[User]
I want to create a parametric puzzle generator using OpenSCAD. I need it to produce puzzles with interlocking pieces, and I want to be able to control various aspects of the puzzle through parameters.

Specifically, I need to be able to adjust:

*   **`piecesize`**: The average size of a single piece, in millimeters. This should let me define the scale of the puzzle.
*   **`rows`**:  The number of rows of pieces in the puzzle.
*   **`columns`**: The number of columns of pieces in the puzzle.
*   **`thickness`**: The thickness of the puzzle pieces in millimeters.
*  **`bezwidth`**:  The space between the pieces, also in millimeters. This represents how tight the fit is.

I also need to be able to control the shape of the interlocks (the nubs and legs). I need parameters for this, but I also want a little variation between pieces so they don't look too uniform. The existing code uses Bezier curves to define the shape, so the parameters need to control the shape of those curves. The current parameters include:

* **Nub Parameters** (all based on `piecesize`):
    *   **`bezaw`**, **`bezah`**: The start/end point of the nub.
    *   **`bezbw`**, **`bezbh`**: The narrow part of the nub.
    *   **`bezcw`**, **`bezch`**: The wide part of the nub.
    *   **`bezdw`**, **`bezdh`**: The top of the nub.

* **Leg Parameters** (also based on `piecesize`):
    *   **`bezlegax`**, **`bezlegay`**: Start of leg.
    *   **`bezlegbx`**, **`bezlegby`**: First control point of the leg
    *   **`bezlegcx`**, **`bezlegcy`**: Second control point of the leg.
    *  **`bezlegdx`**, **`bezlegdy`**: The end of the leg.
    * **`bezlegex`**, **`bezlegey`**: Another control point to help smooth the transition

*   **`stdev`**: A standard deviation for the random variation of the nub shape. This controls the amount of variation.
*    **`mean`**: the mean to use when varying pieces

I also need to use the Bezier curve library from thing:86713 in order to create the curved interlocks; specifically, I need the `BezWall` module which takes a list of control points and creates a wall based on it, and supporting functions like `PointAlongBez`, `PerpAlongBez`, and `hodograph`.

The final puzzle should be created using `difference()` operations to cut the interlocks out of a rectangular prism. The program should generate a new and different puzzle each time it is run using `rands()`.

Essentially, I need a program similar to what I've described that generates a flat 2D puzzle with nubs and legs on the edges of the pieces and uses `rands()` to create random variations between the pieces. I should be able to control all these pieces with parameters, too.

[Assistant]
PuzzleGeneratorV2.scad:
```
// Average piece size in mm
piecesize=25; // [10:50]
// How many rows of pieces
rows=3; // [2:10]
// How many columns of pieces
columns=3; // [2:10]
// Piece thickness in mm
thickness=5; // [1:100]
// Space between pieces in mm
bezwidth=0.2;

/* [Hidden] */
// Determine puzzle width
cubex=piecesize*columns;
// Determine puzzle height
cubey=piecesize*rows;
// Make sure cuts all the way through puzzle
bezheight=thickness+1;
// Resolution, higher=better quality,more time to render
bezsteps=20;

// These variable control the nub of the piece
// beza is the start and end point of the nub
bezaw=0.28*piecesize;
bezah=0.0*piecesize;
// bezb is the narrow part of the nub
bezbw=0.72*piecesize;
bezbh=0.08*piecesize;
// bezc is the wide part of the nub
bezcw=0.12*piecesize;
bezch=0.12*piecesize;
// bezd is the top of the nub
bezdw=0*piecesize;
bezdh=0.54*piecesize;

// These variable control the legs of the piece
bezlegax=0*piecesize;
bezlegay=0*piecesize;
bezlegbx=0.1*piecesize;
bezlegby=-0.04*piecesize;
bezlegcx=0.2*piecesize;
bezlegcy=-0.04*piecesize;
bezlegdx=0.24*piecesize;
bezlegdy=0*piecesize;
bezlegex=0.28*piecesize;
bezlegey=0*piecesize;

// variables that control how much variation is in the pieces
stdev=0.006*piecesize;
mean=1;

// creating a normal distribution for nub variability
function sd(stdev,mean)=(rands(-1,1,1)[0]+rands(-1,1,1)[0]+rands(-1,1,1)[0])*stdev+mean;

// module to creat nub
module nub(xpos,ypos,piecesizex,piecesizey,bezwidth,bezheight,bezsteps,bezaw,
    bezah,bezbw,bezbh,bezcw,bezch,bezdw,bezdh,signx,signy,flipx,flipy) {
  BezWall( [
    [xpos+flipx*bezaw, (ypos+flipy*bezah)], // A-L
    [xpos+sd(stdev,mean)*flipx*bezbw, (ypos+sd(stdev,mean)*flipy*bezbh)], // B-L
    [xpos+sd(stdev,mean)*flipx*bezcw, (ypos+sd(stdev,mean)*flipy*bezch)], // C-L
    [xpos+sd(stdev,mean)*flipx*bezdw, (ypos+sd(stdev,mean)*flipy*bezdh)], // D-L
    [xpos+piecesizex+sd(stdev,mean)*flipx*(signx*bezdw), ypos+piecesizey+sd(stdev,mean)*flipy*(signy*bezdh)], // D-R
    [xpos+piecesizex+sd(stdev,mean)*flipx*(signx*bezcw), ypos+piecesizey+sd(stdev,mean)*flipy*(signy*bezch)], // C-R
    [xpos+piecesizex+sd(stdev,mean)*flipx*(signx*bezbw), ypos+piecesizey+sd(stdev,mean)*flipy*(signy*bezbh)], // B-R
    [xpos+piecesizex+flipx*(signx*bezaw), ypos+piecesizey+flipy*(signy*bezah)], // A-R
  ] , width = bezwidth, height = bezheight, steps = bezsteps, centered = true );
}

// module to create nub legs
module legs(xpos,ypos,piecesizex,piecesizey,bezwidth,bezheight,bezsteps,
    bezlegax,bezlegbx,bezlegcx,bezlegdx,bezlegex,bezlegay,bezlegby,bezlegcy,
    bezlegdy,bezlegey,left,right,flipx,flipy) {
  BezWall( [
    [xpos+piecesizex+flipx*(left*bezlegax), ypos+piecesizey+flipy*(right*bezlegay)], //
    [xpos+piecesizex+sd(stdev,mean)*flipx*(left*bezlegbx), ypos+piecesizey+sd(stdev,mean)*flipy*(right*bezlegby)], //
    [xpos+piecesizex+sd(stdev,mean)*flipx*(left*bezlegcx), ypos+piecesizey+sd(stdev,mean)*flipy*(right*bezlegcy)], //
    [xpos+piecesizex+flipx*(left*bezlegdx), ypos+piecesizey+flipy*(right*bezlegdy)], //
    [xpos+piecesizex+flipx*(left*bezlegex), ypos+piecesizey+flipy*(right*bezlegey)], //
  ] , width = bezwidth, height = bezheight, steps = bezsteps, centered = true );
  // this cylinder is added to help make a smooth connection between legs and nub
  translate([xpos+bezlegex,ypos+bezlegey,-0.5]) cylinder(r=bezwidth/2,
     h=bezheight);
}

difference() {
  // create puzzle to be cut
  cube(size=[cubex, cubey, .01]);

  // can also use an stl, be sure to set your puzzle piece size and col/rows so they match up
  // translate([14.959,15.481,0.001]) import("L3RightPanelPuzIn.stl");
  // In case your stl has holes and needs a backer board
  // union() {
  //   translate([0.501,0.501,0.001]) cube(size=[28.916, 29.960, 0.6]);
  //   translate([14.709,16.131,0.002]) import("L3RightPanel.stl");
  // }

  // cut the rows
  for (xpos=[0:piecesize:cubex-piecesize],
    ypos = [piecesize:piecesize:cubey-piecesize])
  {
      // flip nub up or down
	  assign (flipy= rands(-1,1,1)[0]>0 ? 1 : -1)
      {
	    nub(xpos,ypos,piecesize,0,bezwidth,bezheight,bezsteps,bezaw,bezah,bezbw,
           bezbh,bezcw,bezch,bezdw,bezdh,-1,1,1,flipy);

        legs(xpos,ypos,0,0,bezwidth,bezheight,bezsteps,bezlegax,bezlegbx,bezlegcx,
          bezlegdx,bezlegex,bezlegay,bezlegby,bezlegcy,bezlegdy,bezlegey,1,1,1,flipy);

        legs(xpos,ypos,piecesize,0,bezwidth,bezheight,bezsteps,bezlegex,bezlegdx,
          bezlegcx,bezlegbx,bezlegax,bezlegey,bezlegdy,bezlegcy,bezlegby,
          bezlegay,-1,1,1,flipy);
	  }
  }

  // cut the columns
  for (xpos = [piecesize:piecesize:cubex-piecesize],
         ypos = [0:piecesize:cubey-piecesize])
  {
	  assign (flipx= rands(-1,1,1)[0]>0 ? 1 : -1)
      {
        nub(xpos,ypos,0,piecesize,bezwidth,bezheight,bezsteps,bezah,bezaw,bezbh,
          bezbw,bezch,bezcw,bezdh,bezdw,1,-1,flipx,1);

        legs(xpos,ypos,0,0,bezwidth,bezheight,bezsteps,bezlegay,bezlegby,bezlegcy,
          bezlegdy,bezlegey,bezlegax,bezlegbx,bezlegcx,bezlegdx,bezlegex,1,1,flipx,1);

        legs(xpos,ypos,0,piecesize,bezwidth,bezheight,bezsteps,bezlegay,bezlegby,
          bezlegcy,bezlegdy,bezlegey,bezlegax,bezlegbx,bezlegcx,bezlegdx,
          bezlegex,1,-1,flipx,1);
	  }
  }
}
// End of puzzle cut program

// ***************************************************
// For customizer to work I had to include a portion of this library from ckirby thing 86713

/*
  Bezier functions for OpenScad
  Generated from BezierScad.coffee from darwin at Fri May 10 2013 22:59:02 GMT-0700 (PDT)
  Supports Bezier interpolation with 1-8 controls
  Sources/Inspirations:
    http://en.wikipedia.org/wiki/Bézier_curve
    http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/Bezier/bezier-der.html
    http://www.thingiverse.com/thing:8443

Copyright (c) 2013 Chad Kirby

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/

module BezWall(
  ctlPts,
  width = 1,
  height = 1,
  steps = 16,
  widthCtls = [],
  heightCtls = [],
  centered = false,
  showCtlR = 1
) {
  hodoPts = hodograph(ctlPts);
  if (showCtlR > 0) {
    for (pt = ctlPts) {
      % translate([pt[0], pt[1], 0]) circle(showCtlR);
    }
  }
  triangles = [ [0,2,1], [0,3,2], [0,4,5], [0,1,4], [0,6,3], [0,5,6], [4,6,5], [4,7,6], [1,2,7], [1,7,4], [2,3,6], [2,6,7], ];
  for(step = [steps-1 : 1])
  {
    assign(
      t1 = step/(steps-1),
      t0 = (step-1)/(steps-1)
    ) {
    assign(
      hgt0 = len(heightCtls) > 0 ? BezI(t0, heightCtls) : height,
      hgt1 = len(heightCtls) > 0 ? BezI(t1, heightCtls) : height,
      wid0 = len(widthCtls) > 0 ? BezI(t0, widthCtls) : width,
      wid1 = len(widthCtls) > 0 ? BezI(t1, widthCtls) : width
    ) {
      if (centered) {
        assign(
          p0 = PerpAlongBez(t0, ctlPts, dist = -wid0/2, hodograph = hodoPts),
          p1 = PerpAlongBez(t0, ctlPts, dist = wid0/2, hodograph = hodoPts),
          p4 = PerpAlongBez(t1, ctlPts, dist = wid1/2, hodograph = hodoPts),
          p5 = PerpAlongBez(t1, ctlPts, dist = -wid1/2, hodograph = hodoPts)
        ) {
          if (hgt0 == 0 && hgt1 == 0 ) {
            polygon([ p5, p0, p1, p4 ]);
          } else if (hgt0 == hgt1) {
            linear_extrude(height = hgt0, convexity = 2) polygon([ p5, p0, p1, p4 ]);
          } else {
            polyhedron(
              points =[
                [p0[0],p0[1],0], // 0
                [p1[0],p1[1],0], // 1
                [p1[0],p1[1],hgt0], // 2
                [p0[0],p0[1],hgt0], // 3
                [p4[0],p4[1],0], // 4
                [p5[0],p5[1],0], // 5
                [p5[0],p5[1],hgt1], // 6
                [p4[0],p4[1],hgt1], // 7
              ],
              triangles = triangles,
              convexity = 2
            );
          }
        }
      } else {
        assign(
          p0 = PointAlongBez(t0, ctlPts),
          p1 = PerpAlongBez(t0, ctlPts, dist = wid0, hodograph = hodoPts),
          p4 = PerpAlongBez(t1, ctlPts, dist = wid1, hodograph = hodoPts),
          p5 = PointAlongBez(t1, ctlPts)
        ) {
          if (hgt0 == 0 && hgt1 == 0 ) {
            polygon([ p5, p0, p1, p4 ]);
          } else if (hgt0 == hgt1) {
            linear_extrude(height = hgt0, convexity = 2) polygon([ p5, p0, p1, p4 ]);
          } else {
            polyhedron(
              points =[
                [p0[0],p0[1],0], // 0
                [p1[0],p1[1],0], // 1
                [p1[0],p1[1],hgt0], // 2
                [p0[0],p0[1],hgt0], // 3
                [p4[0],p4[1],0], // 4
                [p5[0],p5[1],0], // 5
                [p5[0],p5[1],hgt1], // 6
                [p4[0],p4[1],hgt1], // 7
              ],
              triangles = triangles,
              convexity = 2
            );
          }
        }
      }
    } }
  }
}

function PointAlongBez(t, ctlPts) =
  len(ctlPts) == 1 ? PointAlongBez1(t, ctlPts) :
  len(ctlPts) == 2 ? PointAlongBez2(t, ctlPts) :
  len(ctlPts) == 3 ? PointAlongBez3(t, ctlPts) :
  len(ctlPts) == 4 ? PointAlongBez4(t, ctlPts) :
  len(ctlPts) == 5 ? PointAlongBez5(t, ctlPts) :
  len(ctlPts) == 6 ? PointAlongBez6(t, ctlPts) :
  len(ctlPts) == 7 ? PointAlongBez7(t, ctlPts) :
  len(ctlPts) == 8 ? PointAlongBez8(t, ctlPts) :
  [];

function BezI(t, ctls) =
  len(ctls) == 1 ? BezI1(t, ctls) :
  len(ctls) == 2 ? BezI2(t, ctls) :
  len(ctls) == 3 ? BezI3(t, ctls) :
  len(ctls) == 4 ? BezI4(t, ctls) :
  len(ctls) == 5 ? BezI5(t, ctls) :
  len(ctls) == 6 ? BezI6(t, ctls) :
  len(ctls) == 7 ? BezI7(t, ctls) :
  len(ctls) == 8 ? BezI8(t, ctls) :
  [];

function PointAlongBez1(t, ctlPts) = [
  BezI1(t, [ctlPts[0][0]]),
  BezI1(t, [ctlPts[0][1]])
];
function PointAlongBez2(t, ctlPts) = [
  BezI2(t, [ctlPts[0][0], ctlPts[1][0]]),
  BezI2(t, [ctlPts[0][1], ctlPts[1][1]])
];
function PointAlongBez3(t, ctlPts) = [
  BezI3(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0]]),
  BezI3(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1]])
];
function PointAlongBez4(t, ctlPts) = [
  BezI4(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0], ctlPts[3][0]]),
  BezI4(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1], ctlPts[3][1]])
];
function PointAlongBez5(t, ctlPts) = [
  BezI5(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0], ctlPts[3][0], ctlPts[4][0]]),
  BezI5(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1], ctlPts[3][1], ctlPts[4][1]])
];
function PointAlongBez6(t, ctlPts) = [
  BezI6(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0], ctlPts[3][0], ctlPts[4][0], ctlPts[5][0]]),
  BezI6(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1], ctlPts[3][1], ctlPts[4][1], ctlPts[5][1]])
];
function PointAlongBez7(t, ctlPts) = [
  BezI7(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0], ctlPts[3][0], ctlPts[4][0], ctlPts[5][0], ctlPts[6][0]]),
  BezI7(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1], ctlPts[3][1], ctlPts[4][1], ctlPts[5][1], ctlPts[6][1]])
];
function PointAlongBez8(t, ctlPts) = [
  BezI8(t, [ctlPts[0][0], ctlPts[1][0], ctlPts[2][0], ctlPts[3][0], ctlPts[4][0], ctlPts[5][0], ctlPts[6][0], ctlPts[7][0]]),
  BezI8(t, [ctlPts[0][1], ctlPts[1][1], ctlPts[2][1], ctlPts[3][1], ctlPts[4][1], ctlPts[5][1], ctlPts[6][1], ctlPts[7][1]])
];

function PerpAlongBez(t, ctlPts, dist = 1, hodograph = []) =
  len(ctlPts) == 2 ? PerpAlongBez2(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 3 ? PerpAlongBez3(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 4 ? PerpAlongBez4(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 5 ? PerpAlongBez5(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 6 ? PerpAlongBez6(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 7 ? PerpAlongBez7(t, ctlPts, dist, hodograph) :
  len(ctlPts) == 8 ? PerpAlongBez8(t, ctlPts, dist, hodograph) :
  [];

function PerpAlongBez2(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez2(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez1( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez3(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez3(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez2( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez4(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez4(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez3( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez5(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez5(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez4( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez6(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez6(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez5( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez7(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez7(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez6( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function PerpAlongBez8(t, ctlPts, dist = 1, hodograph = []) =
  pSum(
    PointAlongBez8(t, ctlPts),
    rot90cw(
      normalize(
        PointAlongBez7( t, (len(hodograph) > 1) ? hodograph : hodograph(ctlPts) ),
        dist
      )
    )
  );

function hodograph(p) =
  len(p) == 2 ?
    [ pDiff(p[1], p[0]) ] :
  len(p) == 3 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]) ] :
  len(p) == 4 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]), pDiff(p[3], p[2]) ] :
  len(p) == 5 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]), pDiff(p[3], p[2]), pDiff(p[4], p[3]) ] :
  len(p) == 6 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]), pDiff(p[3], p[2]), pDiff(p[4], p[3]), pDiff(p[5], p[4]) ] :
  len(p) == 7 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]), pDiff(p[3], p[2]), pDiff(p[4], p[3]), pDiff(p[5], p[4]), pDiff(p[6], p[5]) ] :
  len(p) == 8 ?
    [ pDiff(p[1], p[0]), pDiff(p[2], p[1]), pDiff(p[3], p[2]), pDiff(p[4], p[3]), pDiff(p[5], p[4]), pDiff(p[6], p[5]), pDiff(p[7], p[6]) ] :
  [];

function BezI1(t, ctls) =
  (ctls[0])
  ;

function BezI2(t, ctls) =
  ((1-t) * ctls[0]) +
  (t * ctls[1])
  ;

function BezI3(t, ctls) =
  (pow(1-t, 2) * ctls[0]) +
  (2 * t * (1-t) * ctls[1]) +
  (pow(t, 2) * ctls[2])
  ;

function BezI4(t, ctls) =
  (pow(1-t, 3) * ctls[0]) +
  (3 * t * pow(1-t, 2) * ctls[1]) +
  (3 * pow(t, 2) * (1-t) * ctls[2]) +
  (pow(t, 3) * ctls[3])
  ;

function BezI5(t, ctls) =
  (pow(1-t, 4) * ctls[0]) +
  (4 * t * pow(1-t, 3) * ctls[1]) +
  (6 * pow(t, 2) * pow(1-t, 2) * ctls[2]) +
  (4 * pow(t, 3) * (1-t) * ctls[3]) +
  (pow(t, 4) * ctls[4])
  ;

function BezI6(t, ctls) =
  (pow(1-t, 5) * ctls[0]) +
  (5 * t * pow(1-t, 4) * ctls[1]) +
  (10 * pow(t, 2) * pow(1-t, 3) * ctls[2]) +
  (10 * pow(t, 3) * pow(1-t, 2) * ctls[3]) +
  (5 * pow(t, 4) * (1-t) * ctls[4]) +
  (pow(t, 5) * ctls[5])
  ;

function BezI7(t, ctls) =
  (pow(1-t, 6) * ctls[0]) +
  (6 * t * pow(1-t, 5) * ctls[1]) +
  (15 * pow(t, 2) * pow(1-t, 4) * ctls[2]) +
  (20 * pow(t, 3) * pow(1-t, 3) * ctls[3]) +
  (15 * pow(t, 4) * pow(1-t, 2) * ctls[4]) +
  (6 * pow(t, 5) * (1-t) * ctls[5]) +
  (pow(t, 6) * ctls[6])
  ;

function BezI8(t, ctls) =
  (pow(1-t, 7) * ctls[0]) +
  (7 * t * pow(1-t, 6) * ctls[1]) +
  (21 * pow(t, 2) * pow(1-t, 5) * ctls[2]) +
  (35 * pow(t, 3) * pow(1-t, 4) * ctls[3]) +
  (35 * pow(t, 4) * pow(1-t, 3) * ctls[4]) +
  (21 * pow(t, 5) * pow(1-t, 2) * ctls[5]) +
  (7 * pow(t, 6) * (1-t) * ctls[6]) +
  (pow(t, 7) * ctls[7])
  ;

function x(p) = p[0];
function y(p) = p[1];
function dx(p1, p2) = x(p1) - x(p2);
function dy(p1, p2) = y(p1) - y(p2);
function sx(p1, p2) = x(p1) + x(p2);
function sy(p1, p2) = y(p1) + y(p2);

function dist(p1, p2 = [0,0]) = sqrt( pow( dx(p1,p2), 2) + pow( dy(p1,p2), 2) );
function normalize(p, n = 1) = pScale( p, n / dist( p ) );

function pSum(p1, p2) = [sx(p1, p2), sy(p1, p2)];
function pDiff(p1, p2) = [dx(p1, p2), dy(p1, p2)];
function pScale(p, v) = [x(p)*v, y(p)*v];

function rot90cw(p) = [y(p), -x(p)];
function rot90ccw(p) = [-y(p), x(p)];
function rot(p, a) = [
  x(p) * cos(a) - y(p) * sin(a),
  x(p) * sin(a) - y(p) * cos(a),
];
function rotAbout(p1, p2, a) = pSum(rot(pDiff(p1, p2), a), p2); // rotate p1 about p2

```


[User]
Hi there, I'm looking to design a parametric turtle robot shell in OpenSCAD, and I need some help. I've been playing around with a design, but it's not quite where I want it, and I think you could do a much better job.

The basic idea is a rounded shell, sort of like a turtle's carapace, but with openings on the sides. I'd like it to be fully parametric so I can easily adjust the size and proportions for different robot builds. The original design I made was based on a sphere, but I think there is a better way to do it.

Here's what I'm envisioning:

*   **Overall Shape:** It should be mostly spherical, but slightly elongated along one axis (like a squashed sphere), which in my original code is controlled by a scaling factor along the x-axis
*   **Main Shell:** I'd like this to have a controlled thickness, so I can define the shell's outer radius, and the inner shell radius separately. The outer shell should be somewhat faceted, maybe around 12 facets, while the inner shell should be smooth (e.g. 100 facets). I want to be able to adjust the difference between the inner and outer radius to control the wall thickness.
*   **Side Openings:** There should be two symmetrical openings on the sides, kind of like large ports. I want the openings to be circular and their radius to be a parametric variable. I'd also like their position to be parametric along the long axis, and the thickness of the shell around the port to be controllable, so I can increase or decrease the border thickness.
*   **Bottom:** The bottom should be a flat surface. I was using a difference operation with a large cube to remove the bottom half of my original sphere. I'm wondering if there's a better way, maybe by using some kind of rotation to build a half sphere?
*   **Parameters:** I'd like to be able to control the following parameters:
    *   `overall_radius`:  This should be like the major radius for the shell, the equivalent of the `shell_radius` in my code.
    *  `elongation`: This would be the scale factor for the x-axis to control how squashed the sphere is.
    *   `shell_thickness`: The difference between the outer and inner shell radii.
    *   `side_opening_radius`: The radius of the circular openings on the sides.
    *   `side_opening_position`: How far the openings are from the center along the elongated axis.
    *   `border_thickness`: How thick the border around the openings is.
   * `facet_count`: How many facets to use for the outer shell (e.g. 12)
*   **Techniques:** I really liked the use of `hull()` and `rotate_extrude()` to make those pancake borders in my code and would appreciate seeing those or similar techniques used in the new design. I also like how my code used a difference operation to create the port openings, but I wonder if there is a better way.
*   **Libraries:** I'm not using any external libraries currently, but I'd be happy to use MCAD or BOSL libraries if you think they'd make the code more efficient or easier to read. I'm also familiar with some other libraries, so if you recommend something I can probably figure it out.

I think that covers the basics. I'm really excited to see what you can come up with! Please let me know if you need any more details.

[Assistant]
turtle1v3.scad:
```

// preview[view:south west, tilt:bottom diagonal]

// Radius of cube in mm (center to faceted surface along short axis)
shell_radius=25;

border_radius=shell_radius/8;
cut_radius=shell_radius/3;

rotate([180,0,0])
scale([1.5,1,1])
difference() {
	union() {
		//outer shell, intentionally chunky
		sphere(shell_radius, $fn=12);
		// spin a circle in another circle for donut,
		// then "hull" it for pancake.  This is the
		// border around the bottom
		hull() {
			rotate_extrude($fn=100)
			translate([shell_radius, -border_radius/2, 0])
			circle(r = border_radius, $fn=40);
		}
		// spin a circle in another circle for donut,
		// then "hull" it for pancake.  Then rotate and
		// translate it out to the sides for border around
		// end openings (x2 with opposite translations)
		scale([1,1.5,1])
		rotate([0,90,0])
		translate([0,0,shell_radius-border_radius/2])
		hull() {
			rotate_extrude($fn=100)
			translate([cut_radius, -border_radius, 0])
			circle(r = border_radius, $fn=40);
		}
		scale([1,1.5,1])
		rotate([0,90,0])
		translate([0,0,-shell_radius+border_radius/2])
		hull() {
			rotate_extrude($fn=100)
			translate([cut_radius, border_radius, 0])
			circle(r = border_radius, $fn=40);
		}
	}

	// Difference away the inner sphere (smooth for strength)
	sphere(shell_radius-shell_radius/10, $fn=100);

	// Difference away bottom half to make it a half-shell
	translate([-shell_radius*2,-shell_radius*2,0]) cube(shell_radius*4);

	// Difference away cylinder for end openings
	rotate([0,90,0]) translate([0,0,-shell_radius*2]) scale([1,1.5,1]) cylinder(h=shell_radius*4,r=cut_radius,$fn=30);

	// Difference away a little at the ends to make them smooth
	translate([shell_radius-shell_radius/50-border_radius/2,-shell_radius,-shell_radius]) cube(shell_radius*2);
	translate([-shell_radius*3+shell_radius/50+border_radius/2,-shell_radius,-shell_radius]) cube(shell_radius*2);
}

```


[User]
I'd like to create a parametric model of a Reuleaux tetrahedron, sometimes called a Meissner tetrahedron, in OpenSCAD. I've seen some simple examples, but I need something more flexible.

Essentially, I want a solid shape formed by the intersection of four spheres. The centers of these spheres should form the vertices of a regular tetrahedron. I need to be able to control the overall size of the resulting shape, which should be as measured across its widest points. It's also important that the model be oriented in such a way that it's centered on the origin and the "bottom" of the tetrahedron faces the negative Z axis.

Could you provide an OpenSCAD file that allows me to specify this size parameter, and accurately creates the Reuleaux tetrahedron? I'm okay with a high `$fn` value for smoother curves - something around 50 would be great, and it'd be helpful to have that parameter settable too. I'd prefer not to rely on any external libraries, just the built-in OpenSCAD functionality.

[Assistant]
meissner3.scad:
```
// meissner object
// based on tetrahedron

// size of object in ALL directions
size = 40;

m = 2 * sqrt(2);

$fn = 50;

scale(size / m)
	translate([0, 0, m / 2])
		intersection() {
			translate([1, 1, 1]) sphere(m);
			translate([1, -1, -1]) sphere(m);
			translate([-1, 1, -1]) sphere(m);
			translate([-1, -1, 1]) sphere(m);
		}

// eof

```


[User]
I'd like to create a customizable, hollow Jack-o'-lantern in OpenSCAD. I have some specific ideas for how I want the customization to work.

First, I want to be able to choose from different shapes for the eyes, nose, and mouth. For eyes, I'd like to select between circles, triangles, ovals, and squares. The same shapes should be available for the nose, and for the mouth, I'd like the same options as the eyes *plus* a rectangle shape.

I also want a "snaggle tooth" option that's either on or off, and a "carved" option, which will determine if the face features are cut all the way through the pumpkin or not.

Then for sizes, I'd like to adjust the size of each eye individually, the size of the nose, and the size of the mouth. Triangle shapes won't need individual size adjustments, just the standard shape. I don't have any other specific size requirements.

The pumpkin itself should be a hollow, somewhat round shape, and have a stem coming out the top that can be twisted.

I'm not sure exactly how I want the code structured so you've got some flexibility there. I'm not using any libraries right now, but if it'd be easier to use one, I'm fine with that.

[Assistant]
hollow_pumpkin_working.scad:
```
//hollow pumpkin and stem
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

/* [Shapes] */
eye_shape = "eye_oval"; //[eye_circle: Circle Eyes, eye_triangle: Triangle Eyes, eye_oval: Oval Eyes, eye_square: Square Eyes]
nose_shape = "nose_circle"; //[nose_circle:Circle Nose, nose_triangle:Triangle Nose, nose_oval:Oval Nose, nose_square:Square Nose]
mouth_shape = "mouth_circle"; //[mouth_circle: Circle Mouth, mouth_triangle:Triangle Mouth, mouth_rectangle:Rectangle Mouth, mouth_oval:Oval Mouth]

//**works best with large mouth sizes selected**
snaggle_tooth = "yes"; //[no, yes]

//Carve completely through?
carved = "no"; //[no, yes]

//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

/* [Sizes (Triangle Shapes not adjustable)] */

left_eye = 7; //[0:7]

right_eye = 7; //[0:7]

nose_size = 4; //[0:4]

mouth_size = 6; //[0:6]

//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
difference(){

union(){

//		hollow center start
difference(){
translate([0,0,-22])
	cylinder (h=40, r=22);

translate([0,0,-23])
	cylinder (h=42, r=21);
}
//		hollow center end

//		left side
 difference(){
 scale([1.15, 1, 1.25])
 translate([9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		right side
 difference(){
 scale([1.15, 1, 1.25])
 translate([-9, 0, 0])
	sphere(r=20,$fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		left side front
 difference(){
 rotate([0,0,55])
 scale([1.15, 1, 1.25])
 translate([9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
}

//		left side back
 difference(){
 rotate([0,0,-50])
 scale([1.15, 1, 1.25])
 translate([9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		back
 difference(){
 rotate([0,0,-100])
 scale([1.15, 1, 1.25])
 translate([9, 0, 0])
	sphere(r=20, $fn=52);

translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		front
 difference(){
 rotate([0,0,-80])
 scale([1.15, 1, 1.25])
 translate([-9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		right front
 difference(){
 rotate([0,0,-35])
 scale([1.15, 1, 1.25])
 translate([-9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		right back
 difference(){
 rotate([0,0,45])
 scale([1.15, 1, 1.25])
 translate([-9, 0, 0])
	sphere(r=20, $fn=52);

 translate([0,0,-26])
	cylinder (h=40, r=22);
 }

//		stem
difference(){
linear_extrude(height = 32, convexity = 2, twist = -400)
translate([1, -1, 0])
	circle(r = 3.5);

translate([0,0,-26])
	cylinder (h=40, r=22);
}
}

//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

//~~~Eyes~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~***

if (eye_shape=="eye_triangle")
		{
	//triangle eyes
		translate([0,-10,27])
		rotate([90, 90, 0])
		linear_extrude(height = 25)
		polygon([[10,10.5],[20,5],[20,15]]);

	//triangle eyes
		translate([0,-35,27])
		rotate([0, 90, 90])
		linear_extrude(height = 25)
		polygon([[10,10.5],[20,5],[20,15]]);
		}

else if (eye_shape=="eye_circle")
	{
	//		left eye
	translate([11,0,11])
	rotate([90,0,0])
		cylinder(35, left_eye, left_eye);

	//		right eye
	translate([-11,0,11])
	rotate([90,0,0])
		cylinder(35, right_eye, right_eye);
	}

else if (eye_shape=="eye_oval")
	{
	//	left eye oval
	translate([11,0,11])
	rotate([90,0,0])
	scale([.8,1.1,1])
		cylinder(35, left_eye, left_eye);

	//	right eye oval
	translate([-11,0,11])
	rotate([90,0,0])
	scale([.8,1.1,1])
		cylinder(35, right_eye, right_eye);
	}

else if (eye_shape=="eye_square")
	{
	//	left eye square
	translate([6,-15,7])
	rotate([90,0,0])
		cube([9, left_eye, 19]);

	//	right eye square
	translate([-15,-15,7])
	rotate([90,0,0])
		cube([9, right_eye, 19]);
	}

//~~~Nose~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~***
//Customizable Nose Shapes
	if (nose_shape=="nose_circle")
	{
	//	nose_circle
	translate([0,-15,1])
	rotate([90,0,0])
		cylinder(23, nose_size, nose_size);
	}
	else if (nose_shape=="nose_square")
	{
		//nose_square
		translate([-3.5,-20,-2.5])
		rotate([90,0,0])
			cube([7,nose_size,17]);
	}
	else if (nose_shape=="nose_triangle")
	{
		//triangle nose
		translate([-10.5,-15,17])
		rotate([90, 90, 0])
		linear_extrude(height = 25)
		polygon([[10,10.5],[20,5],[20,15]]);
	}
	else if (nose_shape=="nose_oval")
	{
	//	nose_oval
	translate([0,-15,1])
	rotate([90,0,0])
	scale([.8,1.2,1])
		cylinder(23, nose_size, nose_size);
	}

//~~~Mouth~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~***
//Customizable Mouth Shapes
	if (mouth_shape=="mouth_circle")
	{
	//		circle mouth
	translate([0,-15,-12])
	rotate([90,0,0])
		cylinder(23, mouth_size, mouth_size);
	}
	else if (mouth_shape=="mouth_oval")
	{
	//		oval mouth
	translate([0,-10,-12])
	rotate([90,0,0])
	scale([1.7,1,1])
		cylinder(23, mouth_size, mouth_size);
	}
	else if (mouth_shape=="mouth_rectangle")
	{
		//		rectangle mouth
	translate([-9,-20,-15])
	rotate([90,0,0])
	scale([1.7,1.5,1])
		cube([11, mouth_size, 14]);
	}
	else if (mouth_shape=="mouth_triangle")
	{
		//triangle mouth
		translate([10,-15,-27])
		rotate([90, 270, 0])
		linear_extrude(height = 25)
		polygon([[12,10.5],[20,0],[20,20]]);
	}
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
//Guts
	//sphere to hollow out
	translate([0,0,-3.75])
	sphere(r=26, $fn=52);

	//sphere to hollow out face
	translate([0,2,2])
	scale([0,1.5,0])
	sphere(r=21, $fn=52);

	//sphere to hollow out face
	translate([0,1,3])
	scale([1.3, 1.4, .85])
	sphere(r=21, $fn=52);
	}

//~~~Teeth~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~***
//tooth
	if (snaggle_tooth=="yes")
	{
		translate([-6.5,-27,-10.5])
		rotate([80,-8,0])
			cube([5,6,4]);
	}
	else if (snaggle_tooth=="no"){
	}
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
//partially or completely carved

	if (carved=="no")
	{
	difference(){
//thin layer for face negative
	translate([0,-5,-1])
	scale([1.3, 1.2, 1.2])
	sphere(r=21, $fn=52);

//thin layer for face positve
	translate([0,-4,-2])
	scale([1.3, 1.2, 1.2])
	sphere(r=21, $fn=52);

//thin layer for face negative
	translate([0,-3,-2])
	scale([1.3, 1.2, 1.2])
	 sphere(r=21, $fn=52);
	}
	}
	else if (carved=="yes")
	{
	}

//~~~To Play~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

```


[User]
I need a parametric design for a headset holder that clamps onto a tabletop. I've got a few specific requirements in mind, but I want it to be adjustable for different table thicknesses and headset sizes.

Here's what I need:

*   **Table Clamp:** The holder should attach to the table with a clamp mechanism, not just sit on top. The clamping part needs to be adjustable to accommodate different table thicknesses. I'd like to specify the table thickness as a parameter. The clamp should use flat surfaces and have enough area to create good friction against the tabletop.
*   **Headset Support:** The part that actually holds the headset should be a cradle, basically a half cylinder that is wide enough to accommodate different headbands. I'd like to set the width of the headband as a parameter. It should have a small lip to prevent the headset from sliding off, kind of like a shallow trough.
*   **Parametric Design:** It should be entirely parametric so I can easily change the dimensions for various table thicknesses, headset headband widths, the height the holder extends below the table, the depth of the half-cylinder that holds the headset, and the thickness of the clamp material itself. I'd like to set the length the holder extends out from the table's edge, too.
*   **Materials:** The material should be optimized for 3D printing, so make sure it doesn't have any unnecessary supports. Assume I am printing in PLA, so shrinkage is a factor when clamping.

Also, can you make sure to include a build plate module so I can see the part on a standard printer bed (like a Replicator 2) and also let me specify a custom size? I've seen some designs use a `build_plate.scad` file for this - could you use that? This should be optional, for visual purposes and not required for printing.

I'd like to be able to specify these things as user-adjustable parameters in the code:

*   `thickness_of_tabletop`: The thickness of the table the clamp is being attached to.
*   `width_of_headband`: The width of the headset's headband.
*   `holder_length`: The distance the holder extends from the edge of the table.
*   `holder_width`: The width of the half-cylinder cradle part.
*   `holder_strength`: The thickness of the material used for the clamp parts.
*  `holder_height`: The height of the small lip of the half cylinder cradle.
*  `build_plate_selector`: for choosing between printer build plates (Replicator 2, Replicator, Thingomatic, and manual), using an integer.
*   `build_plate_manual_x`: x dimension of a manual printer bed.
*   `build_plate_manual_y`: y dimension of a manual printer bed.

I'd like the build plate options to be handled in the `build_plate.scad` file.

I'd appreciate it if the main file used the `use <build_plate.scad>` for the build plate module, rather than include its code directly in the main file.

Thanks!

[Assistant]
headset_holder_rotated.scad:
```
// Filename: parametric_headset_holder.scad
// Author: Steffen Pfiffner
// Date: 06/10/2014
// Email: s.pfiffner@gmail.com
// Web: http://www.thingiverse.com/FiveF

// Project: Parametric Headset Holder

use <build_plate.scad>

/* [Basic] */
//Normally the thickness of the table should be chosen slightly bigger than the real thickness because material shrinkage. (for PLA about 0.1mm)
thickness_of_tabletop = 35;
width_of_headband = 45;

holder_length = 40;
holder_width = 40;
holder_strength = 3;

holder_height = 10;

/* [Quality] */
//$fa is the minimum angle for a fragment. Even a huge circle does not have more fragments than 360 divided by this number. The default value is 12 (i.e. 30 fragments for a full circle). The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.
$fa = 5.0;

//$fs is the minimum size of a fragment. Because of this variable very small circles have a smaller number of fragments than specified using $fa. The default value is 2. The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.
$fs = 1.0;

/* [Advanced] */

/* [Hidden] */
width_of_headset = width_of_headband + 2*holder_strength;

//Build plate:

//for display only, doesn't contribute to final object
build_plate_selector = 0; //[0:Replicator 2,1: Replicator,2:Thingomatic,3:Manual]

//when Build Plate Selector is set to "manual" this controls the build plate x dimension
build_plate_manual_x = 100; //[100:400]

//when Build Plate Selector is set to "manual" this controls the build plate y dimension
build_plate_manual_y = 100; //[100:400]

build_plate(build_plate_selector,build_plate_manual_x,build_plate_manual_y);

//Build plate END

//half cylinder
module half_cylinder(){
	difference(){
		translate([0,-holder_length/2-width_of_headset/2,thickness_of_tabletop+holder_strength]){
			rotate(a=90, v=[1,0,0]){

				cylinder (h = width_of_headset-2*holder_strength, r=holder_width/2, center = true);
			}

		}

		translate([0,-holder_length/2-width_of_headset/2,holder_width/2+thickness_of_tabletop-holder_strength*2+0.5]){
			cube([holder_width,width_of_headset+5,holder_width/2], center = true);
		}
	}
}

//HOLDER START
//thickness_of_tabletop+holder_strength/2+holder_strength
translate([holder_length/2,-thickness_of_tabletop/2,holder_width/2]){
	rotate(a=180, v=[0,1,0]){
		rotate(a=90, v=[0,0,1]){
			rotate(a=90, v=[0,1,0]){
				difference(){
					union(){

						translate([0,0,0]){
							cube([holder_width,holder_length,holder_strength], center = true);
						}

						translate([0,0,thickness_of_tabletop+holder_strength]){
							cube([holder_width,holder_length,holder_strength], center = true);
						}

						translate([0,-holder_length/2-holder_strength/2,thickness_of_tabletop/2+holder_strength/2]){
							rotate(a=90, v=[1,0,0]){
								cube([holder_width,thickness_of_tabletop+2*holder_strength,holder_strength], center = true);
							}
						}

						half_cylinder();

						translate([0,-holder_length/2-width_of_headset+holder_strength/2+holder_strength,-holder_height+0.25]){
							resize([holder_width+holder_height,holder_strength,0], auto=true){
								half_cylinder();
							}

						}
					}

					union(){

						//the following line remove stuff
						//bottom
						translate([0,-holder_length/2-width_of_headset/2,holder_width/2+thickness_of_tabletop-holder_strength*2]){
							cube([holder_width*2,width_of_headset*5,holder_width/2], center = true);
						}

						//sides
						//left
						translate([holder_width/2 + 20,0,0]){
							cube([40,500,500], center = true);
						}

						//right
						translate([-holder_width/2 - 20,0,0]){
							cube([40,500,500], center = true);
						}

					}
				}
			}
		}
	}
}

//HOLDER END

```


[User]
Hey, I'm looking to create a customizable flag design in OpenSCAD, similar to the one I saw on Thingiverse and YouMagine. I've got the basic idea, but I need it to be fully parametric so I can easily change all the dimensions and text.

Essentially, it's a flag with a curved, wavy shape, kinda like a sine wave if you look at it from the side, and it has text on both sides. The flag needs to have a cylindrical base with a clip that will attach to Modio stick parts (I can provide the dimensions for that clip, I think I'll just need a cylindrical connector with an extra cutout for the stick itself).

Here’s a breakdown of what I need:

*   **Flag Body:** The main part of the flag should have a curved, wavy shape, not just a simple flat rectangle. I'd like to define the overall height, the radius for the curves, and the thickness of the flag material. The curves look like they’re made with quarter-cylinders.
*   **Flag Base:** The base needs to be a cylinder that can connect to the other modio parts, which should be pretty standard. It should connect to the flag body with a small cylinder connecting the base to the flag, and there should be a small sphere on top of the cylinder. The base should have a slot cutout in its body as well as cones cut out from the top and bottom of it. The connection for the modio part itself should have the additional cutout.
*   **Text:** I need to add customizable text on both sides of the flag. The text should be sized to fit the flag, and I need to be able to adjust the text height and the distance from the surface. The text needs to be "cut" out of the flag using difference operators. I want to use custom fonts, so I'll need to use the `write()` function from some sort of library that lets me load in .DXF files for the font. It also looks like I'll need to be able to translate the text up a bit to compensate for descending letters like "y" or "g".
*   **Parametric Design:** I need to easily adjust all of these dimensions: flag height, curve radius, flag thickness, text, font, and the ability to compensate for descending lower-case letters (the library's text method).
*   **Libraries:** I think I'll need a text library (like `write/Write.scad`) to handle the fonts.

I’d like to see something that would be easily customizable for different word lengths and sizes. Could you provide the necessary OpenSCAD files?

[Assistant]
modio-flag-web2.scad:
```
//Cusomizable Modio flag by Mark G. Peeters 10-7-2014
//Notes: the text is resized to fit the flag, so keep the message short, initials, a single word etc. I have uploaded this in these places:
// https://www.youmagine.com/designs/modio-customizable-flag
// http://www.thingiverse.com/thing:492155

// preview[view:south, tilt:top diagonal]

use<write/Write.scad>
//NOTE: Do not use too many letters, they will get too small to print legibly.
initials="modio";
//ONLY USE for descending lowercase letters(like y,g,p,etc), this will move the text up so they are not cut off. BUT if you do not have descending lower case letters then this will cut the tops off.
loweryes=0;//[0:NO descending lowercase,1:descending lowercase letters]
//zero for no lowers, 1 for lower case letters use 0.2*y-dimension translation
//Choose your font
font = "Letters.dxf";//[write/Letters.dxf:Letters, write/BlackRose.dxf:Black Rose, write/knewave.dxf:Knewave, write/orbitron.dxf:Orbitron]

/* [hidden] */
//how tall is the flag in mm
flag_height=10;
//radius for the curve, don't go crazy
flag_radius=6;
//how thick is the flag in mm
flag_thick=1.2;
//the letters will just be 0.8 flag thick

textadjust =(loweryes==0)? 0 : 0.2;//if-then to set value of textadjust, used to move text up to keep lower case letter from being chopped off
$fn=100;
fod=flag_radius+flag_thick;//flag outer radius
fid=flag_radius;//flag inner raduis
movr=(fid+fod)*cos(45);

//flag body
difference(){
union(){
translate([-7,5.5,0])cylinder(h=flag_height,r=5);
//translate([-7,5.5,flag_height])cylinder(h=2,r1=5,r2=2);
color("blue")translate([0,0,0])sinwave(fid,fod,flag_height);
}//end union
translate([-7,5.5,-1])cylinder(h=flag_height+2,r=1.8);
hull(){//out cylinder wedge
translate([-7.5,5.5,-1])cylinder(h=flag_height+2,r=1);
translate([-14,5.5,-1])cylinder(h=flag_height+2,r=4);
}
translate([-7,5.5,flag_height/2])sphere(r=3.2);//center sphere
translate([-12,5.5-1.75,-1])cube([5,3.5,flag_height+2,]);//slot out
translate([-7,5.5,-1])cylinder(h=2.5,r1=2.8,r2=1.7);//bottom cone out
translate([-7,5.5,flag_height-1.5])cylinder(h=2.5,r1=1.7,r2=2.8);//top cone out
//notch falg end
translate([movr*3.4,0,flag_height/2])rotate([0,45,0])cube([3,10,3]);
translate([movr*3.4,0,flag_height/6])rotate([0,45,0])cube([3,10,3]);
translate([movr*3.4,0,flag_height/1.2])rotate([0,45,0])cube([3,10,3]);
}//end diff

//add text front
translate([0,-flag_thick*.8,0])
difference(){
translate([0,fod,textadjust*flag_height])rotate([90,0,0])resize([movr*3.4,flag_height,0])write(initials,h=flag_height,t=fod,font=font);
//part to trim front text
sinwave_cutout(fid,fod,flag_height);
}//end diff

//add text back
translate([0,flag_thick*.8,0])
difference(){
//translate([(fid+fod)*cos(45)*3.5,(fid+fod)*cos(45)-fid-monogram_thick,0])
translate([movr*3.4,0,textadjust*flag_height])rotate([90,0,180])resize([movr*3.4,flag_height,0])write(initials,h=flag_height,t=fod,font=font);
//part to trim front text
sinwave_cutout(fid,fod,flag_height);
}//end diff

//modules----------------------------------
module sinwave(fid,fod,flag_height){//this is the flag sin shape
movr=(fid+fod)*cos(45);
circqr(fid,fod,flag_height,45);
translate([movr,movr,0])circqr(fid,fod,flag_height,45+180);
translate([movr*2,0,0])circqr(fid,fod,flag_height,45);
translate([movr*3,movr,0])circqr(fid,fod,flag_height,45+180);
}//end mod sinwave

module sinwave_cutout(fid,fod,flag_height){//this is a cube with sine carved out used to trim text
movr=(fid+fod)*cos(45);
difference(){
translate([-fod*1.5,-fod/3,-flag_height*0.5])cube([fod*7,fod*2,flag_height*2]);
sinwave(fid,fod,flag_height);
}//end diff
}//end mod sinwave_cutout

module circqr(rin,rout,height,rot){//this is the 1/4 part of cylinders used to make flag shape
rotate([0,0,rot])difference(){   //diff1
cylinder(h=height,r=rout);
translate([0,0,-1])cylinder(h=height+2,r=rin);
translate([0,0,-1])difference(){    //diff2
translate([-rout,-rout,0])cube([rout*2,rout*2,height+2]);
rotate([0,0,1])cube([rout,rout,height+2]);
rotate([0,0,-1])cube([rout,rout,height+2]);}//end diff2
}//end diff1
}//end module
```


[User]
I'd like to create a rounded rectangle, similar to what's in the example you gave, but I need it to be parametric.

Specifically, I need to control the length, width, and height of the main rectangular portion. I also need to control the radius of the rounded corners. I'd like a single module, say `rounded_rectangle()`, that takes these parameters. The parameters should be named `length`, `width`, `height`, and `radius`.

Could you generate the necessary OpenSCAD code? I don't need any documentation or comments for now, just the working code. I think the `minkowski()` operator is what's needed here.

[Assistant]
rounded_rectangle.scad:
```

$fn=50;
minkowski() {
cube([20,15,3]);
// rounded corners
cylinder(r=2,h=2);
}
```


[User]
Hey, I'm trying to design some modular lamp shade panels that are compatible with the Modio system. I've got a basic window panel in mind that I'd like to be able to customize, and I'd like it to use the same peg system as Modio so they'll all fit together.

Basically, I want a rectangular panel with a peg on one side, that can plug into the standard Modio holes. I'm imagining something like the attached SCAD file, but I need it to be more parametric. I'd like to be able to specify the following:

*   **Panel width**: The overall width of the rectangular panel.
*   **Panel height**: The overall height of the rectangular panel.
*   **Panel thickness**: The thickness of the panel itself.
*   **Peg diameter**: The diameter of the peg that inserts into Modio holes.
*   **Peg length**:  How far the peg sticks out from the panel.
*   **Peg offset**:  The offset (x and y) of the peg from the center of the panel.

I'd like the peg to be a cylinder, with a small cube at the base that overlaps the panel, that way there are no crazy overhangs to print. I guess you could say I want a "T" shaped peg.

Also, it would be great if I could control the number of faces on the cylinder for the peg – you know, to make it smoother or keep the polycount down for previewing.

Ideally, all these things should be configurable in the OpenSCAD file, using variables. Is this something you can help me with? I think it would be cool if I could do things like create a small 4-sided panel, or a long 2-sided one - whatever I can dream up.

I'm not super familiar with libraries like MCAD or BOSL - is it possible to do this without using them? I'm fine using other libraries, though.

[Assistant]
modio-window.scad:
```
//	Window Width
width = 38;
//	Window height
height = 44;
//	The smaller this number the more light that will be let through
thickness= 1.5;
// The default is for modio parts printed at 100% scale
post_diameter=3;

cube([width, height, thickness], center=true);
translate([0,.5*height+2,-.5*thickness])
difference(){
translate([0,0,.75])rotate([90,0,0])cylinder(10,post_diameter/2,post_diameter/2,$fn=40,center=true);
translate([0,0,-10])cube([20,12,20],center=true);
};
```


[User]
Okay, I need to create a parametric honeycomb generator in OpenSCAD. I'd like it to be able to generate both open and closed cell honeycombs, where you can specify the overall dimensions of the grid and the individual cell characteristics. Specifically:

*   **Cell Shape:** The cells should be hexagonal.
*   **Cell Type:** I need to be able to choose between "open" and "closed" cells. Open cells would be a simple hexagonal cylinder with thin walls. Closed cells would have a solid base and then three angled triangles above, forming a more pointed shape. The height should be specified separately from the other radius/thickness parameters.
*   **Cell Dimensions:** I need to specify the cell radius, cell height, and the cell wall thickness.
*   **Grid Dimensions:** I need to specify the number of rows and columns for the honeycomb grid.
*   **Wall Overlap:** This is a bit tricky. I want a parameter that lets me choose if all the walls are the same thickness, or if the interior walls are thicker and the perimeter walls are thinner. This is to allow the pieces to fit together nicely if I'm generating multiple grids that should be connected side-by-side. If this option is selected, internal wall thickness = the specified cell wall thickness; external walls should have half the thickness.
*   **Parametric:** Everything should be parametric, so I can easily change all these values.
*   **Output:** I expect a single .scad file (or a few .scad files if modularity makes sense) containing the full implementation. I don't want to rely on any external libraries.

Can you generate that for me? Thanks!

[Assistant]
honeycomb_maker_v3.scad:
```
/* model honeycomb
Gian Pablo Villamil
October 2014

Customizable honeycomb generator. You can choose open or closed ended cells.
The overlap parameter controls the wall thickness of internal vs. external borders. If overlap is true, all walls will be same thickness. If overlap is false, then the
internal borders will be thicker and external thinner, so if you put two sections
together, they will mesh correctly.

 */

// Cell Radius mm
cellrad = 6;
// Cell Depth mm
cellheight = 20;
// Cell Wall Thickness mm
cellthick = 0.8;

// Rows
rows = 6;
// Columns
cols = 5;

// Open or closed cells?
celltype = "open"; // [open,closed]
// Inner and outer cell walls same thickness?
overlaptype = "yes"; // [yes,no]

closed = (celltype == "closed") ? true : false;
overlap = (overlaptype == "yes") ? true: false;

module flatcube(x,y,z) {
	translate([0,0,z/2]) cube([x,y,z],center=true);
}

module closedcell(radius,height,thickness) {
	difference() {
		cylinder(r=radius,h=height,$fn=6);
		for (i=[-1:1]) {
			translate([0,0,height]) rotate([0,-30,i*120]) flatcube(cellrad*3,cellrad*3,10);
		}
		translate([0,0,-1])
		difference() {
			cylinder(r=radius-thickness,h=height-thickness,$fn=6);
			for (i=[-1:1]) {
				translate([0,0,height-thickness]) rotate([0,-30,i*120]) flatcube(cellrad*3,cellrad*3,10);
			}
		}
	}
}

module opencell(radius,height,thickness) {
	difference() {
		cylinder(r=radius,h=height,$fn=6);
		translate([0,0,-0.5]) cylinder(r=radius-thickness,h=height+1,$fn=6);
	}
}

module honeycomb(rows,cols,closed) {
	cellsize = overlap ? cellrad-cellthick/2 : cellrad ;
	voff = cellsize*1.5;
	hoff = sqrt(pow(cellsize*2,2)-pow(cellsize,2));

	for (i=[0:rows-1]) {
		for (j=[0:cols-1]){
			translate([j*hoff+i%2*(hoff/2),i*voff,0])
			rotate([0,0,30])
			if (closed==true) {closedcell(cellrad,cellheight,cellthick);}
				else
			{opencell(cellrad,cellheight,cellthick);}
		}
	}
}

honeycomb(rows,cols,closed);

//opencell(cellrad,cellheight,cellthick);
//closedcell(cellrad,cellheight,cellthick);
```


[User]
Hey, I need some help designing a replacement loop for my water bottle. The original one broke, and I'd like to 3D print a new one.

Essentially, it's a loop with a smaller loop extending off one side. The main loop needs to be adjustable in size to fit different bottles. The smaller loop should be a fixed size for attaching a keyring carabiner.

Here are some specific details:
*   The main loop will be a circle, and the size should be a parameter, let's call it `main_hole_diameter`.
*   The loop should have a thickness of 1mm. (So the radius of the main loop will be `main_hole_diameter/2 + 1`).
*   The small loop that sticks out should be roughly circular, and attached tangentally to the large loop.
* The smaller loop should be around 9mm in radius, with a hole roughly 5mm radius.
*   The thickness of the main and small loops should be 2mm.
*   I want it to have a 1 mm bevel on the top and bottom to make it look nicer. So, the total height should be 4 mm with the main object being 2mm high.
*   I plan on printing this with ABS, but PLA should work too. I need this to be strong enough for daily use.

Could you generate an OpenSCAD file for this? I'm not using any specific OpenSCAD libraries so no need to import anything.

[Assistant]
Water_Bottle_Loop.scad:
```
//Diameter of ring opening in mm
hole=50;

/* [Hidden] */
$fn=60;

difference() {
	hull() {
		cylinder(r=hole/2+7,h=2);
		translate([hole/2+7+5,0,0]) cylinder(r=9,h=2);
	}
	translate([0,0,-1])cylinder(r=hole/2,h=4);
	translate([hole/2+7+5,0,-1])cylinder(r=5,h=5);
}

```


[User]
I'd like to design a parametric LED ring for my delta printer using OpenSCAD. I want to be able to customize a few things, like the size of the ring, the number of LEDs, and how to mount it.

Specifically, I envision a ring with:
*   An adjustable inner radius
*   A definable ring width. I might want to have multiple concentric rings with LEDs too, so that should be configurable.
*   A configurable number of LEDs, and they will be evenly spaced on each ring.
*   An option for mounting ears – I want to be able to set how many ears I want and their dimensions. Also I need to be able to specify the mounting hole radius for those ears
*   I need to be able to define the dimensions of the LEDs, like the radius and height of the bulb.
*   I also need a way to make a channel for the wires between the LEDs on each ring. I need to be able to configure the depth and width of that channel.
*   Finally, I'd like to be able to define the height of both an inner edge and an outer edge if I need those. I need to be able to set both the inner and the outer edge height separately.

I'd like this to be parametric, so that all of these parameters are easily adjustable. So when I change one parameter, the model updates, so I can tweak the design as needed.
I also want the ability to use an inner edge, outer edge, or the mounting ears as options to mount the ring, not all at once.

I'm thinking I'd need at least two modules: one for the mounting ears and the main module for the LED ring. Do I need to include any special libraries for something like this? I'm not seeing any required here, but I just wanted to make sure. Can you do this for me?

[Assistant]
Delta_Led_Ring_v2.scad:
```
/* [Led Ring] */
//What is the radius of the outside of the ring
inner_radius = 60;

//What is the width of the ring
ring_width = 10;

//How many leds do you want to place per ring
number_of_leds = 6;

//How many rings do you want?
number_of_rings = 2;

//What is the radius of the led
led_r = 2.5;

//How high is the led (bulb)
led_height = 5;

//How deep is the cable hole
cable_dept = 2;

//how width is the cable hole
cable_width = 3;

//How many ears do you want to add to the right
number_of_mounting_ears = 3;

//What size is the ear
mounting_ear_size = 11;

//What is the radius of the mounting hole in the ear
mounting_ear_mount_r = 1.7;

//How high in the inner edge
inner_edge_height = 5;

//How high in the outer edge
outer_edge_height = 5;

/* [Hidden] */
development = 1; //[0=no, 1=yes]
outer_radius = inner_radius + (ring_width * number_of_rings);
angle_per_led = number_of_leds <= 0 ? 0 : 360 / number_of_leds;
angle_per_ear = number_of_mounting_ears <= 0 ? 0 : 360 / number_of_mounting_ears;
ear_height = outer_edge_height > 0 ? outer_edge_height + led_height : led_height;

module ear()
{
	difference()
	{
		hull()
		{
			translate([mounting_ear_size/2-2,mounting_ear_size/2-2,0])
			cylinder(r=2, h=ear_height, center=true,$fn=24);

			translate([mounting_ear_size/2-2,-mounting_ear_size/2+2,0])
			cylinder(r=2, h=ear_height, center=true,$fn=24);

			translate([-1,0,0])
			cube([mounting_ear_size - 1,mounting_ear_size, ear_height], center=true);
		}
		cylinder(r=mounting_ear_mount_r, h=ear_height*2+1, center=true,$fn=24);
	}
}

translate([0,0,led_height/2])
{
	difference()
	{
		union()
		{
			cylinder(r=outer_radius, h=led_height, center=true,$fn=72);

			if(number_of_mounting_ears > 0)
			for(j = [0 : number_of_mounting_ears])
			{
				rotate([0,0,angle_per_led/2 + (angle_per_ear * j)])
				{
					if(outer_edge_height > 0)
					{
						translate([outer_radius + mounting_ear_size/2 - 1,0,outer_edge_height/2]) ear();
					}
					else
					{
						translate([outer_radius + mounting_ear_size/2 - 1,0,0]) ear();
					}
				}
			}
		}

		cylinder(r=inner_radius, h=led_height + 1, center=true,$fn=72);

		if(number_of_leds>0)
		{
			for(rn = [1 : number_of_rings])
			{
				if(outer_edge_height < cable_dept)
				{
					translate([0,0,led_height/2])
					{
						difference()
						{
							cylinder(r=((inner_radius + (rn * ring_width) - ring_width/2)) + cable_width/2, h=cable_dept*2, center=true,$fn=72);
							cylinder(r=((inner_radius + (rn * ring_width) - ring_width/2)) - cable_width/2, h=(cable_dept*2)+1, center=true,$fn=72);
						}
					}
				}

				for(i = [0 : number_of_leds])
				{
					rotate([0,0,(angle_per_led/2 * rn) + (angle_per_led * i)])
					{
						translate([inner_radius + (rn * ring_width) - ring_width/2,0,0])
						{
							cylinder(r=led_r,h=led_height+1,center=true,$fn=12);
							translate([0,0,led_height/2])
							{
								cylinder(r=led_r + 1,h=led_height/2,center=true,$fn=12);
							}
						}
					}
				}
			}
		}

		if(outer_edge_height > 0)
		{
			translate([0,0, led_height + (outer_edge_height) / 2 ])
			{
				cylinder(r=outer_radius, h=outer_edge_height + led_height, center=true,$fn=72);
			}
		}
	}
}

if(inner_edge_height > 0)
{
	translate([0,0,(inner_edge_height + led_height) / 2])
	{
		difference()
		{
			cylinder(r=inner_radius, h=inner_edge_height + led_height, center=true,$fn=72);
			cylinder(r=inner_radius - 1, h=inner_edge_height + led_height + 1, center=true,$fn=72);
		}
	}
}

if(outer_edge_height > 0)
{
	translate([0,0,(outer_edge_height + led_height) / 2])
	{
		difference()
		{
			cylinder(r=outer_radius + 1, h=outer_edge_height + led_height, center=true,$fn=72);
			cylinder(r=outer_radius, h=outer_edge_height + led_height + 1, center=true,$fn=72);
		}
	}
}
```


[User]
I need an OpenSCAD design for a customizable jar cap, something I can use to reuse old jars. I want to be able to control the diameter of the cap's base, the diameter of the small holes on top, and the number of rows of holes. I also need to control the overall height of the cap.

Ideally, it would have a slightly wider top than base, sort of like a frustrum and the bottom of the cap should have a recessed area to fit over the mouth of a jar. It should also have a catch or lip to keep it from just falling off. I’m not sure if that is a proper catch. I'd also like to adjust the width of the top rim, or have it automatically calculated for a small increase. I also need to be able to control the space between the holes and how big the lip is. I'm trying to be able to modify these values so I can easily make caps for all sorts of different sized jars I have lying around.

I don’t need any special libraries but please use the standard OpenSCAD functions.

[Assistant]
Customizable_Jar_Cap.scad:
```
// preview[view:south west, tilt:bottom]

/* [General] */

// Base diameter (bottom part)
diameter = 51.5;

// Diameter of single hole
holeDiameter = 1.8;

// Number holes rows with central hole
holeRings = 6; // [0:20]

/* [Advanced] */

// Use -1 for auto.
rimWidth = -1;

// Total cap height
height = 16; // [1:20]

// Modifier for space around holes
holeSpace = 1;

// Set 4 to disable catch
catchSize = 10; // [4:20]

// calculated
bottomRadius = diameter/2;
topRadius = rimWidth == -1 ? bottomRadius * 1.04 : bottomRadius + rimWidth;
basePocketRadius = bottomRadius - 2;
basePartHeight = height / 2;
catchCenterX = topRadius + 2;
holeRadius = holeDiameter / 2;
catchCogCylinderRadius = topRadius - catchSize / 2.8 + 1;
catchHeight = height > 10 ? 7 : height * 0.7;
catchCogHeight = height > 10 ? 3 : height * 0.3;

module base() {
	cylinder(h=basePartHeight, r1=topRadius, r2=bottomRadius);
	translate([0, 0, basePartHeight])
	cylinder(h=basePartHeight, r=bottomRadius);
}

module basePocket() {
	if (height > 1)
	translate([0, 0, 1])
	cylinder(h=height, r=basePocketRadius);
}

module grooveCylinder() {
	translate([catchCenterX, 0, 0])
	cylinder(h=catchHeight, r=catchSize);
}

module catchPocket() {
	translate([catchCenterX, 0, -1])
	cylinder(h=catchHeight, r=catchSize-2);
}

module catchCogCylinder() {
	translate([0, 0, 0])
	cylinder(h=catchCogHeight, r1=catchCogCylinderRadius, r2=catchCogCylinderRadius-1);
}

module hole(x, y) {
	translate([x, y, -1])
	cylinder(r=holeRadius, h=height+2);
}

module holes() {
	if (holeRings > 0)
		hole(0, 0);

	if (holeRings > 1) {
		for (ring = [1:holeRings-1]) {
			for (i = [1:6*ring]) {
				assign(x=sin(i*60/ring+90)*ring*holeSpace*holeRadius*4.2)
				assign(y=cos(i*60/ring+90)*ring*holeSpace*holeRadius*4.2)
				if (pow(x - catchCenterX, 2) + pow(y, 2) > pow(catchSize+holeRadius, 2))
				if (pow(x, 2) + pow(y, 2) < pow(basePocketRadius-holeRadius, 2))
				hole(x, y);
			}
		}
	}
}

module emptyBase() {
	difference() {
		base();
		basePocket();
	}
}

module emptyBaseWithHoles() {
	difference() {
		emptyBase();
		holes();
	}
}

module groove() {
	intersection() {
		base();
		grooveCylinder();
	}
}

module baseWithGroove() {
	union() {
		emptyBaseWithHoles();
		groove();
	}
}

module baseWithCatch() {
	difference() {
		baseWithGroove();
		catchPocket();
	}
}

module catchCog() {
	intersection() {
		catchPocket();
		catchCogCylinder();
	}
}

module fullBase() {
	union() {
		baseWithCatch();
		catchCog();
	}
}

$fa = 2;
$fs = 0.3;
fullBase();

```


[User]
Hey, I'm looking to generate some customizable 3D printable columns using OpenSCAD. I'd like a few features included.

First, I need to be able to specify the overall height of the column and the ratio of its height to its width. I'd like the base to be a simple block and the top to have a customizable capital. The capital needs to be selectable from at least four options - Tuscan, Doric, Ionic, and Corinthian.

I also want to customize the fluting style on the column's shaft, either Greek, Roman, or no fluting at all. And, ideally, it would be great to also have an option for spiral fluting at some point in the future, but it's not critical for now.

I'm not super familiar with OpenSCAD libraries, but are there any libraries available that would help with creating the different capital styles, particularly the Corinthian one? I'd prefer to not code those from scratch if possible. I'd also like to have all the different styles of columns in the same file. Thanks!

[Assistant]
Column_1.2.scad:
```
//Customizable Column v1.2
//v1.2 Customizer fix, added ionic capital
//v1.0 had 10 downloads
//v1.1 had 381 downloads
//Created by Ari M. Diacou, October 2014
//Shared under Creative Commons License: Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
//see http://creativecommons.org/licenses/by-sa/3.0/

//The ratio of the height to the width of the column
ratio=5;
//The length of the column including the base and capital
height=20;
//Stripes that go up the column
fluting="roman";//[roman,greek,none]
capital="ionic";//[corinthian,simple,ionic]

						/*[Hidden]*/
///////////////// Variables //////////////////////////
pi=3.1415+0;
ep=0.001+0;
width=height/ratio;
capital_height=(capital=="corinthian")
				  ? width*1.3
				  : width*0.25;
//types=["tuscan","doric","ionic","corinthian"]+0;
//chosen_type="tuscan";//["tuscan","doric","ionic","corinthian"]+0;
//x=search(chosen_type,types)+0;
//echo(x);

////////////////// Main() ///////////////////////////
column();
//////////////// Functions ////////////////////////////
module column(){
	bottom();
	top();
	shaft();
	}

module top(){
	translate([0,0,height-ep]){
        if(capital=="corinthian"){
            corinthian_capital();}
        if(capital=="ionic"){
            ionic_capital();}
        if(capital=="simple"){
            cube([width*1.25,width*1.25,width*0.25],center=true);}
        }
	}

module bottom(){
	translate([0,0,width*0.125])
		cube([width*1.25,width*1.25,width*0.25],center=true);
	}

module shaft(){
	difference(){
		cylinder(h=height, r=width/2,$fn=72);
		if(fluting=="greek" || fluting=="roman"){
			for(i=[0:23]){
				translate((width/2)*[sin((360/24)*i),cos((360/24)*i),0])
					cylinder(h=height,
								r=(fluting=="greek")? (pi*width/2/24):(pi*width/2/36),
								$fn=24);
				}
			}
		}
	}

module ionic_capital(){
    x=width*0.5+capital_height;
    y=width*.625;
    z=-0.5*capital_height;
    cube([width+2*capital_height,width*1.25,capital_height],center=true);
    translate([x,y,z])
        rotate([90,0,0])
            cylinder(h=width*1.25,d=capital_height*2,$fn=12);
    translate([-x,y,z])
        rotate([90,0,0])
            cylinder(h=width*1.25,d=capital_height*2,$fn=12);
    }
module corinthian_capital(){
    z=capital_height;
	ep=.001;
	resize([1.2*z,1.2*z,z])
	translate([0,0,-4])
	union(){
		difference(){
			for(i=[1:12]){
				rotate([0,0,(i+0.0)*30]) petal(3);
				rotate([0,0,(i+0.5)*45]) petal2(3);
				rotate([0,0,(i+0.5)*90]) petal3(3);
				}
			cube([16,16,8],center=true);
			}
		translate([0,0,7+6+.5-ep]) cube([12,12,1],center=true);
		}
	}
module petal(x){
	translate([0,-x,0])
	linear_extrude(height = 7, center = false, convexity = 10, scale=[1,2], $fn=24)
		translate([0, x, 0])
			circle(r = 1.5);
	}

module petal2(x){
	translate([0,-x,3])
	linear_extrude(height = 7, center = false, convexity = 10, scale=[1,2], $fn=24)
		translate([0, x, 0])
			circle(r = 1.5);
	}

module petal3(x){
	translate([0,-x,6])
	linear_extrude(height = 7, center = false, convexity = 10, scale=[1,1.98], $fn=24)
		translate([0, x, 0])
			circle(r = 2.5);
	}
```


[User]
I need a parametric spool holder for 3D printing filament. It should have a base, two stands, and an axle. I want to be able to adjust the size of the holder based on the spool and hole dimensions of the filament I am using.

Here are the parameters I'd like to be able to control:

*   **axle\_diameter**: The diameter of the hole in the center of the spool in millimeters.
*   **spool\_diameter**: The diameter of the entire spool in millimeters.
*   **spool\_width**: The width of the spool in millimeters.
*   **axle\_tolerance**: Extra space between the axle and the spool opening in millimeters (this should be a little larger than the diameter, so the spool spins freely).
*   **spool\_tolerance**: Extra space from the spool to the ground in millimeters.
*   **spool\_padding**: Extra space between the stands and the spool in millimeters.
*   **stand\_thickness**: Thickness of the stands and base in millimeters.
*  **stand\_balance**: Extra base width for stability in millimeters.
*  **part**: Allows choosing to print only the axle, stands, base or all parts. (string value, "axle", "stands", "base", "all")

I want the design to be done in OpenSCAD. The base should be a flat rectangle with cutouts for weight reduction and the stands should be attached to this base, with cutouts that interlock. The axle should be a cylinder that fits between the two stands. I'd like to use the built-in OpenSCAD modules (i.e. `cube()`, `cylinder()`, `difference()`, etc.), and no external libraries.

[Assistant]
FilamentHolder.scad:
```
/**
 * Parametric Spool Holder
 * By Chris London
 *
 * based on: http://www.thingiverse.com/thing:293623
 */

/* [Standard] */
/* [Global] */

// Which part would you like to see?
part = "all"; // [axle:Axle Only,stands:Stands Only,base:Base Only,all:All]

// The diameter of the hole in the center of the spool in millimeters.
axle_diameter = 32;

// The diameter of the entire spool in millimeters
spool_diameter = 100;

// The width of the spool in millimeters
spool_width = 60;

/* [Advanced] */

// Extra space between the axle and the spool opening in millimeters
axle_tolerance = 2;

// Extra space from the spool to the ground in millimeters
spool_tolerance = 25;

// Extra space between the stands and the spool in millimeters
spool_padding = 20;

// Thickness of the design in millimeters
stand_thickness = 8;

// Extra base width for stability in millimeters
stand_balance = 68;

/* [Hidden] */

axleRadius =  (axle_diameter - axle_tolerance) / 2;
spoolRadius = spool_diameter / 2 + spool_tolerance;
standWidth = spool_width + (2 * spool_padding);
pegDistance = (axleRadius / 1.3) > 8 ? axleRadius / 1.3 : 8;

print_part();

module print_part() {
	if (part == "axle") {
		axle();
	} else if (part == "stands") {
		flatStands();
	} else if (part == "base") {
		base();
	} else if (part == "all") {
		all();
	} else {
		all();
	}
}

// Draw the base
module base() {
	difference() {
		translate([-(stand_balance + axle_diameter) / 2, -standWidth / 2, 0])
		cube([stand_balance + axle_diameter, standWidth, stand_thickness]);

		translate([2.25, -standWidth / 2 + stand_thickness, -stand_thickness / 2])
		cube([(stand_balance + axle_diameter) / 2 - stand_thickness - 2.25, standWidth - stand_thickness * 2, stand_thickness * 2]);

		translate([-(stand_balance + axle_diameter) / 2 + stand_thickness, -standWidth / 2 + stand_thickness, -stand_thickness / 2])
		cube([(stand_balance + axle_diameter) / 2 - stand_thickness - 2.25, standWidth - stand_thickness * 2, stand_thickness * 2]);

		translate([-pegDistance, -41, 2])
		equiTriangle([10, stand_thickness * 2]);

		translate([pegDistance, -41, 2])
		equiTriangle([10, stand_thickness * 2]);

		translate([-pegDistance, 51, 2])
		equiTriangle([10, stand_thickness * 2]);

		translate([pegDistance, 51, 2])
		equiTriangle([10, stand_thickness * 2]);
	}
}

// Draw two stands in their upright position
module stands() {
	translate([0, standWidth / 2 - stand_thickness / 2, 0])
	stand();

	translate([0, -standWidth / 2 + stand_thickness / 2, 0])
	stand();
}

// Draw two stands in their flat printing position
module flatStands() {
	translate([-(axleRadius + stand_thickness) - 10, 0, 0])
	rotate(90, v=[1,0,0])
	stand();

	translate([(axleRadius + stand_thickness) + 10, 0, 0])
	rotate(90, v=[1,0,0])
	stand();
}

// Draw a single stand in an upright position
module stand() {
	pegOffset = -5.8;

	difference() {
		translate([0, 0, stand_thickness]) union() {
			translate([-(axleRadius + stand_thickness), -stand_thickness / 2, 0])
			cube([(axleRadius + stand_thickness) * 2, stand_thickness, spoolRadius]);

			translate([-(axleRadius + stand_thickness), 0, 0])
			cylinder(spoolRadius, stand_thickness / 2, stand_thickness / 2);

			translate([(axleRadius + stand_thickness), 0, 0])
			cylinder(spoolRadius, stand_thickness / 2, stand_thickness / 2);

			translate([-pegDistance, stand_thickness / 2, pegOffset])
			equiTriangle([9.5, stand_thickness]);

			translate([pegDistance, stand_thickness / 2, pegOffset])
			equiTriangle([9.5, stand_thickness]);
		}

		translate([-axleRadius - stand_thickness / 2, -stand_thickness, stand_thickness * 2])
		cube([axleRadius * 2 + stand_thickness, stand_thickness * 2, spoolRadius - axleRadius - (stand_thickness * 2)]);

		rotate(90, v=[1,0,0])
		translate([0, spoolRadius + stand_thickness - 2, -stand_thickness])
		cylinder(stand_thickness * 2, axleRadius, axleRadius);

		translate([-axleRadius, -stand_thickness, spoolRadius + stand_thickness - 2])
		cube([axleRadius * 2, stand_thickness * 2, axleRadius * 2]);
	}
}

// Draw an axle in the upright position
module axle() {
	cylinder(standWidth, axleRadius, axleRadius);
}

module all() {
	base();
	stands();

	rotate(90, v=[1,0,0])
	translate([0, spoolRadius + stand_thickness - 1.5, -standWidth / 2])
	axle();
}

module equiTriangle(coords) {
	height = coords[0] / 2 * sqrt(3);
	rotate(90, v=[1,0,0])
	linear_extrude(coords[1], true, coords[1], 0)
	polygon(points=[[0,height], [-coords[0]/2, 0], [coords[0]/2, 0]]);
}

```


[User]
Hey there, I'm looking to create a customizable logarithmic spiral column, similar to the one I saw online (Spiral_1.0.scad), but I need it to be a bit more robust and flexible for my project. I'd like to be able to easily tweak its overall dimensions and have some better control over the individual components, like the spherical nodes and cylindrical segments.

Here’s what I'm thinking:

1.  **Logarithmic Spiral:** The base structure should still be a logarithmic spiral defined by `r = a * exp(b * theta)`, where `a` and `b` are adjustable parameters.
2.  **Number of Loops & Segments:** I'd like to specify the number of loops and the number of segments per loop as separate parameters. This allows for fine-tuning the spiral's density and overall length.
3.  **Spherical Nodes:** At each segment endpoint, there should be a sphere. The diameter of the spheres should be proportional to the radius of the spiral at that point, maybe something like `d = r/k`, where `k` is another adjustable parameter to manage sphere size.
4.  **Cylindrical Segments:** The segments connecting the spherical nodes should be cylinders. The diameters of these cylinders should match the diameters of the connected spheres, and their length should be calculated as the arc length between the nodes.
5.  **Fudge Factors:** Similar to the example code I saw, I'd like to have fudge factors for the radial and rotational alignment of the cylinders. These factors should allow for small adjustments to avoid issues where the cylinders do not precisely line up with the spheres.
6.  **Overall Height:** I would like to have control over the height of the column by setting the distance between successive points along the z-axis as it spirals upwards.
7.  **Libraries:** I think using the `BOSL2` library would be beneficial for some of the mathematical operations and possibly for the sphere and cylinder generation.

I'd prefer a fully parametric design, so that each of these parameters can be easily adjusted. Could you design an OpenSCAD file or set of files that implement this? Thanks!

[Assistant]
Spiral_1.0.scad:
```
//Customizable Column v1.1
//v1.0 had 10 downloads
//Created by Ari M. Diacou, October 2014
//Shared under Creative Commons License: Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
//see http://creativecommons.org/licenses/by-sa/3.0/

loops=3;
steps_per_loop=20;
//A logarthmic Spiral has the form r=a*exp(b*theta);
a=0.4;
b=0.2;
//How much detail on the curves
$fn=30;
//If segments dont line up with spheres, use this to move segments in and out. Vary between [-0.5,0.5].
rad_fudge=0.30;
//If segments dont line up with spheres, use this to rotate segments. Vary between [-0.5,0.5].
deg_fudge=-0.10;

						/*[Hidden]*/
////////////////// Variables //////////////////////////
pi=3.1415+0;
//////////////////// Main() ///////////////////////////
for(i=[0:loops*steps_per_loop]){
	translate([r(rad(i))*cos(deg(i)),r(rad(i))*sin(deg(i)),0])
		color("pink") sphere(d=d(i));
	translate([
					r(rad(i+rad_fudge))*cos(deg(i+0.5)),
					r(rad(i+rad_fudge))*sin(deg(i+0.5)),
					0])
		rotate([90,0,deg(i+deg_fudge)])
			cylinder(d2=d(i),d1=d(i+1),h=arc_length(i-1),center=true);
	}
////////////////// Functions //////////////////////////
function deg(n)=360*n/steps_per_loop;
function rad(n)=2*pi*n/steps_per_loop;
function arc_length(n)= //The length of a line segment = sqrt( (y2-y1)^2 + (x2-x1)^2 )
		sqrt(
			pow(
				r(rad(n+1))*sin(deg(n+1)) -
				r(rad(n))*sin(deg(n))
				,2)
			+
			pow(
				r(rad(n+1))*cos(deg(n+1)) -
				r(rad(n))*cos(deg(n))
				,2)
			);
function r(th)=a*exp(b*th);
function d(i) =r(rad(i))/3;
```


[User]
Hey there! I'm looking to create a parametric nose cone for an RC plane, and I'd like it to be customizable. I've got a bunch of parameters I need to be able to tweak, and I'd like to use OpenSCAD.

Here are the dimensions:

*   **`diameterPlane`**: This is the diameter of the base of the nose cone where it attaches to the plane's fuselage.
*   **`diameterProp`**: This is the diameter of the nose cone where the propeller mounts.
*   **`diameterMotorHole`**: This is the diameter of the hole in the front of the nose cone for the motor shaft.
*   **`heightSocket`**: The length of the base portion of the nose cone that has the `diameterPlane` diameter.
*   **`heightTotal`**: The total length of the nose cone.
*   **`thickness`**: This defines the wall thickness.

Then, there are also these decorative elements:

*   **`ellipses`**: The number of decorative ellipses around the propeller end.
*   **`thicknessEllipses`**: The thickness of the ellipses.
*   **`scaleEllipses`**: A scale factor for the width of the ellipses.
*   **`text`**:  A string of text that will be embossed onto the socket portion of the cone. I want to use the "orbitron.dxf" font.

I'm hoping to be able to use a couple of libraries for this, specifically:

*   A `build_plate.scad` library that can draw a build plate, and can account for Replicator 2, Replicator, Thingomatic, and Manual build plate sizes. I also need to be able to set the manual x and y dimensions of the build plate.
*   A `Write.scad` library with a `writecylinder` function that lets me add text along a cylinder's surface.

It would be great if the main design was in a module called `nose()`, which is basically two joined cylinders and some cutouts. Also, the text should be embossed along the first, wider, cylinder section. Finally, the decorative ellipses should sit proud on the front face of the cone. Thanks for your help!

[Assistant]
nose.scad:
```
/******************************************************************************************
* Nose Generator for RC model planes                                                      *
* by Thomas Rößler, http://www.geekair.at                                                 *
*                                                                                *
* This work is licensed under the Creative Commons Attribution 4.0 International License. *
* To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.      *
*                                                                                *
* Please attribute to www.geekair.at                                                      *
******************************************************************************************/
use <utils/build_plate.scad>
use <write/Write.scad>
//use <../../lib/write.scad/write.scad>
// preview[view:north, tilt:bottom diagonal]

/* [Sizes] */
// Diameter of the nose on rc plane side
diameterPlane = 128;
// Diameter of the nose on propeller side
diameterProp = 80;
// Diameter of the propeller hole
diameterMotorHole = 40;
// length of wide side
heightSocket = 55;
// Total length of the nose
heightTotal = 110;
// thickness of the walls
thickness = 1;

/* [Decoration] */
// number of ellipses on propeller side
ellipses = 54;
// thickness of the ellipse layer
thicknessEllipses = 1;
// scale factor for ellipse width
scaleEllipses = 0.13;
// text on socket
text = "www.geekair.at";

/* [Build Plate] */
//for display only, doesn't contribute to final object
build_plate_selector = 0; //[0:Replicator 2,1: Replicator,2:Thingomatic,3:Manual]
//when Build Plate Selector is set to "manual" this controls the build plate x dimension
build_plate_manual_x = 100; //[100:400]
//when Build Plate Selector is set to "manual" this controls the build plate y dimension
build_plate_manual_y = 100; //[100:400]

/* [Hidden] */
$fn = 120;
effectiveThicknessEllipses = ellipses > 0 ? thicknessEllipses : 0;

module noseShape(dPlane, dProp, extraHeight) {
	cylinder(r=dPlane/2, h=heightSocket+extraHeight);

	translate([0, 0, heightSocket])
	cylinder(r1=dPlane/2, r2=dProp/2, h=(heightTotal-heightSocket)+extraHeight);
}

module nose() {
	width = (diameterProp - diameterMotorHole) / 2;

	color("orange")
	translate([0, 0, heightTotal]) {
		for(i = [1 : ellipses]) {
			rotate([0, 0, 360/ellipses * i])
			translate([0, (width + diameterMotorHole) / 2, 0])
			scale([scaleEllipses, 1, 1])
			cylinder(r=width/2, h=effectiveThicknessEllipses);
		}
	}

	color("orange")
	writecylinder(text=text,where=[0,0,0],font="orbitron.dxf",h=10,radius=(diameterPlane+thickness)/2,height=heightSocket);

	difference() {
		noseShape(diameterPlane+thickness, diameterProp+thickness, 0);

		translate([0, 0, -thickness])
		noseShape(diameterPlane, diameterProp, 0.1);

		translate([0, 0, heightTotal])
		cylinder(r=diameterMotorHole/2, h=thickness*2, center=true);
	}
}

translate([0, 0, heightTotal+effectiveThicknessEllipses])
rotate([180, 0, 0])
nose();

build_plate(build_plate_selector,build_plate_manual_x,build_plate_manual_y);
```


[User]
I need a design for a rope end cap, you know, like the little plastic or metal things that go on the ends of shoelaces or drawstrings.

The basic shape should be a cylindrical base with a slightly rounded top. The cap needs to have a hole going all the way through for the rope to pass through and then get knotted to keep it from pulling out. The top rounded part should be essentially a slightly smaller diameter sphere blended smoothly into the cylindrical part, making the top of the cap taper a bit towards the rounded end.

I want to be able to control several things as parameters:

*   The overall diameter of the cap (let's call it `cap_diameter`).
*   The overall height of the cap (`cap_height`).
*   The diameter of the hole for the rope (`hole_diameter`).
*   The thickness of the cap's wall (`wall_thickness`).

I need the interior of the cap to be hollowed out, obviously, so the wall thickness applies to the thickness of all the walls, and the top of the rounded part.

Could you generate an OpenSCAD file for this design? I would like to be able to use all of the parameters that I described above.

[Assistant]
rop_end.scad:
```
$fn = 1*50;

//Diameter of rop end cap
rop_diam = 15.3;
//Hight of rop end cap
rop_hight = 16.24;
//Hole for rope
rop_hole_diam = 4;//[2:6]
//Thikness of rop end cap
rop_thikness = 1.5;

difference() {
	hull () {
		translate ([0, 0, rop_hight]) sphere (d = rop_diam-rop_diam/5);
		cylinder (h = rop_hight, d1 = rop_diam, d2 = rop_diam-rop_diam/5);
	}
	hull () {
		translate ([0, 0, rop_hight]) sphere (d = rop_diam-rop_thikness*2-rop_diam/5);
		cylinder (h = rop_hight, d1 = rop_diam-rop_thikness*2, d2 = rop_diam-rop_thikness*2-rop_diam/5);
	}
	translate ([0, 0, rop_hight+(rop_diam-rop_diam/5)/2-rop_thikness-1]) cylinder (h = rop_thikness+2, d = rop_hole_diam );
}
```


[User]
Okay, I have a kind of complex design in mind and I'm hoping you can help me create the necessary OpenSCAD files. It's a 10-digit puzzle, where each digit is made from a 5x3 grid of what I'm calling "boxels."

Here are the specifics:

*   **Boxels:** Each boxel is a square, and I need several types:
    *   Empty
    *   Full square
    *   Half square (diagonal)
    *   Pointy dent (a square with a point pushed inwards on one side)
    *   Full dented (a square with an inward point and the corners pulled in slightly)
*   **Digit Definition:** Each digit (0-9) is composed of 5 rows of 3 boxels. I'll provide the data for this (boxel type and rotation in 90-degree increments) as an array.
*   **Puzzle Solution:** The puzzle has a "solved" configuration. This includes a specific rotation and translation for each digit. Again, this data will be provided as an array.
*   **Printing Configuration:** I also need a "print" configuration, which orients the digits for easy printing and doesn't give away the puzzle's solution.  This, too, is defined with a rotation and translation for each digit, stored as an array.
*   **Box:**  The puzzle sits within a box. I need the ability to render and not render the box. The box has an adjustable thickness, height, and a little extra space to ease insertion of the digits.
*   **Parametric:** All dimensions like boxel size, element height, box thickness, extra space, and the "ease" parameter for the dented boxels should be parametric.
*   **Color:** I would like a toggle to have each digit be a different color, or not be colored.

I'm basically envisioning several interconnected SCAD files:

1.  **Core definitions:** A file to set the parameters for the boxel sizes, dimensions of elements, box properties, and definitions of the basic boxel types. This should include the data arrays for the digit definitions, translations, and rotations for both the solved state and the print configuration. It will also store the color array.
2.  **Boxel generation:** A file to handle the creation of the different boxel types. It should take the boxel type index as an input and output a 2D shape, ready to be extruded.
3.  **Digit generation:** A file to construct each digit from the given boxel arrangement.
4.  **Main assembly:** A top-level file that includes all the above and instances the digits. This will need to render the box according to parameters, place the digits in either the "solved" or "print" state, and apply colors according to parameters.

I also need to note that the goal is to create manifold parts suitable for printing, and so I'm currently scaling the boxels by 1.001, but if there is a more general approach to address that issue I would appreciate learning about it. I am not using any external libraries.

I'm looking forward to seeing what you can create!

[Assistant]
10_digit_puzzle_eased.scad:
```
//digits are made of 3x5 'boxels'. specify boxel size (mm)
boxel_size=8;
//elements height (mm)
elem_height=5;
//Display solved puzzle
solved=0;
//render box
box=1;
//box_thickness (mm)
box_thickness=2;
//extra space in box to ease insertion (mm)
space=1;
//ease in the dented boxels. keep this very small (~0.05)
jeu=0.05;
//box height (mm)
box_height=2;
//render colors (0 fot no / 1 for yes)
colored=0;
boxel=[
	[],							//empty
	[[-0.5,-0.5],[0.5,-0.5],[0.5,0.5],[-0.5,0.5]],		//full
	[[-0.5,-0.5],[0.5,-0.5],[0.5,0.5]],			//half (diagonal)
	[[-0.5+jeu,-0.5],[0.5-jeu,-0.5],[0,-jeu]],				//pointy dent
	[[-0.5,-0.5+jeu],[-0.5,0.5],[0.5,0.5],[0.5,-0.5+jeu],[0,jeu]]	//full dented
];

//digits definitions. 5 x 3 pairs, each pair is [boxel index , Z rotate x 90°]
digit=[
[  //0
 [[2,0],[1,0],[2,3]],
 [[1,0],[0,0],[1,1]],
 [[3,0],[0,0],[4,3]],
 [[1,0],[0,0],[1,0]],
 [[2,1],[1,0],[2,2]]
],
[ //1
[[3,0],[0,0],[0,0]],
[[1,0],[0,0],[0,0]],
[[4,3],[0,0],[0,0]],
[[1,0],[0,0],[0,0]],
[[3,2],[0,0],[0,0]]
],
[ //2
 [[3,1],[1,0],[2,3]],
 [[0,0],[0,0],[1,0]],
 [[2,0],[1,0],[2,2]],
 [[1,0],[0,0],[0,0]],
 [[2,1],[1,0],[3,3]]
],
[ //3
 [[3,1],[1,0],[2,3]],
 [[0,0],[0,0],[1,0]],
 [[3,1],[1,0],[4,1]],
 [[0,0],[0,0],[1,0]],
 [[3,1],[1,0],[2,2]]
],
[ //4
 [[3,0],[0,0],[3,0]],
 [[1,0],[0,0],[1,0]],
 [[2,1],[1,0],[4,1]],
 [[0,0],[0,0],[1,0]],
 [[0,0],[0,0],[3,2]]
],
[ //5
 [[2,0],[1,0],[3,3]],
 [[1,0],[0,0],[0,0]],
 [[2,1],[1,0],[2,3]],
 [[0,0],[0,0],[1,0]],
 [[3,1],[1,0],[2,2]]
],
[ //6
 [[2,0],[1,0],[3,3]],
 [[1,0],[0,0],[0,0]],
 [[4,3],[1,0],[2,3]],
 [[1,0],[0,0],[1,0]],
 [[2,1],[1,0],[2,2]]
],
[ //7
 [[3,1],[1,0],[2,3]],
 [[0,0],[0,0],[1,1]],
 [[0,0],[0,0],[4,3]],
 [[0,0],[0,0],[1,0]],
 [[0,0],[0,0],[3,2]]
],
[ //8
 [[2,0],[1,0],[2,3]],
 [[1,0],[0,0],[1,0]],
 [[4,3],[1,0],[4,1]],
 [[1,0],[0,0],[1,0]],
 [[2,1],[1,0],[2,2]]
],
[ //9
 [[2,0],[1,0],[2,3]],
 [[1,0],[0,0],[1,0]],
 [[2,1],[1,0],[4,1]],
 [[0,0],[0,0],[1,0]],
 [[3,1],[1,0],[2,2]]
]
];

//Rotate to solve
rsolved=[
	[  0	,  0	,  0	],	//  0
	[  0	,  0	,-90	], 	//  1
	[  0	,180	,-90	],	//  2
	[  0	,  0	, 90	],	//  3
	[  0	,  0	, 90	],	//  4
	[  0	,  0	,  0	],	//  5
	[  0	,  0	,-90	],	//  6
	[  0	,  0	, 90	],	//  7
	[  0	,  0	,  0	],	//  8
	[  0	,  0	,-90	]	//  9
	];

//Translate to solve
tsolved=[
	[ 7	, 1	, 0	],	//  0
	[ 4	,-2	, 0	], 	//  1
	[ 0	, 2	, 0	],	//  2
	[ 6	, 6	, 0	],	//  3
	[ 2	, 6	, 0	],	//  4
	[ 3	, 3	, 0	],	//  5
	[ 6	, 4	, 0	],	//  6
	[ 6	, 0	, 0	],	//  7
	[-1	, 5	, 0	],	//  8
	[ 0	, 0	, 0	]	//  9
	];

//Rotate to print
rprint=[
	[  0	,0	,  0	],	//  0
	[  0	,0	,  0	],	//  1
	[  0	,0	,  0	],	//  2
	[  0	,0	,  0	],	//  3
	[  0	,0	,  0	],	//  4
	[  0	,0	, 90	],	//  5
	[  0	,0	,  0	],	//  6
	[  0	,0	, 90	],	//  7
	[  0	,0	,-45	],	//  8
	[  0	,0	,  0	],	//  9
	];

//Translate to print
// (a bit messy, but minimizes footprint & travel time without showing the solution)
tprint=[
	[-3	, 6.0	,0	],	//  0
	[ 0.15	, 5.4	,0	],	//  1
	[ 1.3	, 5.9	,0	],  	//  2
	[ 3.45	, 5.9	,0	],  	//  3
	[-3	, 1.8	,0	],  	//  4
	[ 2.5	, 1.1	,0	],	//  5
	[-3.6	,-1.8	,0	],  	//  6
	[ 1.1	, 1.8	,0	],  	//  7
	[ 2.83	,-1.9	,0	],	//  8
	[-0.9	,-2.2	,0	]   	//  9
	];

dcolor=[[0.5,0.5,0],[0.5,0,0.5],[0,0.5,0.5],[1,0,0],[0,1,0],[0,0,1],[1,1,0],[0,1,1],[1,0,1],[0.5,1,0.8],];

//--------------------------------------------------------------
// render digit n° nd
//--------------------------------------------------------------
module mkdigit(nd) {
	for ( row = [0 : 4] )
		{
		for ( col = [0 : 2] )
			{
			translate([(col-1)*boxel_size,(2-row)*boxel_size,0])
			scale([boxel_size,boxel_size,1])
			rotate([0,0,digit[nd][row][col][1]*90])
					scale(1.001) //for manifold... avoids adjacent faces
					linear_extrude(height = elem_height, center = true, convexity = 10)
					polygon(points=boxel[digit[nd][row][col][0]]);
			}
		}

 };

//--------------------------------------------------------------
// render and place all digits
//--------------------------------------------------------------
 for (digitnum=[0:9])
 {
	color(colored*dcolor[digitnum]+(1-colored)*[0.5,0.8,1])
	union() {
	translate([0,0,elem_height/2]+(box*solved*[0,0,box_thickness]))
	translate((1-solved)*tprint[digitnum]*boxel_size)
	translate(solved*boxel_size*(tsolved[digitnum]-[3,3,0]))
		rotate(solved*rsolved[digitnum])
		rotate((1-solved)*rprint[digitnum])
			mkdigit(digitnum);
	}
}

//--------------------------------------------------------------
// render box
//--------------------------------------------------------------
scale(box)
translate((1-solved)*[boxel_size*9.5+box_thickness*2+space,boxel_size*2,0])
translate([0,0,(box_height+box_thickness)/2])
rotate((1-solved)*[0,0,90])
difference(){
	cube(size=[boxel_size*11+box_thickness*2+space,boxel_size*9+box_thickness*2+space,box_height+box_thickness],center=true);
	translate([0,0,box_thickness])cube(size=[boxel_size*11+space,boxel_size*9+space,box_height+box_thickness],center=true);
}
```


[User]
Hey, I'm looking to create a parametric design for a paper fastener, the kind you use to hold a stack of papers together. I'd like to be able to adjust various aspects of it for different use cases.

Essentially, it's a peg that goes through the paper, and a washer that keeps it from sliding back out. The peg part has a cylindrical base, then a smaller cylinder extending from that which is meant to go through the papers, and then a wider rounded stopper at the end to keep it from sliding back out. There's also a cutout on the side of the peg for flexibility when pushing it through the washer. The washer is just a simple ring with a hole in the middle that the peg pushes through.

Here's what I'm thinking about for parameters:

*   `peg_base_radius`: Radius of the base of the peg
*   `hole_radius`: Radius of the hole that the peg goes through (and radius of the cylindrical portion of the peg)
*   `peg_tag_height`: Height of the base of the peg (and the washer)
*   `paper_width`: The thickness of the paper stack it will be fastening, this will control length of the peg's cylindrical portion.
*   `stopper_increment`: How much larger the rounded stopper at the end of the peg is compared to the `hole_radius`. This affects how secure the fastener is.
*   `cutout_width`: The width of the cutout on the side of the peg to allow flex when inserting the peg into the washer.

I think that should cover it. I'd really appreciate it if you could generate the OpenSCAD code for this. I'm not using any specific libraries right now, but if you think any would be useful, I'm open to suggestions.

[Assistant]
Fastner.scad:
```
//fastner radius
lR = 7.5;
//hole radius
iR = 2.25;
//fastner height of tags
h = 1.5;
//paper width
pW = 3;
//increment of stopper to fasten
dH=1;

module fastnerPeg(){
difference(){
 union(){
	cylinder(r=lR,h=h);
	translate([0,0,h]) cylinder(r=iR,h=pW+h);
	translate([0,0,2*h+pW]) sphere(r=iR+dH/2);
	}
	translate([-(dH*1.25)/2,-(iR*2+dH)/2,h]) cube([dH*1.25,iR*2+dH,h+pW+iR+dH/2]) ;
}
}

module fastnerWasher(){
	difference(){
		cylinder(r=lR,h=h);
		// increase r if your printer prints smaller holes.
		cylinder(r=iR+dH/2+0.3,h=h);
	}
}

fastnerPeg();

translate([lR *2 + 2,0,0])
fastnerWasher();
```


[User]
I'm trying to design a sort of spiral gun, inspired by a video where a ball is accelerated along a spiral path. I've got a basic concept in OpenSCAD, but it's failing to render because it involves a lot of small spheres and I think my approach might not be the best.

Essentially, I need a design where a ball can travel along a spiral groove. The core idea is a flat, circular base, and a spiral path cut into it. Imagine a vinyl record, but instead of a groove that goes around and around in a circle, it needs to be a spiral starting from the center and going outwards. A ball would then sit in that groove.

Here's what I had in mind for the parameters:

*   **Main Radius (r):** The overall radius of the base.
*   **Ball Radius (br):** The radius of the ball that will travel in the groove.
*   **Revolutions Count (n):** The number of revolutions the spiral makes.
*   **Angular Step (s):** The angle increment between each sphere used to create the spiral path. A smaller value will make for a smoother spiral.
*   **Initial Radius (ir):** The starting radius of the spiral.
*   **Border:** The thickness of the material beyond the outer spiral edge of the circular base.
*   **Floor:**  The thickness of the bottom of the base.

I think the most problematic part in my attempt was using spheres to "cut" the spiral path. I feel like there should be a better way to generate this kind of spiraling groove, perhaps by using linear extrusion or something. It would be great if you could generate a parametric design for this, focusing on the creation of the groove along the spiral path, with the parameters exposed.

I'm not sure if this helps, but my previous version used `difference()` to subtract the spheres from a base cylinder, along with a big for loop which is what I think was killing the rendering process. I'm hoping we can do better than that this time. I don't think any special libraries are needed for this, but please let me know if you think it's required. I'd prefer to keep it in plain OpenSCAD if possible.

[Assistant]
spiral_gun.scad:
```
//main radius
r=80;
//ball radius
br=4;
//revolutions count
n=5;
//angular step
s=2;
//initial radius
ir=6;
//border
border=3;
//floor thickness
floor=1;
nsteps=(360*n)/s;
rdelta=(r-ir)/nsteps;

difference()
{
	translate([0,0,-br-floor])cylinder(r=r+br+border,h=br+floor);
	for ( i = [0 : nsteps] )
		{

		rotate([0,0,s*i])translate([ir+(i*rdelta),0,0]) sphere(r=br);
		}

}
```