Generate Perspective Transformation Matrix?: Page 2

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Generate Perspective Transformation Matrix?

xyz

@gauntlet said:

@xyz said:

What did you use with values from gimp?

I used the basic formula for applying the transformation to coordinates:

x' = (xh0 + yh1 + h2) / (xh6 + xh7 + 1) y' = (xh3 + yh4 + h5) / (xh6 + xh7 + 1)

I don't actually need to set the values in the matrices, I just need to be able to extract the values since the application is just the simple equations above.

Right. It's equivalent to matrix multiplication, just flattened out.

Now that you've shown what you're actually doing... yeah, you won't be able to achieve that with neither Transform2D nor the script @cybereality linked...

gauntlet

@xyz said: Ok so here's the system of equations that needs to be solved

x0h0 + y0h1 + h2 - u0x0h6 - u0y0h7 = u0 x0h3 + y0h4 + h5 - u0x0h6 - u0y0h7 = v0

x1h0 + y1h1 + h2 - u1x1h6 - u1y1h7 = u1 x1h3 + y1h4 + h5 - u1x1h6 - u1y1h7 = v1

x2h0 + y2h1 + h2 - u2x2h6 - u2y2h7 = u2 x2h3 + y2h4 + h5 - u2x2h6 - u2y2h7 = v2

x3h0 + y3h1 + h2 - u3x3h6 - u3y3h7 = u3 x3h3 + y3h4 + h5 - u3x3h6 - u3y3h7 = v3

where: x, y are coordinates of original points u, v are coordinates of distorted points h0-h7 are variables you need to solve for, these then go directly into the matrix

Thank you for this. I think I have a pretty good approximation.

h6 & h7 will have to be assumed to be 0. Since the true image is rectangle, we can assume that x0, y0, x2, and y1 are all 0. The remaining x, y, u, and v values are not 0 but are known.

We can solve for the h values in order with basic math, since there is only one unknown in each.

h2 =u0, h5 =v0, h0 = (u1 - h2)/x1 h3 = (v1 - h5)/x1 h1 = (u2 - h2)/y2 h4 = (v2 - h5)/y2

I believe this means that I can write a basic Godot function for this approximation. The only error is coming from assuming that h6 and h7 are 0. But I don't think the effect will be very significant in my case.

xyz

@gauntlet Hopefully, I didn't screw something up when writing these :)

If your shorthand still proves not to be adequate, there's another possible option... Peek into source code of any Python library that implements linear equation solving, like Numpy or SymPy.solvers, and just copy-paste the functions. Most of these libraries support several standard numerical methods for solving such systems. There may be some dependent code to drag along and some adjustments to be made. But adapting it could be worth the effort if everything else fails. And you could afterwards publish the whole thing as a proper Godot addon :)

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