regular and irregular multi resolution terrain models a comparison n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Regular and Irregular Multi-resolution Terrain Models: a Comparison PowerPoint Presentation
Download Presentation
Regular and Irregular Multi-resolution Terrain Models: a Comparison

Loading in 2 Seconds...

play fullscreen
1 / 34

Regular and Irregular Multi-resolution Terrain Models: a Comparison - PowerPoint PPT Presentation


  • 143 Views
  • Uploaded on

Regular and Irregular Multi-resolution Terrain Models: a Comparison. Leila De Floriani * Paola Magillo Department of Computer Science University of Genova, Genova (Italy) * currently at the University of Maryland, College Park, MD. Outline. Motivations

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Regular and Irregular Multi-resolution Terrain Models: a Comparison' - tudor


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
regular and irregular multi resolution terrain models a comparison

Regular and Irregular Multi-resolution Terrain Models: a Comparison

Leila De Floriani * Paola Magillo

Department of Computer Science

University of Genova, Genova (Italy)

* currently at the University of Maryland, College Park, MD

outline
Outline
  • Motivations
  • Related Work
  • Regular and Irregular Multi-Triangulations (MTs)
    • Vertex-Based Multi-Triangulation (Vertex-based MT)
    • Hierarchy of Right Triangles (HRT)
  • Level-Of-Detail (LOD) Queries for Terrain Modeling
  • Data Structures
  • Experimental Results and Comparisons
  • Summary and Future Work
why multi resolution terrain models
Why Multi-resolution Terrain Models?
  • Large-size terrain data sets
    • high storage requirements and high processing times
  • Multi-resolution terrain models
    • encompass a collection of terrain representations at different levels of resolutions
why multi resolution terrain models1
Why Multi-resolution Terrain Models?
  • Multi-resolution terrain models
    • allow extracting terrain representations at a variable resolution
regular and irregular multi resolution models
Regular and Irregular Multi-Resolution Models
  • Data on a grid versus scattered data
  • Regular versus irregular multi-resolution models:
    • Regular models: based on a nested domain decomposition
    • Irregular models: compact way of encoding the steps performed by a simplification process applied to an irregular triangle mesh
regular and irregular multi resolution models1
Regular and Irregular Multi-Resolution Models
  • Both are instances of a common framework: the Multi-Triangulation
  • Our objective: compare and analyze regular and irregular multi-resolution models
  • Comparison:
    • size of the models
    • space requirements of their encoding structures
    • efficiency in extracting meshes at variable resolution: Level-Of-Detail (LOD) queries
related work
Related Work
  • Regular multi-resolution models:
    • Triangle quadtrees (Gomez and Guzman, 1979; Dutton, 1983)
    • Restricted quadtrees (Von Herzen and Barr, 1987; Sivan and Samet, 1992)
    • Hierarchies of right triangles (Duchaineau et a., 1997; Evans et al., 2001; Lindstrom et al., 1996; Pajarola, 1998)
  • Irregular multi-resolution models:
    • Nested meshes (De Floriani and Puppo, 1995; Scarlatos and Pavlidis, 1994)
    • Pyramidal triangle meshes (De Berg and Dobrindt, 1995; De Floriani, 1989)
    • Progressive meshes (Hoppe, 1996; Taubin et al., 1998)
    • Continuous LOD models (Hoppe, 1998; Xia et al., 1997; Maheshvari et al.,1997; El Sana and Varshney 1999: De Floriani et al., 1998)
basic concepts modifications
Basic Concepts: Modifications
  • Modification of a triangle mesh: replace a connected set of triangles with other triangles covering the same region
basic concepts dependencies
Basic Concepts: Dependencies
  • A modification M2 depends on a modification M1 iff M2 changes some triangles that have been changed by M1

M2 depends on M1

M2 does not depend on M1

the multi triangulation mt
The Multi-Triangulation (MT)
  • A base mesh
  • A set of modifications
  • A partial order (dependency relation)
the multi triangulation mt1
The Multi-Triangulation (MT)
  • Vertex-Based Multi-Triangulation (Vertex-based MT):
    • Scattered data
    • Modification: vertex insertion
  • Hierarchy of Right Triangles (HRT):
    • Data on a grid
    • Modification: simultaneous bisection of two adjacent right triangles
lod queries
LOD Queries
  • A set of basic queries for analysis and visualization of a terrain at different levels of detail
  • Instances of selective refinement:

extract from a Multi-triangulation a mesh with the smallest possible number of triangles satisfying some user-defined criterion based on LOD

  • LOD based on approximation error
  • LOD can be uniform on the whole domain,or variable at each point of the domain.
data structures for multi triangulations
Data Structures for Multi-Triangulations
  • They must support efficiently:
    • do/undo modifications on the extracted mesh
    • test dependency links (to decide whether a modification can be applied)
  • Data Structures for Vertex-Based MTs:
    • Procedural encoding of modifications
    • Partial order represented as a Directed Acyclic Graph (DAG)
    • Approximation error associated either with triangles or with modifications
procedural encoding of modifications in a vertex based mt
Procedural Encoding of Modifications in a Vertex-based MT
  • To insert a vertex:
    • Recognize the triangles to be deleted – hard
    • Create triangles incident in the new vertex – easy
  • To remove a vertex:
    • Delete triangles incident in the vertex – easy
    • Reconstruct the triangles inside the hole – hard
encoding a triangulated polygon
Encoding a Triangulated Polygon
  • Encode an anchor edge
  • Perform a depth-first traversal as a tree
  • Encode the traversal as a bit stream

10 00 11 11

building a vertex based mt
Building a Vertex-based MT
  • A vertex-based MT is built through error-driven techniques based on
    • coarsening an initial mesh through vertex insertion (VI)
    • decimating the full-resolution mesh through vertex removal
      • iterative removal of a single vertex (VR)
      • removal of a set of independent vertices (IVR):
  • Shape of a vertex-based MT (number of triangles, size of modifications) depends on its construction strategy
  • Size of the modifications with different strategies:
    • MT-VI : each modification creates 5 triangles on average
    • MT-IVR: each modification creates 5.5 triangles on average
    • MT-VR : each modification creates 6 triangles on average
encoding a hierarchy of right triangles
Encoding a Hierarchy of Right Triangles
  • Modifications and dependency links are implicitly represented
  • Each triangles is uniquely identified by a binary location code
  • From the location code of a triangle t we can retrieve:
    • vertex coordinates and height values
    • modifications involving t
    • dependency links for such modifications
  • Only height values and errors (associated with triangles) are stored
comparison storage costs of the data structures
Comparison:Storage Costs of the Data Structures
  • Full-resolution mesh (encoded in a standard triangle- based data structure) : 54n bytes
  • Vertex-based MT: 27n (error on modifications)

33n bytes (error on triangles)

    • between 1/2 and 3/5 of the space required by mesh at full resolution
  • Hierarchy of right triangles:6n bytes
    • 1/5 of the space required by a vertex-based MT
    • 1/9 of the space required by mesh at full resolution
comparison level of detail lod queries
Comparison:Level-Of-Detail (LOD) Queries
  • Uniform LOD across the domain
  • Variable LOD:
    • Domain-based LOD: max resolution inside a window
    • Field-based LOD: max resolution for selected contour values
  • Best solution = fewer extracted triangles for the same error value
comparison uniform lod
Comparison: Uniform LOD
  • MT-VI is the best one
  • MT-VR, MT- IVR, HRT are comparable
  • Motivation: error-driven construction strategy

HRT -

VI -

IVR -

VR -

HRT -

VI -

IVR -

VR -

Mount Marcy

Devil Peak

comparison uniform lod1
Comparison: Uniform LOD

error = 1.3% of height range

HRT 22045 triangles MT-VI 16208 triangles

comparison uniform lod2
Comparison: Uniform LOD

error = 6.7% of height range

HRT 3648 triangles MT-VI 1951 triangles

comparison variable lod
Comparison: Variable LOD
  • HRT is the best one
  • MT-VI, MT-IVR are comparable (MT-IVR slightly better)
  • MT-VR is the worst one
  • Motivation: smaller modifications, fewer dependency links

(HRT = each modification creates 4 triangles)

HRT -

VI -

IVR -

VR -

HRT -

VI -

IVR -

VR -

Window focus

Mount Marcy

Devil Peak

comparison variable lod1
Comparison: Variable LOD
  • HRT gives the best results
  • MT-VI, MT-IVR are comparable (MT-VI slightly better)
  • MT-VR give the worst results
  • Motivation: smaller modifications, fewer dependency links

(HRT = each modification creates 4 triangles)

HRT -

VI -

IVR -

VR -

HRT -

VI -

IVR -

VR -

Field

focus

Mount Marcy

Devil Peak

comparison variable lod2
Comparison: Variable LOD

error = 1.3% of height range, focused inside a window

HRT 1614 triangles MT-VI 2072 triangles

comparison variable lod3
Comparison: Variable LOD

error = 1.3% of height range, focused on a field value

HRT 6697 triangles MT-VI 7138 triangles

summary
Summary
  • Both can generate meshes with topology (triangle-triangle adjacency links)
current and future work
Current and Future Work
  • Out-of-core techniques for a vertex-based MT: data structures, simplification methods, query algorithms
  • 3D extension for volume data visualization:
    • Efficient neighbor-finding techniques for a hierarchy of tetrahedra (Lee, De Floriani and Samet, 2001)
    • Compact data structures for irregular 3D MTs (De Floriani et al., 2002)
    • Analysis and comparison of regular and irregular 3D MTs on large volume data sets
generating a vertex based mt
Generating a Vertex-based MT
  • Error-driven vertex insertion (VI)top-down
    • At each step insert the data point corresponding to the maximum error (maximum vertical distance from the existing surface)
  • Error-driven vertex removal (VR) bottom-up
    • Start with a full-resolution mesh
    • At each step remove the vertex whose removal causes the least error increase (minimum vertical distance from the new surface)
  • Error-driven independent vertex removal (IVR) bottom-up
    • Start with a full-resolution mesh
    • At each step remove an independent set of vertices selected as the ones causing the least error increase
generating a vertex based mt1
Generating a Vertex-based MT
  • Error-driven vertex insertion (VI)top-down
    • At each step insert the data point corresponding to the maximum error (maximum vertical distance from the existing surface)
generating a vertex based mt2
Generating a Vertex-based MT
  • Error-driven vertex removal (VR) bottom-up
    • Start with a full-resolution mesh
    • At each step remove the vertex whose removal causes the least error increase (minimum vertical distance from the new surface)
generating a vertex based mt3
Generating a Vertex-based MT
  • Error-driven independent vertex removal (IVR) bottom-up
    • Start with a full-resolution mesh
    • At each step remove an independent set of vertices selected as the ones causing the least error increase
space requirements for a vertex based mt
Space Requirements for a Vertex-based MT
  • Storage cost:
    • 27n bytes (errors associated with modifications)
    • 33n bytes (errors associated with triangles)

where n = number of vertices in the data set

by assuming (pessimistic experimental estimates)

    • number of triangles = 4n
    • number of arcs in the DAG = 3n
  • Size (number of triangles) depends on the error-driven MT construction strategy:
    • vertex insertion (VI)
    • vertex removal (VR)
    • removal of a set of independent vertices (IVR)