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Rail deserts
Evening all,
It frequently strikes me, when considering the geography of the terra incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) [1]. That's a huge area, about equal to the area encircled by the Inner Ring Road, and densely populated. It's shocking there's no railway service there - but perhaps not suprising when you consider that it's also largely a very deprived area. When the stations on the Holborn line were open, it was a lot smaller, but still pretty huge. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Twice the size of the Walworth desert, although currently containing a lot of industrial land. Most of the outer suburbs of London are like this, i suppose - the surprising thing about the Walworth one is that it's so central. I'm trying to figure out how to program a computer to find these automatically. And then overlay them on a population density map or something. tom [1] You can of course draw arbitrarily large shapes like that wherever you like, by avoiding stations, but this is no such trick - as evidenced by the fact that the polygon you've drawn is convex, at least roughly. -- Come on thunder; come on thunder. |
Rail deserts
On Oct 25, 6:17 pm, Tom Anderson wrote:
If a girl ever told me that she lived at Thornton Heath our relationship ended with the full stop that ended that sentence. Apart from the fact that the area is like a cross between Threads and The Equalizer, the only way to get there is by abseiling down from a rented Zeppelin. Mottingham, famous only for its obviously fictional name, is another can't-get-in, can't-get-out area. |
Rail deserts
On Thu, 25 Oct 2007 18:17:04 +0100, Tom Anderson
wrote: Evening all, It frequently strikes me, when considering the geography of the terra incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) [1]. That's a huge area, about equal to the area encircled by the Inner Ring Road, and densely populated. It's shocking there's no railway service there - but perhaps not suprising when you consider that it's also largely a very deprived area. When the stations on the Holborn line were open, it was a lot smaller, but still pretty huge. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Twice the size of the Walworth desert, although currently containing a lot of industrial land. Most of the outer suburbs of London are like this, i suppose - the surprising thing about the Walworth one is that it's so central. Isn't this down to the tram network that existed in South London, which limited penetration by the Underground and also overground railways? Maybe a tram map from c.1900 might help? -- Terry Harper Website Coordinator, The Omnibus Society http://www.omnibussoc.org |
Rail deserts
On Oct 25, 9:26 pm, Terry Harper wrote:
On Thu, 25 Oct 2007 18:17:04 +0100, Tom Anderson wrote: Evening all, It frequently strikes me, when considering the geography of the terra incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) [1]. That's a huge area, about equal to the area encircled by the Inner Ring Road, and densely populated. It's shocking there's no railway service there - but perhaps not suprising when you consider that it's also largely a very deprived area. When the stations on the Holborn line were open, it was a lot smaller, but still pretty huge. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Twice the size of the Walworth desert, although currently containing a lot of industrial land. Most of the outer suburbs of London are like this, i suppose - the surprising thing about the Walworth one is that it's so central. Isn't this down to the tram network that existed in South London, which limited penetration by the Underground and also overground railways? Maybe a tram map from c.1900 might help? It's also an area that will benefit from the Crossriver tram if that ever gets off the ground. Though a station at Camberwell Green (and perhaps another at Walworth) on the Blackfriars line would also be welcome. That area is actually pretty well served by buses, though. I lived down there for four years and so got out of the habit of getting the tube that even though I now live in King's Cross, which is hardly short of tubes, I still tend to either bus it or walk everywhere. Jonn |
Rail deserts
In message . com,
Offramp writes On Oct 25, 6:17 pm, Tom Anderson wrote: If a girl ever told me that she lived at Thornton Heath our relationship ended with the full stop that ended that sentence. Apart from the fact that the area is like a cross between Threads and The Equalizer, A phrase I seem to recall coining many years ago to describe my one and only visit to Wembley Central....... the only way to get there is by abseiling down from a rented Zeppelin. When I was studying in London, I stayed in Thornton Heath. The rail service was pretty good (fantastic for a non-Londoner) and buses did everything I needed, too. It was the pubs that put me off the area, not the transport! -- Ian Jelf, MITG Birmingham, UK Registered Blue Badge Tourist Guide for London and the Heart of England http://www.bluebadge.demon.co.uk |
Rail deserts
Offramp wrote:
On Oct 25, 6:17 pm, Tom Anderson wrote: If a girl ever told me that she lived at Thornton Heath our relationship ended with the full stop that ended that sentence. Apart from the fact that the area is like a cross between Threads and The Equalizer, the only way to get there is by abseiling down from a rented Zeppelin. Is this a different Thornton Heath from the one in South London that has 8 trains per hour in each direction? -- Richard J. (to e-mail me, swap uk and yon in address) |
Rail deserts
Tom Anderson wrote:
Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. That one partly exists because of the closure of the Crystal Palace High Level branch. The obvious (to me) one is around Roehampton Vale. Admittedly it's mostly parkland, but if you live in the middle you are a long way from a station. Yeading is another one. |
Rail deserts
On 25 Oct, 18:17, Tom Anderson wrote:
incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) The Aylesbury Estate? Notorious for being a railway ghetto. The Cross River Tram has a branch straight through this area. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Chelsea. If you're standing on Albert or Battersea Bridge you're a good mile from any sort of station. I'm trying to figure out how to program a computer to find these automatically. And then overlay them on a population density map or something. If you have the NR and tube station overlays (from Keyhole BBS) loaded into Google Earth, it's pretty easy to see where the gaps are. I see a big one south of Woolwich, a big hole north of the Olympic site (where Lea Bridge used to be). There's a huge one around Richmond Park. The East London Line extension cuts through the middle of a big hole too. U -- http://londonconnections.blogspot.com/ A blog about transport projects in London |
Rail deserts
On Oct 26, 5:40 am, Mr Thant
wrote: On 25 Oct, 18:17, Tom Anderson wrote: incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) The Aylesbury Estate? Notorious for being a railway ghetto. The Cross River Tram has a branch straight through this area. The Aylesbury is in the area described above. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Chelsea. If you're standing on Albert or Battersea Bridge you're a good mile from any sort of station. I'm trying to figure out how to program a computer to find these automatically. And then overlay them on a population density map or something. If you have the NR and tube station overlays (from Keyhole BBS) loaded into Google Earth, it's pretty easy to see where the gaps are. I see a big one south of Woolwich, a big hole north of the Olympic site (where Lea Bridge used to be). There's a huge one around Richmond Park. The East London Line extension cuts through the middle of a big hole too. Northern Havering is pretty poorly served, too. Rise Park, Noaks Hill and Harold Hill are all a good mile or two from either the Shenfield line or the Hainult branch. Jonn |
Rail deserts
On Oct 25, 11:51 pm, Ian Jelf wrote:
In message . com, Offramp writesOn Oct 25, 6:17 pm, Tom Anderson wrote: Thornton Heath ... is like a cross between Threads and The Equalizer ... A phrase I seem to recall coining many years ago to describe my one and only visit to Wembley Central....... And far too good to be reserved for a single usage. I have mentioned the phrase before as one that I liked, probably here. If I did a guide to London then that phrase would be the description of a 'no-star' rating for an area. |
Rail deserts
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Rail deserts
In message om,
Offramp writes On Oct 25, 11:51 pm, Ian Jelf wrote: In message . com, Offramp writesOn Oct 25, 6:17 pm, Tom Anderson wrote: Thornton Heath ... is like a cross between Threads and The Equalizer ... A phrase I seem to recall coining many years ago to describe my one and only visit to Wembley Central....... And far too good to be reserved for a single usage. I have mentioned the phrase before as one that I liked, probably here. I wasn't claiming copyright it anything! :-)) If I did a guide to London then that phrase would be the description of a 'no-star' rating for an area. Tell me, have you ever been to Rotherham?! -- Ian Jelf, MITG Birmingham, UK Registered Blue Badge Tourist Guide for London and the Heart of England http://www.bluebadge.demon.co.uk |
Rail deserts
In message , Tom
Anderson writes There was certainly a tram route along the Old Kent Road. The tram network in South London was very extensive and included services along most main roads in the inner south-east of London. But surely the main age of growth of the railways was before the age of trams? True, but back then there were inner-city stations on a number of lines and most of these were closed at an early date as a result of competition from the trams. But of course there were then, as now, some areas that were not served by railways, and that's where the various tram networks really came into their own. -- Paul Terry |
Rail deserts
On Oct 26, 11:45 am, wrote:
On Oct 26, 5:40 am, Mr Thant wrote: On 25 Oct, 18:17, Tom Anderson wrote: incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) The Aylesbury Estate? Notorious for being a railway ghetto. The Cross River Tram has a branch straight through this area. The Aylesbury is in the area described above. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Chelsea. If you're standing on Albert or Battersea Bridge you're a good mile from any sort of station. I'm trying to figure out how to program a computer to find these automatically. And then overlay them on a population density map or something. If you have the NR and tube station overlays (from Keyhole BBS) loaded into Google Earth, it's pretty easy to see where the gaps are. I see a big one south of Woolwich, a big hole north of the Olympic site (where Lea Bridge used to be). There's a huge one around Richmond Park. The East London Line extension cuts through the middle of a big hole too. Northern Havering is pretty poorly served, too. Rise Park, Noaks Hill and Harold Hill are all a good mile or two from either the Shenfield line or the Hainult branch. Jonn There's a difference between the areas which simply lack lines and stations and the Elephant, Peckham etc area, which is that the latter is surrounded by stations which have services that only run at certain times, such that if you go out by train, you can't necessarily get home. In Havering, you can trek across to one of the lines at any time of any day and find trains running (OK, replacement bus). |
Rail deserts
On 25 Oct, 18:17, Tom Anderson wrote:
Evening all, It frequently strikes me, when considering the geography of the terra incognita called 'South London', that there is an amazingly large region with no railway stations in the Walworth area. If you draw a line through Elephant & Castle, Kennington, Oval, Stockwell, Brixton, Loughborough Junction, Denmark Hill, Peckham Rye, Queen's Road Peckham, South Bermondsey, Bermondsey, Borough, and back to Elephant, you have an area within which there are no other railway stations of any sort (other than disused, anyway) [1]. That's a huge area, about equal to the area encircled by the Inner Ring Road, and densely populated. It's shocking there's no railway service there - but perhaps not suprising when you consider that it's also largely a very deprived area. When the stations on the Holborn line were open, it was a lot smaller, but still pretty huge. Anyway, are there any other notable rail deserts like this? There's one around Dulwich, but a lot of that's open ground, so it probably has fewer people in it. There's another huge one in the Thames Gateway, south of the District line, north of the Beckton branch of the DLR, east of the Stratford branch (a year ago, east of the NLL), and west of, crumbs, Dagenham Dock? Twice the size of the Walworth desert, although currently containing a lot of industrial land. Most of the outer suburbs of London are like this, i suppose - the surprising thing about the Walworth one is that it's so central. I'm trying to figure out how to program a computer to find these automatically. And then overlay them on a population density map or something. tom [1] You can of course draw arbitrarily large shapes like that wherever you like, by avoiding stations, but this is no such trick - as evidenced by the fact that the polygon you've drawn is convex, at least roughly. -- Come on thunder; come on thunder. I remember when I first moved to South London being surprised that Camberwell had no station, despite the dense population, and evidence of a former station at Camberwell. Apparently there is no capacity for a station here, but I believe that Southwark Council are pushing for one, and may agree to the closure of Loughborough Junction to create the capacity. Are there any updates on this? |
Rail deserts
In article , Tom
Anderson writes I'm trying to figure out how to program a computer to find these automatically. The approach I've taken in the past is very simple. Start with a grid representing the entire area (to make it easy, say 1000 x 1000 with one unit on the grid being 100 metres). Set up a list of locations of all the stations. Then: for each grid cell best := infinity for each station on the list d := (distance from station to cell) squared if d best then best := d cell value := sqrt (best) You can optimize things slightly by using a lookup table for the square roots rather than calculating them each time. When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. -- Clive D.W. Feather | Home: Tel: +44 20 8495 6138 (work) | Web: http://www.davros.org Fax: +44 870 051 9937 | Work: Please reply to the Reply-To address, which is: |
Rail deserts
Offramp wrote:
On Oct 25, 6:17 pm, Tom Anderson wrote: If a girl ever told me that she lived at Thornton Heath our relationship ended with the full stop that ended that sentence. Apart from the fact that the area is like a cross between Threads and The Equalizer, the only way to get there is by abseiling down from a rented Zeppelin. Mottingham, famous only for its obviously fictional name, is another can't-get-in, can't-get-out area. So the railway station called "Mottingham" is where exactly (answers of the form "one stop from Lee on the Sidcup line" are not helpful)? Robin |
Rail deserts
On 29 Oct, 11:04, "Clive D. W. Feather" cl...@on-the-
train.demon.co.uk wrote: When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. I actually did a map like this on Friday: http://londonconnections.blogspot.co...ndon-gaps.html I loaded all the station locations into a MySQL database, then wrote a PHP script to generate an SVG file. I didn't bother calculating distances - it just does separate passes to make the quarter mile discs appear on top of the half mile discs, which achieves a similar effect. U -- http://londonconnections.blogspot.com/ A blog about transport projects in London |
Rail deserts
On Mon, 29 Oct 2007 11:04:56 +0000, Clive D. W. Feather wrote:
The approach I've taken in the past is very simple. Start with a grid representing the entire area (to make it easy, say 1000 x 1000 with one unit on the grid being 100 metres). Set up a list of locations of all the stations. Then: 1 for each grid cell 2 best := infinity 3 for each station on the list 4 d := (distance from station to cell) squared 5 if d best then best := d 6 cell value := sqrt (best) Why does the distance need to be squared in line 4? -- jhk |
Rail deserts
"R.C. Payne" wrote in message ... Offramp wrote: On Oct 25, 6:17 pm, Tom Anderson wrote: If a girl ever told me that she lived at Thornton Heath our relationship ended with the full stop that ended that sentence. Apart from the fact that the area is like a cross between Threads and The Equalizer, the only way to get there is by abseiling down from a rented Zeppelin. Mottingham, famous only for its obviously fictional name, is another can't-get-in, can't-get-out area. So the railway station called "Mottingham" is where exactly (answers of the form "one stop from Lee on the Sidcup line" are not helpful)? Robin |
Rail deserts
In article . com, Mr
Thant writes I loaded all the station locations into a MySQL database, then wrote a PHP script to generate an SVG file. I didn't bother calculating distances - it just does separate passes to make the quarter mile discs appear on top of the half mile discs, which achieves a similar effect. Oo, crafty. Let existing graphics software do all the heavy work. -- Clive D.W. Feather | Home: Tel: +44 20 8495 6138 (work) | Web: http://www.davros.org Fax: +44 870 051 9937 | Work: Please reply to the Reply-To address, which is: |
Rail deserts
In article , Jarle H Knudsen
writes 1 for each grid cell 2 best := infinity 3 for each station on the list 4 d := (distance from station to cell) squared 5 if d best then best := d 6 cell value := sqrt (best) Why does the distance need to be squared in line 4? What is the formula for distance between two points on a Cartesian grid? -- Clive D.W. Feather | Home: Tel: +44 20 8495 6138 (work) | Web: http://www.davros.org Fax: +44 870 051 9937 | Work: Please reply to the Reply-To address, which is: |
Rail deserts
Clive Feather:
When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. With suitable travel-time assumptions, you can make an "isochronic map" like this one, which I occasionally use as a screen background: http://www.mysociety.org/2006/travel...big-1177px.png Delete the last component of the URL to see other examples by the same people, and discussion. Google on "isochronic map" to see examples by other people. -- Mark Brader, Toronto | I am a mathematician, sir. I never permit myself | to think. --Stuart Mills (Carr: The Three Coffins) |
Rail deserts
|
Rail deserts
On 2 Nov, 00:45, (Mark Brader) wrote:
Clive Feather: When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. With suitable travel-time assumptions, you can make an "isochronic map" like this one, which I occasionally use as a screen background: http://www.mysociety.org/2006/travel...al-london-big-... Delete the last component of the URL to see other examples by the same people, and discussion. Google on "isochronic map" to see examples by other people. According to your link Surbiton Station is nowhere near a station. |
Rail deserts
On Thu, 1 Nov 2007 17:26:38 +0000, Clive D. W. Feather wrote:
In article , Jarle H Knudsen writes 1 for each grid cell 2 best := infinity 3 for each station on the list 4 d := (distance from station to cell) squared 5 if d best then best := d 6 cell value := sqrt (best) Why does the distance need to be squared in line 4? What is the formula for distance between two points on a Cartesian grid? d = sqrt((x2 - x1)^2 + (y2 - y1)^2). But that does not explain (to me) why you do d^2 in line 4. -- jhk |
Rail deserts
On Sat, 3 Nov 2007 01:24:15 +0100,
Jarle H Knudsen wrote: On Thu, 1 Nov 2007 17:26:38 +0000, Clive D. W. Feather wrote: In article , Jarle H Knudsen writes 1 for each grid cell 2 best := infinity 3 for each station on the list 4 d := (distance from station to cell) squared 5 if d best then best := d 6 cell value := sqrt (best) Why does the distance need to be squared in line 4? What is the formula for distance between two points on a Cartesian grid? d = sqrt((x2 - x1)^2 + (y2 - y1)^2). But that does not explain (to me) why you do d^2 in line 4. It's an optimization. You only have to calculate a square root once per cell. Tim. -- God said, "div D = rho, div B = 0, curl E = - @B/@t, curl H = J + @D/@t," and there was light. http://tjw.hn.org/ http://www.locofungus.btinternet.co.uk/ |
Rail deserts
On Mon, 29 Oct 2007 11:04:56 +0000,
Clive D. W. Feather wrote: In article , Tom Anderson writes I'm trying to figure out how to program a computer to find these automatically. The approach I've taken in the past is very simple. Start with a grid representing the entire area (to make it easy, say 1000 x 1000 with one unit on the grid being 100 metres). Set up a list of locations of all the stations. Then: for each grid cell best := infinity for each station on the list d := (distance from station to cell) squared if d best then best := d cell value := sqrt (best) You can optimize things slightly by using a lookup table for the square roots rather than calculating them each time. I'd have thought a more useful optimization would be: If D(x,y) = x^2 + y^2 then D(x+1, y) = D(x, y) + 2x + 1 D(x, y+1) = D(x, y) + 2y + 1 D(x-1, y) = D(x, y) - 2x + 1 D(x, y-1) = D(x, y) - 2y + 1 But optimizing without profiling is generally a complete disaster and you've done this before but I haven't. ;-) Tim. -- God said, "div D = rho, div B = 0, curl E = - @B/@t, curl H = J + @D/@t," and there was light. http://tjw.hn.org/ http://www.locofungus.btinternet.co.uk/ |
Rail deserts
In message , Mark Brader
writes Clive Feather: When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. With suitable travel-time assumptions, you can make an "isochronic map" like this one, which I occasionally use as a screen background: http://www.mysociety.org/2006/travel...london-big-117 7px.png That, Mark, is seriously excellent! (And could also get you at the very least a shortlisting for the Turner Prize!) In all seriousness, a *very* interesting exercise. -- Ian Jelf, MITG Birmingham, UK Registered Blue Badge Tourist Guide for London and the Heart of England http://www.bluebadge.demon.co.uk |
Rail deserts
On Sat, 3 Nov 2007, Ian Jelf wrote:
In message , Mark Brader writes With suitable travel-time assumptions, you can make an "isochronic map" like this one, which I occasionally use as a screen background: http://www.mysociety.org/2006/travel...big-1177px.png That, Mark, is seriously excellent! (And could also get you at the very least a shortlisting for the Turner Prize!) Or rather, for Tom Steinberg and, posthumously, Chris Lightfoot, who i believe did the map. tom -- Science which is distinguishable from magic is insufficiently advanced |
Rail deserts
On Sat, 3 Nov 2007, Tim Woodall wrote:
On Mon, 29 Oct 2007 11:04:56 +0000, Clive D. W. Feather wrote: In article , Tom Anderson writes I'm trying to figure out how to program a computer to find these automatically. The approach I've taken in the past is very simple. Start with a grid representing the entire area (to make it easy, say 1000 x 1000 with one unit on the grid being 100 metres). Set up a list of locations of all the stations. Then: for each grid cell best := infinity for each station on the list d := (distance from station to cell) squared if d best then best := d cell value := sqrt (best) You can optimize things slightly by using a lookup table for the square roots rather than calculating them each time. Possibly. This is not as sure-fire a trick as it once was - you're saving arithmetic operations, but giving your data cache a rough ride. I'd have thought a more useful optimization would be: If D(x,y) = x^2 + y^2 then D(x+1, y) = D(x, y) + 2x + 1 D(x, y+1) = D(x, y) + 2y + 1 D(x-1, y) = D(x, y) - 2x + 1 D(x, y-1) = D(x, y) - 2y + 1 This would only work if you inverted the loops, though, so you iterated over stations on the outside, and grid cells on the inside. If you did that, though, yes, this would be what we call 'strength reduction', a venerable optimisation trick. Very well spotted that it can be applied here! A better optimisation, though, would be to start off by putting the stations in a quadtree or some other spatial data structure (something clever involving the Voronoi diagram?), so that you can find the nearest station (or at least a small number of candidates) to each grid cell with a fast lookup, rather than having to grind through every station in the list. Or at least, this would be true if there were a million stations. If there are only a few hundred, brute force might still be quicker. Most unsatisfying. tom -- Science which is distinguishable from magic is insufficiently advanced |
Rail deserts
On Mon, 29 Oct 2007, Mr Thant wrote:
On 29 Oct, 11:04, "Clive D. W. Feather" cl...@on-the- train.demon.co.uk wrote: When you've finished, the grid holds the distance to the nearest station. Convert it to a GIF and fiddle with the colour map and, for example, you can have a map where places within 1km of a station are green, within 2km are yellow, and more than 2km are red. I actually did a map like this on Friday: http://londonconnections.blogspot.co...ndon-gaps.html I posted a similar, but much less pretty, map, a few months ago. Can't find it now - i think i must have deleted it. Oh well. But i want an actual readout of polygons, with lists of bounding stations and exact areas. My OCD requires this. Then i need a map and/or dataset showing the population density across London. If you did want to do it with pure graphics, the best way i can think of would be to do a Voronoi tesselation (using some code off the internet or something [1]), split the regions into triangles centred on the stations, then make postscript of the triangles with a graduated fill getting darker/redder/etc as it goes out from the station [2]. That would look pretty sweet. I loaded all the station locations into a MySQL database, then wrote a PHP script to generate an SVG file. I didn't bother calculating distances - it just does separate passes to make the quarter mile discs appear on top of the half mile discs, which achieves a similar effect. The thing that excites me most is that you have the coordinates of all the stations from Google Earth dudes - i've been using Clive's grid references for tube stations and manually adding them for railway stations, which is very tedious. I will be obtaining the dataset you used forthwith! tom [1] Such as: http://www.qhull.org/ [2] Like so: http://redgrittybrick.org/postscript/gradient.html -- Science which is distinguishable from magic is insufficiently advanced |
Rail deserts
In uk.transport.london message ,
Mon, 29 Oct 2007 11:04:56, Clive D. W. Feather clive@on-the- train.demon.co.uk posted: In article , Tom Anderson writes I'm trying to figure out how to program a computer to find these automatically. The approach I've taken in the past is very simple. Start with a grid representing the entire area (to make it easy, say 1000 x 1000 with one unit on the grid being 100 metres). Set up a list of locations of all the stations. Then: for each grid cell best := infinity for each station on the list d := (distance from station to cell) squared if d best then best := d cell value := sqrt (best) You can optimize things slightly by using a lookup table for the square roots rather than calculating them each time. Square root is an FPU operation nowadays, so minimising them is only of minor importance. But there's no need to store distance in each cell while finding the best; store the square, and root only for display. A quick test in Javascript shows that the language can calculate a million distance^2 in five seconds (P4 3GHz); so for N stations the distances^2 would need 5N seconds; double that for details, and divide it by a fairly large number if using a compiled language. N is under 1000, IIRC. The conclusion seems to be that there's no point, for a one-off calculation (stations don't move about much), in doing other than simple reliable brute force, testing of course with subset data first; if one cannot do the final full run over dinner at home, one needs a better cook. Unless, of course, one has an already-developed more subtly algorithm to hand and knows how to use it. If course, that's just for distances. The nearest station to Ham House must be Twickenham or St Margarets; but the nearest by foot alone is probably Richmond, possibly Teddington. -- (c) John Stockton, Surrey, UK. Turnpike v6.05 MIME. Web URL:http://www.merlyn.demon.co.uk/ - FAQish topics, acronyms, & links. Proper = 4-line sig. separator as above, a line exactly "-- " (SonOfRFC1036) Do not Mail News to me. Before a reply, quote with "" or " " (SonOfRFC1036) |
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