Level of Detail:Choosing and Generating LODsDavid LuebkeUniversity of Virginia

Recap: Generating LODs

Simplification operator:– Cell collapse– Vertex removal– Edge collapse

Full edge collapse Half edge collapse Vertex-pair merge a.k.a. “virtual edge

collapse”

Generating LODs

Simplification algorithm– Outer optimization: where to simplify

No optimization Ex: uniform grid cells

Greedy optimization Ex: floating cell clustering Ex: sort edge collapses by error, resort on collapse

Lazy optimization Ex: sort edge collapses by error, dirty bit on

collapse

– Inner optimization: how to simplify Ex: placement of new vertex, retriangulation

Basic Greedy Edge Collapse Algorithm

Sort all edges (by some metric)

repeatCollapse edge

choose edge vertex (or compute optimal vertex)

Fix-up topology

until (no edges left)

Recap: Measuring Error

Most LOD algorithms measure error geometrically– What is the distance between the original and

simplified surface?– What is the volume between the surfaces?– Etc

Really this is just an approximation to the actual visual error, which includes:– Color, normal, & texture distortion– Importance of silhouettes, background

illumination, semantic importance, etc.

Measuring Visual Error

Measuring error– Image-based ideas

Lindstrom & Turk, SIGGRAPH 2000

– Perceptually-based ideas Luebke & Hallen, EGRW 2001 Williams, Luebke, Cohen, Kelley & Schubert,

I3D 2003

Perceptually Driven LOD

Idea: measure local simplification operations against a perceptual model to predict whether the user can could see the effect of simplification

Model: contrast sensitivity function

Perception 101: Contrast Sensitivity Function

Contrast grating tests produce a contrast sensitivity function– Threshold contrast

vs. spatial frequency– CSF predicts the

minimum detectablestatic stimuli

Campbell-Robson Chart by Izumi Ohzawa

Your Personal CSF

Perceptual Graphics:Where To Next?

Incorporate eccentricity, velocity (attention?)

Protect copyrighted media: imperceptible “watermarking” via mesh distortion

Interactive ray tracing…

Measuring Geometric Error

Measuring error– Hausdorff distance

One-sided:

Two-sided:

– Common approximations: Measure vertex-vertex distance, vertex-plane

distance METRO: Sample H(A,B) by sprinkling points on

triangles Quadric Error Metrics: a variation of vertex-plane

distance that works well in practice

( , ) max minb Ba A

h A B a b

( , ) max ( , ), ( , )H A B h A B h B A

Edge Collapse Algorithm

V1

V2 V2Collapse

Edge Collapse Benefits

Edge collapse operation is simple Supports non-manifold topology:

Edge Collapse vs. Vertex-Pair Merging

Even better: vertex-pair merging merges two vertices that:– Share an edge, or– Are within some threshold distance t

Q: What does vertex-pair merging enable over edge collapse?

Quadric Error Metric

Minimize distance to all planes at a vertex Plane equation for each face:

0 :p DCzByAx

v

1

z

y

x

DCBAT vp

Distance to vertex v :

Squared Distance At a Vertex

)(

))((vplanesp

TT vppv

)(

)(vplanesp

TT vppv

vppvvplanesp

TT

)(

)(

2 )()(vplanesp

T vpv

Quadric Derivation (cont’d)

ppT is simply the plane equation squared:

The ppT sum at a vertex v is a matrix, Q:

vQvv T )(

2

2

2

2

DCDBDAD

CDCBCAC

BDBCBAB

ADACABA

ppT