Spatial Interpolation  

Voronoi polygons

Thiessen polygons

Maps = Power

Waldseemüller map 1507

Gemma Frisius 

(born Jemme Reinerszoon)

December 9, 1508 – May 25, 1555

Geographic Information Science

Interpolation

Voronoi polygons
Tessellation

Data = Confidence

Geographic
Information
Systems

Title Text

GIS Body of Knowledge

Foundational Concepts

Knowledge Economy

Data Capture and Management

Programming and Development

Analytics and Modeling

Cartography and Visualization

GIS&T Society

Domain Applications

What might we find here?

Tobler's First law of Geography: 

Everything is related to everything else but

near things are more related than distant things.

interpolation

The estimation of surface values at unsampled points based on known surface values of surrounding points.

Interpolation

Think carefully about the data and real-life phenomena before you pick a specific interpolation method.

Geographic
Information
Science

Geographic Information Science

  • The field that seeks to redefine geographic concepts and their use in the context of GIS. 
  • Interrogates fundamental themes traditionally found in spatially oriented fields
  • Study the impacts of GIS on society and societies impacts on GIS (Mark, 2003)

from: MacEachren, Alan M. 1992. "Visualizing uncertain information." Cartographic Perspectives. 13: 10-19.

Clay soil

Clay soil

Clay soil

Clay soil

Wetland soil

High Active Clay soil

Organic soil

Wetland soil

Spodic soil

High Active Clay soil

?

Voronoi polygons

Draw a line equal distance between two points,

generating a cell around each point.

Control Points

hypothetical points within a polygon likely to share value with control point.

"Area of influence polygons"

Set of known points

Control points

example: Weather stations, soil samples

Tesselation

MC Escher. Two Fish (No. 41)

1941 Pencil, ink, watercolor. Improved 1963.

Nature

Social Science Examples

  • social service access
  • epidemiology
  • marketing

London 1854

Red dots cholera deaths.

Blue dots water pumps.

John Snow maps entered into GIS by John Macdenzie

Other names for Voronoi diagrams include...

  • Thiessen polygons
  • Dirichlet tessellation

Many disciplines use voronoi and similar techniques

  • geology
  • computational geometry
  • ecology
  • archaeology
  • meteorology
  • video game design

Computer Vision 

Architecture 

Geography 

point-->surface

Isoline Map 

Strengths

  1. relatively easy to interpret and execute
  2. 2D and 3D space
  1. irregular boundaries and edges
  2. does not take into account...

Weakness

Network Voronoi Diagram

Manhattan Distance

Future Lessons

Network analysis 

 

One hour service area, hospitals in rural British Columbia, Canada

Several interpolation methods used in GIS 

 

Nearest Neighbor

Kringing

Spline

Inverse Distance Weight (IDW)

Inverse of Voronoi is Delaunay Triangulation

Delaunay Triangulation commonly used to make Triangulated Irregular Network (TIN)

Future Lessons

Learn from history

Apply to new forms of spatial media

Dank u wel.

Voronoi

By Britta Ricker

Voronoi

This presentation will introduce the interpolation method often known as Voronoi.

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