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I couldn't understand the description in the post, but I read the pdf. It sounds like you could accomplish this with a boundary surface. A screen-shot of your two end conditions might help.
there is no equiv. of this feature in SolidWorks. You can achieve the same result but would need to create some additional geometry in SW and then use Boundary or Loft. Here's a sphere that is blended (lofted) to a rectangular profile (see attached.)
Perhaps there is an easier way in SW to achieve what you're after, but of course, you'd have to show us what you're trying to achieve.
It seems I did not need to use an equivalent of a 'section to surface blend'. I was able to solve the problem using other techniques.
I am working on a project for a client, and the mold tooling will need to be replaced in the next year. The SolidWorks version will need to closely match the origional part (surface scan of part created by hand). The part file will need to be revised once the 3-D CAD file is complete, and I have more experience using Pro-E in similar types of projects for surfacing
My first attempt was to trim the top of the handle grip and join the section to the domed feature. However, I did a mutual trim on the two surfaces and added a surface fillet. The part is actually plastic, not metal, but is is easier to see selecting a metal material when modeling.
The right-hand part will look similar, and I need to add ribs & bosses after shelling out the inside. I may consider trimming away the surface near the fillet and using a 'fill' feature to improve the appearance.