Shape Optimization Using Reflection Lines

Elif Tosun, Yotam I. Gingold, Jason Reisman, Denis Zorin
In Proceedings of SGP 2007, Barcelona, Spain, July 2007.

Paper (PDF, 13M)
Presentation (PDF, 15M)


Many common objects have highly reflective metallic or painted finishes. Their appearance is primarily defined by the distortion the curved shape of the surface introduces in the reflections of surrounding objects.

Reflection lines are commonly used for surface interrogation, as they capture many essential aspects of reflection distortion directly, and clearly show surface imperfections that may be hard to see with conventional lighting. In this paper, we propose the use of functionals based on reflection lines for mesh optimization and editing. We describe a simple and efficient discretization of such functionals based on screen-space surface parameterization, and we demonstrate how such discrete functionals can be used for several types of surface editing operations.

Video MP4 (24M):


 author    = {Elif Tosun and Yotam Gingold and Jason Reisman and Denis Zorin},
 title     = {Shape optimization using reflection lines},
 booktitle = {Proceedings of the fifth Eurographics Symposium on Geometry processing},
 series    = {SGP '07},
 year      = {2007},
 isbn      = {978-3-905673-46-3},
 location  = {Barcelona, Spain},
 pages     = {193--202},
 numpages  = {10},
 publisher = {Eurographics Association},
 address   = {Aire-la-Ville, Switzerland, Switzerland}

An addendum:

A Note on the Triangle-Centered Quadratic Interpolation Discretization of the Shape Operator

Jason Reisman, Eitan Grinspun, Denis Zorin
Technical Report, New York University, 2007.

Paper (PDF, 0.8M)


In this note we consider a simple shape operator discretization for general meshes, based on computing an interpolating quadratic function passing through vertices of a triangle and its edge-adjacent neighbors. This approximation is computationally simple and consistent for a broad class of meshes. However, its convergence properties in the context of mesh optimization problems are not as good as some of the previously proposed techniques and it suffers from instabilities for certain point configurations.


  author      = {Jason Reisman, Eitan Grinspun, Denis Zorin},
  title       = {A note on the triangle-centered quadratic interpolation discretization of the shape operator},
  institution = {New York University},
  year        = {2007},