Geometry Clipmaps: Terrain Rendering Using Nested Regular Grids

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Geometry ClipmapsTerrain Rendering Using Nested
Regular Grids
Frank Losasso Stanford University
Hugues Hoppe Microsoft Research
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Terrain Rendering Challenges
Mount Rainier
Primary Dataset United States at 30m spacing20
Billion samples
Olympic Mountains

• Concise storage ? No paging hick-ups
• Real-Time frame rates ? 60 fps
• Visual continuity ? No temporal pops

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Previous Work

• Irregular Meshes (e.g. Hoppe 98)
• Fewest polygons
• Extremely CPU intensive
• Bin-trees (e.g. Lindstrom et al 96)
• Simpler data structures / algorithms
• Still CPU intensive
• Bin-tree Regions (e.g. Cignoni et al 03)
• Precomputed regions ? Decreased CPU cost
• Temporal continuity difficult

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Previous Work

• Texture Clipmaps Tanner 1998
• Infinitely large textures
• Clipped mipmap hierarchy
• Modeling for the Plausible Emulation of Large
  Worlds Dollins 2002
• Quadtree LOD around viewer
• Terrain synthesis

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Geometry Clipmaps

• Store data in uniform 2D grids
• Level-of-Detail from nesting of grids
• Refine based on distance
• Main Advantages
• Simplicity
• Compression
• Synthesis

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Terrain as a Pyramid

• Terrain as mipmap pyramid
• LOD using nested grids

Coarsest Level
Finest Level
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Puget Sound
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Individual Clipmap Levels

• Uniform 2D grid
• Indexed triangle strip
• Efficient caching
• 60 M triangles/second
• 255-by-255 grid
• Expected Soon
• Vertex Textures

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Inter-Level Transitions

• Between respective power-of-2 grids

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Inter-Level Transitions
No transition
Geometry transition
Geometry texture transition
Gaps in geometry
Gaps in texturing/shading
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Inter-Level Transitions

• Vertex shader ? blend geometry
• Pixel shader ? blend textures
• Both are inexpensive

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Clipmap Update

• For each level
• Calculate new clipmap region
• Fill new L-shaped region
• Use toroidal arrays for efficiency

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Clipmap Update

• Update levels coarse-to-fine
• Use limited update budget
• Only render updated data
• Fine levels may be cropped
• Rendering load decreases as update load becomes
  to large for the budget

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Filling New Regions

• Two Sources
• Computed on-demand ? at 60 frames/second

Decompressed explicit terrain
Synthesized new terrain
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Clipmap Update

• Fine level from coarse level
• U is a 16 point C1 smooth interpolant
• For synthesized terrain, X Gaussian noise
• For explicit terrain, X compression residual

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Terrain Synthesis

• Adds high frequency detail
• Upsample then add Gaussian noise
• Precomputed 50-by-50 noise texture
• Per-octave amplitude from real terrain

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Texture Synthesis
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Subdivision Interpolant
Bilinear Interpolant (C0)
16-point Interpolant (C1)
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Terrain Compression

• Create mipmap fine-to-coarse
• D found from data such that

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Terrain Compression

• Calculate residuals coarse-to-fine
• Upsample and compute inter-level residual
• Quantize and compress residual
• Replace approximation
• ? Prevent error accumulation

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Compression Results

• U.S height map
• 30m horizontal spacing
• 1m vertical resolution
• 216,000-by-93,600 grid
• 40GB uncompressed
• 350MB compressed ? factor of over 100
• rms error 1.8m (6 of sample spacing)

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Compression Results
LOD scheme Number of samples Runtime space Bytes per sample
Hoppe 98 8 M 50 MB 6.0
Lindstrom 02 256 M 5.0 GB 19.5
Cignoni et al 02 64 M 115 MB 1.8
Geometry Clipmaps 20 G 375 MB 0.02
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Level-of-detail Error

• Analyzed statistically ? See paper
• For U.S. terrain (640-by-480 resolution)
• rms error 0.15 pixels
• max error 12 pixels
• 99.9th percentile 0.90 pixels

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United States of America
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Graphics Hardware Friendly

• Can be implemented in hardware
• Clipmap levels as high-precision textures
• Subdivision and normal calculation Losasso et al
  03
• Morphing already done in hardware
• Noise from Noise() or from texture
• Uploaded on-demand
• Decompressed terrain

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Limitations

• Statistical error analysis
• Assumes bounded spectral density
• Unnecessarily many triangles
• Assumes uniformly detailed terrain
• but, allows for optimal rendering throughput

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Advantages

• Simplicity
• Optimal rendering throughput
• Visual continuity
• Steady rendering
• Graceful degradation
• Compression
• Synthesis