# 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

**G**eographic

**I**nformation

**S**ystems

## 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.

**G**eographic

**I**nformation

**S**cience

# 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

- relatively easy to interpret and execute
- 2D and 3D space

- irregular boundaries and edges
- 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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