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

Introduction x (x) x

Motivation

MLS

Our Line Integral

Understanding MLS MLS Amenta, Kil, SIGGRAPH 2004 e(x,a) n(x)

Energy Field of MLS a Amenta, Kil, SIGGRAPH 2004 Gaussian Weight a

Vector Field of MLS a n MLS (x) Amenta, Kil, SIGGRAPH 2004

Extremal Surface Amenta, Kil, SIGGRAPH 2004 Energy on

An Energy and Vector Field (not MLS) e n

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 c c c Normalized Gaussian Weight

n COM

Vector Field and Surface

Estimated Distance Function x

Estimated Distance Field

Estimated Distance Function

Line Integral Intro

Line Integral n I (x) a x

n I Vector Field

Ideal Stream Lines

n I Stream Lines

Surface and Stream Lines

Overall View MLSCenter of Mass e DIST & n I Vector Field Energy Field Surface

Conclusion Analyze various energy and vector fields. n COM works well except at sharp corners. e DIST approximates distance well. n I works well, but expensive (Not recommend for 3D).

Thank you. Updated paper and slide: Defining Surface plugin (to appear):

Estimated Distance and Line Integral

MLS

e DIST n I

MLS Circular plot example

MLS Energy e(x,a)

Energy + Field

MLS Surface

Surface with maxima

MLS Surface with maxima