Progressive Meshes

Progressive MeshesProgressive Meshes

A Talk by Wallner and Wurzer for A Talk by Wallner and Wurzer for the overfull MathMeth auditoriumthe overfull MathMeth auditorium

2 / 27Wallner and Wurzer Vienna University of Technology

What it‘s all about...What it‘s all about...


OverviewOverview

Advantages PM‘sAdvantages PM‘s Definition and Basics Definition and Basics GeoMorphsGeoMorphs Mesh CompressionMesh Compression Selective RefinementSelective Refinement ConstructionConstruction


Let‘s start off...Let‘s start off...


Advantages of PM‘sAdvantages of PM‘s

Mesh SimplificationMesh Simplification LOD ApproximationLOD Approximation Progressive TransmissionProgressive Transmission Mesh CompressionMesh Compression Selective RefinementSelective Refinement


Definition and Basics (1)Definition and Basics (1)

A A cornercorner is a (vertex,face) tuple is a (vertex,face) tuple

We are speaking of a We are speaking of a sharp edgesharp edge if if it is a boundary adgeit is a boundary adge the adjacent faces have different discrete the adjacent faces have different discrete

values orvalues or adjacent corners have different scalar adjacent corners have different scalar

valuesvalues


Definition and Basics (2)Definition and Basics (2) Traditional MeshTraditional Mesh

Progressive MeshProgressive Mesh

(M(M00,{Vsplit,{Vsplit00… Vsplit… Vsplitn-1n-1})})

KK VV

MM00


Definition and Basics (3)Definition and Basics (3)

lossless !lossless !

vvll vvrr

vvtt

vvss

vvssvvll vvrr’’

vsplit

ecol


Definitions and Basics (4)Definitions and Basics (4)

M ... Full-Detailed Mesh (all vertices)M ... Full-Detailed Mesh (all vertices)^̂

MM00 ... Minimal Detailed Version ... Minimal Detailed Version

13,54613,546 500500 152152 150150

MM00MM11MM175175

ecolecol00ecolecoliiecolecoln-1n-1

M=MM=Mnn^̂


GeomorphGeomorph Smooth visual transition between two Smooth visual transition between two

meshes Mmeshes Mff, M, Mcc

vv11

vv22

vv33

vv44

vv55

vv66

vv77

vv88

MMff

vv11

vv22

vv33

MMcc

VV FF

MMffcc

VV

PM with geomorph


Geomorph (2)Geomorph (2)


Mesh CompressionMesh Compression

vvssvvll vvrr

vvll vvrr

vvtt’’

vvss’’

Record deltas:Record deltas: vvtt - v - vss vvs s - v- vss ……

’’’’

vspl(vvspl(vs s ,v,vl l ,v,vr r ,,

vvss ,,vvtt ,…),…)’’ ’’


Selective RefinementSelective Refinement

MM00 vsplvspl00 vsplvspl11 vsplvspli-1i-1 vsplvspln-1n-1


Selective Refinement (2)Selective Refinement (2) RulesRules for the vertex splits: for the vertex splits:

All involved vertices are All involved vertices are present present

doRefine(v) == TRUE doRefine(v) == TRUE neighbours neighbours should be further refinedshould be further refined

vertex is vertex is absentabsent a previous vertex split a previous vertex split was not executed, based on the two was not executed, based on the two upper rulesupper rules


Selective Refinement (3)Selective Refinement (3)

View Frustum

...which makes this vertex „not present“

Split not performed...

...because this split wasnot performed...


Selective Refinement (4)Selective Refinement (4)

View Frustum

if this would be present


ConstructionConstructionTask: Task:

Construct MConstruct Mn-1n-1, M, Mn-2n-2, ... M, ... M00

Naive Algorithm:Naive Algorithm:

{{

select random edge to collapse until resolution select random edge to collapse until resolution MM00 faces faces

}}


Construction (2)Construction (2) Problems of naive algorithm:Problems of naive algorithm:

1.1. Geometry is not preservedGeometry is not preserved

2.2. Color, Normals etc. are not preservedColor, Normals etc. are not preserved

3.3. Discontinuities are not preservedDiscontinuities are not preserved


Construction (3)Construction (3) Better algorithm:Better algorithm:

(Re-)Sample object (Re-)Sample object Simplify ObjectSimplify Object Use energy function to measure Use energy function to measure

accuracy accuracy Extend to preserve...Extend to preserve...

surface geometrysurface geometry color and normals color and normals discontinuitiesdiscontinuities


Energy FunctionEnergy Function

E(V)= EE(V)= Edistdist(V) + E(V) + Espringspring(V) + E(V) + Escalarscalar(V)+E(V)+Ediscdisc(V)(V)

E negative E negative perform split perform split

(= less energy used for simplified mesh)(= less energy used for simplified mesh) furtherexplanations


With better algorithm...With better algorithm...


SummarySummary

PM have many advantages:PM have many advantages: losslesslossless captures discrete attributescaptures discrete attributes captures discontinuitiescaptures discontinuities

continuous-resolutioncontinuous-resolution smooth LODsmooth LOD space-efficientspace-efficient progressiveprogressive


Links (1)Links (1)

Progressive MeshesProgressive Meshes

[ Hoppe ][ Hoppe ]http://research.microsoft.com/~hoppe/http://research.microsoft.com/~hoppe/

((all images in this talk except those explicitly labeled all images in this talk except those explicitly labeled courtesy of H. Hoppe)courtesy of H. Hoppe)


Links (2)Links (2) quadric error metric scheme quadric error metric scheme

[ Garland and Heckbert ][ Garland and Heckbert ]http://graphics.cs.uiuc.edu/~garland/papers.htmlhttp://graphics.cs.uiuc.edu/~garland/papers.html

memoryless schemememoryless scheme

[ Lindstrom and Turk ][ Lindstrom and Turk ]http://www.cs.gatech.edu/gvu/people/Phd/Peter.Lindstrom.htmlhttp://www.cs.gatech.edu/gvu/people/Phd/Peter.Lindstrom.html

Thank you for your attention !Thank you for your attention !

Progressive MeshesProgressive MeshesWallner and WurzerWallner and Wurzer


Discussion NoteDiscussion Note Problem of this approach:Problem of this approach:

pictures courtesy of Markus Gross


Discussion NoteDiscussion Note Better Approach:Better Approach:

pic

ture

court

esy

of

Mark

us

Gro

ss

Progressive Meshes

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