Levels of Detail

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Levels of Detail

• COMP 770
• 3/25/09

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Problem

• Models can be very detailed
• Look great when close up
• Last week we explored one way of attacking this
  problem

13M Triangles
8M Elevation Points
1M Triangles
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Problem
Q Why else might we want to reduce the working
set size?

• Even after visibility culling we can have too
  many visible triangles
• Wont this problem go away with faster GPUs?
• The real world has virtually infinite complexity
• Our ability to model and capture this complexity
  outpaces rendering performance

372M Triangles
100M Triangles
270M Elevation Points
82M Triangles
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Levels of Detail

• Basic Idea Render using fewer triangles when
  model is farther from viewer
• Methods
• Multi-resolution modeling
• Remeshing
• Parametric Surfaces
• Subdivision Surfaces
• Polygonal Simplification
• Image Impostors

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LOD Hierarchy

• Clark76 First LOD paper
• Replace each object in the scene graph with a
  hierarchy of objects at differing resolutions
• Select LOD based on size of screen-space
  projection
• Integrates VFC with LOD search
• Supports out-of-core rendering
• Most LOD systems today are based on this basic
  concept

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Polygonal Simplification

• Method for reducing the polygon count of mesh
• Local Operators
• Vertex Clustering
• Vertex Removal
• Edge Collapse
• Triangle Collapse
• Global Operators
• Low-Pass Filtering
• Morphological Operators
• Alpha-Hull

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Vertex Clustering

• Rossignac Borrel 93
• Weight vertices by
• Inverse of max angle between edges (why?)
• Size of largest adjacent face (why?)
• Impose a grid on the model
• Compute weighted average vertex in each cell
• Triangles become
• Triangles
• Lines
• Points
• Keep the unique primitives

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Vertex Clustering

• How do we create a set of LODs?
• What are the limitations on this method?
• Main Benefits

• Hard to target a polygon count
• Poor error control
• Not invariant to rotation or translation
• Mixed primitive types

• Simple
• Robust

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Vertex Clustering

• Low Tan 97
• Improve on RB in a several ways including
• Floating-cell clustering
• Improved angle weight draw it
• Rendering using thick lines

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Vertex Removal

• Schroeder et al. 92
• Designed for Marching Cubes Output
• Remove a triangle and re-triangulate hole
• Ignores non-manifold vertices
• Properties
• Preserves topology
• Uses original vertices
• Linear

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Edge Collapse

• Introduced by Hoppe93
• Variation Half-Edge Collapse

edge collapse
b
c
a
vertex split
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Foldovers

• Collapsing an edge can flip a face

edge collapse
b
a
c
vertex split
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Virtual Edge Collapse

• Extension of edge collapse to two vertices not
  connected by an edge
• Allows topological simplification
• Also known as vertex-pair collapse
• Usually limited to small distance to avoid O(n2)
  virtual edges

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Edge Collapse

• Allows geomorphs
• Fine-grained 2 triangles removed for manifold
  case
• Topology preserving
• Half-edge collapse preserves vertex set

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Low-Pass Filtering

• He et al. 96
• Convert polygon mesh to volumetric representation
• Apply low-pass filter to volumetric data
• Reconstruct the mesh using marching cubes

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Morphological Operators

• Nooruddin99
• Convert polygon mesh to volumetric representation
• Apply dilation operator followed by erosion
  operator
• Reconstruct with marching cubes
• Apply polygonal simplifcation

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Topological Simplification Using Alpha-Hulls

• El-Sana and Varshney 98
• Definition
• Set of points P
• Spherical ball b with radius alpha
• If b is placed such that it does not intersect P
  it is empty
• The alpha-hull is the complement of empty balls

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Topological Simplification Using Alpha-Hulls

• Intuitively, we roll a ball around the points to
  define the new surface
• If the ball does not fit into a concavity it is
  filled
• If the ball does not fit in to a hole it is
  closed
• If the ball does not fit between two objects it
  is closed
• What if alpha0?
• What if alphainfinity?
• Show paper images

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Discrete LOD

• Use local or global operators to compute a set of
  LOD meshes
• At runtime select an LOD mesh and render it
• Possible Criteria
• Distance to user
• Fraction visible
• Eccentricity
• Visual Importance
• Extension HLODS Erikson01

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Continuous LOD

• Progressive Meshes Hoppe96
• Iteratively decimate a mesh using edge collapse
  operator
• Store the inverse vertex split for each collapse
• The most simplified mesh (base mesh) and vsplit
  records form the progressive mesh M0?M1 ? ? Mn

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Continuous LOD

• Rather than a few discrete LODs we have a full
  range
• Vertex split does not require much storage
• Can geomorph between LODs
• Show video

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View-Dependent LOD

• So far we have
• Discrete LOD fixed models at various fidelities
• Continuous LOD a progression of meshes from
  coarse to fine
• Consider a case like this

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View-Dependent LOD

• Create an LOD representation at runtime according
  to view-parameters
• What view-dependent criteria can we use?

More detail close to the viewer Preserve the
silhouette of the object Preserve specular
highlights Aggressively simplify the backfaces
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View-Dependent LOD

• Organize the simplification operations as a
  hierarchy
• Compute a front in the hierarchy
• Use temporal coherence
• LuebkeErikson97 use octree clustering
• Hoppe96 uses edge collapse
• Show video

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View-Dependent LOD

• View-Dependent LOD has fidelity advantages but
  not generally used.
• Why?

• Expensive to traverse hierarchy front
• Dynamically generated geometry difficult to
  render optimally

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CHPM

• Yoon et al. 2004
• Addresses problems of vertex hierarchy
• Same framework used for LOD collision detection

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CHPM

• Video
• http//gamma.cs.unc.edu/QVDR
• Collision
• http//gamma.cs.unc.edu/MRC

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Simplification Error

• Why measure error?
• Better quality LOD
• Know the quality of the LOD
• Usually, we want to measure appearance
• Generally, we use a geometric measure as a proxy
• Error measures are used in three ways
• To pick which operation to perform
• To determine resulting surface from an operation
  (e.g. position of replacement vertex)
• To pick an LOD at runtime
• Two common LOD selection criteria
• Target framerate
• Target quality

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Hausdorff Distance
A
B

• A measure of surface deviation
• h(A,B)maxaminb(a-b)
• H(A,B)max(h(a,b),h(b,a))
• h is sometimes called the one-sided Hausdorff
  distance
• Provides a bound on the maximum possible error
• Project to screen space to get deviation in pixels

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Vertex Plane Distance

• Ranford 96
• One metric is the max distance between the vertex
  and the planes of the supported triangles

• Emaxp(pv)

v
a
b
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Quadric Error Metric

• Garland Heckbert 97
• Use sum of squared distance rather than max
  distanceE?(pv)2 ?(vTp) (pTv)vT?(p pT)v
  vT?Qpv vTQv
• Additional plane can be incorporated by a 4x4
  matrix addition
• Cost to compute the error given a quadric and
  vertex is constant

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Attributes

• Vertices have more than just position
• Colors
• Normals
• Texture Coords
• And now varying input to programs
• Vertices may lie at a discontinuity
• Different Textures
• Different Material Properties
• Different Shaders

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Attributes

• Hoppe98 introduces the idea of wedges
• Wedges separate discrete attributes at a vertex
• A wedge disappears when all its triangles collapse

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Attributes

• Earlier algorithms ignored attributes or simply
  propagated their values
• Can simply use the same metric as for position
• Normals in Euclidean space
• Colors in RGB space
• Better
• Normals in spherical domain
• Colors in a perceptually linear color space
• Generally total error is a weighted sum of
  position and attribute errors

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Normal cones

• Luebke Erikson 97
• Used in view-dependent LOD to determine
  likelihood that a vertex represents the
  silhouette or be at a specular highlight

cluster
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GAPS

• Erikson99
• Uses a threshold distance t
• Vertex pairs within distance t are candidates
• t grows over simplification process
• Allows topological simplification at all scales

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Image Driven Simplification

• Render the object from a sampling of view-points
• Measure error as RMS of pixels
• Only redraw relevant triangles
• Benefits?
• Drawbacks?

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Simplification Envelopes

• Compute interior and exterior offset surfaces at
  distance e
• Remove vertices and retriangulate if new surface
  does not intersect envelopes
• Limitations?

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Other Forms of LOD

• Image impostors
• Warping (e.g. Rafferty98)
• Texture Depth Meshes (e.g. Aliaga99)
• Shader LOD
• Number of shaders
• Number of textures
• Simulation LOD
• Time steps
• Simulation resolution
• Number of particles
• Lighting
• Number and type of lights used

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Resources

• LOD Book Luebke et al.
• www.lodbook.com
• Surveys
• http//www.cs.cmu.edu/afs/cs/user/garland/www/mult
  ires/survey.html
• http//www.cs.umd.edu/class/spring2005/cmsc828v/pa
  pers/surveyMINGLE.pdf
• http//citeseer.ist.psu.edu/247479.html
• http//www.cs.virginia.edu/luebke/publications/pd
  f/cga.2001.pdf