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Arizona Lineaments derived from 10m DEM Multi-Directional Hillshade


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Created: Jul 09, 2025 at 11:20 p.m. (UTC)
Last updated: Aug 03, 2025 at 9:23 a.m. (UTC)
Published date: Aug 03, 2025 at 9:23 a.m. (UTC)
DOI: 10.4211/hs.6972730012384cc788bb5b3d0e686083
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Abstract

This dataset contains lineament features automatically extracted using the LINE algorithm in Catalyst (PCI Geomatica) Focus Module from a 10m resolution Multi-Directional Hillshade (MDHS) derived from a 1/3 arcsecond DEM of Arizona. The lineaments were extracted from the MDHS using a low pass filter to smooth noise, and then processed with the LINE algorithm. The resulting lineaments were cleaned to remove artificial features, and a lineament density raster was created.

Lineaments—linear or curvilinear surface features—often correspond to underlying faults, fractures, or lithologic boundaries, and are important indicators of secondary permeability. As such, lineament density has been widely used to identify zones of enhanced infiltration and potential groundwater recharge, particularly in karst and fractured-rock terrains.

This dataset supports integrated hydrogeologic analysis, especially in regions lacking detailed subsurface data, by providing a proxy for structural controls on groundwater movement.

More details can be found here:
https://github.com/Ryan3Lima/Arizona_10m_Lineaments**

**currently a private repository to be made public after publication

Subject Keywords

Coverage

Spatial

Coordinate System/Geographic Projection:
WGS 84 EPSG:4326
Coordinate Units:
Decimal degrees
Place/Area Name:
Arizona
North Latitude
37.1982°
East Longitude
-108.8082°
South Latitude
31.5442°
West Longitude
-114.9607°

Content

README.md

Dataset Title

Arizona Lineaments derived from 10m DEM Multi-Directional Hillshade

Version

v.1.0: July 2025

Authors

  • Ryan E Lima (Northern Arizona University, 0000-0002-5352-7215) Ryan.lima@nau.edu
  • Calvin A. Mako (Arizona Geological Survey , ORCHID) cmako@arizona.edu
  • Temuulen T. Sankey (Northern Arizona University, 0000-0002-7859-8394 )
  • Abraham E. Springer (Northern Arizona University, 0000-0003-4826-9124)

Dataset Description

This dataset contains lineament features automatically extracted using the LINE algorithm in Catalyst (PCI Geomatica) Focus Module from a 10m resolution Multi-Directional Hillshade (MDHS) derived from a 1/3 arcsecond DEM of Arizona. The lineaments were extracted from the MDHS using a low pass filter to smooth noise, and then processed with the LINE algorithm. The resulting lineaments were cleaned to remove artificial features, and a lineament density raster was created.

Lineaments—linear or curvilinear surface features—often correspond to underlying faults, fractures, or lithologic boundaries, and are important indicators of secondary permeability. As such, lineament density has been widely used to identify zones of enhanced infiltration and potential groundwater recharge, particularly in karst and fractured-rock terrains.

This dataset supports integrated hydrogeologic analysis, especially in regions lacking detailed subsurface data, by providing a proxy for structural controls on groundwater movement.

Methods

DEM Processing

  1. A mosaic was created using the 1/3 arcsecond DEM tiles from the National Map
  2. the Spatial Analyst/filter tool was used with a Low pass filter type to smooth noise from the DEM
  3. raster functions/hillshade was completed using multi-directional type and z = 5 (5x vertical exaggeration) resulting in a MDHS raster
  4. The smoothed DEM MDHS was broken up into 9 tiles for processing using the split raster tool

PCI Geomatica

  1. The tiles were opened in Catalyst (PCI Geomatica) focus module using the python scripting tool and the attached Batch_PCI_Line.py script was run

Parameters

|PARAM| Value| Parameter Description | |------|------|---------------------------| | radi|[10]| Filter Radius| | gthr|[100]| Edge Gradient Threshold| | lthr|[45]| Curve Length Threshold| | fthr|[3]| Line Fitting Threshold| | athr|[15]| Angular Difference Threshold| | dthr|[35]| Linking Distance Threshold|

  1. Lineaments were exported as shapefiles for all 9 tiles

Shapefile Post-Processing

  1. the 9 lineament shapefiles were loaded in ArcGIS pro, and combined with the merge tool.
  2. A 500m Buffer around the Arizona Boundary shapefile was used to erase artifact lineaments at the edge of the DEM using the erase tool
  3. a 200m buffer was created around the 1M -Highways shapefile from the National Map, and a 50m buffer was created alon gthe 1M- Rail line feature class from the national map, each was used to erase lineaments along roads and railroads with the erase tool.
  4. Manual cleaning was then conducted, where mining areas, major roads, railroads, and large urban areas were spot checked and artificial or human-made lineaments were removed.

Starting Lineament Layer 220,697 Features

after State Boundary Buffer Erase 219,671 features

After erasing features in Rail 50m Boundary 219,643 features

After erasing features within 200m Road Buffer 218,434 features

After Manual cleaning 217,288 features

Calculating Lineament Density

  1. The line density tool was run using the cleaned lineaments feature class, tool params, RADI = 1000, CellSize = 30, Units = square km

Accuracy Assessment

see Notebooks/Lineament_Accuracy.ipynb and Pylines/AccuracyAssessment.py

Accuracy Assessment

Rose Diagram Analysis

We compare the rose diagrams for each study area for both the reference lineaments and the predicted lineaments. Overall, the predicted lineaments show a similar distribution to the reference lineaments, particularly in the Woods Canyon and N36W113 study areas, less so in Thorn Peak. However the predicted lineaments often differ in frequency particularly in the largest study area N36W113, where many more lineaments were predicted then were present in the reference data.

Thorn Peak Lineament Rose Diagram

Rose Diagrams for Thorn Peak

Woods Canyon Lineament Rose Diagram

Rose Diagrams for Woods Canyon

N36W113 Lineament Rose Diagram

Rose Diagrams for N36W113

Buffer Intersection Analysis

For each set of Reference Lineaments, a buffer was created around the lines to create a polygon. Then the predicted lineaments were compared to the reference lineaments using the Intersect tool resulting in the following table of accuracy metrics:

| Metric relative to REF | Thorn Peak | Woods Canyon | N36W113 | |------------------------|------------|--------------|---------| | True Positive | 0.274 | 0.585 | 0.557 | | False Positive | 0.714 | 0.482 | 0.711 | | False Negative | 0.647 | 0.252 | 0.166 | | Precision | 0.286 | 0.518 | 0.289 | | Recall | 0.298 | 0.699 | 0.777 | | F1 | 0.292 | 0.595 | 0.422 |

Hausdorff Distance Analysis

Hausdorff distance is an algorithm that calculated the maximum distance between two sets of points in metric space Hausdorff 1914. Freire and others 2002 used Hausdorff distance to compare mapped contour lines to remotely sensed contours, and Karimi and Karimi 2017 suggested Hausdorff distance as a metric for measuring the similarity sets of lineaments. The equation for calculating Hausdorff distance is shown below:

$$ d_H(A, B) = \max \left( \sup_{a \in A} \inf_{b \in B} \|a - b\|,\; \sup_{b \in B} \inf_{a \in A} \|b - a\| \right) $$

Where: * $(A, B)$ are two sets of points

  • $\|a - b\|$ is the distance (Euclidean) between points where $a$ is an element of set $A$ and $b$ is an element of set $B$; $a \in A \quad \text{and} \quad b \in B$

  • The expression finds the maximum distance of closest approach between the two sets.

For our analysis we compared $d_H (REF,PRED)$ for each study area with the results shown in table x

| metric | Thorn Peak | Woods Canyon | N36W113 | |------------------|------------|--------------|------------| | PRED LINES n | 306 | 967 | 6719 | | REF LINES n | 365 | 552 | 622 | | Mean REF->PRED | 500.71 m | 547.99 m | 1962.27 m | | Median REF->PRED | 453.75 m | 445.87 m | 1444.95 m | | Max REF->PRED | 1558.02 m | 6899.74 m | 20175.15 m | | Mean PRED->REF | 1201.83 m | 503.72 m | 1560.40 m | | Median PRED->REF | 824.76 m | 479.14 m | 1243.74 m | | Max PRED->REF | 5051.90 m | 1450.23 m | 9164.82 m |

The results show that in the Thorn Peak and Woods Canyon areas where there was less class imbalance between the number of Predicted and Reference lines, moderate spatial agreement between predicted and reference lineaments. The N36W113 area however had relatively poor spatial agreement and a very high false positive rate. This may be due to the manual analysis taking place over a much larger area where much larger features were highlighted at the expense of smaller features. Furthermore, in the N36W113 area major faults from the Statewide 1:500,000 scale map were added, some without any surface expression, and without surface expression they would be difficult to segment using topographic data alone.

Manual Assessment of Extracted Lineaments

Finally, we assessed the lineaments manually in the Thorn Peak Quad, and then in an area not previously assessed. Manual assessment involved looking at the DEM and the extracted lineaments and labeling lineaments as Correct, Partially Correct, or Incorrect. Correct was used for predicted lineaments that appeared to accurately show a linear feature such as a fault or fracture. Partially Correct were predicted lineaments that captured part or partly captured a fault or fracture visible from the DEM. Predicted lineaments were deemed "incorrect" if they did not align with either an obvious fault or fracture. Often times these "incorrect lineaments" lined up with high-points or ridgelines, which may be related to faulting, but could just as easily be the result of erosional surface processes.

Figure x. Shows the Thorn Peak Quad area (A) on the left, and another previously un-evaluated area in SE Arizona (B). Predicted lineaments were compared to the Multi-Directional Hillshade as labeled as correct (Green), incorrect (Red), or partially correct (Yellow).

Manual Accuracy Values

| Category | Count | Percent of Total (n = 759) | |-------------------|-----------|--------------------------------| | Correct | 363 | 47.8% | | Partially Correct | 138 | 18.2% | | Incorrect | 258 | 34.0% |

Geographic Coverage

|Bounding Dimension|Coordinates| |------------------|---------------------| |Top| 4,098,982.787900m| |Bottom| 3,466,522.787900m| |Left| 145,110.251800m| |Right| 685,410.251800m|

Projected Coordinate System NAD 1983 (2011) UTM Zone 12N Projection Transverse Mercator WKID 6341 Previous WKID 102059 Authority EPSG Linear Unit Meters (1.0) False Easting 500000.0 False Northing 0.0 Central Meridian -111.0 Scale Factor 0.9996 Latitude Of Origin 0.0

Files:

|File Name | Description | File Type | Size | |---------------------|--------------------------------------------------|-----------------|-----------------| |AZ10m_MDHS_lopass_z5.tif | 10m DEM after low pass filter, with hillshade tool run, using multidirectional and z=5 | .tif (uint8) |3,740,243 KB| |Lineaments_10m_AZ.shp | merged, and cleaned lineament shapefile for Arizona | .shp || |AZ_lineament_density_DEM10m_res30m.tif | Line Density tool params, RADI = 1000, CellSize = 1000, Units = square km, 30 x 30m resolution| .tif (float 32)|| |AZLineament_Density10_res30_INT |reclassified Lineament density using 6 geometric classes 5 - 10, 30 x 30m resolution |.tif (uint8)| |Lineaments_10m_Thorn.shp|Identified Statewide lineaments clipped to the Thorn Peak area, used for accuracy assessment|.shp|| |N36W113_Bounds.shp|Boundary for the N36W113 study area used to clip Lineaments_10m_AZ.shp for the accuracy assessment|.shp||

References

  1. Al-Adamat, R. (2012). The Use of GIS and Google Earth for Preliminary Site Selection of Groundwater Recharge in the Azraq Oasis Area—Jordan. Journal of Water Resource and Protection, 04(06), 395–399. https://doi.org/10.4236/jwarp.2012.46045

  2. Chenini, I., Mammou, A. B., & El May, M. (2010). Groundwater Recharge Zone Mapping Using GIS-Based Multi-criteria Analysis: A Case Study in Central Tunisia (Maknassy Basin). Water Resources Management, 24(5), 921–939. https://doi.org/10.1007/s11269-009-9479-1

  3. Chowdhury, A., Jha, M. K., & Chowdary, V. M. (2010). Delineation of groundwater recharge zones and identification of artificial recharge sites in West Medinipur district, West Bengal, using RS, GIS and MCDM techniques. Environmental Earth Sciences, 59(6), 1209–1222. https://doi.org/10.1007/s12665-009-0110-9

  4. Fathi, S., Hagen, J. S., & Haidari, A. H. (2020). Synthesizing existing frameworks to identify the potential for Managed Aquifer Recharge in a karstic and semi-arid region using GIS Multi Criteria Decision Analysis. Groundwater for Sustainable Development, 11, 100390. https://doi.org/10.1016/j.gsd.2020.100390

  5. Freire, A. A. R., Antunes, M. A. H., De Barros, M. M., De Souza, W. D., De Sousa Da Silva, W., & De Souza, T. M. (2022). Similarity Analysis between Contour Lines by Remotely Piloted Aircraft and Topography Using Hausdorff Distance: Application on Contour Planting. Remote Sensing, 14(14), 3269. https://doi.org/10.3390/rs14143269

  6. Hausdorff, F. (1914). Grundzuge der mengenlehre (Vol. 61). American Mathematical Soc.

  7. Karimi, B., & Karimi, H. A. (2017). An Automated Method for the Detection of Topographic Patterns at Tectonic Boundaries. Patterns 2017. The Ninth International Conferences on Pervasive Patterns and Applications.

  8. Kresic, N. (1995). Remote Sensing of Tectonic Fabric Controlling Groundwater Flow in Dinaric Karst. Remote Sensing of Environment, 53. https://doi.org/10.1016/0034-4257(95)00042-Y

  9. Mallast, U., Gloaguen, R., Geyer, S., Rödiger, T., & Siebert, C. (2011). Semi-automatic extraction of lineaments from remote sensing data and the derivation of groundwater flow-paths [Preprint]. Groundwater hydrology/Remote Sensing and GIS. https://doi.org/10.5194/hessd-8-1399-2011

  10. Meijerink, A. M., Bannert, D., Batelaan, O., Lubczynski, M., & Pointet, T. (2007). Remote sensing applications to groundwater (Vol. 16). Unesco Paris.

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  12. Ni, C., Zhang, S., Liu, C., Yan, Y., & Li, Y. (2016). Lineament Length and Density Analyses Based on the Segment Tracing Algorithm: A Case Study of the Gaosong Field in Gejiu Tin Mine, China. Mathematical Problems in Engineering, 2016, 1–7. https://doi.org/10.1155/2016/5392453

  13. Nyborg, M., Berglund, J., & Triumf, C.-A. (2007). Detection of lineaments using airborne laser scanning technology: Laxemar-Simpevarp, Sweden. Hydrogeology Journal, 15(1), 29–32. https://doi.org/10.1007/s10040-006-0134-0

  14. O’leary, D. W., Friedman, J. D., & Pohn, H. A. (1976). Lineament, linear, lineation: Some proposed new standards for old terms. Geological Society of America Bulletin, 87(10), 1463--1469. https://doi.org/10.1130/0016-7606(1976)87

  15. Rutzinger, M., Maukisch, M., Petrini-Monteferri, F., & Stötter, J. (2007). Development of algorithms for the extraction of linear patterns (lineaments) from airborne laser scanning data. Proceedings of the Conference ’Geomorphology for the Future’ Obergurgl, 1–8. Scopus.

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  17. Wang, Y., Han, Y., Guo, Y., Wang, J., Wang, N., & Abdelkareem, M. (2025). The use of radar-optical remote sensing data and geographic information system–analytical hierarchy process–multicriteria decision analysis techniques for revealing groundwater recharge prospective zones in arid-semi arid lands. Open Geosciences, 17(1), 20220666. https://doi.org/10.1515/geo-2022-0666

  18. Wilson, J. L., & Guan, H. (2004). Mountain-block hydrology and mountain-front recharge. In J. F. Hogan, F. M. Phillips, & B. R. Scanlon (Eds.), Water Science and Application (Vol. 9, pp. 113–137). American Geophysical Union. https://doi.org/10.1029/009WSA08

Disclaimer

This dataset was generated using automated lineament extraction from 10-meter resolution DEMs, and its accuracy was evaluated against manually delineated geologic lineaments in just one area in the basin and range. Though we invite comparison with other mapped products. You can find the jupyter notebook with the functions to evaluate accuracy in the same manner at this github repository https://github.com/Ryan3Lima/Arizona_10m_Lineaments.git

Evaluated accuracies were relatively low, likely due to limitations in the spatial resolution of the input data and a high incidence of false positive lineaments that reflect surface geomorphology rather than subsurface geologic structures. As such, the dataset is best suited for broad-scale or statewide analyses, such as groundwater recharge suitability mapping.

Licensing

GNU GENERAL PUBLIC LICENSE

Citation

Lima, R.E., Mako, C.A., Sankey, T.T., Springer, A.E. (2025). Arizona 10 meter Lineament Density, July 2025 [Dataset]. HydroShare. https://doi.org/10.xxxx/xxxxx

Funding

Arizona Board of Regents for funding this research through the Technology and Research Initiative Fund (TRIF) through the Arizona Tri-University Recharge and Water Reliability Project (ATUR)

Credits

Funding Agencies

This resource was created using funding from the following sources:
Agency Name Award Title Award Number
Arizona Board or Regents

How to Cite

Lima, R. (2025). Arizona Lineaments derived from 10m DEM Multi-Directional Hillshade, HydroShare, https://doi.org/10.4211/hs.6972730012384cc788bb5b3d0e686083

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written offer to provide the Corresponding Source. This
alternative is allowed only occasionally and noncommercially, and
only if you received the object code with such an offer, in accord
with subsection 6b.

d) Convey the object code by offering access from a designated
place (gratis or for a charge), and offer equivalent access to the
Corresponding Source in the same way through the same place at no
further charge. You need not require recipients to copy the
Corresponding Source along with the object code. If the place to
copy the object code is a network server, the Corresponding Source
may be on a different server (operated by you or a third party)
that supports equivalent copying facilities, provided you maintain
clear directions next to the object code saying where to find the
Corresponding Source. Regardless of what server hosts the
Corresponding Source, you remain obligated to ensure that it is
available for as long as needed to satisfy these requirements.

e) Convey the object code using peer-to-peer transmission, provided
you inform other peers where the object code and Corresponding
Source of the work are being offered to the general public at no
charge under subsection 6d.

A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.

A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling. In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage. For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product. A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

"Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source. The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.

If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information. But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).

The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed. Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.

Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.

7. Additional Terms.

"Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law. If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.

When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it. (Additional permissions may be written to require their own
removal in certain cases when you modify the work.) You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.

Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:

a) Disclaiming warranty or limiting liability differently from the
terms of sections 15 and 16 of this License; or

b) Requiring preservation of specified reasonable legal notices or
author attributions in that material or in the Appropriate Legal
Notices displayed by works containing it; or

c) Prohibiting misrepresentation of the origin of that material, or
requiring that modified versions of such material be marked in
reasonable ways as different from the original version; or

d) Limiting the use for publicity purposes of names of licensors or
authors of the material; or

e) Declining to grant rights under trademark law for use of some
trade names, trademarks, or service marks; or

f) Requiring indemnification of licensors and authors of that
material by anyone who conveys the material (or modified versions of
it) with contractual assumptions of liability to the recipient, for
any liability that these contractual assumptions directly impose on
those licensors and authors.

All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10. If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term. If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.

If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.

Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.

8. Termination.

You may not propagate or modify a covered work except as expressly
provided under this License. Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).

However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.

Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License. If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.

9. Acceptance Not Required for Having Copies.

You are not required to accept this License in order to receive or
run a copy of the Program. Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance. However,
nothing other than this License grants you permission to propagate or
modify any covered work. These actions infringe copyright if you do
not accept this License. Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.

10. Automatic Licensing of Downstream Recipients.

Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License. You are not responsible
for enforcing compliance by third parties with this License.

An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations. If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.

You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.

11. Patents.

A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based. The
work thus licensed is called the contributor's "contributor version".

A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version. For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.

Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.

In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement). To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.

If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients. "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.

If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.

A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License. You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.

Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.

12. No Surrender of Others' Freedom.

If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all. For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.

13. Use with the GNU Affero General Public License.

Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
combined work, and to convey the resulting work. The terms of this
License will continue to apply to the part which is the covered work,
but the special requirements of the GNU Affero General Public License,
section 13, concerning interaction through a network will apply to the
combination as such.

14. Revised Versions of this License.

The Free Software Foundation may publish revised and/or new versions of
the GNU General Public License from time to time. Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.

Each version is given a distinguishing version number. If the
Program specifies that a certain numbered version of the GNU General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation. If the Program does not specify a version number of the
GNU General Public License, you may choose any version ever published
by the Free Software Foundation.

If the Program specifies that a proxy can decide which future
versions of the GNU General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.

Later license versions may give you additional or different
permissions. However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.

15. Disclaimer of Warranty.

THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

16. Limitation of Liability.

IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.

17. Interpretation of Sections 15 and 16.

If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.

<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail.

If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:

<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.

The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".

You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<https://www.gnu.org/licenses/>.

The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

https://www.gnu.org/licenses/why-not-lgpl.html

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