Update to the answer below
I see actually that it has 12 sides, so create 36 segments not 24, and change your edge selections accordingly and the 'Auto Smooth' value
I'm pretty new to Blender and I had a quick go at this using a feature I learned about today "Auto Smooth".
Looking at the lampshade, it looks like it has 6 sides, so I created the UV ...
I guess somebody has to suggest a cloth simulation, although I'm not sure it will meet your specifications. The curves resulting from pinning and tension don't appear to be catenaries, until the tension is wound up to an unrealistic level.
The topology is as shown, with the selected vertex-groups pinned in the simulation:
The edges between planes have also ...
It controls whether to keep intersecting edges perpendicular to the bevel direction.
Loopslide On: gives smoother topology and better results for tight geometry
Loopslide Off: keeps perpendicular edges and even bevel width
When Clamp Overlap isn't enough, Loopslide On can keep the topology in check:
Absolutely nothing wrong with @David Wilson's answer.. this is a more Subdiv. approach..
Under 2 levels of subdivision..
On a 36 sided UV sphere, pole vertices deleted, select every sixth longitude (select 2 edges at the right spacing, CtrlShiftNupad + to progressively select the rest, then Header > Select menu > Loops > Edge loops)
CtrlB Bevel ...
As Duarte said, the Curve Modifier is probably best suited for this.
You can easily edit both the knot and the shape of your tie.
Start with a flat tie. Heavily subdivide it along it's length
Create the Windsor knot using a Bezier curve
Add a Curve modifier to your tie and target the knot
Either Blender is rather non-intuitive, or I'm missing something obvious.
The fastest way I found:
Add a bezier circle and make it non-cyclic (Alt + C)
Rotate the end vertices to form a 3/4 circle
Extrude one of the ends and complete the circle
Clamp Overlap option prevent two bevels overlap each other. Basically it clamps bevel width by the shortest distance between two beveling edges:
If disabling Clamp Overlap reveals bevels, try to remove vertexes that's close to each other.
Select all - press M ⇾ By distance may help
Its sort of unavoidable. You'll need to transition from the single edge (above) to the split/beveled edge (below) somehow.
If you want the bevel to only be on the vertical part, you can add an edge loop (highlighted) just below the current knee joint, and then select the edge below the edge loop and just bevel that. Then the 'fan' that transitions from no-...
Blender makes a distinction between CtrlB, Bevel Edges, and CtrlShiftB, Bevel Vertices.
So, use the other shortcut, or, having reached the Adjust Last Operation panel visible in your illustration, switch at the top from 'Edges' to 'Vertices'.
(In other panels, or the Bevel modifier, it might be a small checkbox - 'Only Vertices')
I didn't realize.. as @...
Add curve extra objects.
Another curve based option is to use the the catenary curve provided. It has an option to "hang" a catenary curve between two objects. Powerlines, cables, etc
Enable the add curve extra objects addon.
In demo below have two cubes at x = +/- 4. With them both selected Add Curve > Knots > Catenary
Blender comes with an add-on called Mesh:LoopTools. Enable it in the Preferences then you will see it in the N-panel (N).
Select the first 2 vertices at the beginning of the ramp and move them down to the floor along the Z-axis. Then select the vertices of the edge loop that you want to smooth. Make sure the vertice at the beginning is the active one (...
The problem is some duplicate vertices - 9 to be exact. Go to edit mode, select all, and select Mesh > Merge By Distance. A little window will pop up in the bottom left corner. Click to expand the little box, and press the arrow on the right side once until the value is 0.0101. They will be removed and the bevel will work cleanly.
EDIT - I'm glad the fix ...
You can start from plane
from bottom extruding (E) on Y axis, scale (S) and repeat process up to top.
add Subsurface Modifier
Sharp edge (Shift+E) = 1 (pink edges)
Unwrap (U) > Project from View
switch to UV Edit layout (from top row) and adjust position on image in edit mode
(if you need more smooth shape increase Modifier)
You can start from Curve ...
Another solution using vertex bevel.
Add an edge top and bottom (for now you can F a temporary face for your object, it will be deleted later)
Select the vertices that define the edges and press Ctrl + Shift + B followed by P to change the profile.
Hide everything except the bevel you just created with H
Alt + Shift select and use Bridge Edge Loops to ...
I'm not sure this is what you want but here is a try, you can use a Boolean with a closed shape (put the Boolean above the Mirror modifier, choose Solver > Fast):
Then apply the modifiers, delete the bottom face (you'll probably need to clean the topology if you plan to add bevels or use a Subdivision Surface, etc), use a Solidify modifier to give ...
Aside from @Jachym's method, you can also do something like it with a custom 2-segment profile, with the central control-point set to Vector, and clipped against one edge of the graph...
... but as you can see from the tilted cube in the illustration, it still means introducing a (bad topology) extra edge.
It would be very nice if Blender had asymmetrical ...
For the moment you can't bevel the edge because you have an inner face, the edge is common to 3 faces and therefore Blender can't guess how to bevel, once the inner face deleted, Ctrl B should work:
If you have a problem of shortcut, you can open the Preferences > Keymap and type "bevel" in the search field, then redefine the shortcuts you want ...
Start with a bezier curve.
Scale each control point to zero (S+0)
Subdivide the curve. A new control point is created. Moving the newly created control point should do what you want. You can specify precisely where to place it by using the numeric controls (Press N to enable the control region)
Or try using Nurf Surfaces.
As someone who tries to avoid booleans, as they result in irregular topology most of the time, I would do this operation with Proportional Editing
Create a few loop cuts, select the edges in the middle, enable proportional editing in Sphere Falloff mode. Then scale on one axis only (in this case, to scale only on the $Y$ axis, press S+Y) and move the mouse. ...
This is happening because you have some faces pointing inwards and some pointing outwards. You can tell by turning on Face Orientation and Face Normals in Overlays:
To fix it, select the whole thing in edit mode and then select Mesh > Normals > Recalculate Outside. You can now bevel as you wish:
You need to lower the radius in the bevel node.
If your cube is 2 units wide and the bevel radius is 1 m, it means the normals are interpolated right to the middle of each face, generating artifacts. Try the default (0.05).
Examples of the effect of the radius field :
I think I found an answer whilst playing around after reading @mma78 answer.
I can snap the 3D cursor to the bottom vertex and then bevel the edge. I can then set the Pivot point to 3D Cursor and scale the bottom vertices back in. This way the bottom is tapered while keeping the shape of the base unchanged.
While this works, it is not very efficient as I ...
The problem is definitely topology. You have a lone vertex that the bevel must eventually reach which, precisely because it's a lone vertex, and not a series of subdivided edges, will never be able to be reached (red arrow). You need a number of subdivisions at that location which matches the number of subdivisions for the row of edges to be beveled (...