1. Chap 10. Geometric Level of Detail
그래픽스 연구실
김수균
Graphics Lab

2. Introduction Concept of LOD Sprites and Billboards
Discrete Level of Detail
Continuous Level of Detail
Simplification Using Quadric Error Metric
The algorithm
Construction of the error metric
Simplification at run time
Selecting Surface Attribute
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3. Switching between models of varying degrees of resolution
Concept of LOD
Switching between models of varying degrees of resolution
Faces :69,459
Faces:2,502
Faces:251
Faces:76
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4. Concept of LOD
The switching is usually associated with distance from eye point to object
#F:76
#F:251
#F:2,502
#F:69,459
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5. Sprites and Billboards
Sprites (sometimes called imposters)
prerendered images of three-dimensional objects
Easy to spot in the rendering
If they represent objects that are close to the eye point or if the eye point moves
The visual anomaly associated with a moving eye point can be rectified in two ways
First way is to have a set of prerendered images of the object calculated from a set of predefined eye points and orientations
The second is to allow a single prerendered image to change orientation depending on eye point location and orientation (called a billboard)
Graphics Lab

6. Discrete Level of Detail
Discrete LOD
advantage
Simplicity of the implementation
Simple programming models
disadvantage
Popping effect
Massive CAD Models
Super-detailed range scans
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7. Discrete Level of Detail
Popping Effect
Switch occurs during rendering it is usually noticeable and not very natural
Reduce the Popping
Morph between two consecutive models in the LOD sequence
2,000faces
10,000faces
50,000faces
Pop
Pop
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8. Continuous Level of Detail
An alternative to discrete LOD is Continuous LOD
CLOD algorithms
Hoppe 1996
Garland and Heckbert 1997,1998
Cohen et al. 1996
Cohen, Olano, and Manocha 1998
Luebke and Erikson 1997
Lindstrom and Turk 1998
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9. Continuous Level of Detail
Advantage
Reduce “Popping effect”
Support progressive
Progressive Meshes[Hoppe 97]
Progressive Forest Split Compression[Taubin 98]
Support View-dependent
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10. Continuous Level of Detail
Vertex Decimation
Removing a vertex and all triangles sharing it
Then retriangulating the hole that produced by removal ( schroeder, Zarge, Lorensen 1992)
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11. Continuous Level of Detail
Vertex Clustering
Involves placing the mesh in a bounding box
Partitioning that box into a lattice of small boses
Collapsing all vertices in each small box into a single vertex, and removing
Rossignac and Borrel 1993
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12. Continuous Level of Detail
Iterative edge contraction
Replacing an edge and its two vertices by a single vertex
Removing the triangles sharing that edge, and adjusting the connectivity information for the triangles adjacent to the ones removed (Hoppe 1996)
Edge
Contraction
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13. Continuous Level of Detail
Simplification Using Quadric Error Metrics
Garland and Heckbert 1997
Sum of squared distances A b c
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14. Continuous Level of Detail
Quadric Form
Optimal Position in the quadric Q1 Q2
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15. Continuous Level of Detail
Algorithm
Select a set of candidate vertex pairs
Assign a cost of contraction to each candidate
Place all candidates in a heap keyed on cost with the minimum cost pair at the top
Repeat until the desired approximation is reached
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16. Continuous Level of Detail
Cessna Model
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17. Selecting Surface Attributes
Normal vectors, texture coordinates, and colors
New surface attributes must be selected for a contracted vertex
Compute the barycentric coordinates of the new vertex with respect to the tetrahedron
Normal vectors at contracted vertices can be computed
Use the barycentric coordinate scheme
By computing a weighted averages of the normals of the triangles sharing the new vertex
Alternative is to view the unit-length normals as points on a sphere
The minimal angle cone containing those points is computed and the axis the cone is used as the new normal
a weighted averages of normals is not geometrically appealing
Graphics Lab