3 rd November 2006

1. PNORMS: Platonic Derived Normals for Error Bound Compression João Fradinho Oliveira, Bernard Buxton(Department of Computer Science, University College London) [Plato ~428 BC] 3rd November 2006

2. PNORMS: Platonic Derived Normals for Error Bound Compression João Fradinho Oliveira, Bernard Buxton(Department of Computer Science, University College London) 3rd November 2006

3. 1- Introduction What is the difference?

4. 1- Introduction What is the difference? Both have 10million triangles 10 million normals of 12 bytes (original) Maximum error of 2.5 degrees 27300 normals of 12 bytes (using 2 byte / 16 bit ids)

5. 1- Introduction 10 million normals x12 bytes = 120 Mbytes 10 million normals x 2 bytes= 20 Mbytes Geometry+normals+colours = 1.3 Gbytes versus739 Mbytes

6. 2- Previous Work (building normal databases) Hexasecting octahedron + spherical coordinates point sampling of functions that parameterize a sphere Deering’ 95 Sloane’ 81 3 bits are used to encode the +/- sign of a normal’s x, y, z, hence determining the octant a normal lies in, 3 bits determine the sextant, and then two 6 bit numbers encode the phi and theta spherical coordinates of a normal (these 18 bits normal indices are then delta encoded) Quadrisecting octahedron (strips) BSP encoding (GPU) Taubin’ et al. 98 Von Rymon-Lipsinki et al. 05 Botsch’ et al. 02 octahedron subdivision [3, 12], use 3 bits(to locate which of 0-7 octants the normal lies in) and several 2 bit pairs, where each pair represents one subdivision (the 2 bits locate one of the 4 subdivided triangles). Each 2 bits requires decoding to evaluate the full normal of a triangle (which can use 13 bits [3] for a x5 subdivided octahedron or 5-8bits when gzipped) Normal clustering (no error) Normal meshes/subd. surf. Deok-Soo et. al 04 Guskov et al. 00 Geographical Information Systems (GIS) Randal’ et al. 02

7. 2- Previous Work (building normal databases) Randal’ et al. 02

8. 3- Building normal databases (different nets)

9. 4- Fast Normal Encoding (error and time) * 500 MGhz PowerBook G4. normalid = level startoffset + ((previous level triangle no -1) x 4) + subtriangle id(ranging from 0-3)).

10. 4- Accurate Normal Encoding (error+symmetry tolerance) subdivision level tol = (subangle) x 1.5 where subangle = subangle of the previous level/3 for the first level of subdivision the subangle corresponds to the solids initial dehidral angle. (cascaded tolerance formula)

11. 4- Normals Encoding (fast vs accurate) * level 0-5 of: 0.05; 0.05; 0.02; 0.02; 0.01; and 0.01 respectively.

12. 5- Results - Error Distribution & Colour compression void geterrorcolour(float &r float &g float &b float res) if (res<=0.345) { r=res; g=res/0.345; b=1.0-res;} else { r=res; g=(1-res) /0.654; b=1.0-res;} Fast encoding x5 icosahedron

13. 5- Results – Performance

14. 5- Results - Shading effects

15. 6- Conclusions monotonic reduction bit-wise error boundsdynamically VR Onefreeing accurate No reconstruction absolute normal indicesthe number error associatedlength in bits icosadronless maximum and mean errorx2.5 more normals scanned statuesCAD model. fast encodingnot require tolerancesaccurate encodingsymmetrycascading tolerances icosahedronsmallest accurately encodemaximum error bound of 1.3˚,fast encodingmaximum error bound of 2.5˚, hierarchical queryingnew normals at run-time unknownwithout actual decoding,implicit mapping VR 739 Mbytes256colour table all

16. 6- Conclusions • We showed that the increasing number of normals resulting from the subdivision of Platonic solids does not necessarily, in all cases, lead to a monotonic reduction in the encoding errors. • We provide an alternative to bit-wise compression, with the following main advantages: • maximum error bounds for yet to be known normals; these normals belong to objects to be added dynamicallyto a scene, or to be produced from soft-deformation animation, or from large • sets of user edited geometry in a VR modeling task. • One single hierachical-multiresolution database for a scene as a whole that allows for fast searches of normal representatives during encoding without using the GPU, freeing the graphics card • to do other tasks. • A slower but more accurate encoding method that caters for the symmetry inherent between adjacent normals of a Platonic solid. • No reconstruction of normal ids required at run-time, again freeing the GPU to do other tasks. • We use absolute normal indices rather than bit-wise compressed indices. We showed how the number of subdivisions of different Platonic solids, affect the • number of normals created, the error associated with the normals distributions, and ultimately the length in bits that bit-wise compression • methods need to use. In particular we showed that the x5 subdivided icosadron has less maximum and mean error in our results, and produces x2.5 more normals than the • x5 subdivided octahedron widely used in the normal compression literature. Consequently we could use absolute 16 bit normal indices, with still 83% memory savings, • with no normal reconstruction required. • We presented results obtained using scanned statues and the UNC power plant CAD model. • We presented a fast encoding scheme that does not require tolerances, and a more accurate encoding method that caters for symmetry by cascading tolerances across the levels of the • database. • The database generated by subdivision of an icosahedron generated the smallest maximum and mean errors of any of those obtained from the 5 Platonic solids. • We plan to make the 2 byte and 4 byte databases of normals available online. The 2 byte indexed database obtained from 5 subdivisions of an icosahedron can be used to • accurately encode normals with a maximum error bound of 1.3˚, or fast encoding of normals with a maximum error bound of 2.5˚, • and the 4 byte indexed database obtained from 9 subdivisions of an icosahedron can be used to accurately encode normals with a maximum error bound of <0.1˚, • or fast encoding of normals with a maximum error bound of 2.5˚which is no better than obtained with the fast encoding using a 5-fold subdivision of 2.5˚ as the fast • encoding does not cater for symmetry like the accurate encoding approach does. • Our method stores normals in the database at all levels of subdivisions so as to allow hierarchical querying of new normals at run-time. This strategy is not only useful for encoding • newunknownnormals of modified or new geometry in the scene, but it is conceivable that algorithms could be developed using purely the 2-byte or 4-byte indices without • actual decoding, since there is an implicit mapping to their 3D orientations. • We note that many computer games are geared to applying rigid transformations such as translation and rotation matrices to essentially unchanged representations of geometry. • We hope that our method can help bring more soft deformation animation of surfaces into applications such as games, and bring memory savings when modelling/editing larger models in VR. • As mentioned in section 5.3, our compression method allowed us to load and view the 28 million triangle • statue of Lucy with a laptop comprised of a maximum of 1 Gbyte of RAM, using just 739 Mbytes instead of the expected 1.3 Gbytes. We found that the 256colour table was sufficient to • store all the colours of the Power Plant model.

17. Acknowledgements: References: Deering, M.,Geometry Compression, SIGGRAPH’95, 13-20 Botsch, M., Wiratanaya, A., and Kobbelt, K., Efficient high quality rendering of point sampled geometry, In Proc. 13th Eurographics Workshop on Rendering, 2002, 53-64 Taubin, G., Horn, W., Lazarus, F., and Rossignac, J. Geometry Coding and VRML. In Proc. of the IEEE, Special issue on Multimedia Signal Processing,86(6),98,1228-43 Randall, D. A., Ringler, T. D., Heikes, R. P., Jones, P., and Baumgardner, J. Climate Modeling With Spherical Geodesic Grids, Computing in Science&Engineering’02 Deok-Soo, K., Youngsong, C., and Hyun, K. Normal vector compression of 3D mesh model based on clustering and relative indexing. Future Generation Computer Systems, Vol .20, 2004, pp. 1241-50. Guskov, I., Vidimce, K., Sweldens, W., and Schroeder, P. Normal Meshes, In Proc.SIGGRAPH00 (2000), pp. 95-102. Sloane, N. J. A. Tables of Sphere Packings and Spherical Codes,IEEETrans.InformationTheory,Vol27,1981,327-38 Woo, M, Davis, and Sheridan, M. B. OpenGL Programming Guide:The Official Guide to Learning OpenGL,V1.2,3rded99 Von Rymon-Lipsinki, B.. Jansen, T., Hanssen, N. and Keeve, E. Interactive Visualization of Large Point Isosurfaces Using GPU-Based Decompression. In Proc. of IEEE/EurographicsSymposiumonPointBasedGraphics’05 Funding: Fundação Calouste Gulbenkian ALFAMICRO JNICT/PRAXISXXI Fundação para a Ciência e a Tecnologia 3D credits: Thanks: Stanford University (Stanford bunny, Thai statue, David) Matt Hall, Jan Kautz, Ben Dias, Stuart Robson Resources available www.cs.ucl.ac.uk/staff/Joao.Oliveira/