1. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Features Dinesh Shikhare National Centre for Software Technology (NCST) Mumbai, India.

2. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Overview Large 3D polygon mesh models Processing tasks for applications Storage, transmission, loading, rendering Special techniques needed due to the large size of models Previous work in Geometry Compression not best suited for large 3D models of engineering class Our contributions Compression of large engineering models using automatic discovery of repeating geometric features Results

3. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Large polygon mesh models

4. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Large polygon mesh models… Walk-through of Massive Power Plant Model (13 million triangles) University of North Carolina, Chapel Hill. ( http://gamma.cs.unc.edu/GigaWalk/) Double Eagle Tanker (82 million triangles)

5. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Large polygon mesh models… Digital Michelangelo Project (Statue of David) 4,128,614 vertices 8,254,150 triangles Digital Michelangelo Project (St. Matthew) 186,810,938 vertices 372,422,615 triangles http://graphics.stanford.edu/projects/mich/

6. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. 3D Data on the Web… Collaborative CAD http://www.cocreate.com Notre Dame Cathedral Walk-through http://www.vrndproject.com

7. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. 3D Data on the Web… Fatehpur Sikri Walkthrough http://rohini.ncst.ernet.in/fatehpur Virtual Trade Fair http://www.cvtf.org.in

8. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Triangle mesh models… Common representation –Shared list of vertices (Geometry) each has xyz coordinates –List of triangles (Connectivity) each has 3 indices into the shared vertex list Size of storage –Vertices: 3 x V x B bits, (B bits per coordinate value) –Triangles: 3 x T x log 2 V (V = no. of vertices) –Typically, T = 2 x V

9. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Large file sizes… Model# Vertices# TrianglesFile size Capitol Bld.52,60687,2581,678,368 Colosseum69,828135,1592,459,844 Helicopter105,079187,9293,516,096 Boeing 74756,36488,7371,741,212 Taj Mahal65,323126,4532,301,312 Even the smallest model will need 204sec to transmit at download speeds of 64kbps At 500,000 triangles/sec, z-buffer hardware can render only 5 frames/sec

10. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Large models need special techniques… Acquisition Healing – adapting the model for application Rendering at interactive speeds Fast interactions – e.g. collision detection Fast transmission Progressive disclosure Compact storage

11. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Compression of Mesh Models Compact encoding of “information” by eliminating “redundancy” in the original data Exploit the special knowledge of “structure” in the data to encode the information Specialized algorithms perform better than PKZIP, gzip, etc. –e.g. JPEG, MPEG, MP3, etc. Polygon meshes have a special structure too!

12. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Previous Work Connectivity compression –Compact encoding of meshes based on graph traversals Geometry compression –Truncation of precision –Prediction of vertex positions –Spectral compression (FT, Wavelets, …) Compression of attributes –Separation of Attributes and their mappings –Quantization of color, normals –Truncation of precision

13. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Connectivity compression In a triangle mesh: –triangle count  2 * (vertex count) –each vertex gets used in 5 to 7 triangles Such large number of repeated references to vertices motivates compression of connectivity information –goal: minimize repeated references to vertices

14. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Triangle strips and fans… (OpenGL) 0 1 2 0 2 3 0 3 4 0 4 5... 0 1 2 3 4 5 0 1 2 3 4 5... 0 1 2 2 1 3 2 3 4 4 3 5... 0 1 4 5 2 3

15. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Generalized triangle strips… (Deering95) Triangle Strip 1 3 5 4 6 2 Triangle Star 7 8 910 11 12 13 14 R1 O2 O3 O4 O5 O6 R7 O8 O9 M10 M11 M12 M13 M14 Independent Triangle 15 16 17 R15 O16 O17 Independent Quad 18 19 20 21 R18 O19 O20 O21

16. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Edge-based traversal…

17. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Traversal is not always smooth…

18. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Dual graph traversal + encoding

19. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Geometry & Attributes Vertex Coordinates –Truncation of precision –Prediction schemes based on the traversal of connectivity parallelogram rule (Touma and Gotsman) butterfly scheme (Pajarola and Rossignac) Vertex Normals –global table of quantized normals Colour –Truncation of precision

20. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Geometry compression… Spectral compression of geometry –Frequency-domain based schemes –Wavelet based schemes –Works only on smooth meshes

21. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Recent years of intense research… Began with Deering ’95 (first geometry compression paper), and to some degree with Turk ‘92, Rossignac&Borrel, ‘92, Hoppe ’93 (the first simplification papers) Papers on connectivity alone –Itai,Rodeh: Representation of graphs, Acta Informatica, 82 –Turan: On the succinct representation of graphs, Discrete Applied Math, 84 –Naor: Succinct representation of general unlabeled graphs, Discrete Applied Math, 90 –Keeler,Westbrook: Short encoding of planar graphs and maps, Discrete Applied Math, 93 –He, Kao,Lu: Linear time succinct encodings of planar graphs, Siam J. Discrete Math, 99 –Chuang, Garg, He, et al: Compact encodings of planar graphs, ICALP, 98 –Deering: Geometry Compression, Siggraph, 95 –Taubin,Rossignac: Geometric compression through topological surgery, ACM ToG, 98 –Taubin,Horn,Lazarus,Rossignac: Geometry coding and VRML, Proc. IEEE, 98 –Touma,Gotsman: Triangle Mesh Compression, GI, 98 –Gumbold,Straßer: Realtime compression of triangle mesh connectivity, Siggraph, 98 –Rossignac: Edgebreaker: Compressing the incidence graph of triangle meshes, TVCG, 99 –Rossignac,Szymczak: Wrap&Zip: Linear decompression of triangle meshes, CGTA, 99 –King&Rossignac: Guaranteed 3.67V Bit Encoding of Planar Triangle Graphs, CCCG, 99 –Bajaj et al.: Single resolution compression of arbitrary triangle meshes, DCC 99 –Cohen-Or: Progressive compression of arbitrary triangle meshes, Visualization 99 –Isenburg&Snoeyink, Mesh Collapse Compression, SIBGRAPI 99 –Snoeyink, VanKreveld: Linear-time reconstruction of Delauney triangulations, ESA 99 –Denny,Sohler: Encoding a triangulation as a permutation of its point set, CCCG, 97 –King, Symczak, &Rossignac: Connectivity Compression for Irregular Quadrilateral Meshes, submitted –Isenburg&Snoeyink: Face-Fixer, Siggraph 2000 Above list does not include the progressive methods, the ones that focus on geometry, ones that change the connectivity

22. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Patents… Companies – Intel, Sun, IBM, Microsoft, Macromedia, Metacreations Startups – Virtue3D, Enbaya, WebGlide, … At least 20 Issued Patents (from http://www.3dcompression.com/patents.phtml) –6,167,159 -- Touma&Gotsman's valence-based mesh compression6,167,159 –6,046,744 -- Hoppe's Selective Refinement of Progressive Meshes6,046,744 –5,793,371 -- Deering's Compression used in Java3D5,793,371 –5,825,369 -- Rossignac&Taubin's Topological Surgery5,825,369 –5,736,987 -- Drucker&Mitchell's compression method for normals5,736,987 –5,818,463 -- Tao et al. -- a method for animated 3D model compression using quads, 19985,818,463 –5,905,507 -- Rossignac&Taubin's Topological Surgery for generalized models5,905,507 –5,929,860 -- Hoppe's Progressive Meshes5,929,860 –5,963,209 -- Hoppe's Progressive Meshes -- Encoding and transmission5,963,209 –5,966,133 -- Hoppe's Progressive Meshes -- Geomorphs and variable resolution5,966,133 –6,009,435 -- Taubin -- level of detail method that sends the highest LOD connectivity6,009,435 –6,031,548 -- Gueziec,Lazarus,Taubin -- Progressive Multi-level transmission6,031,548 –6,016,153 -- Gueziec&Taubin -- Cutting&Stitching6,016,153 –6,169,819 -- Dyer (HP) -- Fast compression of surface normals6,169,819 –6,169,549 -- Burr, 2001, method for continuous LOD control6,169,549 –6,088,034 -- Deering's Java3D -- surface normal decompression6,088,034 –5,870,094 -- Deering's Java3D -- system for transferring compressed 3D5,870,094 –5,867,167 -- Deering's Java3D compression5,867,167 –5,842,004 -- Deering's Java3D decompression5,842,004 –6,028,610 -- Deering's Java3D -- geometry instructions for decompression6,028,610 –5,933,153 -- Deering's Java3D -- mesh buffer for decompression5,933,153 –5,905,502 -- Deering's Generalized Triangle Mesh compression5,905,502

23. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Architectural and Engineering Designs Common Characteristics: –Large number of small meshes. –Many shapes and groups of shapes repeat. –The model has arbitrary grouping of polygons. –Instancing information is not captured and modeled optimally.

24. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Applicability of previous techniques to Engineering Models? Each repeating feature is repeatedly encoded. Predictive encoders perform poorly on engineering CAD models having sharp edges and corners. Spectral methods too can’t handle sharp features. Vertices are repeated to capture texture coordinates, vertex normals. –Hence graph traversals have many short branches in the tree – encoding is not very compact.

25. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Our Approach Attack the redundancy in encoding the shape features that repeat within a 3D model Automatic discovery of repeating shapes at various granularities: –Connected components –Sub-component features –Aggregates of above two types Compactly encode the repetition of features

26. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Our Approach Soup of Polygons Connected Components Component level Instance Detection Aggregate-level Instance Detection Unstructured or arbitrarily grouped collection of polygons along with attributes. Regrouping of polygons to obtain edge-connected components -- “component shapes”. Detection of repeating component shapes using 3D registration techniques. Detection of repeating groups of component shapes (“aggregates”) by looking for iso-transformation instances of component shapes. Sub-component level Instance Detection Detection of repeating features Within and across components using “feature growth” technique. Compact encoding

27. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Preprocessing of Model Removal of duplicated geometry –replicated vertices –overlapping faces Regrouping of the model as a collection of connected components –For the first stage, connected component is the unit for matching and instancing. A single mesh in the original model split into 36 components to make shape matching and instancing possible.

28. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Matching at Component Level Problem: (Top-Down) –Determine whether given two component shapes are near identical (in the sense of a rigid body transformation). –If they are identical, record the transformation (rotation, translation) for instance definition and for later reconstruction. Various approaches: –graph matching, feature extraction and matching, 3D registration.

29. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Matching at Component Level Normalized Orientation –Obtain an orthonormal basis that describes the eccentricities of the component shape. –Use this basis as a pure rotation matrix to bring a shape to its “normalized orientation”.

30. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Matching at Component Level Hotelling Transform Determine the centroid: Compute Covariance Matrix: Determine eigenvectors and eigenvalues of matrix C. Obtain pure rotation matrix R with normalized eigenvectors and translation T -m to get rigid body transformation (R, T -m ). Compute OBB.

31. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Matching at Component Level Matching two component shapes, M 1, M 2 : –Obtain for both shapes, orthonormal bases and centroids: (R 1, T -m1 ) and (R 2, T -m2 ). Also compute OBBs of the shapes. –Proceed only if dimensions of OBBs match. –Proceed if vertex counts and polygon counts match. –Align M 2 with M 1 using the composite transformation: T = T -m1  R 2  R 1 -1  T m2 –Carry out fuzzy comparison of vertices of M 1 and M 2. –If 99.9% of vertices match, create an instance and record T.

32. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Matching at Component Level Feature i DEF Geom+Conn+Attrib Feature j DEF Geom+Conn+Attrib Feature k DEF Geom+Conn+Attrib First Instance Component Shapes Instance USE T1 Instance USE T2 Instance USE Tm Instance USE T3 Instance USE T1 Instance USE Tn Instance USE T2 Instance USE T1 Instance USE T1 Instance USE T4 Instance USE T2

33. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sample Models

34. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Results: Repeating Components

35. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Results...

36. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features Many shape features repeat within and across components. –Examples: Teeth of a gear: geometry and connectivity for each tooth is repeatedly described. Components of mechanical assemblies are merged to obtain a single component, but still has many repeating shapes. Component level discovery cannot detect sub- component level patterns. Previous work –Discovery of repeating motifs in molecular structures

37. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features…

38. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features… Discovery algorithm (Bottom-up) –Assign footprints to all vertices in the model –Create equivalence classes of vertices having identical neighborhoods as identified by their footprints –Starting with vertices of each equivalence class Carry out identical simultaneous breadth-first growth of features Verify that the features are indeed geometrically identical

39. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features… Identical simultaneous growth of repeating features about vertices (seeds) having identical neighborhoods. Vertex 0 indicates the seeds, and the numbering indicates the BFS order of traversal during the growth.

40. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features… Antenna SteeringSpring RotorWheel

41. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Sub-component features… Large number of vertices belonging to repeating features can be compressed effectively using instancing of vertices and triangles connecting them.

42. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Aggregate features Geometry repeats not only at the level of connected features, but also as groups of features –e.g. A pillar in an architectural model consists of multiple component shapes, and the model can have a large number of identical pillars. Key Observation: –USE-instances of all meshes of a structure have identical transformation associated with them. –An iso-transformation set gives us structures that repeat.

43. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Aggregate features… Feature i DEF Geom+Conn+Attrib Feature j DEF Geom+Conn+Attrib Feature k DEF Geom+Conn+Attrib First Instance Features / Shapes Instance USE T1 Instance USE T2 Instance USE Tm Instance USE T3 Instance USE T1 Instance USE Tn Instance USE T2 Instance USE T1 Instance USE T1 Instance USE T4 Instance USE T2 Structure 1 Structure 2

44. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Aggregate features…

45. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Identification of Erroneous Duplicates Feature i DEF Geom+Conn+Attrib Feature j DEF Geom+Conn+Attrib Feature k DEF Geom+Conn+Attrib First Instance Features / Shapes Instance USE T1 Instance USE T2 Instance USE Tm Instance USE T3 Instance USE T1 Instance USE Tn Instance USE T2 Instance USE T1 Instance USE T1 Instance USE I Instance USE T2 Structure 1 Structure 2 Identical Transformations Identity Transformation

46. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Compressed Storage DEF instances compressed using the best available connectivity compression algorithm –e.g. Edgebreaker (Rossignac 1999) USE instances represented as reference to the DEF instance and a rigid-body transformation. A more general transformation may be used –similarity transformation –a sequence of topological operators to take one mesh to another

47. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Compressed Storage Scheme

48. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Result of compression… (1) File sizes in bytes. (2) Note that some models could not be compressed using Edgebreaker algorithm because (a) DIK has textures and (b) others have non-manifold meshes. (3) CR = 1 – C(M) / O(M)

49. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Heritage Lathe Boeing 747

50. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Summary of contributions New algorithms for discovery of repeating geometric features at different levels of granularity A new compression scheme for large 3D models of architectural and engineering class Extension of compression scheme for incorporation of the previously reported compression techniques A new technique for automatically eliminating erroneously replicated geometry

51. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Discussion… Compression ratio –Very high CR for architectural / engg. Models Speed of compression, decompression –Slow compression (… large parallelism) –Fast decompression Lossy compression –Control over lossiness?

52. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Future Work Matching features that have similar geometry but different connectivity Use of more general set of transformation for shape instance detection and encoding More extensive healing techniques Extension to simplification and progressive disclosure Do you have any more ideas?

53. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Outline of the Thesis… 1.Introduction 2.3D Polygon Mesh Models 3.Compression of 3D Models 4.Automatic Discovery of Repeating Geometric Features 5.A New Compression Scheme for Large 3D Models of Engineering Class 6.Conclusions and Future Directions Appendices A.Some claims and proofs B.Implementation Notes C.Sources of data and software tools

54. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Acknowledgements... Thesis Supervisor: Prof. S. P. Mudur Funded projects: –Aeronautical Development Agency (ADA) –Intel Inc. Models: –VISIONS, 3dcafe.com, avalon.viewpoint.com Expert reviews: –SIGGRAPH01, VMV01, Graphical Models Discussions: –colleagues in Graphics & CAD division, NCST

55. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Thank You.

56. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Recent Work… Improvement of Instance Transforms… –error minimization technique for optimization of instance transformation using 3D-3D registration technique [Haralick, Shapiro] Connectivity Compression –Advancing Fan-front algorithm –Fan-based traversal of triangle mesh for compactly encoding –efficient O(n) algorithm

57. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. List of Publications… On Geometric Modeling, Mesh Generation –A Two-phase Technique for Tessellation of Complex Geometric Models –Tetrahedral Discretization of Complex Volumetric Spaces: Implementation, Efficiency, Robustness and Interactive Control. –Zeus: Surface Modeling, Surface Grid Generation and Tetrahedral Volume Discretization.

58. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. List of Publications... On Interactive Visualization –Graphics Pipeline for Interactive Visualization of Very Large 3D Models On Geometry Compression –Discovery of Repeating Feature Patterns in Large 3D Mesh Models –Compression of Large 3D Engineering Models using Discovery of Repeating Geometric Features

59. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. List of Publications… On Geometry Compression… –3D Compression of Engineering Models for Collaborative Computing Applications. –Compression Techniques for Distributed Use of 3D Data -- an Emerging Media-type on the Internet –Advancing Fan-front: An Efficient Connectivity Compression Technique for Large 3D Triangle Meshes.

60. Compression of Large Engineering 3D Models using Automatic Discovery of Repeating Geometric Features. Other Papers… Submitted to a journal… –Automatic Discovery of Repeating Geometric Features with Application to Compression of Large 3D Models of Architectural and Engineering Class. On the anvil… –Advancing Fan-front: an Efficient Connectivity Compression Technique.