rotate an image

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hello!
I have two questions for whoever can help me... I have been searching in the forum and I think that there is no easy solution to my problem, but I will ask anyway. Here are my doubts:

- I have an image made up by a 2D crystal lattice points (see image attached). I would like to rotate the lattice, the points, about the origin at an angle that I decide, which can change. Is there an easy way to do it?

- I would like to 'mirror' the same image not about an axis, but about a line that passes through the origin at, say, 30º, and I would like to be able to change the angle of this mirroring line... Is this possible?

Thanks a lot in advance!
You're in luck. Check out the wikipedia page .http://en.wikipedia.org/wiki/Rotation_matrix Basically you get a 2*2 matrix for a specific rotation Angle and matrix multiply by a 2*N matrix containing the x,y coords for the points. The result gives you the new points. You'll have to put the x, y vals into a 2 column wave with N rows. Then transpose the matrix. Then multiply the transform matrix by the 2*N coord matrix.
No doubt there'll be an inbuilt transform to do the same thing.

Wrt to the mirroring, that should be straightforward as well.

March 21, 2011 at 06:08 am - Permalink

Following on Andy's suggestions, you might look in to the matrix operations for point groups ...

http://en.wikipedia.org/wiki/Molecular_symmetry

.. and equivalent hard copy resources. Once you express your lattice as a [x, y] vector matrix, on hand the proper matrix operation, you can do any form of symmetry operation you want using the MatrixOp abilities in Igor Pro.

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville

March 21, 2011 at 05:30 pm - Permalink

Anna,

Try this. It performs "unitful" rotations (i.e., respecting the x and y scaling) about (0,0). If you want to rotate about a different point, just shift your origin. The output is returned as M_rotated2D. The optional useInterp parameter alters how "jagged" the output is. Try it both ways just to see what I mean.

By the way, the output is automatically resized to preserve the number of points along each edge. The space around your image will just be set to NaN.

Function Rotate2D(w, angle, [useInterp])
    Wave w          // 2D image
    Variable angle  // degrees
    Variable useInterp
    
    if(ParamIsDefault(useInterp))
        useInterp = 1       // default uses interpolation
    endif
    
    angle *= -pi/180    // convert to radians, negative sign for correct direction
    Variable origX0 = DimOffset(w, 0)
    Variable origX1 = DimOffset(w, 0)+DimDelta(w, 0)*(DimSize(w, 0)-1)
    Variable origdX = DimDelta(w, 0)
    Variable origY0 = DimOffset(w, 1)
    Variable origY1 = DimOffset(w, 1)+DimDelta(w, 1)*(DimSize(w, 1)-1)
    Variable origdY = DimDelta(w, 1)
    
    // calculate new x's and y's of the corners
    Variable xc1 = origX0*cos(angle)+origY0*sin(angle)
    Variable yc1 = -origX0*sin(angle)+origY0*cos(angle)
    Variable xc2 = origX0*cos(angle)+origY1*sin(angle)
    Variable yc2 = -origX0*sin(angle)+origY1*cos(angle)
    Variable xc3 = origX1*cos(angle)+origY0*sin(angle)
    Variable yc3 = -origX1*sin(angle)+origY0*cos(angle)
    Variable xc4 = origX1*cos(angle)+origY1*sin(angle)
    Variable yc4 = -origX1*sin(angle)+origY1*cos(angle)
    
    Variable x0 = min(min(xc1, xc2), min(xc3, xc4))
    Variable x1 = max(max(xc1, xc2), max(xc3, xc4))
    Variable y0 = min(min(yc1, yc2), min(yc3, yc4))
    Variable y1 = max(max(yc1, yc2), max(yc3, yc4))
    
    Variable rows = round(   sqrt(  ( DimSize(w, 0)*cos(angle) )^2 + ( DimSize(w, 1)*sin(angle) )^2  )   )
    Variable cols = round(   sqrt(  ( DimSize(w, 0)*sin(angle) )^2 + ( DimSize(w, 1)*cos(angle) )^2  )   ) 
    Make/D/O/N=(rows, cols) M_rotated2D
    SetScale/I x, x0, x1, M_rotated2D
    SetScale/I y, y0, y1, M_rotated2D
    
    // fill the final image
    if(useInterp)
        MultiThread M_rotated2D = InRange(x*cos(-angle)+y*sin(-angle), origX0, origX1) && InRange(-x*sin(-angle)+y*cos(-angle), origY0, origY1) ? Interp2D(w, x*cos(-angle)+y*sin(-angle), -x*sin(-angle)+y*cos(-angle)) : NaN
    else
        MultiThread M_rotated2D = InRange(x*cos(-angle)+y*sin(-angle), origX0, origX1) && InRange(-x*sin(-angle)+y*cos(-angle), origY0, origY1) ? w(x*cos(-angle)+y*sin(-angle))(-x*sin(-angle)+y*cos(-angle)) : NaN
    endif
End
 
ThreadSafe Static Function InRange(val, lim1, lim2)
    Variable val, lim1, lim2
    
    return (val >= lim1 && val < lim2) || (val < lim1 && val >= lim2)
End


Good luck,
Nick

March 22, 2011 at 10:23 am - Permalink