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 ! 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 ! ! 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 Pi β Pnew α 1 d d 2 Pi-1 Pi-2 Pi+1 Pi+2 25 / 28 Individual bits 26 / 28 Individual bits 27 / 28 Individual bits 28 / 28.