"GeoPosition" (Comparison Method)

New in 14.1[Experimental]

Compare geographic positions based on geodesic distances.

Details

The "GeoPosition" comparison method considers two geodetic positions to be equivalent if the geodesic distance between them is within a given distance tolerance.
The distance tolerance should usually be set using the Tolerance option in AssessmentFunction. The default value of zero meters allows only machine precision differences. The tolerance should always be a Quantity with units of length.
The default distance function is GeoDistance, but any other distance metric can be specified for the comparison using the DistanceFunction option in AssessmentFunction.
When the answer key contains multiple possible positions that are within the tolerance range of an answer, the assessment is based on the closest answer key.
For convenience, vectors with two or three components are also accepted as input and treated as arguments to GeoPosition.

Examples

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Basic Examples (3)Summary of the most common use cases

Create an AssessmentFunction for GeoPosition comparison with a nonzero tolerance:

In[1]:=1

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-q7aulv

Out[1]=1

Answers within the tolerance range are marked as correct:

In[2]:=2

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-81ey8o

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-rtvey1

Out[3]=3

Use zero tolerance:

In[1]:=1

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-81r5pe

Out[1]=1

Even nearby locations are marked as incorrect:

In[2]:=2

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-08sqw5

Out[2]=2

Only locations with geo positions within machine precision level are accepted:

In[3]:=3

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-cagvsc

Out[3]=3

Define an assessment for a problem with multiple answers, each with a different score.

In[1]:=1

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-mv537z

Out[1]=1

Try some answers:

In[2]:=2

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-e5jdgz

Out[2]=2

Show detailed information about the answer, including the final score, which corresponds to the closest answer key within the tolerance:

In[3]:=3

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-72rps8

Out[3]=3

Answers matching values with negative scores are marked as incorrect:

In[4]:=4

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-b32kig

Out[4]=4

In[5]:=5

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-2uj207

Out[5]=5

Generalizations & Extensions (1)Generalized and extended use cases

Geographic entities are directly accepted as input:

In[1]:=1

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-4v34ad

Out[1]=1

In[3]:=3

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-sbavb8

Out[3]=3

Options (2)Common values & functionality for each option

The Tolerance can be given as any quantity with units of length:

In[46]:=46

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-ykf54m

Out[46]=46

In[61]:=61

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-5qa5xo

Out[61]=61

Use the TravelDistance instead of the GeoDistance to perform the comparison, including an Echo to see the travel distance:

In[1]:=1

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-gwyu4s

Out[1]=1

Applications (1)Sample problems that can be solved with this function

Create a geographic AssessmentFunction including cities in the northeast United States:

In[1]:=1

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https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-llhg3g

Out[1]=1

Create a QuestionObject for the assessment function:

In[2]:=2

✖

https://wolfram.com/xid/0370hczcl8ji4xrhlmxl3qsr5frm-dgfvii

Out[2]=2

Properties & Relations (2)Properties of the function, and connections to other functions

For convenience, vectors with two or three components are also accepted as input and treated as arguments to GeoPosition. Create an assessment function using three different list forms of geo locations:

In[1]:=1