On 1/21/25 06:39, Bald Eagle wrote:
> 
> "Easiest" and fastest thing to do is stop speculating and crank out some
> numbers.
> 
> Have one shear matrix and another and apply them individually to a VECTOR, and
> spit out the result to #debug with vstr.
> 
> Then have POV-Ray sequentially apply the matrices and spit out the result.
> 
> Apply your matrix transforms to a "matrix" by matrix transforming your basic
> vectors x-hat, y-hat, and z-hat and stack the transform output in the #debug
> stream to see what matrix you're actually applying in both individual cases and
> your compound matrix transform case.
> 
> You can use the result vectors to plot spheres in a scene.
> Match them up with the corners of the checkerboard pattern.
> 
> If anything is mis-matched, it's probably not POV-Ray, but some matrix
> construction error.
> 
> Run all of the calculations with POV-Ray matrix transforms and vectors to check
> and verify your calculations in the above post.
> 
> - BW
> 

Hi Bill,

Your suggestions are reasonable ways we might better see what's 
happening. I suspect I've mislead you into thinking I believe something 
is amiss with how matrix transforms are working or with what I expect 
for a result.

My original surprise at the result in the lower right image over in pbi 
came from setting up a matrix I knew was out of bounds for typical use. 
I didn't expect things to work like two separate shear matrices; I 
didn't know what would happen, but the result surprised me due how 
dramatically it whacked the checker pattern.

I started to wonder what other useful direct matrix transformations 
there might be. The 'matrix form' posted about in this thread looks 
useful too, but I fully admit I'm just poking the matrix with a stick to 
see what happens. To some extent, I wonder about why it does what it 
does, but I care more about whether what it does might be useful.

The isosurface animation was itself another way to verify behavior. 
There is the usual pattern space to function space inversion. I 
un-inverted the rotation so it looked like the checker rotation. I left 
the scaling as is because scaling up of the function's coordinate space 
shrinks the isosurface result here - keeping the results in a fixed 
view/frame, so to speak.

I ran the animation out only to frame 50, but I did spot checks at 
frame_numbers 100 through 900 stepping by 100. An image of those renders 
is attached.

Bill P.

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