Rounded square to point? Is it possible?

Hi. I have been trying a few hours in blender (polygonal modeling) making a rounded square to connect with a vertex at the center (the center is placed lower than the square). Unfortunately I did not manage to get the shape without some weird reflections. I decided to jump back to Rhino to see if the problem was my lack of knowledge in Blender or my lack of knowledge in geometry.

I can see now with rhino that the shape I want to make will always give me some kind of tension towards the corners of the square:

I did a try also in Blender by intersecting an inverted cone to a cube and I could see the intersection is never straight…then I realize I am trying to force geometry to do something not possible.

Being said that, I was wondering if there is any trick I could get around this. I am trying to design a fruit holder where the center of the square is a point lower than the edge of the fruit holder…kind of an inverted cone surface, but with the difference It will connect to a roundish square profile instead a circle.

Maybe I am able to fake this with a displacement map…but geometry wise is this possible?

Try using FitCrv on the curve before the extrusion. Extrude the curve to the point with ExtrudeCrvToPoint.

Have you tried Patch?
The result is a very smooth trimmed surface which its section is not a straight line.
Patch

Thank you! Still showing the same outcome. I guess it has to do with the parameters within the fitcrv.
Do you think I should tweak any of these options:

mm looks good, but I would like to have it as a straight section.

that will not work, since the curvature of the surface has to change due to the perimeter flattening after the corners. at least from how i understand it.

you can cheat a little by incorporating straight section lines into the patch to force it to behave as such, but that is merely a compromise.

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Can I ask how did you manage to get the point end? I am using patch (outer curve + 4 segments you mentioned) and I get a rounded profile.

sorry that was a bit deceptive of course because i left the section curves in the screenshot,

if you change the patch setting to for instance 80 spans each direction and adjust the stiffnes to 0.5 than it approximates the pointy edge more and more. it will stay a compromise though but i can imagine this being a good solution, depending on what you need it for.

@Bruno_Suraski what do you need this for if i may ask? i could not stop braining so i further analysed the issue a bit in regards of keeping a sharp edge on the top.

the problem arising here is that the blue curve will be longer than the green, while both also have several degrees of angle to height difference causing the geometry to naturally bump around the corners since it would have to shorten the isocurves internally.

Bildschirmfoto 2020-03-24 um 14.53.25

you can try doing it manually by inserting a control point in circular direction at midpoint and pulling the longer curves inwards to find a good translation between the change of angle.

patch actually does a good job, but when you are keen on pinning the sharp edge completely, something like mesh relax might do with grasshopper, if meshes are ok. i tried a few approaches but i am still pretty much a noob with that and did not figure it out since it might also need a remeshed mesh to feed into a relax component.

maybe @DanielPiker could be so kind to show a quick and super simple example, i would also be interested.

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I’ll attach something that might be good. Here’s how I built it:
(steps from left to right in my model)
Revolve a shape that has the right downward angle & is close-ish to your square outline.
Use cageedit to modify the outer edges until it is closer to your square outline.
Use matchsrf to fit it to your square. (Match edges by closest points turned on.)

example.3dm (8.1 MB)

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I’d be happy to try and share a relaxed version, but I’m afraid I still don’t entirely understand what shape is being sought here.

If you want all vertical sections through the center point to be straight lines, then the shape is entirely determined by the boundary, which has a big jump in curvature at the rounded corners, and this concentration of curvature will necessarily extend into the surface.
I’m not sure if your boundary curve is just straight lines and arcs, but if it is, you could consider instead using a G2 continuous rounded corner instead (as is famously used by Apple in their icons and hardware).
This will still have more curvature at the corners, but since it eases in and out, the reflections would have less of a kink.
edit - for comparison - on the left arcs/lines, and on the right a closed degree 3 NURBS curve, both just extruded to a point.

I can also imagine a shape with the horizontal section blending from the rounded square to something more circular as it approaches the central point, but the vertical sections through the center would then not be straight lines.

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I am trying to do a fruit holder. The gesture I would like to maintain is this translation between the rounded square and a sharp center. It is like an exercise I started in Blender to show in my portfolio.
Your approach is good, but I get similar results with blender. The pinched reflections…:frowning:

Did not check @DanielPiker suggestion, but your file looks way way better than where I started.
Although I tried to follow and I get this ugly corners…not touching the line.

Actually I was thinking if that approach could work. Can I ask, how did you do those apple corners?
Using Blendcrv and then " by eye " ?

  1. Square
  2. I draw a circle with the center on the corner in order to trim the square at equal distance on both edges.
    3.blendcrv>Curvature and picking closer to the corner of both edges sharing that corner.
  3. Do you tweak the curve manually by pulling the handles?

Do you also get these?

When using match, select Refine Match option. Also post your 3dm file.

I do not see how you can completely avoid this - the sharpish corners necessarily propagate to the surface.

-Pascal

ing.3dm (8.2 MB)

I think its on in the screenshot?

maybe not completely, but the proposals are “closer” to make them seem smooth towards the point. I guess it is impossible to not have little bit…

Maybe the @DanielPiker exemplifies better than my words. Although there is a pinch in the second model the transition between the straight part of the rectangle and the curved one are smooth. Maybe what I should rephrase is that. My goal is to make the surface look as one piece and avoiding splits in their reflections. Another wish is to keep the straight section. I would like to get that inverted cone look.

I only see the ing.3dm file, which looks like it has my curves in it. Where is the 3dm of your original post?

ah, thought you wanted to see my mistake. I place it in red next to yours.