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Applying the Inverse Maximum Ratio-Λ to 3-Dimensional Surfaces

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3D Research

Abstract

The question of contour uniformity on a three-dimensional surface arises in various fields of study. Although many questions related to surface uniformity exist, there is a lack of standard methodology to quantify uniformity of a three-dimensional surface. Therefore, a sound mathematical approach to this question could prove to be useful in various areas of study. The purpose of this paper is to expand the previously validated mathematical concept of the inverse maximum ratio over a three-dimensional surface and assess its robustness. We will describe the mathematical approach used to accomplish this and use several simulated examples to validate the metric.

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Notes

  1. In this and later examples the vertical coordinate (dimension), z, is relative to a planar surface defined by the coordinates x and y. This allows us to directly relate results to our previous 2-dimensional analysis [2]. In the Discussion section, we will address the issue of spherical coordinates.

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    Authors and Affiliations

    1. Milken Institute School of Public Health, The George Washington University, 950 New Hampshire Ave, Washington, DC, 20052, USA

      Avinash Chandran, Derek Brown, Loretta DiPietro & Jerome Danoff

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    1. Avinash Chandran
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    2. Derek Brown
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    3. Loretta DiPietro
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    4. Jerome Danoff
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    Correspondence to Avinash Chandran.

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    Avinash Chandran and Derek Brown have contributed equally in manuscript preparation.

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    Chandran, A., Brown, D., DiPietro, L. et al. Applying the Inverse Maximum Ratio-Λ to 3-Dimensional Surfaces. 3D Res 7, 15 (2016). https://doi.org/10.1007/s13319-016-0094-7

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    • DOI: https://doi.org/10.1007/s13319-016-0094-7

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