## Tuesday, October 22, 2013

### Index transformation between bounding boxes and uniform grids

I end up rewriting this code all the time. It transforms from points in space to grid coordinates world_to_grid() and back grid_to_world(), such that p = grid_to_world( aabb, dim, world_to_grid( aabb, dim, p ) ).  It's simple, but bugs here can mess up lots of things in ways that are hard to detect.  No range checking is performed in order to make it easy to apply custom boundary conditions.

    template< typename real, typename index, typename real3 >
inline real3 _world_to_grid( const real *aabb, const index *dim, const real3 &pos ){
return real3( real(dim[0]-1)*(pos[0]-aabb[0])/(aabb[1]-aabb[0]), real(dim[1]-1)*(pos[1]-aabb[2])/(aabb[3]-aabb[2]), real(dim[2]-1)*(pos[2]-aabb[4])/(aabb[5]-aabb[4]) );
}

template< typename real, typename index, typename real3 >
inline real3 _grid_to_world( const real *aabb, const index *dim, const real3 &pos ){
return real3( aabb[0]+real(pos[0])*(aabb[1]-aabb[0])/real(dim[0]-1), aabb[2]+real(pos[1])*(aabb[3]-aabb[2])/real(dim[1]-1), aabb[4]+real(pos[2])*(aabb[5]-aabb[4])/real(dim[2]-1) );
}  

The code assumes that the dim variable holds the number of points in each direction (e.g. int dim[] = { nx, ny, nz };) and that the first point is coincident with the minimum value of the axis-aligned bounding box with the last point coincident with the maximum value of the bounding box. The aabb parameter is the axis-aligned bounding box defining the grid in world space, e.g. int aabb[] = { xmin, xmax, ymin, ymax, zmin, zmax };