The Domain of a Point Set Surface Nina Amenta and Yong J. Kil University of California at Davis.

The Domain of a Point Set Surface

Nina Amenta and Yong J. Kil

University of California at Davis

Introduction

x (x)

x

(x)

Motivation

MLS

Our Line Integral

Understanding MLS

MLS

Amenta, Kil, SIGGRAPH 2004

e(x,a)

n(x)

Energy Field of MLS

),(),,(),( 2i

iiMLS pxxapaaxe

a

Amenta, Kil, SIGGRAPH 2004

Gaussian Weight

a

Vector Field of MLS

),(argmin)( a axexn MLSMLS

a

nMLS(x)

Amenta, Kil, SIGGRAPH 2004

Extremal Surface

Amenta, Kil, SIGGRAPH 2004

Energy on

An Energy and Vector Field (not MLS)

en

Circular plot

x

n(x)a

||e(x,a)||

MLS Vector Field

MLS Best Fitting Plane

MLS Corner Example

Ideal Stream Lines

MLS Circular Plot

MLS Vector Field

MLS Surface and Vector Field

Optimal Direction via Center of Mass

i

iNi pxp ),(c

c

),() ,,(argmin)( 2a i

iiCOM pxapaxn c

Normalized Gaussian Weight

nCOM

Vector Field and Surface

Estimated Distance Function

i

iNiDIST pxpxdxe ),(),()( 2

x

Estimated Distance Field

High

Low

High

Low

Estimated Distance Field

Estimated Distance Function

Line Integral Intro

Line Integral nI(x)

)),()(),(,

2

axy DISTI xyyeaxe

ax,

),(argmin)( a axexn II

a

x

nI Vector Field

Ideal Stream Lines

nI Stream Lines

Surface and Stream Lines

Overall ViewMLS Center of Mass eDIST & nI

Vector Field

Energy Field

Surface

Conclusion

• Analyze various energy and vector fields.

• nCOM works well except at sharp corners.

• eDIST approximates distance well.

• nI works well, but expensive (Not

recommend for 3D).

Thank you.

Updated paper and slide:http://graphics.cs.ucdavis.edu/~yjkil/pub/domain.html

Defining Surface plugin (to appear):http://www.pointshop3d.com

Estimated Distance and Line Integral

MLS

eDIST nI

eDIST nI

MLS Circular plot example

MLS Energy e(x,a)

Energy + Field

MLS Surface

Surface with maxima

MLS Surface with maxima