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- THOMAS E. CECIL
- 2008

Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. Münzner showed that the four principal curvatures can have at most two distinct mul-tiplicities m 1 , m 2 , and Stolz showed that the pair (m 1 , m 2) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isopara-metric hypersurface of… (More)

- Chris Murphy, Daniel Lindquist, Ann Marie Rynning, Thomas Cecil, Sarah Leavitt, Mark L. Chang
- 15th Annual IEEE Symposium on Field-Programmable…
- 2007

We present a low-cost stereo vision implementation suitable for use in autonomous vehicle applications and designed with agricultural applications in mind. This implementation utilizes the Census transform algorithm to calculate depth maps from a stereo pair of automotive-grade CMOS cameras. The final prototype utilizes commodity hardware, including a… (More)

- L Bhattacharyya, T Cecil, +4 authors R L Williams
- Pharmaceutical research
- 2004

- Thomas Cecil
- 2004

In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries. The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary in R n under mean curvature flow. The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using… (More)

In this paper we extend the two dimensional methods set forth in [4], proposing a variational approach to a path planning problem in three dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. We follow… (More)

In this paper we propose a variational approach to a path planning problem in 2 dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. Unlike typical level set implementations where the interface being… (More)

- THOMAS E. CECIL
- 2000

If M is an isoparametric hypersurface in a sphere S n with four distrinct principal curvatures, then the principal curvatures κ 1 ,. .. , κ 4 can be ordered so that their multiplicities satisfy m 1 = m 2 and m 3 = m 4 , and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible… (More)

- Thomas E. CECIL
- 2008

A hypersurface M n−1 in a real space-form R n , S n or H n is isoparametric if it has constant principal curvatures. For R n and H n , the classification of isoparametric hypersurfaces is complete and relatively simple, but asÉlie Cartan showed in a series of four papers in 1938–1940, the subject is much deeper and more complex for hypersurfaces in the… (More)

- THOMAS E. CECIL
- 1997

- Richard Rezak, David W. McGrail, +19 authors Jeff Payne
- 1982

1982 This volume has been reviewed by the Minerals Management Service and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Service, nor does mention of trade names or commercial products constitute endorsement or recommendation for use. VIA ACKNOWLEDGEMENTS This report reflects the work… (More)