Abstract
The upcoming State Plane Coordinate System of 2022 has spurred considerable interest in design, development, and implementation of large-scale conformal map projections designed at Earth’s surface instead of the reference ellipsoid surface. Such projections address overall linear distortion, which accounts for the combination of scale distortion and ellipsoid height distortion. A method for minimizing root-mean-square (RMS) linear distortion in map projection design is presented. It is based upon least-squares “best fits” of map projection surfaces to Earth’s surface, represented by sets of height data points. Linear distortions, across three common conformal map projections (Lambert conformal conic, transverse Mercator, and Hotine oblique Mercator), are controlled by sets of “critical” parameters that have nonlinear functional relationships with position. These functional relationships are linearized and used in iterative least-squares solutions to find estimates for the parameters that minimize the sum of the squares of linear distortions for the entire input height data point set. The methodology can include weighting for priorities such as population and transportation corridors. Examples are presented and comparisons with existing map projections are made, for both unweighted and population-weighted data sets. It is recognized that there can be design considerations, involving linear distortion, other than or in addition to minimizing its root-mean square.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies (parent files for Columbia, Door, and Waukesha Counties, Wisconsin DEMs are available at https://www.sco.wisc.edu/data/elevationlidar/. The executable module, a data file, and all DLL files necessary for running the software developed during this research are in Appendix S1 . Documentation for installation and use of the software is included in Appendix S2 . The DEM and the population grid file for West Virginia are included in Appendix S3 . A numerical example of the partial derivatives for TM projections appears in Appendix S4 . The ASCII grid file (g2018u0.asc) for GEOID18 (CONUS), necessary for running the executable module, is included in Appendix S5 and is also available at https://www.ngs.noaa.gov/GEOID/GEOID18/downloads.shtml.
Acknowledgments
The Wisconsin State Cartographer’s Office thinned the Columbia, Door, and Waukesha County spot elevations from 0.3-m spacing to 30-m spacing for use in this research.
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Published In
Journal of Surveying Engineering
Volume 148 • Issue 1 • February 2022
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© 2021 American Society of Civil Engineers.
History
Received: Dec 21, 2020
Accepted: Aug 24, 2021
Published online: Nov 11, 2021
Published in print: Feb 1, 2022
Discussion open until: Apr 11, 2022
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