Level of Detail: Choosing and Generating LODs

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Level of DetailChoosing and Generating LODs

• David Luebke
• University of Virginia

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Level of DetailTraditional LOD In A Nutshell

• Create levels of detail (LODs) of objects

69,451 polys
2,502 polys
251 polys
76 polys
Courtesy Stanford 3D Scanning Repository
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Level of DetailTraditional LOD In A Nutshell

• Distant objects use coarser LODs

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Review LOD Frameworks

• Discrete LOD
• Generate a handful of LODs for each object
• Continuous LOD (CLOD)
• Generate data structure for each object from
  which a spectrum of detail can be extracted
• View-dependent LOD
• Generate data structure from which an LOD
  specialized to the current view parameters can be
  generated on the fly.
• One object may span multiple levels of detail
• Hierarchical LOD
• Aggregate objects into assemblies with their own
  LODs

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Review LOD Run-Time Management

• Fundamental LOD issue where in the scene to
  allocate detail?
• For discrete LOD this equates to choosing which
  LOD will represent each object
• Run every frame on every object keep it fast

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Review Choosing LODs

• Describe a simple method for the system to choose
  LODs
• Assign each LOD a range of distances
• Calculate distance from viewer to object
• Use corresponding LOD
• How might we implement this in a scene-graph
  based system?
• Make a switch node that picks which of its
  children to traverse based on LOD thresholds

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Review Choosing LODs

• Whats wrong with this simple approach?
• Visual pop when switching LODs can be
  disconcerting
• Doesnt maintain constant frame rate lots of
  objects still means slow frame times
• Requires someone to assign switching distances by
  hand
• Correct switching distance may vary with field of
  view, resolution, etc.
• What can we do about each of these?

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ReviewMaintaining constant frame rate

• One solution scale LOD switching distances by a
  bias
• Implement a feedback mechanism
• If last frame took too long, decrease bias
• If last frame took too little time, increase bias
• Dangers
• Oscillation caused by overly aggressive feedback
• Sudden change in rendering load can still cause
  overly long frame times

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Choosing LODsMaintaining constant frame rate

• A better (but harder) solution predictive LOD
  selection
• For each LOD estimate
• Cost (rendering time)
• Benefit (importance to the image)

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Choosing LODsMaintaining constant frame rate

• A better (but harder) solution predictive LOD
  selection
• For each LOD estimate
• Cost (rendering time)
• of polygons
• How large on screen
• Vertex processing load (e.g., lighting) OR
• Fragment processing load (e.g., texturing)
• Benefit (importance to the image)

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Choosing LODsMaintaining constant frame rate

• A better (but harder) solution predictive LOD
  selection
• For each LOD estimate
• Cost (rendering time)
• Benefit (importance to the image)
• Size larger objects contribute more to image
• Accuracy no of verts/polys, shading model, etc.
• Priority account for inherent importance
• Eccentricity peripheral objects harder to see
• Velocity fast-moving objects harder to see
• Hysteresis avoid flicker use previous frame
  state

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Choosing LODsFunkhouser Sequin, SIGGRAPH 93

• Given a fixed time budget, select LODs to
  maximize benefit within a cost constraint
• Variation of the knapsack problem
• What do you think the complexity is?
• A NP-Complete (like the 0-1 knapsack problem)
• In practice, use a greedy algorithm
• Sort objects by benefit/cost ratio, pick in
  sorted order until budget is exceeded
• Guaranteed to achieve at least 50 optimal soln
• Time O(n lg n)
• Can even use incremental alg to exploit coherence

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Generating LODs

• Next topic generating LODs
• Several subtopics
• Measuring error
• Hausdorff distance
• Quadrics
• Simplification operator (polygon elision mech)
• Cell collapse
• Vertex removal
• Edge collapse
• Simplification algorithm (high-level approach)

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Edge Collapse Algorithm
V2
V2
Collapse
V1
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Edge Collapse Algorithm

• Sort all edges (by some metric)
• repeat
• Collapse edge
• choose edge vertex (or compute optimal vertex)
• Fix-up topology
• until (no edges left)

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Edge Collapse Benefits

• Edge collapse operation is simple
• Supports non-manifold topology

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Edge Collapse vs. Vertex-Pair Merging

• Even better vertex-pair merging merges two
  vertices that
• Share an edge, or
• Are within some threshold distance t
• Q What does vertex-pair merging enable over edge
  collapse?

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Quadric Error Metric

• Minimize distance to all planes at a vertex
• Plane equation for each face

v




0


p
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Cz
By
Ax

• Distance to vertex v

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Squared Distance At a Vertex
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Quadric Derivation (contd)

• ppT is simply the plane equation squared

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AC
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BD
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• The ppT sum at a vertex v is a matrix, Q

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Using Quadrics

• Construct a quadric Q for every vertex

v2
v1
The edge quadric
Q2
Q1
Q


Q
Q
Q
2
1

• Sort edges based on edge cost
• Suppose we contract to v1
• v1s new quadric is simply

T

Qv
v
cost

edge
1
1
Q
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Optimal Vertex Placement

• Each vertex has a quadric error metric Q
  associated with it
• Error is zero for original vertices
• Error nonzero for vertices created by merge
  operation(s)
• Minimize Q to calculate optimal coordinates for
  placing new vertex
• Details in paper
• Authors claim 40-50 less error

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Boundary Preservation

• To preserve important boundaries, label edges as
  normal or discontinuity
• For each face with a discontinuity, a plane
  perpendicular intersecting the discontinuous edge
  is formed.
• These planes are then converted into quadrics,
  and can be weighted more heavily with respect to
  error value.

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Preventing Mesh Inversion

• Preventing foldovers
• Calculate the adjacent face normals, then test if
  they would flip after simplification
• If so, that simplification can be weighted
  heavier or disallowed.

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8
2
10
A
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9
3
merge
1
5
4
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Quadric Error Metric

• Pros
• Fast! (bunny to 100 polygons 15 sec)
• Good fidelity even for drastic reduction
• Robust -- handles non-manifold surfaces
• Aggregation -- can merge objects

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Quadric Error Metric

• Cons
• Introduces non-manifold surfaces(bug or
  feature?)
• Tweak factor t is ugly
• Too large O(n2) running time
• Correct value varies with model density
• Needs further extension to handle color (7x7
  matrices)

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Measuring Error

• Most LOD algorithms measure error geometrically
• What is the distance between the original and
  simplified surface?
• What is the volume between the surfaces?
• Etc
• Really this is just an approximation to the
  actual visual error, which includes
• Color, normal, texture distortion
• Importance of silhouettes, background
  illumination, semantic importance, etc etc etc

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Measuring Geometric Error

• Hausdorff distance
• Average distance
• Surface-surface vs vertex-surface vs
  vertex-plane vsvertex-vertex
• Quadric error metrics vertex-plane measure that
  works well in practice