Efficient Derivation and Caricature of Urban Settlement Boundaries For

Eﬃcient derivation and caricature of urban settlement boundaries for 1:250k

Andreas Reimer and Christian Kempf

Universit¨at Heidelberg

1 / 28 Can schematisation techniques be used for medium scale generalisation?

2 / 28 Deﬁnition We deﬁne schematisation in cartography as a process that uses cartographic generalisation operators in such a way as to produce diagrams of a lower graphical complexity compared to maps of the same scale; the process aims to maximise task-adequacy while minimizing non-functional detail. In contrast, traditional cartographic generalization can be understood as trying to maximise functional detail with task-adequacy (in the form of legibility) as a constraint.

Schematisations use many unorthodox design principles → carricature etc.

Huh? Schematisation?

3 / 28 Huh? Schematisation?

Deﬁnition We deﬁne schematisation in cartography as a process that uses cartographic generalisation operators in such a way as to produce diagrams of a lower graphical complexity compared to maps of the same scale; the process aims to maximise task-adequacy while minimizing non-functional detail. In contrast, traditional cartographic generalization can be understood as trying to maximise functional detail with task-adequacy (in the form of legibility) as a constraint.

Schematisations use many unorthodox design principles → carricature etc.

3 / 28 Why Strategi?

250k legacy product manually updated no relation to OS Master Map data geometrically ﬁtted to generalised base data

4 / 28 Why Strategi?

5 / 28 Why Strategi?

6 / 28 Approach

ﬁnd out target design rules/constraints empirically reduce input complexity in model generalisation redraw geometries in cartographic generalisation

7 / 28 Observations...

Strategi 2500

2000

1500 quantity 1000

500

0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 number of nodes/perimeter [linelength mm] 8 / 28 Input from OS Master Map

9 / 28 Selection

10 / 28 Buﬀer

11 / 28 Union

12 / 28 Selection by size

13 / 28 Simpliﬁcation: Visvalingam-Whyatt

14 / 28 Angular schematisation

15 / 28 Input and result

16 / 28 Result in context

17 / 28 At viewing scale

18 / 28 

 !                !   #  

          Original Strategi        

     

 

      

  

  !  Grassendale  Storeton Port B5171 A562 ! Hale A557  Thurstaston Irby  B5136 !  B5151 Sunlight Bank     A551 Garston A561      Pensby      Bebington B5138 Barnston  B5137  Bridgewater Canal        4  B5137 Bromborough Speke  Runcorn B5155  A540 A5137    Hale

Heswall    B5155  WIRRAL Eastham A557 Dawpool   A41   Thornton    A533  Bank  Sands Dungeon  Hough M53  Weston   Gayton RIVER W   Banks N  a e RIVER DEE MERSEY v a A557 i ve A533 B5151 B5132 ga r / AFON tio Ri  B5136  n W ve

DYFRDWY Raby Eastham ea r Gayton  B5132 ve M56 M56 er r B5135 st Sands e al  Ince ch n     A41 an Ca Banks  M ip  Parkgate Hooton M53 Sh   7      B5133 r  B5439 Childer  te   B5134 Willaston   s l 

Neston e a 

 Thornton 8  h n 

    c a  Frodsham  B5132 n C  a p M56

B5463 A5032 M i   h  B5151 S Ince

  Ness B5463    Bagillt S  A540 A5032 U B5152 h  n Bank A41 B5132 r   i o Elton Helsby o    n p 

 s

  B5132 C h   i a r   Newton

n e  A56 B5153   a  A5032 l A5117   Burton Ledsham  14   Kingsley     Thornton-le-Moors  Capenhurst 10 Hapsford Alvanley   Puddington  A5117    M53    A550(T)  Stoak  Flin t   A5117 B5132 White   15 B5393

 ! M56 Dunham-on-the-Hill  Sands M 56       Shotwick A41 Wervin 

A548  A511 7(T) Backford Manley     Picton Bridge  Delamere Mouldsworth   Trafford Forest Flint Saughall   Connah's Mollington  M53

 Mountain      A540  Quay  Mickle     A55(T) A41(T)   Trafford  176  B5441  Upton Ashton   A5119   

Wepre !     Sealand Hayes 

Shotton   B5132 B5126 Guilden  ! A494(T)   Northop Northop A5116 A56(T) Sutton Great   Blacon  A54 Kelsall  Hall   Queensferry Barrow      B5125 A548 A56  A5480   Mancot      pshire  Tarvin Willington  Royal Shro Vicarscross  Oscroft

 Sandycroft Ri nion Canal Corner  A ve U A51   fo r ! Ewloe  n De Littleton Soughton/Sychdyn Dy e  A5115 B5129 fr / B5125 dw   A494(T) Hawarden y       A55(T) A51 Quarrybank  River Alyn New B5128 / A # Christleton Utkinton   fon Alun A5119      Brighton  A550 Saltney   A41 Drury B5125   Handbridge !  Duddon    A5104 Rowton  Buckley A55(T) A483 A55(T) 158 Broughton    Lache Waverton Burton Clotton B5128 Bretton   A549 B5130

 A494(T) A55(T) A49  !  

    !               

  19 / 28                     

 !                !   #  

          Our urban regions        

     

 

      

  

Neston e a 

 Thornton 8  h n 

    c a  Frodsham  B5132 n C  a p M56

B5463 A5032 M i   h  B5151 S Ince

  Ness B5463    Bagillt S  A540 A5032 U B5152 h  n Bank A41 B5132 r   i o Elton Helsby o    n p 

 s

  B5132 C h   i a r   Newton

 ! M56 Dunham-on-the-Hill  Sands M 56       Shotwick A41 Wervin 

A548  A511 7(T) Backford Manley     Picton Bridge  Delamere Mouldsworth   Trafford Forest Flint Saughall   Connah's Mollington  M53

 Mountain      A540  Quay  Mickle     A55(T) A41(T)   Trafford  176  B5441  Upton Ashton   A5119   

Wepre !     Sealand Hayes 

 A494(T) A55(T) A49  !  

    !               

  20 / 28                     How does it scale?

O(N) + O(3N) + O(N log N) + O(N log N) + O(N) (1) +O(N) + O(N log N + s) ≈ O(N log N + s)

where N is the size of the original input and s is number of intersections.

n O(c · n2 log n) + O(( + 2) · n log n) 2 (2) +O(n) + O(n2) ≈ O(c · n2 log n)

where n the much reduced size after model generalisation and c is the number of angular changes.

21 / 28 Open problems

22 / 28 Open problems

GI comparison with building simpliﬁcation techniques GI administrative subdivisions and seed points GI acute exteriour angles CG inner rings, intersection free CG optimal solutions?

23 / 28 Thank you for your attention! Thanks to Sheng Zhou, Nico Regnauld and Patrick Revell!

24 / 28 Individual bits

β Pnew

1 d d 2

Pi-1 Pi-2

Pi+1 Pi+2

25 / 28 Individual bits

26 / 28 Individual bits

27 / 28 Individual bits

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