Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Intuitive Exposition of Third Order Surface Behavior

Pushkar Prakash Joshi and Carlo H. Séquin

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2008-125
September 25, 2008

http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-125.pdf

Third order surface analysis is an important aspect of shape interrogation and design. We present a novel parameterization-independent exposition of the geometric behavior of a surface point up to third order. Unlike existing algebraic expositions, our work produces an intuitive explanation of the third order surface behavior, analogous to the principal curvatures and directions that describe second order behavior. We extract four parameters that provide a quick and concise understanding of the third order surface behavior at any given point. Our shape parameters can be used to characterize different third order surface shapes without having to use tensor algebra.


BibTeX citation:

@techreport{Joshi:EECS-2008-125,
    Author = {Joshi, Pushkar Prakash and Séquin, Carlo H.},
    Title = {Intuitive Exposition of Third Order Surface Behavior},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2008},
    Month = {Sep},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-125.html},
    Number = {UCB/EECS-2008-125},
    Abstract = {Third order surface analysis is an important aspect of shape interrogation and design. We present a novel parameterization-independent exposition of the geometric behavior of a surface point up to third order. Unlike existing algebraic expositions, our work produces an intuitive explanation of the third order surface behavior, analogous to the principal curvatures and directions that describe second order behavior. We extract four parameters that provide a quick and concise understanding of the third order surface behavior at any given point. Our shape
parameters can be used to characterize different third order surface shapes without having to use tensor algebra.}
}

EndNote citation:

%0 Report
%A Joshi, Pushkar Prakash
%A Séquin, Carlo H.
%T Intuitive Exposition of Third Order Surface Behavior
%I EECS Department, University of California, Berkeley
%D 2008
%8 September 25
%@ UCB/EECS-2008-125
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-125.html
%F Joshi:EECS-2008-125