When a Surface Container is used on a series of closed straight lines is that surface generated via Bilinear Interpolation?

It seems that the surface created from the surface container is a Bilinear Interpolation.

Could anyone confirm or deny this?

See image, Thank you

Your curve, your polyline curve, have 4 corners?

(it have 5 control points, with first and last being coincident?)

If so, the resulting surface most likely is a simple degree 1 surface and so â€ślinear interpolationâ€ť is probably the case.

Usually for higher degree, say 3, you would need at least degree+1 control points (so 4).

In your case, if the control points are just 4, it means your U and V control points quantity are just 2, and that can only fit a degree 1 surface.

Iâ€™d suggest you using:

for a clear and reliable construction.

Or make a loft between two line geometriesâ€¦

Hi thank you for the quick reply and your help.

Yes this surface was created with the surface container from 4 straight lines.

All I want to know is if the mathematical formulation of the surface is one that matches bilinear interpolation as shown in the equations on the right in the image.

I donâ€™t plan to create this for construction or documentation or fabrication. I want to use this surface in lieu of having to do the math of bilinear interpolation. Perhaps the developers could chime in on this one as well?

Your formula uses a rectangle (the same x1 coordinate is used by 2 corner, and so is x2, y1 and y2)â€¦ and it doesnâ€™t have third axis Z.

The formula seems a weighted average (?)

I can confirm that weighted average returns the same location than evaluating the surface.

linear interpolation.gh (12.0 KB)

Note that you need to reparametrize your surface before evaluating: