Rhino 7 has rhino.inside python package, to Embed Rhino in CPython.

Anticipated workflow:
Integration domain of a curve network was easily created in MoI.
Lineweb-like script creates arrayed points of the curves.
Transfer the network .3dm to Rhino 7, (or the points).
Rhino 7 provides the geometry, (complex number 2D points), of curves in a network of Nurbs curves.
Rhino cmath and scipy apply a transformation to the points for each curve, and saves the interpcurves in a new Nurbs network.3dm.

Open the network.3dm and apply MoI Network command, to create a surface. Perform further surface geometry operations in MoI.

Javascript 2009, ES5 does not have any complex number math, and has limited number of decimals. Attempts to create javascript cPlex complex number math from mathJS has not been accomplished. arcsin(complex_number) does not work. Log(w) is weird. No idea if elliptic integral will work, or if ES5 has enough accuracy...
I doubt that if ES6+ were added to MoI version 5 that ES6+ would be much better with the math than ES5?

I'm 99% ignorant of Rhino7, and Python, but imagine the Rhino geometry commands would correspond analogously to MoI scripts...

Is there any possiblility of using cPython with MoI?
Or "embedding" MoI inside cPython?

Or I could export the 2D Points from MoI, to cPython, produce the new points, and import the new points into MoI?

- Brian
-Spring is comming.

http://moi3d.com/forum/lmessages.php?webtag=MOI&msg=3341.1

Dave did some really cool stuff. Left us before fruition....

Thank you Burr.
His first link ...[EDIT] is dead/hyjacked.... And some other links (His URL) also. Maybe Michael would want to delete it? The fate of "abandoned?" web sites?
I wish he had posted his code...But he left some clues. I have no such skills.

Nothing since 6/4/2016...

- Brian

Hi Brian,

re:
> Is there any possiblility of using cPython with MoI?
> Or "embedding" MoI inside cPython?

Not that I'm aware of myself, I don't know what method Dave was using. I don't know very much about the python runtime environment myself though.


> Or I could export the 2D Points from MoI, to cPython, produce the new points, and import the new points into MoI?

There is ImportPointFile and SavePointFile:
http://kyticka.webzdarma.cz/3d/moi/#ImportPointFile
http://kyticka.webzdarma.cz/3d/moi/#SavePointFile

- Michael

Hi Michael,

Thank you for your help.

I think I'll have another go at ES5/cPlex, and investigate importing saved points into Python.

- Brian

Hi Brian,
Yeah, i should have pointed stuff like that out. He left and dropped what he was doing with the moi community.

His work and documentation for it ended up on github. That is here:

https://github.com/davidmorrill/facets

When he started here, he called it "traits".

Its fruition was named "facets".

He programmed MoI with Python using this and that's why i posted the answer to you "yes, it can be done"....

But you have to know how to do it. I can't tell you and Dave is not here to tell us either...

Anyway.....

Thanks Burr.

Maybe his site is on wayback machine?
I may have looked at his site many years ago...

- Brian

This morning, I re-read Dave Morrill's posts about External Scripting Interface for MoI, written in Python (Traits/Facets), creating Javascript code to perform MoI commands.

It seems that Nodeeditor performs these tasks, without Python.

Now all that is needed is to write part of Nodeeditor in Python ??? Somehow?
Allowing Nodeeditor to access the Python cMath/ NumPy and sciPy functions.

- Brian

Using Nodeeditor and Python to process points from MoI

The purpose of these outline notes is to apply Python complex number math functions to the x and y coordinates of 2d, or 3d, points in the MoI top view. In this case, the z coordinates of the points are either ignored, or zero, but may be used in some other situation. The z value is included for future flexibility. The x values are real, and the y values are real, but are treated as imaginary. Complex number z = x + i*y.

Initial MoI geometry is a network, IntegrationDomain, of a score or so planar curves in the xy plane. Nodeeditor will be used. A new node, which incorporates modified LineWeb style code, will be used to array numerous points on each successive curve. A new node, SavePoint4.js, modeled on the MoI SavePoint script, will export the point coordinates to a CSV1 style text file, with a certain delimiter. The CSV1 file will have a typical CSV format. Each line is a list of 3 coordinates, and curveIndex, for one point. Format: x, y, z, cIdx where x, y, and z are real numbers, and cIdx is an integer which indexes each parent curve, and the new curves to be created later.

Next, in a separate Python program, ComplexTransformMap.py, will import the CSV1 file. Complex number functions in cMath, NumPy, and SciPy will be used.
For each curve index, the x and y values will be converted to the complex number class, essentially an (x, y) pair representing the complex number x + i*y. The appropriate complex number math will be applied to each (x, y) to create a new 3d point, (X, Y, Z, cIdx). Python will then Save (output) all of the (X, Y, Z, cIdx) points to a new CSV2 file, PatchPointNetwork, consisting of the same number of network curves to be created from the new points.

Next, in a separate node program, PatchProcessor, will import CSV2, with node CSV_File4, based upon Karstens Import/CSV_File node, converting the (X, Y, Z) points with matching curve index, into a new curve. All of the new curves will be a new network of curves, PatchNetwork. MoI Network command will be applied, to generate a surface Patch. Then Mirror and Symmetry operations are applied to the surface Patch, to generate the final result.

The hardest part is learning enough Python to write a short Python program.
Google search of "python csv import" yields lots of hits, as does "python csv export".

- Brian

_SavePointNetwork.js script, by Brian E. McMillin, February 2021

This script outputs a CSV style text file containing four fields,
[x, y, z, curveIndex], with "comma" or other delimiter. (No []).
Each row contains the point coordinates for one point on the associated indexed parent curve.
The parent curve entries are also in order.
The values of x, y, and z are real numbers, and iCrv = crvIndex is a positive integer, which could include 0.

Input to the _SavePointNetwork script is a set of curves.
The curves could be in a network representing a surface.
For each sequential curve, a startpoint is arrayed on the curve,
to create numPts number of points, in order, for that curve.

Credits:
Michael's scripts Lineweb, SavePointFile (non-ActiveX version). (Grafted together)

Several hours were spent on an incomplete node version.
This script turned out to be fairly easy and simple, after much effort extracting and comparing parts of the credit scripts.

Yet to be done:
A companion script would be ImportPointNetwork, which does the reverse.
ImportPointFile + Karstens Import/ CSV_File node.

Testing has been very limited...

Python import CSV, Bonnet transformation, and export CSV.

Also attached is the network of curves which is the integration domain.
(This networks represents the Complex number plane, and the points complex numbers.)
The network density could be increased or decreased.
It is associated with bonnet angle in radians of 0.66348297051143481, which is an angle of about 38.0147...~ degrees.

- Brian

To utilize the script, place the .js and .htm files in the command folder of MoI. In my case this is the "additional non-stock script" command folder in AppData.
The _ prefix can be removed, or left in for usage with CustomUI.

The script could be modified to not output the z coordinate.
- Brian

_ImportPointNetwork.js script, by Brian E. McMillin, February 2021

This script inputs a CSV style text file containing four fields,
[x, y, z, curveIndex], with "comma" or other delimiter.
The [] are NOT used in the file.

A three fields version for 2D points, [x, y, curveIndex], was NOT implemented,
due to possible confusion with CSV files without curveIndex.
curveIndex is a positive integer, which could include 0.
Each set of points has a different curveIndex = iCrv.

If the option to form Polyline(s) or ControlPts curve(s) or InterpcurvePts curve(s) is chosen,
then a different Curve is formed for each different iCrv.

Each row contains the point coordinates for one point, plus the curve index.
Rows for a set of points (with same curve index) need to be together, in order.
Companion script is _SavePointNetwork, which could be used to make a quick test file. One 3 curve test file is included in the zip.
It is anticipated that _SavePointNetwork is used to send the point CSV to a third party program, for processing.
The third party program would then export new X,Y,Z,curveIndex points, to be Imported back into MoI, as one of the 3 curve types.
Points could also be the result, but would be a cloud.

Credits:
Michael's scrip ImportPointFile was modified to create different curves.

The script has received only limited testing.
I had a lot of trouble getting the script to work, due to poor programming skills.
The last for loop had to have = instead of <, for some unknown reason, to plot the first point set.
.shift() was used instead of .pop().

No telling what the results would be for a weirdly formatted CSV file...

- Brian

A python program typed into Notepad++ can be run from the Notepad++ screen, with the run key. (Windows 10).
Windows environmental variable (proper path) has to be set up, and the proper command entered into the run window of Notepad++.
The youtube video https://youtu.be/yxTbSTrCn6I explains the requirements, after watching several times.
My notepad++ run entry is C:\XXXX\orcha\AppData\Local\Programs\Python\Python39\python.exe -i "$(FULL_CURRENT_PATH)"
Be sure to include a space before, and also after the -i.
The XXXXX entry is to be replaced with the users "username".
I'll post my python csv import (from MoI savepointnetwork script) and also python csv export (to MoI importpointnetwork script) when completed.
Rudimentary Python scripts do not seem too hard. The worst thing is there are numerous alternate ways to handle csv import, and 3 alternate data structures,
list or array or nparray.

- Brian

Finally got Python paths straightened out, and installed numpy, scipy, and pandas with pip. It is fairly easy, but everything has to be just right, or nothing works.
There are too many permutations and alternatives...

After many challenges, finally was able to Read a CSV text file of point coordinates with Pandas, into a pandas DataFrame(), a type of super Deluxe "array" in Python.
It only took 3 lines of code, but I searched a couple of hundred example lines of code...

A superb link: https://datascienceparichay.com/article/read-csv-files-using-pandas-with-examples/

The math should not be too hard.
Re save to X,Y,Z,curveindex should be fairly easy.

- Brian

After an ordeal of a few days of google web surfing scores of websites, and study of Python and Pandas, I was finally able to get a MoI SavePointNetwork.csv imported into Python 3.9.1.
A grand total of 4 lines of code! So many permutations do not work, and there have been version changes also.

The path will need to be modified to the individuals folder structure. Change orcha to your username. Remove OneDrive folder from path, if it is not used.
Place the gDomain.csv file created from MoI into your Desktop folder. The r needs to stay. The plural and singular names must stay the same. # HashTags are comment lines, like Javascript //
Open Python 3.9.1 from Windows 10 start menu.
Paste in the above code, and hit return, to see the pandas Data Frame, which looks like an excel spreadsheet.
Hit return again, to see the data types of the numbers.
The .csv numbers are text strings.
The Data Frame point coordinates are np.float64, and the cIndex is np.int64. (Javascript numbers are also all 64 bit.)
The row index column on the left, and the column names are not essential, but will be used to access the coordinates.

Attached is a truncated gDomain.csv for testing purposes. It has 10 points for each of 3 parent MoI curves.

- Brian

(Running python code in Notepad++ worked in a super simple case, but does not work in general.)

Success, (pending confirmation of surface created), at creating new surface point network, .csv, and importing the network of curve points back in to MoI interpcurve. MoI>Network>gSurface looks nice. Now to clean up the code...and get the project all together.
There are so many setting possibilities--myriad...
Sill need to apply MoI symmetry and mirror operations...
This python script runs in Python 3.9.1.
Input gDomain.CSV is in Desktop. Output gPatch.CSV is now also in the Desktop.
Plan on doing a denser input mesh of curves...

#gNetP1.py, from gDomain.csv, create gNetP1.csv

import numpy as np
import pandas as pd
import csv
from mpmath import *
mp.dps = 25 #; mp.pretty = True
aScale = 1
#K = 1.68575035481259604287120365779
K = ellipk(0.25)
#Kp = 2.1565156474996432354386749988
Kp = ellipk(0.75)
Kpp = (K*K + Kp*Kp)
#theta = 0.6634829705114348080575689, Bonnet angle, radians, ~38.0147739891°
theta = acot(Kp/K)
kappa = aScale*mp.sqrt(Kpp)/(K*Kp) # normalization constant
EiTheta = complex(mp.cos(theta),mp.sin(theta))
sqrt2 = mp.sqrt(2)
twoSqrt2 = 2 * sqrt2
mod97 = (97+0.24484) - 56 * mp.sqrt(3)
zeta = 1/sqrt2
eta = aScale/4
# Import csv coordinate values and curveIndex
# MODIFY orcha to <username>, and use your gDomain.csv:
csvInPath = r"C:\Users\orcha\OneDrive\Desktop\gDomain.csv"
columns = ['xCol', 'yCol', 'zCol', 'cIndex'] #names of columns
dtypes = {'xCol': np.float64, 'yCol': np.float64, 'zCol': np.float64, 'cIndex': np.int64} #dictionary
gDomain_df = pd.read_csv(csvInPath, header=None, names=columns, dtype=dtypes)

# Setup output gNetP1.csv.
with open('C:\\Users\\orcha\\OneDrive\\Desktop\\gNetP1.csv', "w", newline="" ) as f:
  writer = csv.writer(f)
  for i in range(0, len(gDomain_df)):
    x = gDomain_df.at[i, 'xCol']
    y = gDomain_df.at[i, 'yCol']
    cIdx = gDomain_df.at[i, 'cIndex']
    w = complex(x, y)
    ww = w * w
    wwww = ww * ww
    ww4 =  ww * 4   
    numer1 = w * twoSqrt2
    denom3 = wwww + 1			
    denom1 = mp.sqrt(denom3 + ww4)
    quotientX = (numer1 / denom1)
    quotientY = (((-1)*numer1) / denom1)
    quotientZ = (ww4 / denom3)    
    as1 = asin(quotientX)
    as2 = asin(quotientY)
    as3 = asin(quotientZ)
    myf1 = (ellipf(as1, 0.25))/twoSqrt2
    myf2 = (ellipf(as2, 0.75))/twoSqrt2
    myf3 = (ellipf(as3, mod97))/4
    x1 = kappa*((EiTheta * myf1).real)
    y1 = kappa*((EiTheta * myf2).imag)
    z1 = kappa*((EiTheta * myf3).real)   
    X = float(nstr((-zeta*x1 - zeta*y1), 17, min_fixed=0, max_fixed=0))
    Y = float(nstr((-zeta*x1 + zeta*y1 + 2*eta), 17, min_fixed=0, max_fixed=0))
    Z = float(nstr((z1 + 3*eta), 17, min_fixed=0, max_fixed=0))
    writer.writerow([X, Y, Z, cIdx])

- Brian
Revised 3/2/2021, uses Desktop for location of files.

# gPatch.py is a Python program to create a gyroid surface point network, from a CSV file from MoI.

# Data flow:
# wDomainG.3dm surface curve network is created in MoI.
# wDomainG.3dm > gDomain.csv, (point coordinates), via MoI SavePointNetwork script.
# gDomain.csv > gDomain_df, via gPatch.py program, using Python pandas.
# gDomain_df > gPatch.csv, via gPatch.py program.
# gPatch.csv > gPatchNetwork.3dm, via MoI ImportPointNetwork script, to form a curve network.
# gPatchNetwork.3dm > gPatchSurface > gyroid, with MoI.

# Data structures:

# gDomain.csv, a TEXT file with one [x, y, z, curveIndex] row per point, with no Header row, and no rowIndex. (All elements of any csv file are text.) (The delimiter is a comma.)
# For this particular project, the z values are all zero, and are not needed, and also the x,y points represent the complex number (x + yj).

# gDomain_df, a pandas data frame. Header is (x, y, z, cIndex), rowIndex is a column of integers. x, y, and z are float64. cIndex is int64. (cIndex denotes which curve a point is on.)

# The gPatch.py program calculates the (new) X, Y, and Z, float64 coordinate values.
# gPatch.csv, a TEXT file with one [X, Y, Z, curveIndex] row per point, no Header row, no rowIndex.
# The imported text numbers become Javascript numbers, which are the same as numpy float64.

# Overview of gPatch.py program:
# Ignoring z, each x, y, z, and cIndex element in gDomain_df is processed in turn. Coordinate (x,y) is converted into a complex number "w". Certain complex number math equations are applied to "w" to yield real number values for new surface coordinates (X,Y,Z), for each cIndex. Each [X, Y, Z, cIndex] list is saved to a row of gPatch.csv.

# MoI script ImportPointNetwork.js is used to import the new surface point coordinates, and iCrv, from the gPatch.csv text file. The ImportPointNetwork option to create Interpcurves should be used. The new curves form a network of curves. MoI Network command should then be used to create the fundamental gPatchSurface. Next various MoI commands Mirror and Rotate can be used to create the GYROID UNIT, and then the cubical gyroid unit cell. Join or Boolean...

# Superb links using Iris.csv data, a 1937 flower database:
# https://datascienceparichay.com/article/read-csv-files-using-pandas-with-examples/
# https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_csv.html
# https://songthamtung.medium.com/pandas-csv-cheatsheet-f88abecbe289

Credits:
The complex mathematics for the Python script is based upon three papers by Paul J.F. Gandy, and Jacek Klinowski:

"Exact computation of the triply periodic G ('Gyroid') minimal surface," (& D & P), available at:
https://dokumen.tips/download/link/exact-computation-of-the-triply-periodic-g-gyroid-minimal-surface

https://www.researchgate.net/publication/234138905_Exact_computation_of_the_triply_periodic_D_'diamond'_minimal_surface

https://www.researchgate.net/publication/223147236_Exact_computation_of_the_triply_periodic_Schwarz_P_minimal_surface

(The papers are very similar, and complement each other, but do have some inconsistency errors/ typo's, and some elements that are not entirely understood.)

Symmetry operations will be done in MoI.
Next, the input domains for the D_diamond and Schwarz_P surface will be processed.

- Brian

Low density .3dm of the patch attached. Just perform MoI Network on it...

It has been a few months since I studied the symmetry (mirror) planes, and rotational axi...must review.

Corrected error in code.
Not at all clear where the symmetry planes and rotation axi are, so:
Running the script 12 times, with zeta and eta equations modified, produces all 12 patches.
Should modify the script to run once, and write all 12 csv files.
Or figure out symmetry and rotation, maybe in a node...

Increased density of input domain to 41 curves, 100 points per curve.
Running one patch, 4100 points, only takes a few seconds.

- Brian

Eventually will try to open MoI4 from Python, and pass output 3D CSV and run ImportPointNetwork???

Over a 1cm scale:
12 patches almost fit in a unit cube, but not quite.
Pairs of patches, e.g. netP1 and netP2 join up well, with horn to horn distance of 1cm, but the two vertices are off from the corners of the unit cube by ~0.0167468cm.
After line_line these two vertices, the 3rd vertex is about .023733cm short of the center of the cube.
Patch(P1+P2) does not quite adjoin patch(P3+p4), etc.
Will check number of decimals of point coordinates tomorrow.
- Brian