Proj.4 versus Apache SIS: an accuracy comparison
Proj.4 versus Apache SIS: an accuracy comparison 20/09/2017 user In August 17th 2017, we presented an introduction to Apache SIS in the Free and Open Source Software for Geospatial (FOSS4G) conference. A discussion about accuracy were planed, but skipped because of lack of time. The results that we intended to show are below. Disclaimer: the author of this blog is an Apache SIS contributor. Summary The accuracy of two map projection libraries were compared: Proj.4, a library in the C language. Apache Spatial Information System (SIS), a library in the Java language. The benchmark code was written in Java. The code measured both performance and accuracy. Those two measurements were done together in order to ensure that performance comparisons were applied on equivalent coordinate operations. Results of performance comparisons were presented in a previous blog post. Present blog post is about the accuracy part. Tests done for this blog post expand on the Geospatial Integrity of Geoscience Software (GIGS) tests procedure. We require an accuracy of one centimetre, unless the coordinate operation is documented in the EPSG database as having a larger accuracy. In every cases, we require the results after 100 “forward projection – inverse projection” round trips to drift by less than one meter. However while we used some procedures, we didn’t used GIGS data for this blog. A subset of GIGS tests is executed by the Apache SIS project and a smaller subset is executed in the GeoAPI project for Proj4 and UCAR libraries, but they need to be expanded before further discussion. The ISO 19111 standard recognizes two broad categories of coordinate operations: conversionsand transformations. Those two categories need to be analyzed separately. Coordinate conversions This category includes map projections. For all tested conversions, Apache SIS and Proj.4 are in close agreement. Both implementations show drifts much smaller than one meter (and almost always smaller than 1 millimetre) after 100 “forward projection – inverse projection” round trips. Apache SIS has smaller drifts for projections implemented by exact formulas (mostly projections on sphere), presumably because of stricter trigonometric functions in Java compared to C/C++ and because of Apache SIS aggressive concatenation of linear steps. Proj.4 has smaller drifts (except for Cylindrical Equal Area — “cea”) for projections on Earth approximated by series expansions or iterative algorithms, presumably because of more conservative formulas in series expansions and because of iteration stop conditions controlled by smaller tolerance thresholds. However in both libraries the drift still much smaller than the accuracy requested by EPSG. For map projections on planets having higher eccentricity than Earth (e.g. Jupiter), two behaviors are observed: map projections implemented by iterative algorithms keep a stable accuracy, at the cost of more iterations. But map projections implemented by series expansions have growing errors as the eccentricity increases. For a planet flattened like Jupiter but scaled at Earth size (only for comparison purpose with other projections in this test), the Proj.4 “cea” projection has a drift of 9 km after 100 iterations. Apache SIS drift for the same projection is still below a millimetre, because of SIS dual implementation (series expansion completed by iterations when necessary). Such dual implementation is possible for Mercator (not transverse) and a few other projections. Coordinate transformations This category includes datum shifts. Apache SIS and Proj.4 produce the same results when they use the same operation method with the same Bursa-Wolf parameters, but their results can differ by 1 or 2 meters when those two libraries selected different parameter values. The Bursa-Wolf parameters are the same for tested datum shifts from/to WGS84 except in North America. But the parameters differ for datum shifts between other datums than WGS84, for example Martinique 1938 to RGAF09. In all tested cases, Apache SIS uses the Bursa-Wolf parameters as specified by the EPSG geodetic dataset (late-binding approach) while the Proj.4 early-binding approach puts a 0.9 ± 0.4 meter error in Martinique case, which is about 10 times the expected accuracy. Proj.4 does not give any indication to users about such inaccuracy; currently, only informed users could suspect a problem by inspecting the Proj.4-specific +towgs84 elements in definition strings and guessing how Proj.4 may use them. For coordinate transformations in North America, Apache SIS and Proj.4 may agree or disagree depending on the geographic area. The EPSG registry does not provide Bursa-Wolf parameters covering North America as a whole (both USA and Canada). But it provides parameters for smaller areas, for example a particular state. Apache SIS takes the geographic area in account when selecting Bursa-Wolf parameters, while Proj.4 API does not have this option. Proj.4 may use NADCON grids instead, but has no standard way to tell what it actually does. For this reason, while both Proj.4 and Apache SIS can handle NADCON grids, their usages have not been compared yet. Material and method The comparison has been performed between Proj.4 release 4.9.3 (August 2016) and Apache SIS 0.8-jdk8-SNAPSHOT (August 2017). The environment is Java 1.8.0_144-b01 on MacOS 10.12.6. The comparison program uses the GeoAPI interfaces. GeoAPI 3.0 is an OGC standard which allows to write code once and run it on different implementations. It is similar in this respect to Java DataBase Connectivity (JDBC) interfaces. The “Proj.4 versus Apache SIS: a performance comparison” blog post gives more details about GeoAPI implementations, which Coordinate Reference System (CRS) are used and how operations are instantiated. The table of CRS is repeated here for convenience: SOURCE CRS TARGET CRS EPSG:4053 – International 1924 Authalic Sphere EPSG:3410 – NSIDC EASE-Grid Global EPSG:4326 – WGS 84 EPSG:6933 – WGS 84 / NSIDC EASE-Grid 2.0 Global EPSG:4326 – WGS 84 EPSG:3857 – WGS 84 / Pseudo-Mercator EPSG:4326 – WGS 84 EPSG:3395 – WGS 84 / World Mercator EPSG:4269 – NAD83 EPSG:3978 – NAD83 / Canada Atlas Lambert EPSG:4326 – WGS 84 EPSG:3031 – WGS 84 / Antarctic Polar Stereographic EPSG:4269 – NAD83 EPSG:5070 – NAD83 / Conus Albers EPSG:3994 – WGS 84 / Mercator 41 EPSG:3395 – WGS 84 / World Mercator EPSG:4301 – Tokyo EPSG:4612 – JGD2000 EPSG:4277 – OSGB