## Extreme elevation on a 2-manifold

Publication
, Journal Article

Agarwal, PK; Edelsbrunner, H; Harer, J; Wang, Y

Published in: Discrete and Computational Geometry

January 1, 2006

Given a smoothly embedded 2-manifold in ℝ3, we define the elevation of a point as the height difference to a canonically defined second point on the same manifold. Our definition is invariant under rigid motions and can be used to define features such as lines of discontinuous or continuous but non-smooth elevation. We give an algorithm for finding points of locally maximum elevation, which we suggest mark cavities and protrusions and are useful in matching shapes as for example in protein docking. © Springer 2006.

### Duke Scholars

## Published In

Discrete and Computational Geometry

## DOI

## EISSN

1432-0444

## ISSN

0179-5376

## Publication Date

January 1, 2006

## Volume

36

## Issue

4

## Start / End Page

553 / 572

## Related Subject Headings

- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Agarwal, P. K., Edelsbrunner, H., Harer, J., & Wang, Y. (2006). Extreme elevation on a 2-manifold.

*Discrete and Computational Geometry*,*36*(4), 553–572. https://doi.org/10.1007/s00454-006-1265-8Agarwal, P. K., H. Edelsbrunner, J. Harer, and Y. Wang. “Extreme elevation on a 2-manifold.”

*Discrete and Computational Geometry*36, no. 4 (January 1, 2006): 553–72. https://doi.org/10.1007/s00454-006-1265-8.Agarwal PK, Edelsbrunner H, Harer J, Wang Y. Extreme elevation on a 2-manifold. Discrete and Computational Geometry. 2006 Jan 1;36(4):553–72.

Agarwal, P. K., et al. “Extreme elevation on a 2-manifold.”

*Discrete and Computational Geometry*, vol. 36, no. 4, Jan. 2006, pp. 553–72.*Scopus*, doi:10.1007/s00454-006-1265-8.Agarwal PK, Edelsbrunner H, Harer J, Wang Y. Extreme elevation on a 2-manifold. Discrete and Computational Geometry. 2006 Jan 1;36(4):553–572.

## Published In

Discrete and Computational Geometry

## DOI

## EISSN

1432-0444

## ISSN

0179-5376

## Publication Date

January 1, 2006

## Volume

36

## Issue

4

## Start / End Page

553 / 572

## Related Subject Headings

- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics