Hi Alan,
Yes, the original hyphotesis of continuity lines was that "it improves
the axial system without chalenging its fundaments" (Figueiredo and
Amorim, 2005, p161). Basically, because axial lines are not lines of
sight but they are already curves in 3d space, they could be curves in
2d as well. Continuity lines fixes the high sensitivity to small
deformations in the grid found in the axial maps, as pointed by Ratti.
It has a huge effect on what Bin is showing. For instance, Your paper
with Rui clear power-law tails were found in axial maps. Bin's plots
are completely curved - something went wrong during the map creation.
Regards,
Lucas
On 30/05/07, Alan Penn <[log in to unmask]> wrote:
> Lucas,
>
> I am not quite sure what you mean by 'in hierarchical terms'. The axial line
> is well defined and derived from the built boundary taking account of the
> geometry of that full 2d shape. In this it is different to road centre
> lines, named streets or any other derivations of these where there seems to
> be no definition published, nor a formal derivation from the geometry of the
> space itself... or have I missed one? Continuity lines based on axial maps
> seem to me to be equally well founded, but if derived from road centrelines
> you still have a problem of the foundation being poorly defined in its
> relation to the geometry of the open space you are representing. This may
> all be somewhat pedantic and I would guess has little effect on results of
> the kind that Bin is showing.
>
> Alan
>
> >
> > On 30/05/07, Alan Penn <[log in to unmask]> wrote:
> > > Agreed - an argument for a (comparatively) well defined concept like the
> > > axial line perhaps? :-)
> >
> > In hierarchical terms axial lines are ill defined. Some streets are
> > fragmented into several axial lines while others are not. Therefore
> > axial maps throw streets in both directions in the rank-plot, either
> > fragmenting or aggregating. Without mentioning that many axial lines
> > are projections of curves in the 3D space. Therefore, the
> > fragmentation of curves in 2D is not justifiable.
> >
> > Continuity maps have a unified strategy: aggregate until a threshold,
> > therefore all "streets" are moved to the upper rank. In this sense
> > they are better defined.
> >
> > The question is the threshold. Can we aggregate radial streets and
> > create circles? So on...
> >
> > Regards,
> > Lucas
>
--
Lucas Figueiredo
http://www.flickr.com/photos/lucasfigueiredo/
Mindwalk
http://www.mindwalk.com.br
|