Geometry Compression. By Michael Deering. Presented By Jacob Taylor

Transcription

1 Geometry Compression By Michael Deering Presented By Jacob Taylor

2 Why compress geometry? The main bottleneck in current (circa 95) graphics accelerators is input bandwidth and transmitting compressed geometry will reduce the bottleneck. An isolated triangle can take on the order of 100 bytes or more of storage to describe. Without compression CD s are limited to a few tens of millions of triangles. In one of the examples it takes 200,000 triangles to model an insect.

3 Representing geometry with a generalized triangle strip. The language that the decoder interprets has a few commands and keeps a queue (q) of three vertices {v0,v1,v2} Restart: Restart(Vertex v) Begin describing a new geometry (unconnected to the old one) and construct triangles clockwise. Clears the queue and pushes v Replace Old Vertex: RO(Vertex v) Push v onto q so that Before: q={a,b,c} After: q={v,a,b} Replace Middle Vertex: RM(Vertex v) Push v onto q so that Before: q={a,b,c} After: q={v,a,c} After the queue is filled, and every time after that a triangle is described because each next triangle must share two vertices. You need both RO and RM to specify which two vertices is shared. (If the triangle doesn't share two vertices it should be described after a reset.)

4 Generalized triangle strip Here is a way to describe this geometry with vertices 1-6. Command Restart(7) RO(1) RO(2) RM(3) RM(4) RM(5) RM(6) RM(1) q {_,_,7} {_,7,1} {7,1,2} {7,2,3} {7,3,4} {7,4,5} {7,5,6} {7,6,1} Note that each vertex contains a lot of information: x,y,z positions, RBG colors, and N x,n y,n z normals. Also notice that vertex 1 had to be retransmitted. And that with more complicated geometry many vertices may need to be transmitted twice.

5 Generalized triangle mesh. To reduce size of geometry by up to a factor of two, we implement sort of a sliding window. The decoder will keep a queue of length 16, w, and with each command will be an extra bit declaring if the vertex will be used again and thus should be added to the queue A p will follow a command if the vertex is to be remembered. Square brackets will acess the window 2 3 Command q w Restart(7) RO(1)p {_,_,7} {_,7,1} {} RO(2) {7,1,2} RM(3) RM(4) {7,2,3} {7,3,4} 6 5 RM(5) {7,4,5} RM(6) {7,5,6} RM(w[0]) {7,6,1}

6 Position Representation Positions are represented with 24 bits and an 8 bit exponent. This allows positions to span the known universe with sub atomic accuracy. Clearly far fewer bits are necessary for good accuracy spanning most distances. Thus geometry compression allows positions to be quantized down to as little as one bit, but at a maximum of 16 bits. Positions are delta coded, that is represented by their distance from each other rather than their distance from the origin.

7 Color Representation RGBα color is quantized to less than 16 bits, and all colors are within a RGB color space Colors cannot be compressed as well as they are in advanced image compression techniques. Most assumptions that such techniques rely upon cannot be made for geometry. Pixels are not necessarily arranged in rectangular arrays The display scale relative to a users eye is not fixed.

8 Normal Representation Normals are the angles at which light hits the geometry. The standard is to store three 32 bit normal components N x,n y,n z. This allows for 2 96 points to be measured on the surface of the unit circle. This results in a precision far more exact than the that of the Hubble telescope. Again, Clearly much less accuracy is needed in practice.

9 Normal Representation It turns out that only 100,000 points need be measured on the surface of the unit circle. Using clever indexing these points can be represented in 18 bits. The first three bits are indexes which point to an octant of the unit circle. The next three bits are indexes which point to a sextant of an octant. Two 6 bit numbers(θ and φ) follow which are coordinates within the sextant.

10 Normal Representation To decode the normal:

11 Compression Geometry compression uses three Huffman Codes One code for each: position, color, and normals. The codes have 6 bit tags, resulting in trees with 64 tags each Each tag contains the length of the data that it precedes as well as the type of data (ie. A relative position or a absolute position).

12 Results Compression without compromising visual quality results in compression ratios from 6-10x. The ideas in this paper a clearly effective and useful because they were implemented by Deering in java 3D.