principles of 5d modeling - geospatial world forum van oosterom.pdfmay 05, 2012 · principles of...

5-5-2012

Challenge the future

Delft University of Technology

Principles of 5D modeling

Peter van Oosterom,

GIS technology, OTB, Delft University of Technology

Seminar: 5D Modeling, 27 April 2012, GWF Amsterdam

2 Principles of 5D modeling

Contents

• Introduction

• 3D space+time example: 4D Cadastre

• Scale as dimension

• Conclusion


Previous research: separate

treatment of 3D, Scale and Time

Time

(Kraak, 2006) Scale

(Vermeij, 2003)

3D (Penninga, 2007)


Approach: 3 iterations


• Multidimensional polyhedra

• GISt, TU Delft: Arens, Stoter (2004)

• Regular Polytopes

• GISt, TU Delft: Thompson (2007)

• Simplical Homology

• GISt, TU Delft: Penninga (2008)

Method: Apply mathematical theories on

multi-dimensional data modelling

http://commons.wikimedia.org/wiki/File:Dodecahedron-with-inscribed-cube.svg


Poincaré simplicial homology

Solid mathematical foundation:

A n -simplex Sn is defined as smallest convex set in

Euclidian space Rm of n+1 points v0 , …, vn

(which do not lie in a hyper plane of dimension less than n)


Poincaré simplicial homology

The boundary of simplex Sn is defined as sum of (n-1) dimensional

simplexes (note that ‘hat’ means skip the node):

Sn =

remark: sum has n+1 terms

ni

n

i

i vvv ,...,ˆ,...,)1( 0

0


Contents

• Introduction



• Conclusion


Integration of 3D+time: 4D Cadastre

• In addition to spatial (3D) aspect, rights, restrictions and responsibilities include a temporal aspect

• To be able to manage the dynamics in land administration the

time (fourth) dimension must be handled as well


Conceptual Cadastre Basis

2D: a planar partition of the surface

3D: a partition of space with no overlaps or gaps

4D: no overlaps or gaps in the rights, not only in space but also in parallel the time dimension

Partition: no gaps or overlaps in the parcelation on which the rights are based


Implementation

X

Y

t

t0

t1

t2

State 1 t0 to t1 – 1 parcel

State 2 t1 to t2 – 3 parcels

State 3 t2 to now – 4 parcels

now

2D: partition of the surface based on a 2D topology with

faces, edges and nodes

3D: partition of space based on a complete 3D topological structure based on volumes, faces, edges and nodes

4D: use a 4D space-time topological structure


3D Tunnel registration in Queensland


River is moving over time and legal Boundary follows (true 4D)


More cases:

Timesharing

• 3D volumetric

survey plan

(apartments)

• Timesharing of

40 units/week:

40*52 shares

• Timeshare can

be traded,

mortgaged, etc.

• 3D+time=4D


4D cadastre: separate space and time

or an integrated attribute?

• Advantages of separate attributes: 1. Already able to represent all cases

2. Supported by state-of-the art technology

3. Temporal aspect is more than just one dimension

• Advantages of integrated 4D data type: 1. optimal efficient 4D searching

2. Parent-child becomes topology neighbor query in time


P1

P2 P3

P5

P4

t2

t1

t0

time

y

x

Subdivision

of parcels


4D data type advantages (cont.)

• Advantages of integrated 4D data type: 1. optimal efficient 4D searching

2. Parent-child becomes topology neighbor query in time

3. Foundation of full (4D) partition: no overlaps or gaps in

space and/or time

4. 4D analysis: do two moving cattle rights have spatio-

temporal overlap/touch


t2

t1

t0

time

y

x

P2 P1

Moving

cattle


Contents

• Introduction



• Conclusion


1:10.000 1:100.000 1:50.000

1:250.000 1:500.000

Context of the research


Early use of additional dimension for

scale (importance) representation

• Alternative Reactive-tree

(van Oosterom,

Auto-Carto 10, 1991)


Generalized Area Partitioning-tree


Generalized Area Partitioning-tree

(GAP-tree) history

• Normal GAP-tree (van Oosterom 1993) areas are stored as independent polygons computed redundancy (both at given scales and between scales)

• Vermeij et al. 2003 proposed topological GAP-tree: edges and faces (with importance range, consider as height), reduced redundancy between neighbors scale/imp with 3D prisms


Contents

• Introduction



• Conclusion


Conclusions

• Vario-scale nD maps based on (n+1)D representations and

slicing (selecting) with hyperplanes:

• tGAP structure translates 2D space and 1D scale in an

integrated 3D topological representation: no overlaps and no

gaps (in space and scale)

• Starting with 3D space and adding scale results in 4D

• Starting with 3D space and time (history) and adding scale

results in 5D topological structure (again no gaps/overlaps in

space, time or scale), well defined neighbors in space, time

and scale directions


Questions?


patent pending nr. OCNL 2006630

prepared by Dirk de Jong, European Patent Attorney, Vereenigde

ICA 14th Generalisation Workshop, 30 June-1 July 2011, Paris, France

Towards a true vario-scale structure

supporting smooth-zoom


Non-flat slice mixed scale map

(fish-eye example)

x

y

S=0

S=0.5

source: Harrie et al, 2002, ISPRS Archives 34(4):237–242


Non-horizontal slice mixed scale map

principles of 5d modeling - geospatial world forum van oosterom.pdfmay 05, 2012 · principles of...

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