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 “linear interpolation” 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.
I’d suggest you using:
for a clear and reliable construction.
Or make a loft between two line geometries…
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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 don’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)… and it doesn’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:
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