Geometry Compression

1
Geometry Compression

• Michael Deering
• presented by
• Hamish Carr

2
Geometry Compression

• Compression of geometric models
• Models consist of triangles, each with
• 3 vertices, with
• position (x, y, z) (3 x 4 bytes 12 bytes)
• normal (x, y, z) (3 x 4 bytes 12 bytes)
• colour (R, G, B) (3 x 1 byte 3 bytes)
• Triangle can take nearly 100 bytes storage!

3
Stages of Compression

• 1) Reduce of vertices used
• 2) Quantize position, colour, normal
• 3) Delta-encode quantized values
• (adjacent vertices have similar values)
• 4) Huffman-encode the deltas

4
Lower Bound on Vertices

• How many vertices are needed per triangle?
• Eulers Theorem v f - e 2 g
• Simplifies for triangulations to
• v 0.5 f
• Raw triangles v 3 f
• Triangle Strips v f
• So each vertex is sent twice on average

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Reducing Vertices

• How do we reduce the of vertices sent?
• Use a (small) local buffer of recent vertices
• In each strip, push vertices into the buffer if
  we know we will reuse them
• On a buffer overflow, start a new strip
• Remember, we pre-process to choose strips
• Saves 94 of redundant data (bufsize16)

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Encoding the Strip

• Use the following codes
• R Restart (i.e. start a new strip)
• O Replace oldest vertex in triangle
• M Replace middle vertex in triangle
• p Also push vertex into buffer
• O-n Replace oldest with buffertop - n
• M-n Replace middle with buffertop - n

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An example

• Rp

O
Op
O
O
M
Mp
O
O
Op
M
Mp
Mp
M-3
Op
O-5
O-6
Mp
Op
M-9
O
4
8
5
2
6
4
11
3
10
7
9
1
2
1
3
12
16
13
15
14
5
17
9
8
6
7
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Secondary Information

• Vertex normals colours change
• So three modes exist
• 1) bundled with vertex (explicit)
• 2) state-based (implicit)
• 3) replicate from final vertex

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Position Compression

• Position is assumed to be 32-bit floats
• 16-bit fixed-point is sufficient instead
• Sequential vertices have similar positions
• So we delta-encode the x, y, z coordinates
• Compress deltas with Huffman encoding

10
Colour Compression

• RGBA is assumed to be 32-bit floats
• 12 bit (or even 8 bit) fixed-point adequate
• Again, adjacent vertices are similar
• Delta-encode, then Huffman encode
• Compression only at vertices pixels still
  interpolated in full colour depth

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Normal Compression

• Normals are also assumed to be 32-bit
• This allows 2-46 radian precision
• enough to pick out individual pebbles on Mars!
• Precision of 0.01 radian sufficient
• 100,000 possible values (roughly)
• symmetries reduce this to 2,000 normals
• so store an 18-bit index to lookup table in ROM

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Summary

• Mesh encoding avoids repeated vertices
• Quantization drops data size by 50
• Delta Huffman encoding drop size more
• Compression ratio claimed
• 6x - 10x
• Visual quality almost as good as original