RealTime Continuous Level of Detail Rendering of Height Fields

1
Real-Time Continuous Level of Detail Rendering of
Height Fields

• Peter Lindstrom David Koller William Ribarsky
  Larry F. Hodges Nick Faust Gregory A.
  Turner
• ACM SIGGRAPH 1996

2
Introduction

• Terrain visualization typically requires
  geometric complexity beyond the limits of current
  hardware
• Simplification algorithms are used to generate
  models at various levels of detail
• Display system chooses and renders the
  appropriate LOD model
• This algorithm provides for continuous LOD

3
Introduction

• Works on regularly gridded height fields
• Uses screen-space error threshold
• Two levels of simplification, coarse and fine
• Compute and generate appropriate LOD dynamically
  in real-time
• Achieves interactive frame rates

4
Features

• Large reduction in polygons to be rendered-
  typically orders of magnitude
• Smooth, continuous changes between LODs- both
  number and distribution
• Dynamic generation of LODs in real-time- no
  pre-processing, allows terrain deformation
• User specified image quality metric- image
  accurate to X pixels

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Motivation Criteria

• Geometry should be easily queried at any
  instant- allow for surface following (TINs cant
  do 12)
• Changes to mesh geometry shouldnt kill
  performance
• Localized high frequency data shouldnt have a
  global effect on the complexity of the model
  (bump in block)
• Small changes in the view lead to small changes
  in complexity (ie. Discrete LOD popping)
• Provide a means to bound the loss in image
  quality

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The Height Field

• Height field is a rectilinear grid of points
• Dimensions must be 2n 1
• Smallest is 3x3, group these into 2x2 recursively
  to make larger meshes.
• For any level l, the vertex dimensions are 2l1.
  The mesh at each level is a block or a discrete
  LOD model
• Lower resolution blocks are made by discarding
  every other row and column of four higher
  resolution blocks (make a quadtree)

Lowest level vertices
grouping
decimation
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Simplification
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Fine Grained Simplification

• Combine two smaller co-triangles into one larger
  triangle if conditions are met (normals are
  close)
• Find the maximum vertical distance (?) between
  the two co-triangles and their parent triangle

D
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Project the Delta Segment

• Project the delta segment to find the screen
  space distance p(?) (in pixels)
• If p(?) is smaller than the threshold for any
  triangle co-triangle pair substitute the parent
  triangle
• Continue recursively
• Note error is defined with respect to previous
  iteration, not base mesh

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How many pixels?

• Assume midpoint of delta segment is in center of
  view- more error toward edge of screen
• eviewpoint, ddistance from e to projection
  plane, ?number of pixels per world co-ordinate,
  vmidpoint of ?

Reduces to a few adds and multiplies
Where
(a constant)
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Coarse Grained Simplification

• Not practical to run this on all vertices every
  frame
• If maximum delta projection of all lowest level
  vertices in a block lt threshold, swap in lower
  res
• If we know ?max and the axis aligned bounding box
  for block we can determine if any ? gt threshold
• Determine the smallest ? (?l) that can exceed
  threshold and the largest ? (?h) that can be
  smaller than threshold
• Vertices with ? lt ?l can be tossed, ? gt ?h cant
• Vertices in between must be evaluated with old
  equation

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Icky Math

• We can actually do better
• Find spot in bounding box that maximizes the
  delta projection, and spot that minimizes it
• Compute maximum delta that stays under threshold
  where maximized (?l) and vice versa (?h)
• If ?max lt ?l swap in lower resolution block,
  recurse
• Else if ?max gt ?l swap in 4 higher resolution
  blocks

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What Was That?
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Cleaning Up

• Must handle adjacent blocks of different
  resolution
• If a vertex is enabled on a border of one block,
  it is enabled in any other blocks it is a part of
• Just implemented with pointers to vertices
• Vertex has a locked attribute so that it cant
  be disabled by a neighbouring block

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Results

• 20 FPS on 150 MHz Onyx with 13 million polygons
• Polys rendered depends on complexity of terrain,
  not of polys

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Visuals
Threshold 1 pixel
Threshold 4 pixels
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More Visuals
Threshold 1 pixel
Before Simplification 13,304,214 Polys
After Simplification 64,065 Polys
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Discussion

• Love that screen space error metric!
• Note because of approximations, up to 5 of
  delta projections are bigger than the threshold
• No way to lock in a framerate? (Maybe adjust
  threshold based on previous frametime?)
• Texturing? (Do you need a texture as big as the
  world?)
• Doesnt explicitly take advantage of temporal
  coherence
• Could current hardware be used to project the
  deltas instead of the approximation?

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Fin