Help with a visual effect

[SkripT]

Hi, I want to know what's the simple way to obain this visual effect: a rectangle (for example) that rotates 180 degrees from the Y axis:

Coordinate system                      
                        |Y
                        |
                        |
                        |
                        |_________________ X
                       /
                     /
                   /
                 / Z

Coordinate system                      
                        |Y
                        |
                        |
                        |
                        |_________________ X
                       /
                     /
                   /
                 / Z

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All I want is to emulate the effect of a page (of a book) turning around
I think that I could use openGL but I don't hve much experinece with it, maybe it can be easily achieved with QPainter
Thanks in advance.

[jacek]

If you have a point (x, y, z) and you rotate it around Y axis by a degrees, you'll get (x', y', z') where:
x' = x cos a + z sin a,
y' = y,
z' = -x sin a + z cos a.

Second thing you will need is a projection. In this case it probably will be enough if you use:
xp = x - z
yp = y + z
(where xp, and yp are the painter coordinates).

The algorithm:

• translate the painter so that the (0, 0) point is in the middle of the top edge of the book,
• x1 = width/2, y1 = 0, z1 = 0, (upper corner of the page)
• x2 = width/2, y2 = height, z2 = 0, (lower corner of the page)
• for a = 0, 1, ..., 180:
  
  • calculate new x1, y1, z1, x2, y2 and z2
  • draw a (0, 0)--(x1-z1, y1-z1)--(x2-z2, y2-z2)--(0, height) rectangle

Note that in fact x1 == x2, z1 == z2 and both y1 and y2 are constant.

[SkripT]

Thanks a lot jacek, good knowledge of maths

EDIT: taking a look at this alogrithm carefully, I think that it will paint the rectangle with the correct size in each degree, the problem is that I want to paint an image (texture) on this rectangle and I want that it "deforms" with each degree. Is it still possible with QPainter?

[jacek]

I want that it "deforms" with each degree. Is it still possible with QPainter?

Try QPainter::setMatrix() or QImage::transform().

[wysota]

Wouldn't it be enough to transform the painter matrix to do it all?

Hmm... Looks like QMatrix is just 2x2 in size...

[jacek]

Looks like QMatrix is just 2x2 in size...

No, it's 3x3, but the last column is [0;0;1]. Anyway, it will be enough, since you only have to shear and scale the painter (or image).

[SkripT]

Thanks a lot jacek and wysota for your replies. My question is: so, using QMatrix is enought to do all the rotations/shear/scale that I need applied on the image or the rectangle to simulate the effect that I need? QMatrix seems to work only in 2D and this effect has a 3D component I think....

[jacek]

QMatrix is enought to do all the rotations/shear/scale that I need applied on the image or the rectangle to simulate the effect that I need?

Theoretically, yes.

QMatrix seems to work only in 2D and this effect has a 3D component I think....

Do you have a 3D monitor?

[SkripT]

Theoretically, yes.

Do you have a 3D monitor?

Not, but now I know what to request for christmas .

I will try with QMatrix it and I comment the results

[SkripT]

Hi again, I've been reading carefully and testing what the docs explains from QMatrix class and I don't know how could I use it to obtain the effect that I want . I know that I should call QMatrix::shear and QMatrix::scale in some way because, as the docs says, "...Rotation is achieved by carefully setting both the shearing factors and the scaling factors" but I don't know how
It's clear that I'm not a math expert... Could you please guide me a little bit in how could I configure the QMatrix to get the respective "transformated" rectangle for each angle rotated? Thanks again.

[wysota]

Try those:
http://www.inversereality.org/tutori...wmatrices.html
http://gpwiki.org/index.php/3D:Matrix_Math