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A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^n) from sample data is designed by Professor Li Chen in Computer Science at the University of the District of Columbia (UDC).  This method is based on gradually varied functions discovered by Li Chen in 1989 and the classical difference method. This new method has been applied to real groundwater data and the results have validated the method.  This method is independent from existing popular methods such as the cubic spline method and the finite element method.  The new digital-discrete method has considerable advantages for a large amount of real data applications.  This digital method differs from the classical discrete method that usually uses triangulations.


This method can potentially be used to obtain smooth functions such as polynomials through its derivatives f^{(k)} and the solution for partial differential equations such as harmonic and other important equations.

This research has been partially supported by the USGS seed grants through UDC Water Resources Research Institute (WRRI) and Center for Discrete Mathematics and Theoretical Computer Science

(DIMACS) at Rutgers University.  UDC undergraduate Travis Branham extracted the application data from the USGS database.  Chen was inspired by the Workshop on the Whitney Problem organized by Princeton University and the College of William and Mary in August 2009.  This research was also encouraged by the helpful discussions with the presenters and attendees of this workshop.


Li Chen's website is at www.udc.edu/prof/chen.

The IAPR Newsletter is looking for reviewers for the books listed below.


If you have interest and some knowledge in the topic, email us with your mailing address.  We will send you a copy of the book—which you may keep—and will expect in return a review for the Newsletter

Arjan Kuijper, IAPR Newsletter Associate Editor for Book Reviews



The following title is available to be reviewed:


Airborne and Terrestrial Laser Scanning

Vosselman and Mass

Whittles Publishing, 2010

Approx. 320 pp, liberally illustrated, full colour throughout, hardcover.

ISBN 978-1904445-87-6


Free Books!

A Digital-Discrete Method For Smooth-Continuous Data Reconstruction