Three-dimensional space curve comparison using spatial angle variance metric and applications thereof

A method of comparing shapes of three dimensional space curves, the method corresponding:

• determining tangent vectors at corresponding locations along the first and second space curves;
• determining for corresponding locations a pair of angle differences for each of the first and second space curves that defines the angular relationship between the tangent vectors at the corresponding locations;
• and
• using the variance of the angle difference pairs as an indication of how closely the shapes of the first and second space curves match.

A method of evaluating the accuracy of a database that represents geographic features as space curves in three-dimensions, the method comprising:

• for a first space curve which represents a geographic feature, determining a first set of tangent vectors at locations along the first space curve;
• for a second space curve which is a more accurate representation of the geographic feature, determining a second set of tangent vectors at corresponding locations along the second space curve;
• determining for corresponding locations a pair of angle differences for each of the corresponding locations that defines the angular relationship between the first set and second set of tangent vectors at the corresponding locations;
• computing a variance of the angle difference pairs;
• and
• using the variance to indicate how closely the shape of the geographic feature represented by the first space curve matches the actual shape of the geographic feature represented by the second space curve.