Re: [boost] proposal for efficient geom. vector class

From: Reece Dunn (msclrhd_at_[hidden])
Date: 2003-05-21 11:32:33

Justinas V.D. wrote:

>AFAIK, there're no vector (i mean
>geometrical vectors) classes in boost
>(well, there's uBLAS version of vectors but that's rather a container
>than a geometrical primitive, correct me if i'm wrong).

>idea itself is borrowed from blitz++.

>template< typename T, std::size_t N >
>class tiny_vector { /**/ };

>vector operations are and should be implemented
>inlinely. there should be no inner loops in additions
>substractions, scalar multiplication/division, etc.

>i suppose it would be neat to have boostified vectors
>as we have boostified quaternions, octonions, etc.

>so what about this idea?

I like it. Also, why not extend this to other geometric primitives and 
related types.

I was thinking of creating a library that supported 2D, 3D, 4D and nD 
variants of the following:

boost::geometric::point - represents a location
   point = point +/- vector
   and variants
   NOTE: cannot do point * point (does not make sense mathematically)

boost::geometric::vector - represents a distance between two points
   vector = point - point
   vector = vector +/-/*/div vector
   vector = vector +/-/*/div scalar
   and variants

boost::math::matrixNxN - N x N matrices and related operations
   matrix = matrix +/-/* matrix
   and variants

There should also be the matrix-based functions:
   boost::math::transpose( matrix ) - T( i, j ) = A( j, i )
   boost::math::det( martix ) - the determinant of the matrix
   boost::math::cofactor( matrix, i, j ) - the sub-matrix of the matrix
      at the position ( i, j )
   and others

It should also be possible to perform geometric operations:
   matrix boost::geometric::translate( x, y, z )
      translate an object by this matrix
   matrix boost::geometric::scale( x, y, z )
      enlarge an object by this matrix
      NOTE: identity = scale( 1, 1, 1 )
   matrix boost::geometric::rotate( x, y )
   matrix boost::geometric::rotateX/Y/Z()
      rotate an object about a plane

These operations can then be combined via matrix multiplication and applied 
to a point (or vector?):
   point = point * matrix
   vector = vector * matrix
   and variants

There should also be the facility to project an object from one dimension 
system to another, e.g.
   point2D boost::geometric::project( point2D )

NOTE: These are not precise definitions of how the functions/interface 
should look like, it is just a basic outline.

Regards,
Reece

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