Transcript Using the discrete 3D Voronoi diagram for the modelling of

GIMA MSc Thesis Midterm Presentation
U SING THE DISCRETE 3D V ORONOI
DIAGRAM FOR THE MODELLING OF
3D CONTINUOUS INFORMATION IN
GEOSCIENCES
Tom van der Putte
Supervisors: Hugo Ledoux and Peter van Oosterom
degenerate cases
Contents
• The problem and it’s context
• The research objectives
• The research already performed
• The research still to come
Problem and Context
Modeling continuous fields:
Usually represented in raster format
Ledoux (2006) proposed:
represent continuous field by creating an exact
(vector) Voronoi diagram
The Voronoi Diagram
Interpolation method
Point
dataset:
(seeds)
Voronoi
Diagram:
Why the exact Voronoi diagram?
• It handles anisotropic data well
• It can be interpolated more efficient
• Very easily manipulated!
BUT:
- Struggles with degenerate cases
- It can be relatively slow
What is the discrete Voronoi diagram?
N-dimensional regularly tesselated space
(raster), in which all tesselations
(pixels/voxels) have the value of the closest
‘seed’.
Why the discrete Voronoi diagram?
Expected:
- Same pro’s
BUT:
- No degenerate cases
- Expected to be fast (Park et al, 2006)
Research Objectives
Main objective:
To assess the use of the discrete 3D Voronoi
diagram for the modelling of 3D continuous
information in geosciences.
Research Objectives
Research Questions:
-
How to create a discrete 3D Voronoi diagram?
Which GIS can handle discrete 3D data (raster)?
Which data formats are used?
What functionality is needed for modeling ?
What functionality is provided by the GIS?
Discrete vs. Exact: which is best for what?
Already Done
Creating discrete (3D) VD
Numerous ways to create a discrete VD
Poll every pixel/voxel:
“Which seed is closest ?”
“Grow” Voronoi Cells
(Dilation)
“Growing” Voronoi cells
Through morphological operation: Dilation
Object
Structuring
element
New
Object
“Growing” Voronoi cells
List of points
P1 (x,y,z,a)
P2 (x,y,z,a)
POINT
DATA SET
P…. (x,y,z,a)
Pn (x,y,z,a)
“Growing” Voronoi cells
For each point in a list of points:
IF neighbour has no value:
assign neighbour current value
ELSE IF distances from pixel to seeds are equal:
choose highest/lowest/random
ELSE:
assign value of closest seed
Save changed points in new list
Why this way?
- Conceptually very simpel
- Relatively efficient
- Inserting / removing points very easy and
efficient!
List of points
POINT
P1 (x,y,z,a)
……
From discrete 3D VD to GIS
GIS packages that fully support 3D raster:
Grass
(PCRaster)
3D raster vizualisation:
MayaVi
3D raster storage
VTK file
MayaVi
GRASS
ASCII 3D
RASTER
file
3D POINT
DATA SET
VTK XML
file
DISCRETE 3D VD
Functionality
What functionality is offered?
GRASS
MayaVi
-/+
++
Isosurface
-
++
Slicing
-
++
Analytical functionality
++
n/a
Multi-D Map Algebra
++
n/a
3D - Reclassification
++
n/a
Interpolation (Point)
+
n/a
Visualisation
Functionality
What functionality is NOT offered?
Interpolation
- Resampling
- Natural Neighbour Interpolation
-> Easy because inserting points = quick!
Still to do?
• Adding final functionality
• Comparisson exact VD and discrete VD:
- Which is better suited for what purpose?
- What is the difference in accuracy?
• Summarize problems in current 3D GIS in light
of this research
• Put it all on paper