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- Kenneth A. Brakke
- Experimental Mathematics
- 1992

This version is close but not identical to the published version in Experimental Mathematics, 1 (1992) 141– 165. Some figures have been regenerated, and the bibliography updated. Pagination is different, and the text may not be exactly identical. Abstract The Surface Evolver is a computer program that minimizes the energy of a surface subject to… (More)

- Fengzhu Xiong, Wenzhe Ma, +9 authors Sean G. Megason
- Cell
- 2014

Epithelial cells acquire functionally important shapes (e.g., squamous, cuboidal, columnar) during development. Here, we combine theory, quantitative imaging, and perturbations to analyze how tissue geometry, cell divisions, and mechanics interact to shape the presumptive enveloping layer (pre-EVL) on the zebrafish embryonic surface. We find that, under… (More)

We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the… (More)

The results of computer simulation of random Voronoi tessellations of the plane are presented. Statistics tallied include frequencies, area, and perimeter of n-sided cells, and the frequencies of n-and m-sided cells abutting.

- Robert Phelan, Denis Weaire, Kenneth A. Brakke
- Experimental Mathematics
- 1995

The Surface Evolver has been used to minimise the surface area of various ordered structures for monodisperse foam. Additional features have enabled its application to foams of arbitrary liquid fraction. Early results for the case of dry foam (negligible liquid fraction) produced a structure having lower surface area, or energy, than Kelvin's 1887 minimal… (More)

- Kenneth A. Brakke, James M. Mantock, Keinosuke Fukunaga
- IEEE Transactions on Pattern Analysis and Machine…
- 1982

A systematic feature extraction procedure is proposed. It is based on successive extractions of features. At each stage a dimensionality reduction is made and a new feature is extracted. A specific example is given using the Gaussian minus-log-likelihood ratio as a basis for the extracted features. This form has the advantage that if both classes are… (More)

This paper presents a physics-based modeling approach for the creation of high quality surfaces for application in CAGD. Physics-based modeling is commonly used in animation and scientific modeling, and simulates realistic dynamic motion for computer graphics. We propose a physics-based modeling of liquid surface motion as a means to generate complex… (More)

- Kurt W. Swanson, Kenneth A. Brakke, David E. Breen
- ISVC
- 2008

Physics-based modeling techniques have been shown to be advanced methods for creating high quality surfaces for application in CAGD. In this paper we propose a physics-based Temporal Computational Object (TCO) as a modeling process that simulates a liquid membrane to generate organic free-form models. This process compliments existing solid and elastic… (More)

- Michael W Anderson, Chrystelle C Egger, Gordon J T Tiddy, John L Casci, Kenneth A Brakke
- Angewandte Chemie
- 2005

The formation of complex inorganic superstructures in nature relies on the interaction between organic and inorganic species to direct the inorganic form away from its " usual " morphology. During synthesis the superstructures are soft and dynamic which makes a study of the nature of the ephemeral interface difficult. [1] However, the inorganic skeletons… (More)