Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Minimizing Curvature Variation for Aesthetic Surface Design

Pushkar Prakash Joshi

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2008-129
October 7, 2008

http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-129.pdf

We investigate the usability of functional surface optimization for the design of free-form shapes. The optimal shape is subject to only a few constraints and is influenced largely by the choice of the energy functional. Among the many possible functionals that could be minimized, we focus on third-order functionals that measure curvature variation over the surface. We provide a simple explanation of the third-order surface behavior and decompose the curvature-variation function into its Fourier components. We extract four geometrically intuitive, parameterization-independent parameters that completely define the third order shape at a surface point. We formulate third-order energy functionals as functions of these third-order shape parameters. By computing the energy minimizers for a number of canonical input shapes, we provide a catalog of diverse functionals that span a reasonable domain of aesthetic styles. The functionals can be linearly combined to obtain new functionals with intermediate aesthetic styles. Our side-by-side tabular comparison of functionals helps to develop an intuition for the preferred aesthetic styles of the functionals and to predict the aesthetic styles preferred by a new combination of the functionals. To compare the shapes preferred by the functionals, we built a robust surface optimization system. We represent shapes using Catmull--Clark subdivision surfaces, with the control mesh vertices acting as degrees of freedom for the optimization. The energy is minimized by an off-the-shelf implementation of a quasi-Newton method. We discuss some future work for further improving the optimization system and end with some conclusions on the use of optimization for aesthetic design.

Advisor: Carlo H. Séquin


BibTeX citation:

@phdthesis{Joshi:EECS-2008-129,
    Author = {Joshi, Pushkar Prakash},
    Title = {Minimizing Curvature Variation for Aesthetic Surface Design},
    School = {EECS Department, University of California, Berkeley},
    Year = {2008},
    Month = {Oct},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-129.html},
    Number = {UCB/EECS-2008-129},
    Abstract = {We investigate the usability of functional surface optimization for the design of free-form shapes. The  optimal shape is subject to only a few constraints and is influenced largely by the choice of the energy functional. Among the many possible functionals that could be minimized, we focus on third-order functionals that measure curvature variation over the surface. 

We provide a simple explanation of the third-order surface behavior and decompose the curvature-variation function into its Fourier components. We extract four geometrically intuitive, parameterization-independent parameters that completely define the third order shape at a surface point. We formulate third-order energy functionals as functions of these third-order shape parameters. 

By computing the energy minimizers for a number of canonical input shapes, we provide a catalog of diverse functionals that span a reasonable domain of aesthetic styles. The functionals can be linearly combined to obtain new functionals with intermediate aesthetic styles. Our side-by-side tabular comparison of functionals helps to develop an intuition for the preferred aesthetic styles of the functionals and to predict the aesthetic styles preferred by a new combination of the functionals. 

To compare the shapes preferred by the functionals, we built a robust surface optimization system. We represent shapes using Catmull--Clark subdivision surfaces, with the control mesh vertices acting as degrees of freedom for the optimization. The energy is minimized by an off-the-shelf implementation of a quasi-Newton method. We discuss some future work for further improving the optimization system and end with some conclusions on the use of optimization for aesthetic design.}
}

EndNote citation:

%0 Thesis
%A Joshi, Pushkar Prakash
%T Minimizing Curvature Variation for Aesthetic Surface Design
%I EECS Department, University of California, Berkeley
%D 2008
%8 October 7
%@ UCB/EECS-2008-129
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2008/EECS-2008-129.html
%F Joshi:EECS-2008-129