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Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March...

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Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS
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Page 1: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Vladimir Bulatov,

Shapeways

G4G12March 31,2016

Making Fractal Pendant in ShapeJS

Page 2: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Good Old Times

BASIC code for Mandelbrot set fractal2000 REM Initialize the color palette2030 LET L = 1002040 FOR I = 0 TO 1002050 FOR J = 0 TO 1002060 LET U = I / 50 - 1.52070 LET V = J / 50 - 12080 LET X = U2090 LET Y = V2100 LET N = 02120 LET R = X * X2130 LET Q = Y * Y2140 IF R + Q > 4 OR N >= L THEN GOTO 21902150 LET Y = 2 * X * Y + V2160 LET X = R - Q + U2170 LET N = N + 12180 GOTO 21202200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]2210 PLOT I, J, C 2220 NEXT J2230 NEXT I2240 END

Page 3: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Modern Times

ShapeJS web based IDE

Page 4: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

a torus

function main(args) { w = 12*MM; Rout = 5*MM; Rin = 2*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}

Simple shape

Page 5: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

larger torus

function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}

Simple shape

Page 6: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

fatter torus

function main(args) { w = 12*MM; Rout = 5*MM; Rin = 5*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}

Simple shape

Page 7: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

tilted torus

function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; axis = new Vector3d(-1,0,1); bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout, axis); scene = new Scene(shape,bounds); return scene;}

Simple shape

Page 8: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

twisted torus

function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; axis = new Vector3d(-1,-1,1); bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout, axis); scene = new Scene(shape,bounds); return scene;}

Not much fun

Simple shape

Page 9: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Torus and mirror

Torus + Mirror

Page 10: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Torus and it's siamese twin

Torus + Mirror

Page 11: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Moving original torus.

It's twin moves in opposite direction

Torus + Mirror

Page 12: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Tilting original torus.

It's twin tilts in opposite direction

Torus + Mirror

Page 13: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Going wild - 2 mirrors

Torus + 2 Mirrors

Page 14: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

family of quadruplets

Torus + 2 Mirrors

Page 15: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Motion of original torus moves all siblings

Torus + 2 Mirrors

Page 16: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Changing mirror angle makes larger family

Torus + 2 Mirrors

Page 17: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Changing mirror angle makes larger family

Torus + 2 Mirrors

Page 18: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Changing mirror angle makes larger family

Torus + 2 Mirrors

Page 19: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Moving one family member changes the lookof the whole family

Torus + 2 Mirrors

Page 20: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Moving one family member changes the lookof the whole family

Torus + 2 Mirrors

Page 21: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Going insane!

Using 3 mirrors

Torus + 3 Mirrors

Page 22: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Got infinite family.

But the family is rather orderly and boring

Torus + 3 Mirrors

Page 23: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Got infinite family.

But the family is rather orderly and boring

Very predictable

Torus + 3 Mirrors

Page 24: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Twisting one sibling makes all family do thesame

Torus + 3 Mirrors

Page 25: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Another family made with 3 different mirrors

Torus + 3 Mirrors

Page 26: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Another family made with 3 different mirrors

There are only 3 such families

3, 3, 3

2, 3, 6

2,

4,4

Torus + 3 Mirrors

Page 27: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Can we do better with 4 mirrors?

Torus + 4 Mirrors

Page 28: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

4 mirrors

boring

Torus + 4 Mirrors

Page 29: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

4 mirrors

boring

BORING

Torus + 4 Mirrors

Page 30: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

4 mirrors

boring

BORING

BORING

Torus + 4 Mirrors

Page 31: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

4 mirrors

boring

BORING

BORING

BORING

Torus + 4 Mirrors

Page 32: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Magical spherical mirrors!

Spherical Mirrors

Page 33: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Magical spherical mirrors!

Spherical Mirrors

Page 34: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Magical spherical mirrors!

Spherical Mirrors

Page 35: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Reflection in 2 flat mirrors produce familiarresult

Spherical Mirrors

Page 36: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Addition of 3rd spherical mirror givessomething new

Spherical Mirrors

Page 37: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Addition of 3rd spherical mirror givessomething new

Spherical Mirrors

Page 38: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

All 4 mirrors make shape with fractal boundary

Spherical Mirrors

Page 39: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 40: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 41: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 42: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 43: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 44: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Deformation of mirrors arrangement makesnon trivial change of shape

Spherical Mirrors

Page 45: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

The shape is three dimensional

3D view

Page 46: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

The shape is three dimensional

3D view

Page 47: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

The shape is three dimensional

3D view

Page 48: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

The shape is three dimensional

3D view

Page 49: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 50: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 51: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 52: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 53: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 54: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 55: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 56: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 57: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 58: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 59: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 60: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 61: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 62: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 63: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 64: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 65: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 66: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 67: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 68: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Samples

Page 69: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Final choice for pendant

Page 70: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Fractal boundary is too thin to print

It needs to be "thickened"

Geometry of pendant

Page 71: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Fractal boundary is too thin to print

It needs to be "thickened"

Thickening of boundary

Page 72: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Fractal boundary is too thin to print

It needs to be "thickened"

Thickening of boundary

Page 73: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Fractal boundary is too thin to print

It needs to be "thickened"

Thickening of boundary

Page 74: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Fractal boundary is too thin to print

It needs to be "thickened"

Thickening of boundary

Page 75: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

3D print needs 3D mesh file

Conversion into Mesh

Page 76: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

Bundling 10 pendants in group reducesmaniufacturing cost

Maling a Bundle

Page 77: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set

ShapeJS summary

simple to code (javascript)

volumetric modeling via signed distance function

real time server side 3D rendering

compatible with any device which can run web browser

3D print compatible models

easy model sharing

intellectual property protection

We are actively extending the system by adding new capabilities.

Suggestions are very welcome!


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