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

From: Max Motovilov (max_at_[hidden])
Date: 2008-03-28 09:09:00

> 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).

- 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.

...Max...