Level of Detail Generating LODs CS 446: Real-Time Rendering

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Level of DetailGenerating LODs CS 446
Real-Time Rendering Game Technology

• David Luebke
• University of Virginia

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Demo

• Today Brad Wells
• Thursday Stephen Lawrence

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But first

• Unstructured Lumigraph Rendering
• Buehler, C., Bosse, M., McMillan, L., Gortler,
  S., and Cohen, M., SIGGRAPH 2001
• Generalizes formalizes use of geometric proxies
  in light field reconstruction

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Recap The Big Question

• How should we evaluate and regulate the visual
  fidelity of our simplifications?

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Recap Measuring Fidelity

• Fidelity of a simplification to the original
  model is often measured geometrically

METRO by Visual Computing Group, CNR-Pisa
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Recap 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.

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Measuring Visual Error

• Measuring error
• Image-based ideas
• Lindstrom Turk, SIGGRAPH 2000
• Perceptually-based ideas
• Luebke Hallen, EGRW 2001
• Williams, Luebke, Cohen, Kelley Schubert, I3D
  2003

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Generating LODs

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

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Generating LODs

• Simplification operator
• Cell collapse
• Vertex removal
• Edge collapse
• Full edge collapse
• Half edge collapse
• Vertex-pair merge a.k.a. virtual edge collapse

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Generating LODs

• Simplification operator
• Cell collapse
• Vertex removal
• Edge collapse
• Full edge collapse
• Better fidelity (show why)
• Half edge collapse
• Less memory
• Sort vertices, tris into VAR array for fast
  rendering
• Vertex-pair merge a.k.a. virtual edge collapse
• Merge separate objects

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Measuring Geometric Error

• Measuring error
• Hausdorff distance
• One-sided
• Two-sided
• Common approximations
• Measure vertex-vertex distance, vertex-plane
  distance
• METRO Sample H(A,B) by sprinkling points on
  triangles
• Quadric Error Metrics a variation of
  vertex-plane distance that works well in practice

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Edge Collapse Algorithm
V2
V2
Collapse
V1
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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
D
Cz
By
Ax

• Distance to vertex v

ù
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x


ú
ê



y
T
v
p
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A
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1
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Squared Distance At a Vertex
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Quadric Derivation (contd)

• ppT is simply the plane equation squared

ù
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2
AD
AC
AB
A
ú
ê
2
BD
BC
B
AB
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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
• Requires inverting Q
• 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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Quadric Error Metric

• Pros
• Fast! (bunny to 100 polygons 15 sec in 1997)
• 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
• Garland Heckbert 7x7 matrices for XYZRGB, etc
• Hoppe separate matrices for color, texcoords, etc

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View-Dependent LOD Algorithms

• Many good published algorithms
• Progressive Meshes by Hoppe SIGGRAPH 96,
  SIGGRAPH 97,
• Hierarchical Dynamic Simplification by Luebke
  Erikson SIGGRAPH 97
• Multitriangulation by DeFloriani et al
• Others

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Overview The VDS Algorithm

• Ill describe (surprise) my own work
• Algorithm VDS Implementation VDSlib
• Similar in concept to most other algorithms

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Overview The VDS Algorithm

• Overview of the VDS algorithm
• A preprocess builds the vertex hierarchy, a
  hierarchical clustering of vertices
• At run time, clusters appear to grow and shrink
  as the viewpoint moves
• Clusters that become too small are collapsed,
  filtering out some triangles

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Data Structures

• The vertex hierarchy
• Represents the entire model
• Hierarchy of all vertices in model
• Queried each frame for updated scene
• The active triangle list
• Represents the current simplification
• List of triangles to be displayed
• Triangles added and deleted by operations on
  vertex tree

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The Vertex Hierarchy

• Each node in vertex hierarchy supports a subset
  of the model vertices
• Leaf nodes support a single vertex from the
  original full-resolution model
• The root node supports all vertices
• For each node we also assign a representative
  vertex or proxy

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The Vertex TreeFolding And Unfolding

• Folding a node collapses its vertices to the
  proxy
• Unfolding the node splits the proxy back into
  vertices

Fold Node A
Unfold Node A
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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Vertex Tree Example
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Vertex hierarchy
Triangles in active list
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The Vertex Tree

• At runtime, folds and unfolds create a cut or
  boundary across the vertex tree

This part of the modelis represented at high
detail
This part in low detail
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The Vertex TreeLivetris and Subtris

• Two categories of triangles affected

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Fold Node A
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Unfold Node A
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Node-gtSubtris triangles that disappear upon
folding Node-gtLivetris triangles that just
change shape
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The Vertex TreeLivetris and Subtris

• The key observation
• Each nodes subtris can be computed offline to be
  accessed quickly at run time
• Each nodes livetris can be maintained at run
  time, or lazily evaluated upon rendering

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View-Dependent Simplification

• Any run-time criterion for folding and unfolding
  nodes may be used
• Examples of view-dependent simplification
  criteria
• Screenspace error threshold
• Silhouette preservation
• Triangle budget simplification
• Gaze-directed perceptual simplification

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Screenspace Error Threshold

• Nodes chosen by projected area
• User sets screenspace size threshold
• Nodes which grow larger than threshold are
  unfolded

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Silhouette Preservation

• Retain more detail near silhouettes
• A silhouette node supports triangles on the
  visual contour
• Use tighter screenspace thresholds when examining
  silhouette nodes

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Triangle Budget Simplification

• Minimize error within specified number of
  triangles
• Sort nodes by screenspace error
• Unfold node with greatest error, putting children
  into sorted list
• Repeat until budget is reached

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View-Dependent CriteriaOther Possibilities

• Specular highlights Xia describes a fast test to
  unfold likely nodes
• Surface deviation Hoppe uses an elegant surface
  deviation metric that combines silhouette
  preservation and screenspace error threshold

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View-Dependent CriteriaOther Possibilities

• Sophisticated surface deviation metrics
• Sophisticated perceptual criteria
• Sophisticated temporal criteria

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Implementing VDS Optimizations

• Asynchronous simplification
• Parallelize the algorithm
• Exploiting temporal coherence
• Scene changes slowly over time
• Maintain memory coherent geometry
• Optimize for rendering
• Support for out-of-core rendering

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Asynchronous Simplification

• Algorithm partitions into two tasks
• Run them in parallel

Render Task
Simplify Task

Active Triangle List
Vertex Tree
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Asynchronous Simplification

• If S time to simplify, R time to render
• Single process (S R)
• Pipelined max(S, R)
• Asynchronous R
• The goal efficient utilization of GPU/CPU
• e.g., NV_FENCE extension for asynchronous
  rendering

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Temporal Coherence

• Exploit the fact that frame-to-frame changes are
  small
• Three examples
• Active triangle list
• Vertex tree
• Budget-based simplification

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Exploiting Temporal Coherence

• Active triangle list
• Could calculate active triangles every frame
• Butfew triangles are added or deleted each
  frame
• Idea make only incremental changes to an active
  triangle list
• Simple approach doubly-linked list of triangles
• Better maintain coherent arrays with swapping

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Exploiting Temporal Coherence

• Vertex Tree
• Few nodes change per frame
• Dont traverse whole tree
• Do local updates only at boundary nodes

UnfoldedNodes
Boundary Nodes
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Temporal CoherenceTriangle Budget Simplification

• Exploiting temporal coherence in budget-based
  simplification
• Introduced by ROAM Duchaineau 97
• Start with tree from last frame, recalculate
  error for relevant nodes
• Sort into two priority queues
• One for potential unfolds, sorted on max error
• One for potential folds, sorted on min error

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Temporal CoherenceTriangle Budget Simplification

• Then simplify
• While budget is met, unfold max node
• This is the node whose folding has created the
  most error in the model
• While budget is exceeded, fold min node
• This is the node that introduces the least error
  when folded
• Insert parents and children into queues
• Repeat until errormax lt errormin

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Optimizing For Rendering

• Idea maintain geometry in coherent arrays

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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Swap D with F
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Swap D with F
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Swap D with F
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Move Unfolded/Boundary Marker
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Deactivate Ds children (swap w/
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Deactivate Ds children (swap w/
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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Fold node D Deactivate Ds children (swap w/
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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B
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Fold node D Deactivate Ds children (swap w/
last boundary node)
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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B
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Fold node D Deactivate Ds children (swap w/
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Optimizing For Rendering

• Idea use swaps to maintain coherence

Unfolded nodes
Inactive nodes
Boundary nodes
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B
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F
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Fold node D Deactivate Ds children (swap w/
last boundary node)
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Optimizing For RenderingVertex Arrays

• Biggest win vertex arrays
• Actually, keep separate parallel arrays for
  rendering data (coords, colors, etc)

Unfolded nodes
Inactive nodes
Boundary nodes
Vertex array!
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Optimizing For RenderingVertex Arrays on
GeForce2
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Out-of-core Rendering

• Coherent arrays lend themselves to out-of-core
  simplification and rendering

These need to be in memory
These do not
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Out-of-core Rendering

• Coherent arrays lend themselves to out-of-core
  simplification and rendering
• Only need active portions of triangle and node
  arrays
• Implement arrays as memory-mapped files
• Let virtual memory system manage paging
• A prefetch thread walks boundary nodes, bringing
  their children into memory to avoid glitches

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Summary VDS Pros

• Supports drastic simplification!
• View-dependent handles the Problem With Large
  Objects
• Hierarchical handles the Problem With Small
  Objects
• Robust does not require (or preserve) mesh
  topology

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Summary VDS Pros

• Rendering can be implemented efficiently using
  vertex arrays
• Supports rendering of models much larger than
  main memory

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Summary VDS Cons

• Increases CPU, memory overhead
• Hard to map efficiently onto GPU for efficient
  utilization

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Summary VDS Cons

• Be aware of mesh foldovers

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Summary VDS Cons

• Be aware of mesh foldovers

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Summary VDS Cons

• Be aware of mesh foldovers

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Summary VDS Cons

• Be aware of mesh foldovers
• These can be very distracting artifacts
• Can prevent them at run-time
• Add a normal-flipping test to fold criterion
• Use a clever numbering scheme proposed by El-Sana
  and Varshney

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View-Dependent Versus Discrete LOD

• View-dependent LOD is superior to traditional
  discrete LOD when
• Models contain very large individual objects
  (e.g., terrains)
• Simplification must be completely automatic
  (e.g., complex CAD models)
• Experimenting with view-dependent simplification
  criteria

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View-Dependent Versus Discrete LOD

• Discrete LOD is often the better choice
• Simplest programming model
• Reduced run-time CPU load
• Easier to leverage hardware
• Compile LODs into vertex arrays/display lists
• Stripe LODs into triangle strips
• Optimize vertex cache utilization and such

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View-Dependent Versus Discrete LOD

• Applications that may want to use
• Discrete LOD
• Video games (but much more on this later)
• Simulators
• Many walkthrough-style demos
• Dynamic and view-dependent LOD
• CAD design review tools
• Medical scientific visualization toolkits
• Terrain flyovers (a whole topic unto itself)

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Continuous LOD The Sweet Spot?

• Continuous LOD may be the right compromise on
  modern PC hardware
• Benefits of fine granularity without the cost of
  view-dependent evaluation
• Can be implemented efficiently with regard to
• Memory
• CPU
• GPU

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VDSlib

• Implementation VDSlib
• A public-domain view-dependent simplification and
  rendering package
• Flexible C interface lets users
• Construct vertex trees for objects or scenes
• Specify with callbacks how to simplify, cull, and
  render them
• Available at http//vdslib.virginia.edu

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GLOD

• An easy-to-use library for level of detail in
  OpenGL
• LOD generation
• LOD run-time management
• View-dependent LOD (using VDSlib)
• http//www.cs.jhu.edu/graphics/GLOD

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VDSlibOngoing Work

• Various research projects that have used VDSlib
• Out-of-core LOD for interactive rendering of
  truly massive models
• Perceptually-guided view-dependent LOD, including
  gaze-directed techniques
• Non-photorealistic rendering using VDSlib as a
  framework