Interpolation of sections

This tool linearly interpolate Sections between special Sections known as background or template or reference Sections. The profiles are positioned at the same abscissa as the existing sections. The bottom elevations can be maintained or changed (and then in this case also linearly interpolated between the upstream and downstream template Sections).

Currently the upstream and downstream template sections must be of the same type, and of parameterized types: rectangular, trapezium, circular, culvert, power (sections in width - elevation or abscissa - elevation formats are not yet taken into account). On the other hand, as with the option to change the formats of the sections, you can change the format from Width - Elevation or Abscissa - Elevation to Trapezoidal, this limitation can therefore be raised indirectly.

If no template Section is found, then the upstream and downstream sections of the selected portion are selected as the template Sections, and will be used as such for interpolations.

If only one template Section is found, then for the moment it is kept and the upstream and downstream Sections are added as in the previous case where there is no template Section at all. So we end up with 3 template Sections.

If we have at least 2 template Sections, they will be used to interpolate the Sections between them and according to their characteristics. If the options "Extrapolate at the upstream ..." and / or "Extrapolate at the downstream ..." are activated, and if the selected zone exceeds upstream and/or downstream the zone framed by the first and the last template Section, then these extreme zones will also be modified but not by interpolation between the template Sections, but by extrapolation of the 2 closest template Sections. If the options "Extrapolate at the upstream ..." and/or "Extrapolate at the downstream ..." are not enabled, the interpolations will start at the first template Section and will end at the last template Section, the others extreme upstream and downstream sections out of this template-template area will not be altered, even if they are part of the selection.

The interpolation method is not unique. For example, for a trapezoidal section, we can choose to linearly interpolate the banks slope, which is the most traditional method and easy to implement since this slope is one of the parameters of the section. Ditto for the sections of power form, where we can interpolate the coefficient power. But we can also choose another method which consists of interpolating linearly the top width, which is not a parameter of the section, but a consequence of the other parameters (width at the bottom, banks slope and depth for a trapezoidal section). The two methods are not equivalent in the case where the depth (bank elevation - bed elevation) is not identical in the two sections to be interpolated. An option is therefore available to choose one method or another (checkbox "Interpolate side slope or power coefficient (otherwise top-width)"). For now this option is implemented for trapezoidal sections, but not yet for sections power for which only the power interpolation option works.