Link Knot 6_3_2 took only a few minutes to add z offsets with Blend.
Used G2 Blend on longest segment, G1 on the first 3.

Apply Pipe with radius about 1.8 to thicken lines.
Change colors per taste.

From a 3D slant view, the rings look partly square.

- Brian

The 8_18 knot, a single curve.

A pipe outer radius of 1.5 units is suggested.

- Brian

Here is the 12 crossing knot, re: SVG post, slightly modified. A knot that preserves the crossings, etc, is topologically equivalent. Used the amplitude blend method.
Pipe2 used also.

A crude attempt at 3 dragon pendant, with a knot modification. Pipe2, Taper from about 4 at head, to 0.5 at tail. Blendcap, G3, Head Bulge about 4, Tail Bulge about 5.

Note that Blendcap slider appears as the Blend slider, since Blendcap uses Blend. (Used a Bulge slider mod.)
Note that the Bulge number is not restricted to the slider range. The Bulge number can be manually entered, and can be out of the slider range.

Have yet to make mouth, teeth, ears, eyes, nose, fins/wings, etc.

The heads could start at different points of the knot. The tail end was just roughtly point dragged in Top view.

- Brian

Hi Brian,

Very good information. A good source for a future project in the queue.

Thank you,
Wayne

Here is a node for a Lemniscate curve.

Also, after puzzling over how to use an arithmetic progression to duplicate the "t" parameter for parametric equations, as is often done in scripts,
incorporated in the Lemniscate node is a nodeeditor Macro, to make fractional "t" values, from 0 to 2PI.
First tried with sinewave node.

From the loaded Lemniscate node in the nodeeditor canvas,
the Macro can be right clicked, and Exported to the Appdate>nodeeditor>macros directory, for future use.

Thought I'd apply an "amplitude" Blend to the center line of the "infinity" symbol (FatLines) Lemniscate.

- Brian

I may try to modify (Max's?) FatLines script, with a separate line for the slider.

The BeanSlider is a MoI type of script, not a node. (.js and .htm)
Selecting the Blue question mark has some documentation, including creating other shapes, with numpoints set to 3, 4, 5 or 6, then running MoI command Shoe pts, and dragging them.

In 3D view, Dragging a control point to the Z access seems to require an existing geometry point there, (or e.g. line segment).


Motivation was using the shape for a Template cut away, but using offset of an arc, adding a tangent line segment, and then using Blend, produced a nice cut out completing a Scroll tracing template.

- Brian

The script can be placed in CustomUI, ...%appdata%...>commands folder. (Windows 10 or 11.

- Brian

ps, the old LimaBean.js node file seems to do fine if added to NodeEditorPlus, extensions folder. (Curves2 type of nodes.)

This script is for a "CashewNut" profile curve.

https://math.stackexchange.com/questions/4642098/parametric-curve-resembling-a-bean

It is supposed to be some sort of conformal mapping?

Control point dragging can also be done for low numpoints versions.

I will try the Bean curve from Arc curves next.

- Brian

Here is another "Bean" curve, created with 4 arcs.
The link was given previously, and is also in the .js file.
The math is simple, yet fairly intricate.
The x and y coordinates (lengths) are based upon a right triangle, with the other two angles at 45 degrees.
Radical r = square root of 2.
If the two legs of the triangle are 1, the hypotenuse is r.
If the two legs are r, the hypotenuse is 2.
Pointpicker is used to pick local origin in desired View.
This version moved the cPlane origin from point "O" to point S, which is on the largest arc.
This required adjusting the math for each point.
Point S is offset from point O.
3 point arc factory was used, because center arc factory does not always draw the arc on the desired side.
The center arc factory seems to work "counter clockwise", but as the points move around, some arcs may be on the "wrong" side.
Coordinate Frames, and Local coordinates versus World coordinates are now slightly less confusing.
I was thinking of doing an essay on Coordinate Frames. MoI5beta API, and numerous past posts on the forum were helpful.
Help from Michael from past years was utilized, and Max script techniques were also helpful.
Added some reset pushbuttons.
This version may be considered an "alpha".
It seems to work in MoI4 and MoI5beta.
There is brief documentation by using the Blue ? button.

- Brian

Added an angle rotate parameter and slider to the Bean3ptArc script. (Bean3ptArcR)

Description of scroll spiral template

The scroll TEMPLATE has a red spiral, which has been cut into segments with eraser script. These gaps represent support TABS for the template. (The red curved segments are not quite arcs, but close.) The six blue regions approximate cutouts which enable pencil tracing of the scroll template, onto a block of wood. The desire is to replace the six blue cutouts with more precise curves. On the top right is a Bean arc curve, rotated and sized, into position. (An angle rotate slider was added to the BeanArc script.)
( Script Sliders do not do a smooth or good enough placement. A bit crude. ) On the top left is the remains of a bean curve, cut out by the cyan circle. It matches a portion of the blue curve fairly well. The black piece of bean curve is a much better match than an offset of the red curve. The two green line segments are perpendicular to the scroll spiral segment, and are Blended with the black bean segment, forming the orange curves. The orange/green corner could be filleted a little. A join of the red, orange, black, and orange segments, is one of the desired cutouts.



- Brian