Create a connecting surface to two pipes with the same cross section area

First I divided the pipe into 4 parts, two pairs of symmetrical pieces. Then I built the red and blue curves for the initial loose loft. Loose loft is the easiest way to controllably guarantee continuity in simple cases. The blue lines are actually degree 2 curves with the middle control point weight matching the arc middle control point weight to make sure all iso curves in the resulting surface will be nice and straight.

Then I built the initial Loft with Loose option, and extracted a section in the middle and built a planar surface from it. Used the area (about 315) and the target area (308) to calculate a scale factor (about 0.97) for the section curves. Scaled the section curves (magenta) and finally built another loose loft from all the curves. The cross section area is 308 dot something all the way.


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