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The rst stage of geometry compression is to convert triangle data into an ef cient linear strip form: the generalized triangle mesh This is a near-optimal representation of triangle data, given xed storage The existing concept of a generalized triangle strip structure allows for compact representation of geometry while maintaining a linear data structure That is, the geometry can be extracted by a single monotonic scan over the vertex array data structure This is very important for pipelined hardware implementations, a data format that requires random access back to main memory during processing is very problematic
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Version 11 Alpha 01, February 27, 1998
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Vertex Codes 1 Restart 2 RO 3 RO 4 RO 5 RO 6 RO 7 Restart 8 RO 9 RO 10 RM 11 RM 12 RM 13 RM 14 RM 15 Restart 16 RO 17 RO 18 Restart 19 RO 20 RO 21 RO 22 Restart 23 RO 24 RO 25 RO 26 RO 27 RO 28 RO 29 RM 30 RM 31 RM 32 RM 33 RO
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RO = Replace Oldest RM = Replace Middle
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Figure B-1
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However, by con ning itself to linear strips, the generalized triangle strip format leaves a potential factor of two (in space) on the table Consider the geometry in Figure B-2 While it can be represented by one triangle strip, many of the interior vertices appear twice in the strip This is inherent in any approach wishing to avoid references to old data Some systems have tried using a simple regular mesh buffer to support reuse of old vertices, but there is a problem with this approach in practice: In general, geometry does not come in a perfectly regular rectangular mesh structure
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Generalized Triangle Mesh
Generalized Triangle Strip: R6, O1, O7, O2, O3, M4, M8, O5, O9, O10, M11, M17, M16, M9, O15, O8, O7, M14, O13, M6, O12, M18, M19, M20, M14, O21, O15, O22, O16, O23, O17, O24, M30, M29, M28, M22, O21, M20, M27, O26, M19, O25, O18 Generalized Triangle Mesh: R6p, O1, O7p, O2, O3, M4, M8p, O5, O9p, O10, M11, M17p, M16p, M-3, O15p, O-5, O6, M14p, O13p, M-9, O12, M18p, M19p, M20p, M-5, O21p, O-7, O22p, O-9, O23, O-10, O-7, M30, M29, M28, M-1, O-2, M-3, M27, O26, M-4, O25, O-5 Legend: First letter: R = Restart, O = Replace Oldest, M = Replace Middle Trailing p = push into mesh buffer Number is vertex number, -number is mesh buffer reference where -1 is most recent pushed vertex
Figure B-2
A Generalized Triangle Mesh
The generalized technique employed by geometry compression addresses this problem Old vertices are explicitly pushed into a queue, and then explicitly referenced in the future when the old vertex is desired again This ne control supports irregular meshes of nearly any shape Any viable technique must recognize that storage is nite; thus the maximum queue length is xed at 16, requiring a four-bit index We refer to this queue as the mesh buffer The combination of generalized triangle strips and mesh buffer references is referred to as a generalized triangle mesh The xed mesh buffer size requires all tessellators or restrippers for compressed geometry to break up any runs longer than 16 unique references Since geometry compression is not meant to be programmed directly at the user level, but rather by sophisticated tessellators or reformatters, this is not too onerous a restriction Sixteen old vertices allow up to 94 percent of the redundant geometry to avoid being respeci ed Figure B-2 also contains an example of a general mesh buffer representation of the surface geometry
Version 11 Alpha 01, February 27, 1998