## Introduction

I have written a small but powerful C# application that can scale, rotate, skew and distort an image. This program includes a user control `Canvas`

and a class `FreeTransform`

. `Canvas`

can keep the picture in the center of window always, and let the user zoom the image by mouse wheel. You can pick up the corner of the picture by mouse left button and move it freely in `Canvas`

. Image transformation is done by the class `FreeTransform`

. When you set its `Bitmap`

and `FourCorners`

, you can get the transformed `Bitmap`

. If you like high quality of picture, you can set `IsBilinearInterpolation`

to `true`

. How does it work? The following diagram demonstrates the key to this method:

The shortest distances of point P to image borders are `w1`

, `w2`

, `h1 `

and `h2`

. The position of point P on the original image is supposed to be at:

([w1/(w1+w2)]*imageWidth, [h1/(h1+h2)]*imageHeight)

Then the colors at...

([w1/(w1+w2)]*imageWidth, [h1/(h1+h2)]*imageHeight)

... on the original image were put on the point P and thus the result.

To calculate of the distances, the vector cross product was used:

dab = Math.Abs((new YLScsDrawing.Geometry.Vector(vertex[0], srcPt)).CrossProduct(AB));
dbc = Math.Abs((new YLScsDrawing.Geometry.Vector(vertex[1], srcPt)).CrossProduct(BC));
dcd = Math.Abs((new YLScsDrawing.Geometry.Vector(vertex[2], srcPt)).CrossProduct(CD));
dda = Math.Abs((new YLScsDrawing.Geometry.Vector(vertex[3], srcPt)).CrossProduct(DA));
ptInPlane.X = (float)(srcW * (dda / (dda + dbc)));ptInPlane.Y =
(float)(srcH*(dab/(dab+dcd)));

Thanks for trying it!

## History

- 2
^{nd} May, 2009: Initial post - 8
^{th} May, 2009: Added `Config`

and `Save`

functions

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