JSBSim can't interpolate between n dimensions

[TrentConley]

I've read an implemented Jon's advice here, but it looks like the nester interpolation is not happening, since the GetValue() function called on the parameters provides a double value rather than calling interpolate again. See src/math/FGFunction.cpp at line 691.

For the RC craft I am working on, I'll need at least 6 dimensions to interpolate from to produce 6 distinct aerodynamic coefficients.

Below are two examples of how I was setting up the nested interpolation. Neither worked since they each only interpolated once:

      <function name="aero/coefficient/CD">
        <description>CD Coefficient</description>
        <interpolate1d>
          <p>aero/beta-rad</p>
          <v>-0.3476658503988659</v>
          <interpolate1d>
            <p>aero/alpha-rad</p>
            <v>-0.063651317007977318</v>
            <interpolate1d>
              <p>fcs/rudder-pos-rad</p>
              <v>-0.4690658503988659</v>
              <interpolate1d>
                <p>fcs/left-aileron-pos-rad</p>
                <v>-0.3490658503988659</v>
                <interpolate1d>
                  <p>fcs/right-aileron-pos-rad</p>
                  <v>-0.3490658503988659</v>
                  <v>-0.02731959022</v>
                  <v>0.3490658503988659</v>
                  <v>-0.025771052</v>
                </interpolate1d>
                <v>-0.17453292519943295</v>
                <interpolate1d>
                  <p>fcs/right-aileron-pos-rad</p>
                  <v>-0.17453292519943295</v>
                  <v>-0.01767199402</v>
                  <v>0.17453292519943295</v>
                  <v>-0.01580392049</v>
                </interpolate1d>
                <v>0</v>
                <interpolate1d>
                  <p>fcs/right-aileron-pos-rad</p>
                  <v>0</v>
                  <v>-0.01419396561</v>
                  <v>-0</v>
                  <v>-0.01419396561</v>
                </interpolate1d>
                <v>0.17453292519943295</v>
                <interpolate1d>
                  <p>fcs/right-aileron-pos-rad</p>
                  <v>0.17453292519943295</v>
                  <v>-0.01857091949</v>
                  <v>-0.17453292519943295</v>
                  <v>-0.02048905171</v>
                </interpolate1d>
                <v>0.3490658503988659</v>
                <interpolate1d>
                  <p>fcs/right-aileron-pos-rad</p>
                  <v>0.3490658503988659</v>
                  <v>-0.03070267218</v>
                  <v>-0.3490658503988659</v>
                  <v>-0.03315893703</v>
                </interpolate1d>
              </interpolate1d>

      <function name="aero/coefficient/CLalpha">
        <description>Lift_due_to_alpha</description>
        <interpolate1d>
          <property>aero/beta-rad</property>
          <value>0</value>
          <interpolate1d>
            <property>aero/alpha-rad</property>
            <value>-0.06981317007977318</value>
            <table name="aero/table/CL_aos0_aoa-4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.1904237249  0.1924528268  0.1892048997
                -0.1745  0.1904237249  0.1924528268  0.1892048997
                 0.0000  0.1904237249  0.1924528268  0.1892048997
                 0.1745  0.1941832655  0.1974139496  0.1941832655
                 0.3491  0.1941832655  0.1974139496  0.1941832655
              </tableData>
            </table>
            <value>0</value>
            <table name="aero/table/CL_aos0_aoa0">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.0122966662  0.0113427057  0.0070011182
                -0.1745  0.0122966662  0.0113427057  0.0070011182
                 0.0000  0.0122966662  0.0113427057  0.0070011182
                 0.1745  0.0191698934  0.0140192208  0.0191698934
                 0.3491  0.0191698934  0.0140192208  0.0191698934
              </tableData>
            </table>
            <value>0.06981317007977318</value>
            <table name="aero/table/CL_aos0_aoa4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.1634988660 -0.1652509383 -0.1697671105
                -0.1745 -0.1634988660 -0.1652509383 -0.1697671105
                 0.0000 -0.1634988660 -0.1652509383 -0.1697671105
                 0.1745 -0.1599945592 -0.1642176505 -0.1599945592
                 0.3491 -0.1599945592 -0.1642176505 -0.1599945592
              </tableData>
            </table>
          </interpolate1d>
          <value>0.17453292519943295</value>
          <interpolate1d>
            <property>aero/alpha-rad</property>
            <value>-0.06981317007977318</value>
            <table name="aero/table/CL_aos10_aoa-4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.1941832655  0.1974139496  0.1941832655
                -0.1745  0.1941832655  0.1974139496  0.1941832655
                 0.0000  0.1941832655  0.1974139496  0.1941832655
                 0.1745  0.1941832655  0.1974139496  0.1941832655
                 0.3491  0.1941832655  0.1974139496  0.1941832655
              </tableData>
            </table>
            <value>0</value>
            <table name="aero/table/CL_aos10_aoa0">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.0191698934  0.0140192208  0.0191698934
                -0.1745  0.0191698934  0.0140192208  0.0191698934
                 0.0000  0.0191698934  0.0140192208  0.0191698934
                 0.1745  0.0191698934  0.0140192208  0.0191698934
                 0.3491  0.0191698934  0.0140192208  0.0191698934
              </tableData>
            </table>
            <value>0.06981317007977318</value>
            <table name="aero/table/CL_aos10_aoa4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.1599945592 -0.1642176505 -0.1599945592
                -0.1745 -0.1599945592 -0.1642176505 -0.1599945592
                 0.0000 -0.1599945592 -0.1642176505 -0.1599945592
                 0.1745 -0.1599945592 -0.1642176505 -0.1599945592
                 0.3491 -0.1599945592 -0.1642176505 -0.1599945592
              </tableData>
            </table>
            <value>0.13962634015954636</value>
            <table name="aero/table/CL_aos10_aoa8">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.3507050218 -0.3397064550 -0.3441705437
                -0.1745 -0.3507050218 -0.3397064550 -0.3441705437
                 0.0000 -0.3507050218 -0.3397064550 -0.3441705437
                 0.1745 -0.3507050218 -0.3414932873 -0.3507050218
                 0.3491 -0.3507050218 -0.3414932873 -0.3507050218
              </tableData>
            </table>
            <value>0.20943951023931956</value>
            <table name="aero/table/CL_aos10_aoa12">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.5494569256 -0.5079927118 -0.4597214528
                -0.1745 -0.5494569256 -0.5079927118 -0.4597214528
                 0.0000 -0.5494569256 -0.5079927118 -0.4597214528
                 0.1745 -0.5494569256 -0.5101388931 -0.5494569256
                 0.3491 -0.5494569256 -0.5101388931 -0.5494569256
              </tableData>
            </table>
          </interpolate1d>
          <value>0.3490658503988659</value>
          <interpolate1d>
            <property>aero/alpha-rad</property>
            <value>-0.06981317007977318</value>
            <table name="aero/table/CL_aos20_aoa-4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.3538699263  0.3754433011  0.4255063451
                -0.1745  0.3538699263  0.3754433011  0.4255063451
                 0.0000  0.3538699263  0.3754433011  0.4255063451
                 0.1745  0.3538699263  0.3754433011  0.4255063451
                 0.3491  0.3538699263  0.3754433011  0.4255063451
              </tableData>
            </table>
            <value>0</value>
            <table name="aero/table/CL_aos20_aoa0">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491  0.1758219741  0.1924439093  0.2400010318
                -0.1745  0.1758219741  0.1924439093  0.2400010318
                 0.0000  0.1758219741  0.1924439093  0.2400010318
                 0.1745  0.1758219741  0.1924439093  0.2400010318
                 0.3491  0.1758219741  0.1924439093  0.2400010318
              </tableData>
            </table>
            <value>0.06981317007977318</value>
            <table name="aero/table/CL_aos20_aoa4">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.0104985285  0.0083599241  0.0597596340
                -0.1745 -0.0104985285  0.0083599241  0.0597596340
                 0.0000 -0.0104985285  0.0083599241  0.0597596340
                 0.1745 -0.0104985285  0.0083599241  0.0597596340
                 0.3491 -0.0104985285  0.0083599241  0.0597596340
              </tableData>
            </table>
            <value>0.13962634015954636</value>
            <table name="aero/table/CL_aos20_aoa8">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.2124093169 -0.1853586857 -0.1301135914
                -0.1745 -0.2124093169 -0.1853586857 -0.1301135914
                 0.0000 -0.2124093169 -0.1853586857 -0.1301135914
                 0.1745 -0.2124093169 -0.1853586857 -0.1301135914
                 0.3491 -0.2124093169 -0.1853586857 -0.1301135914
              </tableData>
            </table>
            <value>0.20943951023931956</value>
            <table name="aero/table/CL_aos20_aoa12">
              <independentVar lookup="row">fcs/elevator-pos-rad</independentVar>
              <independentVar lookup="column">fcs/rudder-pos-rad</independentVar>
              <tableData>
                         0.0000000000  0.1745329252  0.3490658504
                -0.3491 -0.4407664491 -0.3964551189 -0.3489947922
                -0.1745 -0.4407664491 -0.3964551189 -0.3489947922
                 0.0000 -0.4407664491 -0.3964551189 -0.3489947922
                 0.1745 -0.4407664491 -0.3964551189 -0.3489947922
                 0.3491 -0.4407664491 -0.3964551189 -0.3489947922
              </tableData>
            </table>
          </interpolate1d>
        </interpolate1d>
      </function>

To resolve this, I am planning on creating a nxm matrix where n is the number of dimensions I am need to interpolate from and m is the number of data points I have. This would be in place of the table. Technically, I could only store n-1 dimensions in the matrix since I am planning on having the last row be the coefficient value. Then, I'll created a new function interpolateNd that can interpolate between the vectors in the matrix.

Any thoughts on a better implementation?

[Octal450]

Maybe I am missing something, but why not use the "table" lookup and breakPoint="" to create a 3D table rather than using interpolate1d?

Kind Regards,
Josh

[TrentConley]

It's fine to create a 3D table. But let's say you have aerodynamic data across 7 control surfaces, now you need at least 7 dimensional data. Currently, JSBSim can't handle that to my understanding. I made a modification to a fork of JSBSim, and I could bring that into main as well. Check out this PR that introduced it:
machindustries#2

[Octal450]

I see,
interesting.

Kind Regards,
Josh

[Octal450]

Took a quick look.

I REALLY like this. Would be awesome to see this move into JSB/FlightGear. I could definitely make use of this in my flight models.

Kind Regards,
Josh

[TrentConley]

Cool! I'll work on integrating it into JSBSim then.