Affine transforms - matrix algebra

[Martin Desruisseaux]

Le 23/07/12 14:01, Pavel Safrata a écrit :
> On 23.7.2012 12:09, Martin Desruisseaux wrote:
> Unlike in J2D our Pts will have three coordinates, right? Or do we 
> want transform2D and transform3D?
Yes, I was thinking about 3D-points. Maybe it is not necessary to 
support 2D-points, since the existing Java2D classes can fit that need...


> I'm not sure about the floats. I don't mind adding those methods but 
> is it OK for us to work with floats here and nowhere else? Shouldn't 
> we then allow for floats at least for all the other arrays in Affine 
> class?
I didn't though about the fact that 'float' are used nowhere else in 
JavaFX... This is a good point.

Does JavaFX plans to support big geometries someday? For example 
world-wide coast lines, in which case using 'float' instead of 'double' 
make a huge difference on memory usage?


> To me this sounds a bit frightening. I may be wrong but I believe that 
> the "ulps" are there to deal with representability of certain numbers 
> in floating-point types but not with different math engines producing 
> different results - I believe the results may be up to one ulp wrong 
> but are reliably stable among all platforms. I'm a bit afraid that 
> providing unstable results would violate at least some unwritten 
> conventions. But I'm not an expert here, I might be wrong.
My (maybe naive) understanding was that StrictMath reliably produces 
stable results among all platforms, while Math allow some 
platform-dependent flexibility. In our implementation of a map 
projection library making extensive use of Math.sin and the like, I do 
have noticed slight platform-dependent variations.

Transform doesn't have to use the "ulps" wording; the actual question is 
whatever Transform should allow hardward accelerations at the expense of 
strict cross-platform stability. It may be worth to note that if my 
understanding of java.lang.Math trigonometric functions is not wrong, 
then this slight cross-platform variability already exists in Transforms 
having a rotation calculated from an angle.


> We may use MAT for the getRow/getCol - it would specify from what 
> matrix the col/row will be taken (each pair of values would provide 
> similar behavior except for one of them allowing to read the last line).
This interpretation works for me. Anyone else?

     Martin