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Transcript of U SING THE DISCRETE 3D V ORONOI DIAGRAM FOR THE MODELLING OF 3D CONTINUOUS INFORMATION IN...
![Page 1: U SING THE DISCRETE 3D V ORONOI DIAGRAM FOR THE MODELLING OF 3D CONTINUOUS INFORMATION IN GEOSCIENCES GIMA MSc Thesis Midterm Presentation Tom van der.](https://reader036.fdocuments.net/reader036/viewer/2022062304/56649eb55503460f94bbd4ba/html5/thumbnails/1.jpg)
USING THE DISCRETE 3D VORONOI DIAGRAM FOR THE
MODELLING OF 3D CONTINUOUS INFORMATION IN GEOSCIENCES
GIMA MSc Thesis Midterm Presentation
Tom van der Putte
Supervisors: Hugo Ledoux and Peter van Oosterom
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degenerate cases
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Contents
• The problem and it’s context
• The research objectives
• The research already performed
• The research still to come
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Problem and Context
Modeling continuous fields:Usually represented in raster format
Ledoux (2006) proposed:represent continuous field by creating an exact (vector) Voronoi diagram
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The Voronoi Diagram
Point dataset:(seeds)
Voronoi Diagram:
Interpolation method
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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
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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’.
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Why the discrete Voronoi diagram?
Expected:
- Same pro’s
BUT:
- No degenerate cases- Expected to be fast (Park et al, 2006)
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Research Objectives
Main objective:
To assess the use of the discrete 3D Voronoi diagram for the modelling of 3D continuous information in geosciences.
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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?
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Already Done
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Creating discrete (3D) VD
Numerous ways to create a discrete VD
Poll every pixel/voxel:“Which seed is closest ?”
“Grow” Voronoi Cells(Dilation)
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“Growing” Voronoi cells
Through morphological operation: Dilation
Object Structuring element
New Object
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“Growing” Voronoi cells
POINT DATA SET
List of points
P1 (x,y,z,a)
P2 (x,y,z,a)
P…. (x,y,z,a)
Pn (x,y,z,a)
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“Growing” Voronoi cells
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
For each point in a list of points:
Save changed points in new list
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Why this way?
- Conceptually very simpel- Relatively efficient- Inserting / removing points very easy and
efficient!
POINT
List of points
P1 (x,y,z,a)……
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From discrete 3D VD to GIS
Grass
GIS packages that fully support 3D raster:
(PCRaster)
3D raster vizualisation:
MayaVi
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3D raster storage
DISCRETE 3D VD
MayaViGRASS
3D POINT DATA SET
ASCII 3DRASTER
file
VTK file
VTK XML file
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Functionality
GRASS MayaViVisualisation -/+ ++
Isosurface - ++
Slicing - ++
Analytical functionality ++ n/a
Multi-D Map Algebra ++ n/a
3D - Reclassification ++ n/a
Interpolation (Point) + n/a
What functionality is offered?
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Interpolation- Resampling- Natural Neighbour Interpolation -> Easy because inserting points = quick!
FunctionalityWhat functionality is NOT offered?
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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