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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)

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 [5, 6] to calculate depth maps from a stereo pair of automotive-grade CMOS cameras. The final prototype utilizes commodity hardware, including… (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)

- 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 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

We prove that any connected proper Dupin hypersur-face in R n is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. We prove the same result for any connected non-proper Dupin hypersurface in R n that satisfies a certain finiteness condition. Hence any taut submani-fold M in R n , whose tube M ǫ satisfies this… (More)

- THOMAS E. CECIL
- 2005

We prove that any connected proper Dupin hypersur-face in R n is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. We prove the same result for any connected Dupin hypersurface in R n that satisfies a finiteness condition. Hence any taut submanifold of R n , whose unit normal bundle satisfies the finiteness… (More)