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How to creat this blend protrusion?


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I believe the behavoiral modeling extension (BMX) can do this for you. I have not used it much but I know that you can create constant area blends so a constant perimeter blend should be possible as well. If you didn't already know the circle section must be divided into four section to match the sections of the square. Just curious but what application are you working on that requires a constant perimeter?
Use boundary blend. Create the circle in four equal sections and you may have to connect the curves (end point of circle segment to end point of square segment )to have some in both directions.

You could also create one quadrant of the circle and one side of the square, connect the ends with a curve to give you four sides, build the surface and use surface transform to copy and rotate the surface segments (3 times) and merge them.

good luck.

Use a General Blend.

I like to sketch my sections 1st as datum-curves so I can use the select-curve option but they can also be sketched on-the-fly.

Each section must have the same number of entities so in the sketch for the circle use the divide option in sketcher (you can insert a pair of centerlines to divide about) to create your 4 entities.

Set up a relation to control your perimeters..
Tough problem.

General blend doesn't work. the perimeter is arbitrary and comes out 12.45 with no opportunity for blend control. Same with the surfaces if you use only the 2 known end conditions. The closest so far is a swept blend. Then redefine, pick blend control, and pick set perimeter. This gives a perimeter of 4*pi +/- .005

You could make a large number of sections to blend though, setting each perimeter, which would help.

BMX should do it but formulating the problem is a little tougher, what do you optimize? Will get back to you on that.

your problem it's in every basic examples.

when you make the circle, make aditional 2 construction lines, rotate with 45 degree from horisontal datum plane.

and brake the circle at every intersection.

after that toggle and make the square. It will work verry well.

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adicar01, be careful not to understate the problem. A simple blend from circle to square is easy but ensuring that EVERy cross section in between has exactly a 4*pi perimeter is not simple. Try it. Make the blend, create an offset plane then a curve at inersection of plane and blend. Measure the length of the curve, It is not constant and not 4*pi. Actually I tried several times to create a perimeter dimension to use for BMX but it either crashed or failed to create the geometry. Weird, it worked without the perimeter dim. kvision has the closest answer so far, the set perimeter option tries to force a linear change between sections so it's close. I think making severl sections and forcing their perimeters to be 4*pi will prob be the best answer.
General blends will work if you insert enough sections.

Unfortunately interpolation will rear it's ugly head and you'll lose control in areas between sections..

This is true with swept-blends also...


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