text line with different angles? MaryamR22-Sep-08 2:40 MaryamR 22-Sep-08 2:40
 the quality of image falls when it rotates? GIS_Developer2-Sep-08 4:39 GIS_Developer 2-Sep-08 4:39
 USE THIS VERSION!!! :P FocusedWolf14-Feb-09 9:40 FocusedWolf 14-Feb-09 9:40
 A version for compact framework? Oxcarz10-Aug-08 4:09 Oxcarz 10-Aug-08 4:09
 Top and left side anti-aliasing wangforforyou5-Nov-07 13:51 wangforforyou 5-Nov-07 13:51
 Re: Top and left side anti-aliasing wangforforyou6-Nov-07 9:44 wangforforyou 6-Nov-07 9:44
 VB.NET version of the RotateImage function tigerwood200628-Feb-07 19:51 tigerwood2006 28-Feb-07 19:51
 Re: VB.NET version of the RotateImage function reso_od_ua30-May-08 13:50 reso_od_ua 30-May-08 13:50
 Re: VB.NET version of the RotateImage function NarutoXD3-Sep-11 7:59 NarutoXD 3-Sep-11 7:59
 Easy way to get the resulting bounds [modified] Quimbo21-Sep-06 5:17 Quimbo 21-Sep-06 5:17
 Alternative timberly13-Jun-06 11:05 timberly 13-Jun-06 11:05
 Re: Alternative T4Top17-Sep-06 0:45 T4Top 17-Sep-06 0:45
 Without antialiasing? thomasa8825-Feb-06 11:28 thomasa88 25-Feb-06 11:28
 Last Visit: 31-Dec-99 19:00     Last Update: 4-Dec-21 1:39 Refresh 123 Next ᐅ