Hierarchical Terrain Models Based on Edge Sorting with Integration of Polygonal Networks

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Hierarchical Terrain Models Based on Edge Sorting
with Integration of Polygonal Networks

• Morten Fimland
• Department of Informatics
• University of Oslo

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Introduction

• Motivation - Data thinning with focus on edges
• Edge collapse techniques
• Data structures for hierarchical terrain models
• Edge sorting criteria
• Examples
• Summary and further work

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Motivation

• Terrain models
• Representations of large data sets
• Scale independence
• Focus on edges
• Integration of polygonal data, e.g. river and
  road networks
• Storage, retrieval and transmission

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Terrain and Networks
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Terrain and Networks
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Terrain and Networks
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Edge collapse (expand)

• Progressive meshes Hoppe
• Operation on platelets
• New edges and triangles. No new vertices
• Legal collapse

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Edge collapse (expand)

• Non-legal collapses

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Edge Sorting Strategy - Measure A

• Assign a weight to each edge
• 2D measure (A), a minimum angle over all
  triangles in the platelet,

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Edge Sorting Strategy - Measure Q

• 3D measure (Q),

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Edge Sorting Strategy - Measure S

• 3D measure (S),

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Algorithm
T
P

• 1)
• Generate (Delaunay)
• Generate weights for edges in based on A,Q,S
• 2)
• for jN-1
• Generate by edge collapses
• Generate weights for edges in based on
  A,Q,S
• Result

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Levels and Platelets
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Data Structure

• Analysis
• Synthesis

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Hierarchical Terrain Models

• Pyramid with lists of triangles

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Examples

• Crater Lake 154.224 points
• 306.860 triangles
• Initial Delaunay triangulation

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Examples 3D (4 Triangles)

• Original triangulation WS

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Examples 3D (0.7 Triangles)

• Original triangulation W0.1A0.9S

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Examples 3D (0.7 Triangles)

• WQ W0.1A0.9Q

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Examples 2D (Smaller Area)
WQ
W0.1A0.9Q
W0.5A0.5Q
WA
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Summary

• Triangle-based surface representations for
  terrain models
• Hierarchical data structures
• Triangulation at each level of the hierarchy is
  based on an edge ordering strategy (edge
  collapse)
• Three measures are used for calculating the
  weights

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Further Work

• Integration of the polygonal networks
• Strategies to resolve network-integration
  conflicts
• Improved measures for edge ordering
• Domain decomposition