My life what have I started! I just hope I can do your efforts justice. However a word of caution here. This may well be an interesting mathematical exercise but the reason for it is to produce a shape that can be used as an electric kettle. Therefore it has to be made to, literally, hold water. So far we have been able to create a solid and a surface model of a spiral but neither can be, respectively shelled or thickened. The reason is that the spiral is by nature a self-intersecting solid. The real 'engineering' trick is to create the conch and then turn it into an injection moulded reality. Now that really is the challenge.
John E Forth
you are right - it is interesting mathematical exercise but it has the geometrical solution.
You can combine geometric and mathematical model and create some conch like I tried.
For example: If you need create thin conch - You can create surface model and then create thin feature.
Remember >> it is not possible create self intersection feature.
With two features I was able to create the geometry below. The first feature is a curve driven by equation (cartesian coordinate system). For those of you familiar with equation-driven curves, you know that there's a variable "t" in the equations which does the same thing as trajpar.
A fibonacci spiral, as we've seen, is similar to what Vladimir used in his models. The spiral you get using the golden rectangles as Vladimir used is a very close approximation. Mathcad is giving us better results but Creo can come close. For true a true fibonacci spiral, the spiral needs to increase by a factor of phi (approx. 1.6180339887) every quarter turn. With a bit of playing around, you can get a curve driven by equation to approximate this behavior.
Once you have a suitable curve, this can be used as the basis for a Thin Swept Blend. This absolutely creates self-intersecting geometry. I humbly differ with Vladimir on this point. In my experience, Creo can create certain types of self-intersecting geometry. In fact, the geometry below self intersects multiple times.
While the outside of this conch looks decent, the 'guts' are a mess of mangled goo. With a better sketch for the swept blend, I think I can overcome that, too. This is preliminary geometry. The equation needs to be tweaked until it's matching the curves created by Mathcad. The swept blend needs to be tweaked to be less mangled inside.But I believe this sets us on a good course for an alternate modeling concept for the conch.
Your model look nice
Note: many times, when I try create a Sweep features with intersection geometry, I had failure geometry - GeomCheck - the feature was created but with errors.
I've been looking extensively into the use of "curves by equations" in Creo. I would be interested in looking at the model mentioned. It appears the link is dead & the educational version of the file is not compatible. Would someone be nice enough to share again?