Christopher DeCoroRenato B. Pajarola

XFastMeshXFastMeshFast View-dependent Meshing from Fast View-dependent Meshing from External MemoryExternal Memory

XFastMeshXFastMeshFast View-dependent Meshing from Fast View-dependent Meshing from External MemoryExternal Memory

cdecoro@cat.nyu.eduhttp://www.cat.nyu.edu/~cdecoro/Center for Advanced TechnologyCourant Institute of Mathematical SciencesNew York University

pajarola@ics.uci.eduhttp://www.ics.uci.edu/~graphics/Computer Graphics LabDept. of Information & Computer ScienceUniversity of California Irvine

Talk OutlineTalk OutlineTalk OutlineTalk Outline

• IntroductionIntroduction– Motivation and applications

– Related work

– Background

• External-memory structureExternal-memory structure

• Main-memory structureMain-memory structure

• Experimental resultsExperimental results

• Future workFuture work

MotivationMotivationMotivationMotivation

• Huge geometric modelsHuge geometric models– Digital 3D scanners

» Digital Michelangelo's David, 8M triangles

– CAD, scientific visualization, GIS

• Limited rendering performanceLimited rendering performance– Graphics hardware accelerators can render a fixed amount of triangles in

real-time– We can acquire huge models that far exceed the capability of graphics

cards in the foreseeable future

• Limited memory sizeLimited memory size– Current models can require more storage than we can afford to spend (or

want to spend)– Multiresolution formats require additional space

Related WorkRelated WorkRelated WorkRelated Work

• View-dependent mesh simplificationView-dependent mesh simplification– binary vertex trees [Xia et al. 96+] and [Hoppe 97+]

– multi-triangulation [DeFloriani et a. 98+]

– vertex clustering hierarchies [Luebke & Erikson 97] and [Schmalstieg & Schaufler 97]

– FastMesh [Pajarola 01]

• External-memory mesh simplificationExternal-memory mesh simplification– El-Sana and Chiang [2001]

– Prince [2000]

Background - Half-edgesBackground - Half-edgesBackground - Half-edgesBackground - Half-edges

• Represents mesh and simplification operations with Represents mesh and simplification operations with half-edges and edge collapses / vertex splitshalf-edges and edge collapses / vertex splits– Three consecutive half-edges form a triangle– Each half-edge stores its reverse half-edge, and starting

vertex– Half-edges allow for efficient local mesh update– Each vertex split introduces 1 vertex and 2 triangle faces

AB

CD

a b

cd

h

BA

CD

ab

cd

hh.v

h.n.v

Edge collapse

Vertex split

Background -Background -Multiresolution HierarchyMultiresolution HierarchyBackground -Background -Multiresolution HierarchyMultiresolution Hierarchy

• Uses a hierarchy of half-edge-collapse operationsUses a hierarchy of half-edge-collapse operations– Each node corresponds to a split/collapse

• Level of detail represented as front through hierarchyLevel of detail represented as front through hierarchy– Detail increases as the front descends the tree

h1

h2h3 h10

h5 h14

h11

h7

Active front F

collapsed

expanded

h4

h6h12h9

h8h13

collapsed edgesand faces

expandedvertex splits

Half-edge collapse hierarchy

Background - Background - Basic Simplification CriteriaBasic Simplification CriteriaBackground - Background - Basic Simplification CriteriaBasic Simplification Criteria

• Out-of-frustum SimplificationOut-of-frustum Simplification

• Back-face SimplificationBack-face Simplification

Background – Background – Heuristic Simplification CriteriaHeuristic Simplification CriteriaBackground – Background – Heuristic Simplification CriteriaHeuristic Simplification Criteria

• Screen-projection SimplificationScreen-projection Simplification

• Normal-angle DeviationNormal-angle Deviation

• Silhouette PreservationSilhouette Preservation

Background - LOD parametersBackground - LOD parametersBackground - LOD parametersBackground - LOD parameters

• Bounding spheresBounding spheres– minimal sphere enclosing

all affected triangles (vertices) and spheres of child nodes

h3

h1

Background - LOD parametersBackground - LOD parametersBackground - LOD parametersBackground - LOD parameters

• Bounding spheresBounding spheres– minimal sphere enclosing

all affected triangles (vertices) and spheres of child nodes

• Bounding normal conesBounding normal cones– minimal bounding cone

around vertex normal enclosing all normal directions of subtree

h1

h2

h3h4

Talk OutlineTalk OutlineTalk OutlineTalk Outline

• IntroductionIntroduction

• External-memory structureExternal-memory structure– Overview

– Initial mesh

– Detail blocks

– Auxiliary data

– Data file construction

• Main-memory structureMain-memory structure

• Experimental resultsExperimental results

• Future workFuture work

External Memory Structure – External Memory Structure – Overview Overview External Memory Structure – External Memory Structure – Overview Overview

• Base mesh stored as-is in external storageBase mesh stored as-is in external storage– Loaded at run-time, kept resident during execution

• Detail stored as discrete blocksDetail stored as discrete blocks– Similar in structure to a B-tree (high-degree nodes)– Links within a block represented implicitly

• All faces/vertices/half-edges given unique IDAll faces/vertices/half-edges given unique ID– ID is used to determine the block number– Block number is used to determine disk location

Detail blocksDetail blocksDetail blocksDetail blocks

• Edge-collapse trees are divided into blocksEdge-collapse trees are divided into blocks– Assumes full subtrees

• Forms “block tree”Forms “block tree”– High-degree nodes, similar to B-tree

• Blocks efficiently encode detailBlocks efficiently encode detail– Intra-block links represented implicitly

Detail blocks – GeometryDetail blocks – GeometryDetail blocks – GeometryDetail blocks – Geometry

• Form disc-like regions on the surfaceForm disc-like regions on the surface– Therefore, block nodes are located spatially close together

– Similar positions and orientation

• Lower level blocks form smaller disksLower level blocks form smaller disks– Parent discs (left) encompass child discs (right)

Detail Blocks - ContentsDetail Blocks - ContentsDetail Blocks - ContentsDetail Blocks - Contents

• Information is stored for each existing nodeInformation is stored for each existing node– Vertex, normal coordinates– Bounding sphere radius, bounding cone angle– Global ordering

» Used for fold-over prevention

– Four Adjacent half-edges» Connectivity; used to place new edges into mesh

• Stores connectivity to other blocksStores connectivity to other blocks– ID of parent node (locates block and node)– ID of all child nodes

• FlagsFlags– Indicates number of nodes present

Detail Blocks - PackingDetail Blocks - PackingDetail Blocks - PackingDetail Blocks - Packing

• High-degree trees will have many leavesHigh-degree trees will have many leaves– As blocks store complete subtrees, leaf blocks will be non-full– Leaf blocks do not need child pointers

• Blocks are packed to remove wasted spaceBlocks are packed to remove wasted space– Only nodes that exist are stored in block– Flags indicate which blocks are available– Maintains complete subtree structure

• Child pointers stored only for non-leaf nodesChild pointers stored only for non-leaf nodes– Also indicated by flag

Auxiliary DataAuxiliary DataAuxiliary DataAuxiliary Data

• HeaderHeader– Fixed sized header indicating locations of

other fields

• Initial MeshInitial Mesh– Base mesh M0 stored explicitly on disk,

loaded at start time

• Block IndexBlock Index– For given block b, stores disk offset of b

– Required because packing scheme results in blocks with varying sizes

– Index itself can be entirely loaded at startup, or accessed through memory-mapping

• Root Block ListRoot Block List– Lists which blocks contain root nodes of

the hierarchy

– Root blocks are loaded at start time and kept resident

Talk OutlineTalk OutlineTalk OutlineTalk Outline

• IntroductionIntroduction

• External-memory structureExternal-memory structure

• Main-memory structureMain-memory structure– Overview

– Block loading

– Block deletion

• Experimental resultsExperimental results

• Future workFuture work

Main-memory Structure - Main-memory Structure - OverviewOverviewMain-memory Structure - Main-memory Structure - OverviewOverview

• Block DirectoryBlock Directory– Points to all loaded blocks

– Similar to a page table

– High bits of ID represent block

– Low bits of ID represents offset in block

• Time Priority QueueTime Priority Queue– Min-queue that stores blocks

by least recently used

– Used for caching blocks

Tree NodeTree NodeTree NodeTree Node

• MeshMesh– Stores additional vertex,

normal coordinates

– Six half-edges, representing two faces introduced by split

• TreesTrees– Links to merge tree nodes

– Links to block tree nodes

• TimestampTimestamp

• Simplification parametersSimplification parameters

Block LoadingBlock LoadingBlock LoadingBlock Loading

• Case 1: Front moves below Case 1: Front moves below “frontier” of loaded blocks“frontier” of loaded blocks– Frontier: lowest point in the

hierarchy for which blocks are loaded

– Given block ID, lookup disk address in block index, read from disk

– Inflate block from disk format; enter into directory, attach to tree

Required Block

Active Front

Currently Loaded Merge Tree

New R equired B lock

Active Front

Currently Loaded M erge Tree

Block LoadingBlock LoadingBlock LoadingBlock Loading

• Case 2: Forced split requires Case 2: Forced split requires load of arbitrary blockload of arbitrary block– Update operations that can be

required to maintain mesh;» results from edge collapses

– From split edge ID, determine block ID; read block

– Use parent ID to load parent block

– Repeat until all blocks are connected into the hierarchy

Pre-existing Tree

Pre-existing M esh

Parent D eta il B lock

D etail B lock

Block DeletionBlock DeletionBlock DeletionBlock Deletion

• Caching is required for acceptable performanceCaching is required for acceptable performance

• Once user-specified quota is reached, blocks will be deletedOnce user-specified quota is reached, blocks will be deleted

• Least-recently-used blocks are removed firstLeast-recently-used blocks are removed first– Marked as unused when front moves above root node of block

– Maintains a priority-queue to determine LRU blocks

Unused Nodes Currently U sed Nodes

Tim e P riority Q ueue

Deleted Nodes Unused Nodes

Talk outlineTalk outlineTalk outlineTalk outline

• IntroductionIntroduction

• External-memory structureExternal-memory structure

• Main-memory structureMain-memory structure

• Experimental resultsExperimental results– Storage cost

– Run-time performance

– Examples

• Future workFuture work

Storage cost Storage cost Storage cost Storage cost

• Cost of data file measured on diskCost of data file measured on disk– Less than 30 bytes/tri

– Compares to our original format (about equal)

– More efficient than previous external methods

Run-time performanceRun-time performanceRun-time performanceRun-time performance

– Results shown are average time per frame

– Block load time is generally dominated by rendering

– Block load time also tends to be much less than the view-dependent operations

– Through caching, load time tends to decrease as a percentage of frame over time

Sun 450MHz UltraSPARC-II CPU, Expert3D PCI graphics

More examplesMore examplesMore examplesMore examples

– Upper row displays view from user’s perspective– Lower row shows same image from outside view (represented as

yellow pyramid)– Threshold adjusted to achieve constant 5 frames / second– Between 50 K – 67 K triangles per frame

Animated exampleAnimated exampleAnimated exampleAnimated example

Future workFuture workFuture workFuture work

• Out-of-core PreprocessOut-of-core Preprocess– Would allow more flexibility in creating models

• Asynchronous disk accessAsynchronous disk access– Parrallelize time spent reading from disk

• Pre-fetchPre-fetch– One solution could be based on predicting path of camera movement– Another could base prefetching based on rate of change in the front

• Geometry CompressionGeometry Compression– Allows more information transferred through disk bottleneck– Tradeoff between processor speed vs. disk speed/storage

ConclusionConclusionConclusionConclusion

• Straight-forward approach to external-memory meshing Straight-forward approach to external-memory meshing can be successful, if implemented efficientlycan be successful, if implemented efficiently– Hierarchy broken into blocks

– Minimal transformations to hierarchy required

• Synchronous disk accessSynchronous disk access– Disk access overhead, when blocks are cached, can be minimized

– Synchronous access does not present excessive overhead

• History-based CachingHistory-based Caching– Least-recently used caching scheme dramatically reduces disk

accesses

– No need to attempt prediction of detail required in upcoming frames