Re: [boost] Preview 2 of a template Geometry Library

From: Barend Gehrels (barend_at_[hidden])
Date: 2008-03-28 16:51:35

Max Motovilov wrote:
>> Linear transformations are intentionally left out because they are 
>> already there, in uBLAS indeed, didn't want to write vector/matrix 
>> calculations again.   
>
> Regarding uBLAS: it doesn't look like it is the best match for the job. 
> While the abstraction penalty there is probably very small or 
> nonexistent for the 2x2, 2x3, 3x3 or 3x4 matrices that are likely to be 
> useful for geometrical transformations (provided static arrays are used 
> as underlying container), it just does not offer enough functionality:
>
> - No general matrix inversion, only triangular solvers. While in general 
> case this may well indeed be out of scope for a foundation library, 
> formulas for small matrices of known size are rather simple. And 
> inverted matrices are extremely useful (at least as long as numeric 
> robustness is not the top priority).
>   
Agree that matrix inversion should be there, it is necessary. In earlier 
sample I used lu_substitute and lu_factorize to invert a uBLAS matrix. 
Don't know the backgrounds of those calculations, but it worked well.
> - No special support for scale+shift matrices (2x3 or 3x4: diagonal + 
> last column). Not that big of a deal, but formulas with them are 
> simpler. More importantly, recognizing this special case as such at 
> compile time helps write good code (e.g. don't want to start rotating 
> raster images unless it is unavoidable...).
>
> - No syntactic sugar: constructors of shift/scale/rotation matrices, 
> classification checks (is it a shift+scale matrix? a rotational matrix? 
> are the X and Y scales identical? is it an invertible matrix? etc...)
>
> None of the above is a real show stopper: missing functionality may well 
> be implemented on top of uBLAS. However I don't really see what 
> non-trivial benefits does uBLAS provide for this specific case -- after 
> all, products are really simple for small matrices of fixed size. 
> Admittedly, I'm as far from uBLAS expert as can be so perhaps someone 
> can point out important things I have missed.
>   
If the general feeling is that uBLAS is not good for this job (I get 
this impression), then it might be time for a (separate) lightweight 
vector/matrix library in Boost. I've still the opinion that it should be 
separate from a geometry library. Any matrix library can be used for 
geometry transformations. For some simple calculations, that are now 
"inline", the geometry library needs a lightweight solution.

The matrix listed in mail of Noah Stein, partly pasted here:
>   Matrix<float, 3, 3> m1, m2, m3;
>    m1 = 1.0f, 2.0f, 3.0f,
>         4.0f, 5.0f, 6.0f,
>         7.0f, 8.0f, 9.0f; 
>   
is looking very good.

Barend Gehrels,
Amsterdam, the Netherlands