mental mesh functional overview 1-13-280109

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mental meshTM Functional Overview

White Paper

Document version 1.13 January 28, 2009



mental mesh

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Copyright c 1986-2009 mental images GmbH, Berlin, Germany.

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mental mesh Functional Overview, doc. 1.13 Copyright c 2009 mental images



Table of Contents

Table of Contents

Introduction 1mental mesh Compression 1

Encoding and Compression 1

Decompression and Decoding 2

Features 3

Benchmarks 4

mental mesh Scene Optimization 10

Optimization process 10

Benchmarks 14

Integration of mental mesh 15

Bibliography 16

Copyright c 2009 mental images mental mesh Functional Overview, doc. 1.13 i



Table of Contents

ii mental mesh Functional Overview, doc. 1.13 Copyright c 2009 mental images



mental mesh Compression— Encoding and Compression

Introduction

Computer hardware now makes it possible to generate, manipulate and render geometric data sets reaching

hundreds of millions of primitives. This huge volume is a major challenge both to software and hardwarerendering algorithms. The two main technologies which mental meshTM provides to tackle this aregeometry compression and scene optimization.

Client-side renderingapplications, suchas 3D players embeddedintowebpages, multi-user gameauthoringsystems, and other mesh-centric software often require the transfer or storage of large meshes whose sizeis undesirably, or even unacceptably, limited by hardware constraints or interactivity requirements. Thetechnology provided by mental mesh 3D compression solves this problem by significantly reducing dataneeded to representa meshwhile preservingtopology and quality. The mental meshcompression algorithmaccepts any triangle mesh as input, including degenerate meshes, and produces a compressed data streamwhich allows reconstruction of the mesh within user-chosen quantization tolerance.

Massive and complex 3D scenes are often not well suited to efficient hardware rendering, mainly becauseof suboptimal vertex layout and numerous small meshes. The technology provided by mental mesh sceneoptimization offers ways to merge, simplify and optimize a set of 3D objects. The optimization algorithmaccepts any triangle mesh as input, including degenerate meshes, and produces a smaller set of objectswell-suited for hardware rendering.

This document outlines the basic approach of mental mesh compression and scene optimization, presentsfeatures of the algorithms developed, andprovides information to substantiate the benefits of mental mesh.

mental mesh Compression

The mental mesh 3D compression algorithm is an improved, proprietary version of the algorithm in [1].

It quantizes mesh vertices and uses a region-growing approach to encode the mesh as a stream of symbolswhich are compressed on-the-fly. Vertex positions may also be losslessly encoded. The compressed meshcan be unpacked in a symmetric decompression and decoding process. More detailed information aboutmesh compression techniques can be found in [1].

Encoding and Compression

The first step of the compression process is standard quantization on the input mesh vertices. Figure 1shows an example input mesh with an area of detailed marked and three different levels of bit precisionused on the vertex coordinates in the marked area.

Figure 1: Input mesh with detail marked and detail area with different levels of quantization.

Copyright c 2009 mental images mental mesh Functional Overview, doc. 1.13 1



mental mesh Compression— Decompression and Decoding

The amount of quantization determines tolerance between the original and resulting meshes, and allowsthe user to control the trade-off between quality versus compression ratio. The error is controlled by thenumber of bits chosen to quantize the mesh. mental mesh supports up to 32-bit quantization and lossless

compression. In lossless mode, the portability for decompressing meshes across different platformsrequires compatibility with the IEEE-754 floating point standard.

In the second step of the compression a data stream is constructed in a region-growing process. This streamincrementally encodes the topology and geometry of the quantized mesh and is compressed on-the-fly bya specialized lossless entropy coder to keep memory requirements low.

mental mesh uses a proprietary algorithm to efficiently encode attributes such as normals and UVcoordinates. The corresponding index-lists and attribute values are all processed during the same passas the mesh geometry. Discontinuities, such as seams in texture space, as well as shared attribute valuesover different regions of the mesh are properly encoded.

Figure 2: Typical compression ratios compared to raw binary storage for lossless floating point encoding andquantization levels 20 and 8.

The result is a binary stream which consumes only a small fraction of space in memory than the inputmesh (see Figure 2 and the Benchmarks section for typical compression ratios).

Decompression and Decoding

A mesh which has been compressed with mental mesh can be recovered by performing entropy decodingon the data stream and decoding the mesh. The result is a mesh which is geometrically identical up to the

specified precision (quantization rate or lossless) during the compression stage.

The decompression process gradually decodes topological and geometrical information as needed andsuccessively reconstructs the input mesh in the same order as during the compression stage.

Once decoding is complete, the quantized vertices which were read are converted to floating-point valuesif necessary.

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mental mesh Compression— Features

Features

The features of mental mesh 3D compression include:

• Acceptance of any indexed triangle mesh as input, including non-manifold meshes with degeneratetriangles

• User-controlled quantization level or lossless compression

• Coherent results across architectures

• Region growing technique which favors entropy coding

• Geometry re-ordering which improves hardware rendering performance

• Compression of mesh attributes with arbitary index-lists

• Up to reordering, the topology of the input mesh and its attributes is fully preserved, includingdegenerate triangles. In particular, no artificial cuts are introduced at non-manifold points.

• Compatibility with the OpenGL ES and M3G 3D programming interfaces

• Optional vertex welding for improved compression of triangle soups

• Optional triangle and vertex map output that maintain the correspondence between original anddecompressed mesh

Any indexed triangle mesh may be used as input to mental mesh. Degenerate meshes, i.e., those whichhave non-manifold edges, non-manifold vertices, degenerate or non-orientable triangles are processedautomatically. Optionally vertices with identical position can be merged to improve compression

performance on highly disconnected sets of triangles.

The compression developed for mental mesh is fully compatible with the OpenGL ES and M3G 3Dprogramming interfaces for mobile devices, which use 8- or 16-bit vertex precision. A choice of 8-bitquantization leads to lossless compression on OpenGL ES mesh data. On M3G 3D data, a choice of 8-bit quantization leads to lossless compression if 8-bit geometry integers are used, where a choice of 16-bitquantization leads to lossless compression if 16-bit geometry integers are used. See [2] for informationregarding OpenGL ES and M3G.

The mental mesh compression algorithm preserves the topology of the incoming mesh. Vertices andtriangles are reordered in a way that is well-suited to techniques which are sensitive to vertex caching, suchas hardware rendering.




mental mesh Compression— Benchmarks

Benchmarks

Benchmark tests were run on a Linux 64-bit machine with two 3.6 GHz processors and 4GB RAM.

Different types of models and quantization levels were used. In general, the more bits were used forquantization, the better the result is visually.

The compression efficiency is compared against a binary storage in an indexed facet set format with 12bytes per vertex and 12 bytes per triangle. Note that 1 Kb = 1024 bytes and 1 Mb = 1024 Kb.

Entertainment Models

Models for entertainment purposes including those for games, movies and commercials are often carefullyhand-modelled. They usually have a well-behaved connectivity and can be processed very efficiently bymental mesh technology.

Model name: Subdivision CastleInput precision: 32 bits/coordinateNumber of triangles: 1.19 millionNumber of vertices: 596 KStorage space (binary): 21.5 MbProperties: genus 0, regular subdivision mesh, no creasesCompression statistics:

# quantization bits/coordinate 8 13 20 lossless

# tris processed/sec (in thousands) 447 197 330 343compressed surface size 186.0Kb 375.8Kb 818.2Kb 1835.8Kbcompression efficiency (bits per vertex) 2.6 5.2 11.2 25.2% of original space required 0.9% 1.8% 3.9% 8.8%

Model name: Human Face

Input precision: 32 bits/coordinateNumber of triangles: 12644Number of vertices: 7267Storage space (binary): 239 KbProperties: genus 0, semi-regular mesh, smooth geometry, no crease angleCompression statistics:


# tris processed/sec (in thousands) 121 180 222 220

compressed surface size 9.9Kb 23.1Kb 39.7Kb 55.8Kbcompression efficiency (bits per vertex) 11.1 26.1 44.8 62.9% of original space required 4.2% 9.9% 17.0% 23.9%





Model name: Jacket

Input precision: 32 bits/coordinateNumber of triangles: 40 K

Number of vertices: 20 KStorage space (binary): 720 KbProperties: genus 0, semi-regular mesh with crease angles and non-manifold edgesCompression statistics:



Laser Scans

Meshes created from laser scans are often of poor quality. The pre-processing done by mental meshaddresses manifold issues and degenerate triangles.

Model name: Stanford Dragon

Input precision: 32 bits/coordinateNumber of triangles: 167 KNumber of vertices: 85 KStorage space (binary): 3 MbProperties: genus 55, poor quality, irregular valences, poor triangle aspect ratios

Compression statistics:# quantization bits/coordinate 8 13 20 lossless






Computer Aided Design (CAD) Models

As in the other cases, Computer Aided Design (CAD) models are compressed efficiently by mental mesh

technology.

Model name: Crapaudine

Input precision: 32 bits/coordinateNumber of triangles: 144 KNumber of vertices: 72 KStorage space (binary): 2.6 MbProperties: genus 0, quasi-regular mesh, smooth transitions, circular patternsCompression statistics:



Model name: DXref

Input precision: 32 bits/coordinateNumber of triangles: 55 KNumber of vertices: 28 KStorage space (binary): 1 Mb

Properties: genus 0, quasi-regular mesh, many crease angles and holesCompression statistics:







Computer Aided Design (CAD) Assemblies

Computer Aided Design (CAD) assemblies pose the problem of possibly hundreds of separate meshes

which together form the model of an object. The compression ratio may drop when the ratio of thenumber of meshes to the total number of triangles is very large. However, this affects the compressiononly slightly, as the numbers below indicate.

Model name: High-Resolution Car

Input precision: 32 bits/coordinateNumber of triangles: 1.2 millionNumber of vertices: 606 KStorage space (binary): 22 MbProperties: 256 meshesCompression statistics:

# quantization bits/coordinate 8 16 20 lossless# tris processed/sec (in thousands) 274 259 309 308compressed surface size 440.9Kb 1136.6Kb 1742.7Kb 2960.4Kbcompression efficiency (bits per vertex) 6.0 15.3 23.5 40.0% of original space required 2.1% 5.4% 8.3% 14.1%

Model name: High-Resolution Car Door

Input precision: 32 bits/coordinateNumber of triangles: 117 KNumber of vertices: 82 K

Storage space (binary): 2.2 MbProperties: 3200 meshesCompression statistics:



Limited Input Precision Models

In some settings, such as applications run on mobile devices, low resolution models may be used as input.The compression technology in mental mesh performs very well on such meshes and can easily be madelossless by choosing an appropriate number of quantization bits. The models in the following exampleshave byte coordinates, i.e. are models with input precision of 8 bits per vertex coordinate, meaning that8-bit quantization results in lossless compression.





Figure 3: Decompressed Diesel engine component that was compressed to 16% of input size at quantization level12 (left ) and to 38.8% with lossless compression (right ), which illustrates that at already this quantization rate, themeshes are hardly distinguishable.

Model name: Whale

Input precision: 8 bits/coordinateNumber of triangles: 9441Number of vertices: 5035Storage space (binary): 173 KbProperties: genus 0, simple game mesh, manifoldCompression statistics:

# quantization bits/coordinate 6 8# quantization bits/coordinate 6 8# tris processed/sec (in thousands) 200 149compressed surface size 4.7Kb 6.4Kbcompression efficiency (bits per vertex) 7.7 10.5% of original space required 2.8% 3.8%

Detailed benchmarks on CAD models with mesh attributes

This section shows detailed compression statistics for typical industrial meshes with normals andtexture coordinates. Naturally, the compression ratio depends on the topological quality and geometricredundancy. CAD meshes tesselated from NURBS patches often consist of a large number of connectedcomponents and contain a significant amount of artificial boundary edges. On the other hand, tesselatorsmay produce very irregular triangles that also vary strongly in size.

The following three test cases list compression results from moderate to high mesh irregularity.

The table columns contain the bits per vertex spent to encode the connectivity (topo), the attribute values(values) and information needed to reuse previously encoded attribute values (reuse).





Model name: Motorbike

Number of triangles: 321,445 Number of vertices: 290,541Number of normals: 147,416 Number of texture coordinates: 306,033

Storage space (binary): 19.2Mb # triangles processed/s: 220KProperties: 13259 components, mostly manifold, shared normals and clean

texture parametrization, strongly varying triangle size, sharpangles.

Compression statistics:

Quant. Geometry Normals Texture coords total

level topo values topo values reuse topo values reuse in Kb in %

12 2.49 13.40 1.01 14.17 3.425 0.61 8.00 0.172 1,535.3 8.016 2.36 24.22 1.01 20.17 3.413 0.60 15.26 0.168 2,383.4 12.3

lossless 2.55 56.68 1.01 36.97 3.415 0.60 33.34 0.171 4,778.9 25.1

Model name: Diesel Engine component

Number of triangles: 177,823 Number of vertices: 209,032Number of normals: 533,469 Number of texture coordinates: 209,032Storage space (binary): 16.9Mb # triangles processed/s: 140KProperties: 21729 components, NURBS tesselation, large number of artifi-

cial cuts, highly irregular trianglesCompression statistics:


level topo values topo values reuse topo values reuse in Kb in %

12 2.32 16.23 0.80 71.37 0.31 0.05 15.05 86.00 2,704.5 16.0

16 2.29 26.17 0.80 94.62 0.31 0.05 22.90 86.00 3,751.3 22.2lossless 2.37 50.65 0.80 162.59 0.31 0.05 40.82 86.72 6,569.6 38.8

Model name: Diesel Engine

Number of triangles: 822,906 Number of vertices: 1,114,668Number of normals: 1,114,668 Number of texture coordinates: 1,114,668Storage space (binary): 65Mb # triangles processed/s: 130KProperties: 164971 components, many artificial cuts, attributes aligned to

mesh layoutCompression statistics:


level topo values topo values reuse topo values reuse in Kb in %12 2.26 17.60 0.05 27.34 0.1 0.05 15.04 0.1 8,532.4 13.016 2.23 28.92 0.05 37.21 0.99 0.05 22.88 0.099 12,476.3 19.1

lossless 2.32 58.09 0.05 64.95 0.1 0.05 40.61 0.1 22,644.1 34.7




mental mesh Scene Optimization— Optimization process

Figure 4: Welding with large epsilon for vertex clustering. Left: original mesh, 158k vertices. Right: welded meshwith 29k vertices.

mental mesh Scene Optimization

The current generation of graphics hardware is sensitive both to the number of triangles and vertices sentto the GPU and to the number of driver calls, such as OpenGL primitives.

Most entertainment or CAD scenes consist of scores of sub-elements, usually small in size anddisconnected, which sum to millions of triangles. In order to take advantage of the GPU, large scenes mustbe pre-processed to remove some of the complexity and to recover as much connectivity as possible.

Optimization process

The mental mesh optimization pipeline may be described in three steps, all of which are optional.

1. Object aggregation and welding

2. Geometry simplification

3. Hardware specific geometry optimization

Welding

Several objects in the input scene can be grouped to form a single entity. Vertices with identical positionscan be automatically identified and welded together. Welding commonly eliminates half of the inputvertices because of redundancy introduced by the workflow of most modeling tools.

Main features:





• High performance. The algorithm is hierarchical and has a computational complexity of O(n log n)with respect to the aggregated input size.

• The identification of points is -tolerant, i.e., points within a user specified distance can be identifiedas well. This may also be used to simplify mesh input with arbitrary topology, for instance trianglesoups, via clustering (see Fig. 4).

• The discontinuities of rendering attributes such as normals, materials and texture coordinates, can bepreserved. A user specified parameter controls the maximum distance at which attributes should beidentified in the parameter domain. This leads to compact attribute storage layout.

• It accepts attributes with different index-lists than the original mesh.

Figure 5: Simplification of a high resolution mesh (≈3mio triangles). Top row: Decimation to 10% and 1%. Bottom

row: Zoomed window at 50%, 10% and 1% respectively.

Simplification

mental mesh offers a high-quality mesh decimation algorithm to simplify over-triangulated objects. For agiven target mesh complexity, it preserves details of visual importance as good as possible or, alternatively,

simplifies the input mesh until further reduction would exceed a prescribed scaling-independent geometricerror.

Main features:

• Optimized for high geometric accuracy (see Figs. 5, 6 and 8).

• High performance. The overall algorithm has a computational complexity of O(n log n) with respectto the mesh size.

• Memory efficiency. Unlike other decimation approaches such as quadric-error-metric basedtechniques, mental mesh simplification does not require temporary data to be stored on meshprimitives to evaluate geometric error at the same accuracy level.





Figure 6: Left: original scene with sofas and table decoration tesselated with 1.03mio triangles. Right: same scenewith meshes simplified to 50k triangles. Rendered with mental ray r.

Figure 7: Effect of intrinsic mesh optimization in planar regions. Left: original scene. Middle: same scene simplifiedwithout intrinsic optimization. Right: same scene simplified with intrinsic optimization. In both cases the targetquality was set to 0.3.





R M B

#vertices, logarithmic

Mesh simplification comparison

mental mesh 1.1qslim 2.1

OpenMesh 1.0Softimage XSI 6

Figure 8: Accuracy comparison with two well-known public mesh simplification tools on a typical laser-scannedmodel with 1mio triangles. (RMB equals −10 log10(root mean square error between original and simplified mesh),i.e., higher values mean better accuracy)

• Inner mesh fairness in flat areas (see Fig. 7).

• Detection and handling of non-manifold geometry.

• Handling and preservation of geometric attributes such as normals and textures with possiblydifferent connectivity. Seams will be preserved.

• Coarsening operations preserve the enclosed volume.

• Customizability. Decimation weights can be passed to the simplifier to locally adjust the effect of the simplifier.

• Fully transfers original attributes to simplified mesh, including attributes with different index-lists.

Hardware optimization

Finally, the simplified scene may be optimized using a proprietary algorithm to maximize the GPUperformance. Input geometry is not altered in any way except to re-order in order to take advantage of the GPU architecture. This algorithm is fast and leads to excellent results for all classes of meshes such aslaser-scans, extracted iso-surfaces and subdivision surfaces. Rendering tests show an average frames persecond increase ranging from 1.5 to more than 20, depending on the scene. Scenes with poor occluding,such as mechanical assemblies with many holes, city models and scenes with transparency, benefit the mostfrom the mental mesh optimization pipeline.

The simplification step is the only one which alters the input geometry. It is optional and targeted forinteractive exploration of data sets that are over-tesselated with respect to the scale of the scene.




mental mesh Scene Optimization— Benchmarks

An additional benefit of the mental mesh optimization pipeline is the fully automated correction of anypossible geometry defect, for instance non-manifold vertices and edges, non-orientable surfaces, anddegenerate primitives. The optimized scene may then be processed with algorithms requiring 2-manifold,

connected geometry, such as mesh waterproofing and signing, shape registration, or curvature estimation.

Benchmarks

Benchmark tests were run on a Linux 64-bit machine with two 3.2 GHz processors and 2GB RAM. AnNVidia Quadro FX 3000 was used for hardware rendering. Several different types of scenes were used.The scenes were simplified so that the total triangle count was reduced by at most 75%.

Model name: Airport

Optimization statistics:

scene state original optimized

# triangles 20 million 5 million# vertices 32 million 6 million# objects 85000 410avg frames/sec (hardware rendering) 0.5 7.2

Model name: City of Berlin



# triangles 3 million 0.8 million# vertices 5 million 1.2 million

# objects 15500 17avg frames/sec (hardware rendering) 3.8 17

Model name: CAD Automobile Dataset



# triangles 6.5 million 1.9 million# vertices 7.8 million 2.2 million# objects 4100 54avg frames/sec (hardware rendering) 2 14




Integration of mental mesh

Integration of mental mesh

The technology contained in mental mesh is available as a library for integration into third-party software.

The C++ interface allows for mesh encoding and compression and for mesh decompression and decoding.Scene optimization is also available. Supported platforms include Windows and Linux, with 32-bit or64-bit architecture.




Bibliography

Bibliography

[1] C. Touma and C. Gotsman. Triangle mesh compression. In Graphics Interface Conference Proceedings,

pages 26 - 34, 1998.

[2] K. Pulli, T. Aarnio, K. Roimela and J. Vaarala. Designing Graphics Programming Interfaces for MobileDevices. IEEE Computer Graphics and Applications, 25(6): 66 - 75, 2005.

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