visualization and graphics research group cipic feb 18, 2003multiresolution (ecs 289l) - winter...

Feb 18, 2003 Multiresolution (ECS 289L) - Winter 2003 1

visualization and graphics research group

CIPIC

Progressive Meshes(SIGGRAPH ’96)

By Hugues Hoppe

Presented byYong Kil and Christopher Co



CIPIC

Previous Work

[Schroeder-etal92] [Schroeder-etal92] (decimation)(decimation)

[Turk92] [Turk92] (re-tiling)(re-tiling)

[Hoppe-etal93] [Hoppe-etal93] (mesh optimization)(mesh optimization)

[Rossignac-Borrel93] [Rossignac-Borrel93] (vertex clustering)(vertex clustering)

[Cohen-etal96] [Cohen-etal96] (simplification envelopes)(simplification envelopes)

... MRA (later)... MRA (later)

13,00013,000

1,0001,000 200200

?



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Introduction• What is Progressive Mesh?

Arbitrary mesh M stored as coarser mesh M0 together with a sequence of n detail records that indicate how to incrementally refine M0 exactly back into the original mesh M = Mn.

150150

MM00 MM11

vsplvspl00

152152

MM175175

500500

… … vsplvsplii … …

13,54613,546

vsplvspln-1n-1

MMnn

progressive mesh (PM)progressive mesh (PM) representation representation

vsplvspl00 … … vsplvsplii … … vsplvspln-1n-1

MM00 MMnn



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Edge Collapse and Vertex Split

ecol(vecol(vs s ,v,vt t , , vvss ))

vvll vvrr

vvtt

vvss

vvssvvll vvrr’’

’’

vspl(svspl(s ,l,l ,r,r ,t, A),t, A)

A = A = (( {v {vs s ,v,vt t }, {discrete values}, {scalar values} }, {discrete values}, {scalar values} ))

Discrete values: associated with Discrete values: associated with facesfaces. . I.e. material identifier such as texture map.I.e. material identifier such as texture map.

Scalar values: associated with Scalar values: associated with corners corners (vertex, face)(vertex, face). . E.g color, normal, texture coordinate.E.g color, normal, texture coordinate.



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PM Construction

13,54613,546 500500 152152 150 faces150 faces

MM00MM11MM175175

ecolecol00ecolecoliiecolecoln-1n-1

MMnn


vvll vvrr

vvtt

vvss

vvssvvll vvrr’’

’’

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



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Mesh Simplification• Which edge to collapse?• Minimize the Energy Function:

– E(M) = Edist(M) + Espring(M) + Escalar(M) + Edisc(M)

• For each potential edge collapse, calculate ∆E and add to priority queue.

• Pop edge from queue (with lowest ∆E) and collapse.• Update affected edges and every pop next edge.

(b) Sampled points X = {x1, x2, …, xn}(a) Object to be sampled

Sample Points X



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Distance Energy

i

vi KxdME |))(|,()( 2distance

2

||

2 ||)(||min|))(|,( iviKb

vi bxKxdi

Surface of M



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Spring Energy

Kkj

kj vvcME},{

2spring ||||)(



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Distance and Spring• Where to collapse to have local minimum energy?

• Mesh Optimization (Hoppe ’93) creates non-linear equations and solves using iterative method.

• PM chooses 3 locations out of the infinite set: {0, 0.5, 1}

vvtt

vvss

vvss’’

vvss

??

’’



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Scalar Energy

i

ivj bxcME 22scalarscalar ||)(||)()(

.attributesscalar



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Discontinuity Energy

Sharp Edge (in yellow)1. Boundary edge2. Two adjacent faces have different discrete

attributes3. Adjacent corners have different scalar

attributes.

xi



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Using PM – LOD

13,54613,546 500500 152152 150 faces150 faces

MM00MM11MM175175MMnn

Each intermediate representation of the meshcan be considered a LOD



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Using PM – Transmission and Compression

• Transmission– Transmit M0, then transmit sequence of vsplit records

• Compression– Use connectivity coding and efficient use of bits

– Use delta-encoding to reduce storage of scalar attributes

– Coherence in mesh attributes can be exploited



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Geomorph

• Alpha blend between different resolutions to avoid “snapping”

• Blending occurs between each pair of vertices related by edge collapses performed (ancestor map)



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Selective Refinement

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



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Selective Refinement

Perform vspl( si, li, ri, Ai ) if:

• (1) vertices {si,li,ri} exist

• (2) REFINE(si) is true

REFINE(si) is defined per application

Relax constraint

• (1’) vertex si and A’(li) and A’(ri) exist

• Perform vspl( si, A’(li), A’(ri), Ai )

A’() is an ancestor map similar to that used by geomorphin



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Previous Work - MRA

• Multiresolution Analysis (MRA)

• Analysis produces base mesh with wavelet coefficients (B) using filter A

• Synthesis produces mesh of desired resolution using a refining filter and a perturbing filter

• Figure courtesy of Lounsbery, et al. (`94)



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PM vs. MRA

• Advantages of MRA– encodes geometry & color independently– supports multiresolution editing– guarantees maximum error bound

• Advantages of PM– lossless– can be more accurate– captures discrete attributes– captures discontinuities (creases)



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Results – PM vs. MRA



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Results – Escalar



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Results – Radiosity Solution



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Conclusion

• Contribution: PM data structure

• Advantages– Solves a variety of problems (LOD, Progressive Transmission,

Selective Refinement, etc.)

– Deals with various mesh attributes aside from geometry

• Disadvantages– Mesh parameterization can be non-intuitive

– Energy function is complex



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Sharing Mesh Attributes

wedgewedge

vertexvertex

faceface

cornercorner



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Vertex Correspondence

MMnn MM00MMccMMff

vv11

vv22

vv33

vv44

vv55

vv66

vv77

vv88

vv11

vv22

vv33

MMf-1f-1

vv11

vv22

vv33

vv44

vv55

vv66

vv77

ecolecol

MMf-2f-2

vv11

vv22

vv33

vv44

vv55

vv66

ecolecol ecolecol



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Select refine

b

aab



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Misc• MRA vs PM?• Review of PM

– Selective refinement as primary contribution.

– What improvements have been made from this paper.• i.e. who refers to this paper?



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Figures



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vertexvertex

cornercorner

faceface



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{f{f11} : { v} : { v11 , v, v22 , v , v33 } }

{f{f22} : { v} : { v33 , v , v22 , v , v44 } }

……

connectivityconnectivity

geometrygeometry{v{v11} : (x,y,z)} : (x,y,z)

{v{v22} : (x,y,z)} : (x,y,z)

……

face attributesface attributes{f{f11} : } : “skin material”“skin material”

{f{f22} : } : “brown hair”“brown hair”

……



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{v{v22,f,f11} : (n} : (nxx,n,nyy,n,nzz) (u,v)) (u,v)

{v{v22,f,f22} : (n} : (nxx,n,nyy,n,nzz) (u,v)) (u,v)

……

corner attrib.corner attrib.

{f{f11} : { v} : { v11 , v, v22 , v , v33 } }

{f{f22} : { v} : { v33 , v , v22 , v , v44 } }

……

connectivityconnectivity

geometrygeometry{v{v11} : (x,y,z)} : (x,y,z)

{v{v22} : (x,y,z)} : (x,y,z)

……

face attributesface attributes{f{f11} : } : “skin material”“skin material”

{f{f22} : } : “brown hair”“brown hair”

……



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PM benefit

PMPM

VVnn

MMnn

MM00

progressive transmissionprogressive transmission continuous-resolutioncontinuous-resolution smooth LODsmooth LOD geometry compressiongeometry compression

losslesslossless

single resolutionsingle resolution

vsplvsplFFnn

attributesattributes



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vvll vvrr

vvtt

vvss

vvssvvll vvrr’’

’’



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Vertex Split

vvssvvll vvrr

vspl(vvspl(vs s ,v,vl l ,v,vr r , , vvss ,,vvtt ,…),…)

vvll vvrr

vvtt

vvss

’’ ’’’’

’’

attributesattributes



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Reconstruction

150150

MM00 MM11

vsplvspl00

152152

MM175175

500500

… … vsplvsplii … …

13,54613,546

vsplvspln-1n-1

MMnn

progressive mesh (PM)progressive mesh (PM) representation representation

vsplvspl00 … … vsplvsplii … … vsplvspln-1n-1

MM00 MMnn

visualization and graphics research group cipic feb 18, 2003multiresolution (ecs 289l) - winter...

Documents

graphics research group

multiresolution ecs

scalar energy slide

e scalar

spring energy slide

m0m0m0m0 mnmnmnmn slide

vspl n

e spring