Please God help me to see this picture deformation formula

This is a picture of the operation, http://blog.csdn.net/jia_zhengshen/article/details/12008371

All you need to see is the formula on page 38th and the 4.4.1.

In addition, this is a Chinese web page, also quoted the formula, and some explanations will be more understandable
http://blog.csdn.net/jia_zhengshen/article/details/12008371

In-picture pixel (pixel) substitution is now possible to deform the image
But I don't really understand how that formula works, so I'm going to sort out my questions roughly as follows:

1. The original pixel coordinates of the picture (before deformation) is U or x?
2. As far as I am aware, I have swept each of the pixel with a for loop, each of these pixel is the coordinates of the x in the formula, after finding U, start to do deformation action, change the original x to u, is this thinking direction correct?

Reply to discussion (solution)

This blog post is clearer than what you gave me. http://www.cnblogs.com/xiaotie/archive/2009/12/08/1619046.html

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The shadow ring represents a circular selection with a radius of rmax. Where point C is the mouse punctuation point, that is, the center of the circle selection. Drag the mouse from C to M, causing the point u in the image to change to X. So, the key question is to find the inverse transformation of the above transformation?? When you give a point x, you can find the coordinate u (exact floating point coordinates) before the transformation, and then interpolate the pixel value of u by using the pixels near the U point before changing the image. In this way, each pixel in the circle selection is evaluated to obtain the transformed image.
And this formula is

This blog post is clearer than what you gave me. http://www.cnblogs.com/xiaotie/archive/2009/12/08/1619046.html

[/URL]
The shadow ring represents a circular selection with a radius of rmax. Where point C is the mouse punctuation point, that is, the center of the circle selection. Drag the mouse from C to M, causing the point u in the image to change to X. So, the key question is to find the inverse transformation of the above transformation?? When you give a point x, you can find the coordinate u (exact floating point coordinates) before the transformation, and then interpolate the pixel value of u by using the pixels near the U point before changing the image. In this way, each pixel in the circle selection is evaluated to obtain the transformed image.
And this formula is

Thank you for the reply, this article I also read, really let me confused, "The key problem is to find the above transformation of the inverse transformation?" When you give a point x, you can find the coordinate before it transforms you "I just do not understand the meaning of this sentence, why you are the coordinates before the transformation, is not already known the coordinates (original picture pixel coordinates)? So we're asking for x? If it's X, the equation will turn into x =??? will become very complex ...

So what should be done?

Non-Also
In the case of a linear transformation (translation) from the U-point to the X-point, the coordinates of the U-point are known
But what you do is deform (non-linear transformations), so you only know that the transformed point x does not know where the point U is before the transformation, so you need to calculate
It's like someone arrives in Taipei now, but you don't know if he's from Tainan or Kaohsiung, and he needs to go through his travel time to figure out which city he's from.

Wow!! You know the place where the station is?

Can I understand you? The example is very clear, but the law? There is doubt, first of all I do not know? The position after the shape x, I only know pixel original position u
Can you xuzuning? What's the Ming? Count?

I've already used a for-circle to get the shadow? Pixel, all the seats? Is it a formula? x? is U?

The use of traditional Chinese is not a problem, generally know, but the writing is not necessarily

First of all, the mouse from C to M, M is OK, then the circle with the center of M rmax radius of each point is determined
This should be no problem, right?
Second, because it is nonlinear deformation, each point in the circle M does not correspond to the point one by one in the corresponding position in the circle C (if the one by one corresponds is not deformed)
This should be no problem, right?

So we need to calculate the specific coordinates of the point U in Circle C based on the point x in the circle m
If it's not deformed, it's panning.
Because of the coefficients, the deformation is created.

Very clear explanation, thank you!

So the X in the formula = a single point in the circle after the circle is moved, so the coordinates are known, and all values (X,RMAX,M,C) are put into the formula to find U
Do I understand this correctly?
Do you pixel replace x pixel as the result of the deformation?

Yes, you are the one that you find
However, it is important to note that you are a decimal number (which is unlikely to be counted) and that he is not real and needs to calculate (interpolate) a specific pixel value from the surrounding four items

Well, specifically, I really appreciate you, and it's been a big favor.

Although I'm not aware of the interpolation, I think it's okay if I fix this part myself.

If you do it or you can't do it, you'll know what's going to end up.

Thanks again ~

To give an error 500 message to the sub: Try it later, okay?

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