[User]
I'm looking to create a set of parametric VTech Smart Wheels track pieces using OpenSCAD. I've got some basic designs in mind, but I need your help creating the actual OpenSCAD files, with all the parameters so I can customize everything nicely. I want to be able to create straight track pieces, curved corner pieces, and cross-section pieces.

First, for the **straight track pieces**:

*   I need a parameter to set the *length* of the straight section, excluding the connectors.
*   I need to be able to choose the *connector type* at the start and end of each straight piece (either male or female).
*   The track width needs to be consistent, which I believe is 78.8 units. I need a way to refer to this width value in the file.
*   The track needs to have the basic raised edges on the side. The edges should be the same as in the provided files for vtech_straight.scad.
*   The center part should be lowered and have the two guiding channels, similar to the vtech_straight.scad file.
*   I need to import external STL files for the male and female connectors. I will provide these files separately, named `vtechsmartwheels_female.stl` and `vtechsmartwheels_male.stl`. These will be used in the `connector` module. Make sure this module has a parameter to switch between the two STL models based on user input.

Second, for the **corner track pieces**:

*   I need a parameter to set the *angle* of the corner, which should be configurable between 0 and 90 degrees.
*   I also need a parameter for the *connector type* on each end of the corner.
*   The edges of the road should be designed with a smooth curve at the corner and consistent with the vtech_corner.scad file.
*   I need to import the same male and female STL files as for the straight piece.

Third, for the **cross-section pieces**:

*   I need to specify a connector type for each of the four directions.
*   The edges of the road should be similar to those in the provided cross-section SCAD file, vtech_cross.scad.
*   Same as above, I need to import the same male and female STL files.

All of the files should use the `$fn` variable for the resolution of the curves, and have a default `$fn=18` for normal use, and allow the user to set this to lower or higher values. Also, please be consistent with the units and scaling used in the provided files. The connector width will be referenced as `w`.

For a basic library dependency, could you ensure that the `import()` function is available, and that `hull()` is used to connect the spheres used to create borders.

I am looking for separate `.scad` files for each of the three piece types, clearly labeled as `vtech_straight.scad`, `vtech_corner.scad`, and `vtech_cross.scad`. Please make these designs parametric, easy to understand, and easy to modify.

[Assistant]
vtech_straight.scad:
```
//Length of the road, without connector
//Female is around 20
//male is almost zero (it fits into the female)

roadlength = 50;

//0 = female, 1 = male
start = 1;
end = 0;

//Grade of details
$fn = 18;

module connector(m)
{
    if(m==0)
    {
      import("vtechsmartwheels_female.stl", convexity=3);
    }

    if(m==1)
    {
      import("vtechsmartwheels_male.stl", convexity=3);
    }
}

module startpiece()
{
  connector(start);
}

module endpiece()
{
  translate([roadlength,0,0])
  rotate([0,0,180])
  {
    connector(end);
  }
}

w = 78.8;

module road()
{
  difference()
  {
    union()
    {
      translate([0,-(w/2),0])
      cube([roadlength,w,8]);

      difference()
      {
        hull()
        {
          translate([0,-(w/2),0])
          border();

          translate([0,-(w/2) + 4.9,0])
          border();
        }
      }

      mirror([0,1,0])
      hull()
      {
        translate([0,-(w/2),0])
        border();

        translate([0,-(w/2) + 4.9,0])
        border();
      }
    }

    translate([2,-(w/2) + 2,0])
    cube([roadlength-4,3,14]);

    mirror([0,1,0])
    translate([2,-(w/2) + 2,0])
    cube([roadlength-4,3,14]);

    translate([2,1,0])
    cube([roadlength-4,14,6]);

    translate([2,1 + 14 + 2,0])
    cube([roadlength-4,14,6]);

    mirror([0,1,0])
    {
      translate([2,1,0])
      cube([roadlength-4,14,6]);

      translate([2,1 + 14 + 2,0])
      cube([roadlength-4,14,6]);
    }
  }
}

module border()
{
	br=1.1;
  translate([0,0 + 1,1])
  sphere(r=br);

  translate([roadlength,1,1])
  sphere(r=br);

  translate([0,1,15.5])
  sphere(r=br);

  translate([roadlength,1,15.5])
  sphere(r=br);
}

startpiece();

road();

endpiece();
```
vtech_cross.scad:
```
//0 = female, 1 = male
road1 = 1;
road2 = 0;
road3 = 1;
road4 = 0;

//Number of steps of the corner
corner_fn = 6;

//Width of the track, just leave it
//It helps to center the connectors
w = 78.8;

$fn = 18;

module connector(m)
{
    if(m==0)
    {
      import("vtechsmartwheels_female.stl", convexity=3);
    }

    if(m==1)
    {
      import("vtechsmartwheels_male.stl", convexity=3);
    }
}

module road1piece()
{
    translate([-w/2,0,0])
    connector(road1);
}

module road2piece()
{
  translate([0,w/2,0])
  rotate([0,0,-90])
    connector(road2);
}

module road3piece()
{
  translate([w/2,0,0])
  rotate([0,0,180])
    connector(road3);
}

module road4piece()
{
  mirror([0,1,0])
  translate([0,w/2,0])
  rotate([0,0,-90])
    connector(road4);
}

module border()
{
  difference()
  {
    hull()
    {
      sphere(r=1);

      translate([0,0,15.5])
      sphere(r=1);

      for(r=[0:(90/corner_fn):90])
      {
        translate([-cos(r) * 6, sin(r) * 6,0])
        {
          sphere(r=1);

          translate([0,0,15.5])
          sphere(r=1);
        }
      }
    }

    translate([-10,-10,-4])
    cube([20,20,4]);

    translate([0,-20,-4])
    cube([20,20,24]);
  }
}

module road()
{
  difference()
  {
    translate([0,0,8/2])
    cube([w,w,8],center=true);

    translate([0,0,8-6.5])
    difference()
    {
      co = 56.3/2;
      cylinder(r=co,h=6.6,$fn=80);
      cylinder(r=co-2,h=6.6,$fn=80);
    }

    translate([0,0,8-6.5])
    difference()
    {
      ci = 76.2/2;
      cylinder(r=ci,h=6.6,$fn=80);
      cylinder(r=ci-2,h=6.6,$fn=80);
    }
  }

  translate([(w/2),(-w/2),0])
  border();

  mirror([1,0,0])
  translate([(w/2),(-w/2),0])
  border();

  mirror([0,1,0])
  translate([(w/2),(-w/2),0])
  border();

  mirror([0,1,0])
  mirror([1,0,0])
  translate([(w/2),(-w/2),0])
  border();
}

color("Orange")
{
  road1piece();
  road2piece();
  road3piece();
  road4piece();

  road();
}
```
vtech_corner.scad:
```
//0 = female, 1 = male
start = 1;
end = 0;

//The angle of the corner, between 0 and 90
angle = 45;

//Number of steps of the corner
corner_fn = 18;

//Width of the track, just leave it
//It helps to center the connectors
w = 78.8;

$fn = 12;

module connector(m)
{
    if(m==0)
    {
      import("vtechsmartwheels_female.stl", convexity=3);
    }

    if(m==1)
    {
      import("vtechsmartwheels_male.stl", convexity=3);
    }
}

module startpiece()
{
    translate([0,-w/2,0])
    connector(start);
}

module endpiece()
{
  rotate([0,0,angle])
  translate([0,-w/2,0])
  rotate([0,0,180])
    connector(end);
}

module border(offset=0)
{
	borderradius=1.0;
  for(t=[(angle/corner_fn):(angle/corner_fn):angle])
  {
    t0 = t - (angle/corner_fn);
    hull()
    {
      translate([sin(t0) * (offset), -cos(t0) * (offset),0])
      {
        sphere(r=borderradius);

        translate([0,0,15.5])
        sphere(r=borderradius);
      }

      translate([sin(t) * (offset), -cos(t) * (offset),0])
      {
        sphere(r=borderradius);

        translate([0,0,15.5])
        sphere(r=borderradius);
      }
    }

    hull()
    {
      translate([sin(t0) * (offset + 5), -cos(t0) * (offset + 5),0])
      {
        sphere(r=borderradius);

        translate([0,0,15.5])
        sphere(r=borderradius);
      }

      translate([sin(t) * (offset + 5), -cos(t) * (offset + 5),0])
      {
        sphere(r=borderradius);

        translate([0,0,15.5])
        sphere(r=borderradius);
      }
    }

    hull()
    {
      translate([sin(t0) * (offset), -cos(t0) * (offset),0])
      {
        translate([0,0,15.5])
        sphere(r=borderradius);
      }

      translate([sin(t) * (offset), -cos(t) * (offset),0])
      {
        translate([0,0,15.5])
        sphere(r=borderradius);
      }

      translate([sin(t0) * (offset + 5), -cos(t0) * (offset + 5),0])
      {
        translate([0,0,15.5])
        sphere(r=borderradius);
      }

      translate([sin(t) * (offset + 5), -cos(t) * (offset + 5),0])
      {
        translate([0,0,15.5])
        sphere(r=borderradius);
      }
    }
  }
}

module road()
{
	union()
	{
	  hull()
	  {
		translate([0,-1,0])
		cube([1,1,8]);

		for(r=[0:angle/corner_fn:angle])
		{
		  translate([sin(r) * (w-5), -cos(r) * (w-5),0])
		  cube([1,1,8]);
		}
	  }
	  border(w - 6);

	  border(1);
	}

}

color("Blue")
{
	union()
	{
	  startpiece();
	  endpiece();
	  difference()
	  {
		  road();

		translate([-10,-100,-1])
		cube([10,100,30]);

		translate([-5,-w,-5])
		cube([w + 5,w + 5,5]);
	  }
  }
}
```


[User]
I need a parametric design for a pipe cover, kind of like a collar, that can be used where pipes come through walls or floors. It should be customizable and I need the option for it to be either a single piece or split into two halves.

Here's a breakdown of the dimensions I need to control:

*   **Pipe Diameter:** The diameter of the pipe the cover will go around.
*   **Base Diameter:** The diameter of the wider base of the cover.
*   **Base Height:** The height of the cylindrical base before the tapered section starts.
*   **Loft Height:** The height of the tapered (or lofted) section between the base and the pipe diameter.
*   **Inner Diameter Decrease at Base:**  The difference between the base's diameter and the starting inner diameter at the base. This creates a wall thickness for the base.
*   **Top Diameter Addition:** The additional diameter to add on to the pipe's diameter to achieve the final inner diameter at the top of the loft. This creates some thickness at the top where the pipe would come through.

Additionally, I need a parameter to control whether the cover is split in half. If it is split, there needs to be a variable for the spacing between the two halves when they are not attached to each other. The two halves should be mirror images of each other.

I'd like to use OpenSCAD for this. I don't have any specific preferences for libraries, but it's fine if you need them.

[Assistant]
pipe_cover_v1.scad:
```
// NOTE: Please refer to the picture with drawing to get all the variables explained in details
/* [Outer Size] */
//Diameter of the pipe
pipe_diameter=28;
//Diameter of the base
base_diameter=70;
//Height of the base, before the loft will start
base_height=10;
// Height of the part with loft from base to to pipe diameter
loft_height=30;
// Note: Total height of part = loft_height + base_height
// Please refer to picture with drawing to better understand the variables, if in doubt
/* [Inner space] */
//Difference of the inner space's diameter to inner space's diameter at base level
base_inner_diameter_decrease=20;
// Difference of top diameter to pipe's diameter
top_add_diameter=5;

/* [ Split into two halves?]*/
split=0; // [1:Yes, 0:No]
// Space between two halves
space=30;
/* [Hidden]*/

if (split) {
// draw base as circle
difference(){
    draw_cap();
//subtract half of cap
translate([-base_diameter/2,0,0]) {
    cube([base_diameter,base_diameter/2,base_height+loft_height],center=false);
}
}
translate ([0,space,0]) {
    rotate ([0,0,180]){
    mirror ([1,0,0]){
difference(){
    draw_cap();
//subtract half of cap
translate([-base_diameter/2,0,0]) {
    cube([base_diameter,base_diameter/2,base_height+loft_height],center=false);
}
}
 }
}
}
}else{
    draw_cap();
}

// make two halfs

module draw_cap(){
     difference(){
    union(){
        //draw the base
        cylinder(h=base_height, r=base_diameter/2, center=false);
        //draw the loft
        translate ([0,0,base_height]){
            cylinder(h=loft_height, r1=base_diameter/2, r2=(top_add_diameter+pipe_diameter)/2, center=false);
        }
    }
    //subtract the inner space
    translate ([0,0,0]){
          cylinder(h=loft_height, r1=(base_diameter-base_inner_diameter_decrease)/2, r2=pipe_diameter/2, center=false);
    }
    translate ([0,0,loft_height]) {
          cylinder(h=base_height, r=pipe_diameter/2, center=false);
    }}

}

```


[User]
I'd like to design a custom swim paddle using OpenSCAD. I've got some basic ideas about the shape and some parameters, but I'd like you to generate the SCAD code for me.

The paddle's main shape will be a smooth, curved outline, kind of like a stretched oval or a stylized bean shape. I'm going to provide you with a set of points that define this shape, and I'd like the code to use a natural cubic spline to interpolate between them, creating the final outline. I'll specify the points in the main .scad file.  I will need the code to include the `splines.scad` library which I have attached, to handle that spline interpolation, and it should also use the `write/Write.scad` library which I've also included to add my name to the design.

I'd like the paddle to have some holes in it, arranged in a grid pattern. I'd like to be able to control the size and spacing of these holes, and the overall number of rows and columns in the grid.

Finally, I'd like to be able to easily adjust the thickness of the paddle itself.

Here are some initial parameters I'm thinking of:

*   **`name`**: A string variable to hold my name, to be printed on the paddle. Let's start with "Lazydog".
*   **`name_x`**, **`name_y`**:  X and Y offsets for positioning the name text. Let's start with 1 for both.
*   **`t`**: The thickness of the paddle. Start with 0.1.
*   **`ys`**: A y-scaling factor for the paddle shape. Start with 1.
*   **`hd`**: The diameter of the holes. Start with 0.1
*   **`hx`**, **`hy`**: X and Y offsets for the hole grid. Start with 1.5 and 5 respectively
*   **`hdx`**, **`hdy`**: X and Y spacing for the holes in the grid. Start with 0.5 for both.
*   **`hnx`**, **`hny`**: Number of holes in the X and Y directions, respectively. Start with 3 and 6.

The initial point list for the paddle shape is:

```
pts = [
[2,0],
[3.2,0.15],
[3.9,0.8],
[4,2],
[3.9,3.3],
[3.6,4.6],
[3.0,5.6],
[2,6],

[4-3.0,5.6],
[4-3.6,4.6],
[4-3.9,3.3],
[4-4,2],
[4-3.9,0.8],
[4-3.2,0.15],
[2,0]
];
```

I'd like the main module to use `difference()` to cut out both the holes and the name from the paddle shape. Can you please generate the SCAD code for this?

[Assistant]
swim.scad:
```
use <write/Write.scad>
// Enter your name
name="Lazydog";
name_x = 1;
name_y = 1;
t=0.1;
ys=1;
hd=0.1;
hx=1.5;
hy=5;
hdx=0.5;
hdy=0.5;
hnx=3;
hny=6;

difference() {
    swim();
    holes();
    name();
}

module name() {
   translate([name_x,name_y,0])
   write(name,h=.5,t=2);
}

module swim() {
// based on 4x6 base size

pts = [
[2,0],
[3.2,0.15],
[3.9,0.8],
[4,2],
[3.9,3.3],
[3.6,4.6],
[3.0,5.6],
[2,6],

[4-3.0,5.6],
[4-3.6,4.6],
[4-3.9,3.3],
[4-4,2],
[4-3.9,0.8],
[4-3.2,0.15],
[2,0]
];

pt2 = nSpline(pts,100);
scale([1,ys,1])
linear_extrude(t)
polygon(pt2);

} // end swim

module holes() {
  for (ix=[1:hnx]) {
    for (iy=[1:hny]) {
      x = hx+hdx*(ix-1);
      y = hy-hdy*(iy-1);
      translate([x,y*ys,0])
         linear_extrude(t)
      circle(hd,$fn=10);
    }
  }
}

////////////////////////////////////////////////////
// splines.scad - library for mulivariate splines
// Implementation: Rudolf Huttary (c), Berlin
//  November 2015
//  commercial use prohibited
//
//  usage scheme - n-dimensional natural cubic spline interpolation
//    A = [[...],[...],[...]]; // define Mxn matrix, M>2, n>1
//    B = nSplines(A, N);      // get interpolated Nxn matrix
//    C = gen_dat(B);          // interpret data and transform into trajectory
//    sweep(B);                // render
//
//  for code examples  see:
//     http://forum.openscad.org/Rendering-fails-difference-between-F5-and-F6-tp15041p15100.html
//     http://forum.openscad.org/general-extrusion-imperfect-tp14740p14752.html
//     knot() example in this file!
//
///// some information functions to measure diameter and bounding box of an interpolated system
//  usage:
//    B = nSplines(A);
//    echo(str("outer diam=",Max(Norm(B))));
//    echo(str("bounding box=",Box(B)));

// testcode
//A = [
//  [-4.3,    .57,   .1,  .3],
//  [-.9,     .32,   1,   .4],
//  [1.5,     .07,   .1,  .5],
//  [2.5,    -1.48,  -1,  1.6],
//  [5.6,    -1.68,  -2,  .7],
//  [6.6,     1 ,    1.5, .4],
//  [4.6,    .5 ,    1,   .3],
//  [-1 ,     -2,    1.3, .7],
//  [-5 ,     -2,    1.5, 1.8]
//  ]*10;

//A= [
//[2*x, 0, 0, 1],
//[x+dx, dy, 0, 1],
//[x, 0, 0, 1],
//[x-dx, dy, 0, 1],
//[0, 0, 0, 1],
//[x-dx, -dy, 0, 1],
//[x, 0, 0, 1],
//[x+dx, -dy, 0, 1],
//[2*x, 0, 0, 1],
//]*40;

module knot()
{
// knot
A = [
  [-5,    0,   0],
  [-1,    0,   0],
  [-.4,    0,   -.2],
  [.3,    .3,   .2],
  [.2,     -.5,   0],
  [0,     0,   -.5],
  [-.2,     .5,   -0],
  [-.3,    -.3,   .2],
  [.4,    0,   -.2],
  [1,    0,   0],
  [5,    0,   0],
  ]*10;

N = 200;

nS = nSpline(A,N);   // 4D-Spline rasterized

translate([0,0,20])
//{
//  plot4D(nS);         // 4D-plot, 4th dim is implicit radius
//  plot4D(A, "red");
//}
plot3D(col3D(nS), r=2); // 3D-plot, radius explicit
plot3D(col3D(nS), r=2); // 3D-plot, radius explicit
plot3D(col3D(A), r=3, c="red");

}

module help() splines_help();

/////////////////////////////////////////////////////////////
// library stuff - modules //////////////////////////////////
module plot3D(A, r=1, c = "yellow")
{
  for(i=[0:len(A)-1])
    color(c)
    translate(A[i])
    sphere(r, $fn=30);
}

module plot4D(A, c = "yellow")
{
  for(i=[0:len(A)-1])
    color(c)
    translate([A[i][0], A[i][1], A[i][2]])
    sphere(A[i][3], $fn=30);
}

module help () help_splines();

module help_splines()
{
  echo("\nModule prototypes:\n
=============\n
  help() - echos help in console
  help_splines() - echos help in console
  plot3D(A, r=1, c = \"yellow\")\n
  plot4D(A, c = \"yellow\")\n\n
  Function prototypes:\n
=============\n
  NxM = nSpline(S, N) - n-dim spline interpolation\n
  t = line_integral(S) - calcs line integral over 3D polygon\n
  coeffs = spline2D(x,y) - caculates coeffs for cubic spline\n
  y = spline2D_eval(coeffs, t, x) - evaluate spline at x\n
  Y = spline2D_rasterize(coeffs, t, N) - \n
  m = Max(A, flat=true) recursive max\n
  m = Min(A, flat=true) recursive min\n
  n = Norm(A) - recursive norm\n
  bb = Box(A) - boundingbox\n
  v = flat3(A, n=0) - flatten structured vector\n

  "
);
}

/////////////////////////////////////////////////////////////
// spline stuff - functions /////////////////////////////////
function nSpline(S, N) =
// Rasterizes a PxM-dim vector sequence S into a NxM-dim sequence
// using a multivariate cubic spline interpolation scheme.
// along   a line integral
// over P-dim polygon cord is used as common x-vector
//  S - is PxM-dim and denotes a seq of M-dim vectors to be
//      used as y-vectors
// returns NxM interpolated M-dim vectors
  let(M=len(S[0]))
  let(t = line_integral(S))
  transpose(
  [for(i=[0:M-1])
    let(C = col(S,i))
    let(coeffs = spline2D(t,C))
    (spline2D_rasterize(coeffs, t, N))]);

/////////////////////////////////////////////////////////////
//////// 2D cubic splines - main functions /////////////////
function spline2D(x,y) =
// calculates coeffs of cubic spline segments
// i.e. all coeffs of eq. systems Ax³+Bx²+Cx+D = y
//    x,y - paired vectors
//    [A, B, C, D]   returned vector values
  let(MT = eq_sys(x,y))
  let(b = concat(0, solve_eq(MT[0], MT[1]), 0))
  let(N = len(x)-2)
  let(dx = [for (i=[0:N])  x[i+1] - x[i]])
  let(A  = [for (i=[0:N]) (b[i+1]-b[i])/(3*dx[i])])
  let(C =  [for (i=[0:N]) (y[i+1]-y[i])/dx[i] - (b[i+1]-b[i])*dx[i]/3 - b[i]*dx[i]])
  [A, b, C, y];

function spline2D_rasterize(coeffs, t, N) =
// evaluates a 2D-spline defined by coeffs for the ordered vector t
// at N equidistant points
// returns N vector containing sequence of interpolation values
  let(T = raster(t,N))
  [for(i=[0:len(T)-1]) spline2D_eval(coeffs, t, T[i])];

function spline2D_eval(coeffs, t, x) =
// evaluate spline represented by coeffs and t at x
// f(x) returned
    let(i = interval_idx(t,x))
    let(x_ = x-t[i])
    pow(x_,3)*coeffs[0][i]+
    pow(x_,2)*coeffs[1][i]+
           x_*coeffs[2][i]+
             coeffs[3][i] ;

/////////////////////////////////////////////////////////////
///stuff need for solving spline specific equation system ///
function eq_sys(x, y) =
//transfers value pairs into eq.system M*x=T
//    x,y - paired vectors
//   [M, T] returned vector values with M - symmetric band (m=1) matrix
//           in sparse lower band Nx2 representation
//   T - right side vector
    let(N = len(x)-3)
    let(T = [for (i=[0:N])
      3*((y[i+2]-y[i+1])/(x[i+2]-x[i+1]) - (y[i+1]-y[i])/(x[i+1]-x[i])) ])
    let(M = [for (i=[0:N])
      [(i==0)?0:(x[i+1]-x[i]), 2*(x[i+2]-x[i]) ]])
    [M, T];

function solve_eq(M,y) =
// solves eq. system M*x = y,
// M symmetric band (m=1) matrix, in sparse lower band representation
// uses Cholesky factorization L'*L*x=y
    let(N = len(M)-1)
    let(L = cholesky(M))
    LLx(L,y);

function LLx(L,y) =
// solve L'Lx=y by first solving L'(Lx) = L'x_ = y and then Lx = x_
  let (N = len(y)-1)
  let (x_ = [ for (i= [0:N]) Lx(i, L, y)])
            [ for (i= [0:N]) Lx_(i, N, L, x_)];
function Lx(i,L,y) =   (i==0)? y[0]/L[0][1]: (y[i] - Lx(i-1,L,y) * L[i][0])/L[i][1];
function Lx_(i,N,L,y) =(i==N)? y[i]/L[i][1]: (y[i] - Lx_(i+1,N,L,y) * L[i+1][0])/L[i][1];

function cholesky(A) =
//  Cholesky factorization - applies only to symmetric band (m=1) matrix
// A - matrix to be factorized in sparse lower band representation
// returns Cholesky matrix in sparse lower band representation
    let(N=len(A)-1)
    [ for(k= [0:N])
      let(Lk_ = Lk(A, k))
      [Lk_[0], Lk_[1]]
    ];
function Lk(A,k) =
// recursive helper of cholesky()
  (k==0)?
    [0, sqrt(A[0][1]), A[0][1]]:
      let(Lk_0  = (A[k][0] / Lk(A, k-1)[1]))
      let(Ak_1  = (A[k][1] - Lk_0*Lk_0))
      let(Lk_1  = sqrt(Ak_1))
    [Lk_0, Lk_1, Ak_1];

/////////////////////////////////////////////////////////////
// some more general matrix and vector functions ////////////
function col(S,c=0) =
// returns column c of matrix S
   [for(i=[0:len(S)-1]) S[i][c]];

function col3D(S) =
// returns first 3 columns of matrix S
   let(n=len(S[0])-1)
   [for(i=[0:len(S)-1])
     [S[i][0], (n>0)?S[i][1]:0, (n>1)?S[i][2]:0]];

function transpose(A) =
  [for(i=[0:len(A[0])-1])
    [for(j=[0:len(A)-1])
      A[j][i]]];

function line_integral(S) = let (M = len(S))
// calculates piecewise line integral over S,
//    S is an ordered sequence of M distinct N-dim vectors
// returns ordered N-sequence of accumulated distances
    [for (i=[0:M-1]) lineT2(S,i)];

function lineT1(S, i, k) =
// recursive helper of lineT2()
    let(t1 = pow((S[i][k]-S[i-1][k]),2))
    k==0 ? t1 : t1 + lineT1(S, i, k-1);

function lineT2(S, i) =
// recursive helper of line_integral()
    let(N = len(S[0]))
    let(t1  = pow(lineT1(S,i,N-1), .25))
    (i==0)? 0: (i==1) ? t1 : t1 + lineT2(S,i-1);

function raster(t,N=100) =
// splits interval covered by ordered vector t
//    into N equ.dist. intervals
// returns raster as ordered N vector
   let(d = t[len(t)-1]-t[0])
    [for (i=[0:N-1]) t[0]+i*d/(N-1)];

function interval_idx(t, x) =
// returns index of interval containing real number x
// in ordered interval sequence defined by vector t
   let(N= len(t)-1)
  [for(i=[0:N-1])
    if(t[0]>x || (t[i]<=x && (t[i+1])>=x) || i==N-1) i][0];

// if flat == true
//    max(vec of ... vec)
// else
//    vec of (max(vec))
function Max(A, flat=true) =
    let (m =
      len(A[0])>1?
         [for(i=[0:len(A)-1]) Max(A[i])]:
          max(A) )
       flat?max(m):m;

////////////////////////////////////////////////////////////////////
///// some information functions to measure diameter and bounding box of an interpolated system
//  usage:
//    B = nSplines(A);
//    echo(str("outer diam=",Max(Norm(B))));
//    echo(str("bounding box=",Box(B)));

// if flat == true min(vec of ... vec) else vec of (min(vec))
function Max(A, flat=true) =
    let (m =
      len(A[0])>1?
         [for(i=[0:len(A)-1]) Max(A[i])]:
          max(A) )
       flat?max(m):m;

// if flat == true max(vec of ... vec) else vec of (max(vec))
function Min(A, flat=true) =
    let (m =
      len(A[0])>1?
         [for(i=[0:len(A)-1]) Min(A[i])]:
          min(A) )
       flat?min(m):m;

// norm of vec of vec ... vec3D
function Norm(A) =
  let (m =
    len(A[0])>1?
       [for(i=[0:len(A)-1]) Norm(A[i])]:
        norm(A)) m;

// calculate bounding box over vec of ... vec3D as [[x,y,z], [X,Y,Z]]

function Box(A) = [
    [min(flat3(A,0)), min(flat3(A,1)), min(flat3(A,2))],
    [max(flat3(A,0)), max(flat3(A,1)), max(flat3(A,2))],
    ];

// flatten  vec of vec of ... vec3D into vec of vec3D
function flat3(A, n=0) =
      A[0][0][0] ==undef? A[n]:
      [for (i=[0:len(A)-1])
        for (j=[0:len(A[i])-1])
          flat3(A[i][j], n)];

```


[User]
Okay, so I'm looking to generate a bunch of different snowflake cookie cutter designs, and I'd like the OpenSCAD code to be parametric so I can customize different aspects. I really like the idea of having a random seed to generate unique snowflakes each time, but also being able to input my own seed if I find a design I like and want to recreate it. I'd also like the ability to control the branchiness, how much the snowflake overlaps itself, the fuzziness, how often it has rings, and some things about the shape of the branches like length and width. It'd also be great to adjust how thick the branches are, how pointy the corners are, how organic or mathematically perfect they look, and how many design steps there are. Finally, I need to control the thickness of the inset layer (for the cookie dough to sit in), the height of the cutter itself, and the approximate overall diameter of the cookie cutter, as well as the nozzle width of my 3D printer.

I'd really like to be able to see an output of the random seed, as well, so I can replicate it later if desired.

The basic idea for how the snowflake is made seems to be building it up in steps. Each step can be either a branch or a plate, and there seems to be some random variation for things like the placement of the branches. It also looks like it uses a `hull()` function a lot, so that's something important to incorporate, I think. The final output should be a 2D shape that I can extrude to make the cutter, as well as a very slightly smaller shape to create the inset area for the cookie dough.

I would like the core algorithm to include these steps:

1.  Start with a hexagon.
2.  Add branches or plates to each of the 6 points.
3.  Repeat step 2 for several steps to grow the snowflake.
4.  Optionally, add branches or plates to the end of each of the other branches/plates.
5. Use `linear_extrude` on this shape to get the cookie cutter.
6. Output the random seed used.

The `branch` module creates the actual branch with a `hull` and offsets. The `plate` module creates a hex plate, optionally with additional rings. The `tripleBranch` module creates three branches coming off of one point, with some fuzziness, and the `flatFlake` module is the core generator.

I don't have any particular preference for how you organize the files, so long as it's organized. I would expect the output to be a collection of SCAD files that I can use. I'm not requesting or expecting you to use any particular existing library for this design, so you don't need to worry about that.

Also, could you please make sure that the comments in the code are pretty detailed? That would be very helpful.

[Assistant]
snowflakerator-COOKIES.scad:
```
// THE SNOWFLAKE MACHINE - FOR COOKIES
// mathgrrl snowflakerator

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// RANDOM SEED

/* [Make a Flake!] */

// USE THIS ONE WITH OPENSCAD
// comment this out if using Customizer
// OpenSCAD chooses a random seed
//random_seed = floor(rands(1,9999999,1)[0]);

// USE THIS ONE WITH CUSTOMIZER
// comment this out if using OpenSCAD
// Click anywhere in the slider to make a flake. If your flake has disconnected pieces or if you'd prefer another design, then click again to make a new one. When you like a flake then save it before it melts away!
random_seed = 8707098; // [1:1:9999999]

// OR TYPE IN A SEED MANUALLY
// Overrides the slider seed unless set to 0
custom_seed = 0*0;
// a dozen nice ones
//custom_seed = 8707098; // 1
//custom_seed = 2425545; // 2
//custom_seed = 3830701; // 3
//custom_seed = 5731231; // 4
//custom_seed = 4685353; // 5
//custom_seed = 4598248; // 6
//custom_seed = 4116185; // 7
//custom_seed = 8180448; // 8
//custom_seed = 6088999; // 9
//custom_seed = 0448431; // 10
//custom_seed = 6461073; // 11
//custom_seed = 1832808; // 12

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// FIXED SETTINGS

// Likelihood of branching
branchy = 8*1;
// Amount of overlapping
full = -1*1;
// Chance of extra branch spikes
fuzzy = 1*1;
// Chance of extra plate rings
ringed = 0*1;
// Tendency for long branches
long = 5*1;
// Tendency for wide plates
wide = 1*1;
// Thickness of the branches
fat = 40*1;
// Pointiness of the corners
sharp = 5*1;
// Random/natural style (set to 0 for mathematially perfect flakes)
organic = 0*1;
// Number of design steps
steps = 4*1;
// Thickness of the inset layer
thickness = 1*1;
// Height of cutter
cutterHeight = 8*1;
// Approximate desired diameter of snowflake cookie cutter
target_diameter = 70*1;
// Set this to your 3D printer's nozzle width for best performance
nozzle = .4*1;
// set size of flake before the cutter is made
flakeScale = 1*1;

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// DETERMINED PARAMETERS

// modify fat to be smaller when organic is activated
fatness = max(fat-1.5*organic/7,0);

// branch Diameter
// minimum=nozzle, when fatness=1
// maximum to be nice with target diameter, when fatness=10
bDiam = nozzle+(target_diameter/600)*(fatness-1);
bRad = bDiam/2;

// corner radius
// minimum=0.01, when sharp=10
// maximum=bRad, when sharp=1
cRad = (bRad)*(1/15)*(10-sharp)+0.01;

// branch length bounds
// minimum depending on branch radius
// maximum to get to target diameter
minLen = 5*bRad;
maxLen = nozzle+(target_diameter/13);

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// RANDOM SEQUENCE PARAMETERS

// generate a sequence of random numbers
// even-index entries determine type
// odd-index entries determine length
// e.g. random[2] determines type of 2nd step
// and random[3] determines length of 2nd step
// use the same list to get organic circle variation
// and to put in extra fuzz and ring variation

// set the random snowflake seed
seed = (custom_seed==0) ? random_seed : custom_seed;

// construct the main random sequence
maxSteps=300*1;
// make a sequence of random numbers with the chosen seed
random = rands(0,10,maxSteps,seed);

// type sequence for choosing branch or plate
// true=branch, false=plate
type = [for(i=[0:steps]) random[2*i]<=branchy];

// size sequence for size of each step
size = [for(i=[0:steps]) random[2*i+1]];

// branch length sequence
bLen = [for(i=[0:steps]) floor((1+long/8)*(maxLen-minLen)*size[i]/10+minLen)];

// plate radius sequence
pRad = [for(i=[0:steps]) floor((.5+wide/10)*(maxLen-minLen)*size[i]/10+minLen)];

// Define the lenghts for each growth step
// Takes into account whether the step is a branch or a plate
// thanks to ricswika, Parkinbot, EvilTeach, samkass, daozenciaoyen, and many more
// for replying to my OpenSCAD forum question about how to generate a list defined recursively
// http://www.thingiverse.com/groups/openscad/topic:3916#comment-732582
function stepLocation(k) =
    (k==0 ? pRad[0]-(bRad-cRad)
          : (type[k]==true) ? stepLocation(k-1)+bLen[k]+cRad
                            : stepLocation(k-1)+2*pRad[k]-2*(bRad-cRad));
stepLocation = [for (i=[0:steps]) stepLocation(i)];
// uncomment to visualize the step locations
//for (i=[0:steps]) translate([stepLocation[i],0,0]) cylinder(h=3,r=1,$fn=48);
//echo(stepLocation);

// circle variation sequence
wiggle = [for(i=[0:98]) (organic/7)*nozzle*random[i]/10];

// create a string to output the random seed
// thank you laird for showing me how to do this with your code
// from http://www.thingiverse.com/thing:188481
labelString=str(floor(seed/1000000)%10, floor(seed/100000)%10, floor(seed/10000)%10,
                floor(seed/1000)%10, floor(seed/100)%10, floor(seed/10)%10, floor(seed/1)%10);

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// ECHO

echo(labelString);

///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// RENDERS

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

// MAKE THE FLAKE!
color("white")
linear_extrude(height=thickness)
difference(){
    offset(r=2) scale(flakeScale) flatFlake();
    offset(r=-.3) scale(flakeScale) flatFlake();
}
color("lightgray")
linear_extrude(height=cutterHeight)
difference(){
    offset(r=.45) scale(flakeScale) flatFlake();
    offset(r=-.3) scale(flakeScale) flatFlake(); // total thickness .75
}

// SIZE TESTING
//%circle(target_diameter/2);
//%translate([0,10.825,0]) cylinder(r=.8/2,h=10,$fn=40);

/////////////////////////////////////////////////////
// module for unextruded flake

module flatFlake(){
    color("lightgrey")
    rotate(-1*(wiggle[42]+wiggle[43]+wiggle[44]+wiggle[45]+wiggle[46]+wiggle[47]))
    difference(){
        // the snowflake
        union(){
            // STEP 0: create inner hexagon
            zeroStep();
            // STEP 1: create the first branch/plate step
            firstStep(stepLocation[0]);
            // STEPS 2 and beyond: create the next branch/plate step
            for(k=[2:steps]){
                if(k<=steps){
                    nextStep(k,stepLocation[k-1]);
                }
            }
            // the outer loop, if desired
            //if(loop=="yes"){loopOutside();}
        }
        // the inner loop, if desired
        //if(loop=="yes"){loopInside();}
    }
}

/////////////////////////////////////////////////////
// module for hexagon with given radius and position

module hexagon(xPos,yPos,size){
    //difference(){
        // main hexagon shape
        translate([xPos,yPos])
            hull(){
                for(i=[0:5]){
                    translate([size*cos(60*i),size*sin(60*i)])
                        circle(r=cRad+3*wiggle[i],$fn=24);
                }
            }
}

/////////////////////////////////////////////////////
// module for hexagonal plate with rings

module plate(xPos,yPos,size,ring){
    hexagon(xPos,yPos,size);
    // first-level extra rings
    if(ring+ringed>=9 && size-4*bRad>=6*bRad){
        hexagon(xPos,yPos,size-3.5*bRad);
    }
    // second-level extra rings (less likely)
    if(ring+ringed>=12 && size-7*bRad>=8*bRad){
        hexagon(xPos,yPos,size-7*bRad);
    }
}

/////////////////////////////////////////////////////
// module for branch with given start position, angle, length, and orientation

module branch(xPos,yPos,angle,length,orientation){
    xOff = cos(90+angle)+2*wiggle[70];
    yOff = sin(90+angle)+2*wiggle[71];
    xPush = cos(angle);
    yPush = sin(angle);
    rotation =
        (orientation=="left")  ?  60+wiggle[52] :
        (orientation=="right") ? -60+wiggle[53] :
                                  0;
    //linear_extrude(height=thickness)
    translate([xPos,yPos])
    rotate(rotation,[0,0,1])
        hull(){
            // one side of base
            translate((bRad-cRad)*[xOff,yOff])
                circle(r=cRad+wiggle[12],$fn=24);
            // other side of base
            translate(-(bRad-cRad)*[xOff,yOff])
                circle(r=cRad+2*wiggle[13],$fn=24);
            // one side of arrow
            translate((bRad-cRad)*[xOff,yOff]+length*[xPush,yPush])
                circle(r=cRad+wiggle[14],$fn=24);
            // other side of arrow
            translate(-(bRad-cRad)*[xOff,yOff]+length*[xPush,yPush])
                circle(r=cRad+wiggle[15],$fn=24);
            // center tip of arrow
            if(orientation=="center"){
                translate((length+1*(1/sqrt(3))*(bRad-cRad))
                          *[xPush+.5*wiggle[19],yPush+.5*wiggle[21]])
                    circle(r=cRad+wiggle[16],$fn=24);
            }
            if(orientation=="left"){
                translate(-(bRad-cRad)*[xOff,yOff]
                          +(length+2*(1/sqrt(3))*(bRad-cRad))
                          *[xPush+.5*wiggle[51],yPush])
                    circle(r=cRad,$fn=24);
            }
            if(orientation=="right"){
                translate((bRad-cRad)*[xOff,yOff]
                          +(length+2*(1/sqrt(3))*(bRad-cRad))
                          *[xPush+.5*wiggle[58],yPush])
                    circle(r=cRad,$fn=24);
            }
        }
}

/////////////////////////////////////////////////////
// module for triple of branches

module tripleBranch(xPos,yPos,angle,length,fuzz){
    branch(xPos,yPos,angle,length+2*wiggle[80],orientation="left");
    branch(xPos,yPos,angle,length,orientation="center");
    branch(xPos,yPos,angle,length-wiggle[82],orientation="right");
    // first-level extra fuzz
    if(fuzz+fuzzy>=9 && 2*length/3>=5*bRad){
        branch( xPos+cos(angle)*length/3,yPos+sin(angle)*length/3,angle,
                2*length/3-wiggle[44],orientation="left");
        branch( xPos+cos(angle)*length/3,yPos+sin(angle)*length/3,angle,
                2*length/3+2*wiggle[45],orientation="right");
    }
    // second-level extra fuzz (less likely)
    if(fuzz+fuzzy>=12 && length/3>=5*bRad){
        branch( xPos+cos(angle)*2*length/3,yPos+sin(angle)*2*length/3,angle,
                length/3+2*wiggle[46],orientation="left");
        branch( xPos+cos(angle)*2*length/3,yPos+sin(angle)*2*length/3,angle,
                length/3-wiggle[47],orientation="right");
    }
}

/////////////////////////////////////////////////////
// module for k=0 inner hexagon step

module zeroStep(){
    plate(xPos=0,yPos=0,size=pRad[0],ring=random[71]);
}

/////////////////////////////////////////////////////
// module for k=1 branch/plate step

module firstStep(startLength){
    // IF FIRST STEP = BRANCH
    if(type[1]==true){
        circle(pRad[0]+1.3);
        for(i=[0:5]){
            rotate(60*i+10*wiggle[42+i],[0,0,1])
                tripleBranch(xPos=pRad[0]-bRad+cRad,yPos=0,angle=0,
                             length=bLen[1],fuzz=random[87]);
        }
    }
    // IF FIRST STEP = PLATE
    else{
        circle(pRad[0]+1.3);
        for(i=[0:5]){
            rotate(60*i+10*wiggle[42+i],[0,0,1])
                plate(xPos=startLength+pRad[1]-(bRad-cRad),yPos=0,size=pRad[1],ring=random[72]);
        }
    }
}

/////////////////////////////////////////////////////
// module for k>=2 branch/plate steps

module nextStep(k,startLength){
    // IF TYPE = BRANCH
    if(type[k]==true){
        for(i=[0:5]){
            rotate(60*i+10*wiggle[42+i],[0,0,1])
            union(){
                // center triple
                tripleBranch(xPos=startLength,yPos=0,angle=0,
                             length=bLen[k],fuzz=random[3*k]);
                // IF PREVIOUS TYPE = BRANCH
                if(type[k-1]==true && bLen[k]<=bLen[k-1]*sqrt(2-1)*full/3){
                    // left triple
                    translate(-(bLen[k-1]+cRad)*[cos(-60),sin(-60)])
                        tripleBranch(xPos=startLength,yPos=0,angle=60,
                                     length=bLen[k],fuzz=random[3*k]);
                    // right triple
                    translate(-(bLen[k-1]+cRad)*[cos(60),sin(60)])
                        tripleBranch(xPos=startLength,yPos=0,angle=-60,
                                     length=bLen[k],fuzz=random[3*k]);
                }
                // IF PREVIOUS TYPE = PLATE
                if(type[k-1]==false && bLen[k]<=2*pRad[k-1]*sqrt(2-1)*full/3){
                    // left triple
                    translate(-(pRad[k-1]-(bRad-cRad))*[cos(60),sin(60)])
                        tripleBranch(xPos=startLength,yPos=0,angle=-60,
                                     length=bLen[k],fuzz=random[3*k]);
                    // right triple
                    translate(-(pRad[k-1]-(bRad-cRad))*[cos(-60),sin(-60)])
                        tripleBranch(xPos=startLength,yPos=0,angle=60,
                                     length=bLen[k],fuzz=random[3*k]);
                }
            }
        }
    }
    // IF TYPE = PLATE
    else{
        for(i=[0:5]){
            rotate(60*i+10*wiggle[42+i],[0,0,1])
            union(){
                // center hex
                plate(xPos=startLength+pRad[k]-(bRad-cRad),yPos=0,
                      size=pRad[k],ring=random[4*k]);
                // IF PREVIOUS TYPE = BRANCH
                if(type[k-1]==true && pRad[k]<=bLen[k-1]*sqrt(2-1)*full/6){
                    // left hex
                    translate(-(bLen[k-1]+pRad[k]-(bRad-2*cRad))*[cos(60),sin(60)])
                        plate(xPos=startLength+pRad[k]-(bRad-cRad),yPos=0,
                              size=pRad[k],ring=random[4*k]);
                    // right hex
                    translate(-(bLen[k-1]+pRad[k]-(bRad-2*cRad))*[cos(-60),sin(-60)])
                        plate(xPos=startLength+pRad[k]-(bRad-cRad),yPos=0,
                              size=pRad[k],ring=random[4*k]);
                }
                // IF PREVIOUS TYPE = PLATE
                if(type[k-1]==false && pRad[k]<=pRad[k-1]*sqrt(2-1)*full/3){
                    // left hex
                    translate(-(pRad[k-1]+pRad[k]-2*(bRad-cRad))*[cos(-60),sin(-60)])
                        plate(xPos=startLength+pRad[k]-(bRad-cRad),yPos=0,
                              size=pRad[k],ring=random[4*k]);
                    // right hex
                    translate(-(pRad[k-1]+pRad[k]-2*(bRad-cRad))*[cos(60),sin(60)])
                        plate(xPos=startLength+pRad[k]-(bRad-cRad),yPos=0,
                              size=pRad[k],ring=random[4*k]);
                }
            }
        }
    }
}

```


[User]
I'd like to create a custom soap mold with a text label embedded in it, and I'd like the design to be parametric. The mold should be a simple rectangular block with a cavity for the soap, and a raised text label within that cavity.

Here's what I envision:

**Overall Mold:**
*   **Shape:** A rectangular block.
*   **Dimensions:** The user should be able to define the overall width, height and thickness of the mold.
*   **Cavity:** A rectangular indentation in the mold to form the soap. This cavity will be slightly smaller than the mold's overall dimensions, creating a wall around the soap.
*   **Drafting:** The sides of the soap cavity should have a slight draft angle to aid in removing the soap. This will be done by scaling a cavity, and the amount of the scaling should be a user-defined parameter.
*   **Floor:** The bottom of the cavity should be set off the base of the mold by a user-defined distance to create a floor thickness.
*   **Label:** The text label should be centered in the soap cavity. The user should be able to specify the text, font, font size, and label depth. There should be options for fast rendering and smoothed lettering.

**Smoothing:**
*   If the user selects the smoothing option, the text should be rounded via Minkowski addition with a sphere (a user-defined radius).

**Texturing:**
*   If the user does not select the fast render option, then a waffle texture should be added to the bottom of the mold to assist in releasing the mold.  It should be an array of conical shapes with user-defined depth, base size, and center-to-center distance.

**Parameters:**
*   `labelString`: Text of the label.
*   `fast`: Boolean (0 or 1). 1 = fast rendering (no smoothing or texture), 0 = smoothed lettering and texture.
*   `pourHeight`: Height of the soap cavity.
*   `pourWidth`: Width of the soap cavity.
*   `pourThick`: Thickness/Depth of the soap.
*   `taper`: Amount of draft angle on the cavity walls (as a scale factor).
*   `labelDepth`: How far the label protrudes from the floor of the cavity.
*   `labelSmooth`: Radius for smoothing of the label.
*   `fontSize`: Font size of the label.
*   `moldWall`: Thickness of the walls of the mold.
*   `texDepth`: Depth of the waffle texture cones.
*   `texLine`: Thickness of the waffle texture cones.
*   `texC2C`: Center-to-center distance of the waffle texture cones.

**Libraries:**
*   I expect this will be using the built-in OpenSCAD library only, plus a little helper library I'm familiar with for outset, inset, fillet and rounding: here is the code for that:
```
// Copyright (c) 2013 Oskar Linde. All rights reserved.
// License: BSD
//
// This library contains basic 2D morphology operations
//
// outset(d=1)            - creates a polygon at an offset d outside a 2D shape
// inset(d=1)             - creates a polygon at an offset d inside a 2D shape
// fillet(r=1)            - adds fillets of radius r to all concave corners of a 2D shape
// rounding(r=1)          - adds rounding to all convex corners of a 2D shape
// shell(d,center=false)  - makes a shell of width d along the edge of a 2D shape
//                        - positive values of d places the shell on the outside
//                        - negative values of d places the shell on the inside
//                        - center=true and positive d places the shell centered on the edge

module outset(d=1) {
	// Bug workaround for older OpenSCAD versions
	if (version_num() < 20130424) render() outset_extruded(d) children();
	else minkowski() {
		circle(r=d);
		children();
	}
}

module outset_extruded(d=1) {
   projection(cut=true) minkowski() {
        cylinder(r=d);
        linear_extrude(center=true) children();
   }
}

module inset(d=1) {
	 render() inverse() outset(d=d) inverse() children();
}

module fillet(r=1) {
	inset(d=r) render() outset(d=r) children();
}

module rounding(r=1) {
	outset(d=r) inset(d=r) children();
}

module shell(d,center=false) {
	if (center && d > 0) {
		difference() {
			outset(d=d/2) children();
			inset(d=d/2) children();
		}
	}
	if (!center && d > 0) {
		difference() {
			outset(d=d) children();
			children();
		}
	}
	if (!center && d < 0) {
		difference() {
			children();
			inset(d=-d) children();
		}
	}
	if (d == 0) children();
}

// Below are for internal use only

module inverse() {
	difference() {
		square(1e5,center=true);
		children();
	}
}
```
I think that should be everything.  Thanks!

[Assistant]
NameSoap.scad:
```

labelString = "Dustin";
fast        = 1;   // [0:Smoothed Text, 1:Fast Render]
pourHeight  = 35;  // [5:1:200]
pourWidth   = 90;  // [5:1:300]
pourThick   = 12;  // [1:1:150]
taper       = 0.8; // [0.1:0.01:1.0]
labelDepth  = 2;   // [0.5:0.1:25]
labelSmooth = 0.5; // [0.2:0.1:2.0]
fontSize    = 15;  // [2:1:80]
moldWall    = 6;   // [1:1:12]
moldWidth   = pourWidth  + moldWall*2;
moldHeight  = pourHeight + moldWall*2;
floorThick  = moldWall   + labelDepth;
moldThick   = pourThick  + floorThick;
texDepth    = 2*1;
texLine     = 1*1;
texC2C      = 8*1;
texWidth    = texC2C/sin(60)-texLine;
extra       = 1*1;

difference()
  { moldBlock();
    union()
      { pourCavity();
        if ( fast > 0.5 )
          fastLetters();
        if ( fast <= 0.5 )
          { letters();
            texture();
          }
      }
  }

module pourCavity()
{ translate( [0,0,floorThick] )
    linear_extrude( height=pourThick+extra, scale=1/taper )
      translate( [-pourWidth*taper/2,-pourHeight*taper/2] )
        square( [pourWidth*taper,pourHeight*taper] );
}

module moldBlock()
{ translate( [-moldWidth/2,-moldHeight/2] )
    linear_extrude( moldThick )
      square( [moldWidth,moldHeight] );
}

module letters()
{ font1 = "Baloo Bhai:style=Bold"; // here you can select other font type
  $fn=8;
  translate( [0,0,moldWall] )
    minkowski()
      { linear_extrude( height=(labelDepth+extra-labelSmooth) )
          fillet( labelSmooth )
            rounding( labelSmooth )
              rotate( [0,180,0] )
                text( labelString, font = font1, size = fontSize, direction = "ltr", spacing = 1, halign="center", valign="center" );

        sphere( labelSmooth );
      }
}

module fastLetters()
{ font1 = "Baloo Bhai:style=Bold"; // here you can select other font type
  translate( [0,0,moldWall] )
    linear_extrude( height=(labelDepth+extra-labelSmooth) )
      rotate( [0,180,0] )
        text( labelString, font = font1, size = fontSize, direction = "ltr", spacing = 1, halign="center", valign="center" );
}

// Waffle like cuts to make removal from build plate easier
module texture()
{ wid = moldWidth;
  hei = moldHeight;
  translate( [-wid/2,-hei/2] )
  {
  vo = sin(60)*2;
  for ( i = [wid/2:texC2C:wid] )
    for ( j = [0:texC2C*vo:hei+texC2C*vo] )
      translate( [i,j,0] )
        textureCone( texDepth );
  for ( i = [wid/2+texC2C/2:texC2C:wid] )
    for ( j = [texC2C*vo/2:texC2C*vo:hei+texC2C*vo] )
      translate( [i,j,0] )
        textureCone( texDepth );

  for ( i = [wid/2:-texC2C:0] )
    for ( j = [0:texC2C*vo:hei+texC2C*vo] )
      translate( [i,j,0] )
        textureCone( texDepth );
  for ( i = [wid/2-texC2C/2:-texC2C:0] )
    for ( j = [texC2C*vo/2:texC2C*vo:hei+texC2C*vo] )
      translate( [i,j,0] )
        textureCone( texDepth );
  }
}

module textureCone( h=1 )
{ translate( [0,0,-0.001] )
    linear_extrude( height=h,scale=0.5 )
      polygon(points=[[cos(030)*texWidth/2,sin(030)*texWidth/2 ],
                      [cos(090)*texWidth/2,sin(090)*texWidth/2 ],
                      [cos(150)*texWidth/2,sin(150)*texWidth/2 ],
                      [cos(210)*texWidth/2,sin(210)*texWidth/2 ],
                      [cos(270)*texWidth/2,sin(270)*texWidth/2 ],
                      [cos(330)*texWidth/2,sin(330)*texWidth/2 ]],
              paths =[[0,1,2,3,4,5,0]] );

}

// Copyright (c) 2013 Oskar Linde. All rights reserved.
// License: BSD
//
// This library contains basic 2D morphology operations
//
// outset(d=1)            - creates a polygon at an offset d outside a 2D shape
// inset(d=1)             - creates a polygon at an offset d inside a 2D shape
// fillet(r=1)            - adds fillets of radius r to all concave corners of a 2D shape
// rounding(r=1)          - adds rounding to all convex corners of a 2D shape
// shell(d,center=false)  - makes a shell of width d along the edge of a 2D shape
//                        - positive values of d places the shell on the outside
//                        - negative values of d places the shell on the inside
//                        - center=true and positive d places the shell centered on the edge

module outset(d=1) {
	// Bug workaround for older OpenSCAD versions
	if (version_num() < 20130424) render() outset_extruded(d) children();
	else minkowski() {
		circle(r=d);
		children();
	}
}

module outset_extruded(d=1) {
   projection(cut=true) minkowski() {
        cylinder(r=d);
        linear_extrude(center=true) children();
   }
}

module inset(d=1) {
	 render() inverse() outset(d=d) inverse() children();
}

module fillet(r=1) {
	inset(d=r) render() outset(d=r) children();
}

module rounding(r=1) {
	outset(d=r) inset(d=r) children();
}

module shell(d,center=false) {
	if (center && d > 0) {
		difference() {
			outset(d=d/2) children();
			inset(d=d/2) children();
		}
	}
	if (!center && d > 0) {
		difference() {
			outset(d=d) children();
			children();
		}
	}
	if (!center && d < 0) {
		difference() {
			children();
			inset(d=-d) children();
		}
	}
	if (d == 0) children();
}

// Below are for internal use only

module inverse() {
	difference() {
		square(1e5,center=true);
		children();
	}
}

```


[User]
I'd like an OpenSCAD design for a cookie cutter, and I've got some specific requirements. The cookie cutter needs to be parametric, so I can adjust things like the height and the overall size.

Essentially, I want a cookie cutter with these features:

*   **Cookie Shape:** I should be able to define the shape of the cookie, either by providing a list of 2D points for a polygon or by uploading an image file (a white cookie shape on a black background). If I use an image, it should support interior cutouts.
*   **Cutting Edge:**  The cutting edge needs to be 0.5mm thick.
*   **Walls:** The walls of the cutter should be 1mm thick.
*   **Top Lip:** There needs to be a 3mm wide and 2mm deep lip around the top of the cutter.
*   **Total Height:** I need to be able to specify the total height of the cookie cutter.
*   **Smoothing:** It would be useful to have a smoothing function that can be applied to the shape, so rough edges can be made smoother.

Here are the specifics of how the cutter should be constructed:

1.  **Base Shape:** The base cookie shape (either from the polygon definition or image) will be the inner shape of the cutter.
2.  **Lip:** The lip on top should be created by offsetting the base shape outwards by 3mm and then extruding upwards by 2mm.
3.  **Walls:** The walls of the cutter are constructed by extruding the base shape. There needs to be an outer wall and a cutting edge. The cutting edge is the base shape offset by 0.5mm, and the wall is created by offsetting the base shape by 1mm.
4.  **Cutting Edge:** The cutting edge should extend slightly below the wall.
5.  **Smoothing Function:** The smoothing should be implemented by offsetting the base shape inwards and then outwards again by the given smoothing parameter.
6.  **Image Processing:** If an image is used, the image needs to be converted into a 2D shape that can be used as the base. The image should be centered.

I think that about covers it. I need to be able to specify the shape, the height of the cutter, and the smoothing amount. The overall size of the cookie should be controlled by a scale parameter. I do not need to have image processing libraries - I want to have all the code contained within the files provided.

[Assistant]
cookie_cutter.scad:
```
// cookie shape
shape = [[[-30,30],[0,15],[30,30],[15,0],[30,-30],[0,-15],[-30,-30],[-15,0]],[[0,1,2,3,4,5,6,7]] ]; //[draw_polygon:100x100]

// do you want to sketch a drawing of the cookie? or upload an image?
source = "drawing"; // [drawing, image]

// cookie shape image file. It should be a white cookie on a black background.
shape_file = ""; // [image_surface:100x100]

// drawing scale, 1.0 gives a maximum cookie size of 10cm
scale = 1.0;

// smoothing factor, increase this number to smooth out rough edges, but beware that it might remove small features (eg try 10)
smooth = 0.0;

// cutter total height in mm, 2mm of that height is the lip around the top
height = 15;

/* [Hidden] */

$fn=60;

module cookie_cutter(h=10) {
    difference() {
        union() {
            linear_extrude(height=2, convexity=10)
                offset(r=3)
                    children();
            translate([0,0,2])
                linear_extrude(height=h-4, convexity=10)
                    offset(r=1)
                        children();
            for (y=[0.9 : -0.1 : 0.5])
            translate([0,0,h+1.6-y*4])
            linear_extrude(height=0.4, convexity=10)
                offset(r=y)
                children();
        }
        translate([0,0,-1])
            linear_extrude(height=h+2, convexity=10)
                children();
    }
}

module smooth_2d(s=smooth) {
    offset(r=-s)
    offset(r=s)
    children();
}

module image_2d(file) {
    projection(cut = true)
    translate([0,0,-50])
    surface(file = file, center = true, invert = false);
}

module dat_2d(file) {
    projection(cut = true)
    translate([0,0,-5])
    scale([1,1,10])
    surface(file = file, center = true, invert = true);
}

module main() {
    mirror([1,0,0])
    cookie_cutter(h=height) {
        scale(scale)
        smooth_2d() {
            if (source == "image") {
                dat_2d(file = shape_file);
            } else {
                polygon(points = shape[0], paths = shape[1]);
            }
        }
    }
}

main();

```


[User]
I'm looking to get a custom design for a hand-weaving shuttle, something like the straight shuttles used in lap looms. I need it to be parametric, so I can adjust the size and other features.

Specifically, I need to control the following dimensions:

*   **Overall length of the shuttle**
*   **Overall width of the shuttle**
*   **Overall height/thickness of the shuttle**
*   **The length of the notch** that holds the yarn. It should be a symmetric notch in the middle of the shuttle on each side.
*   **The width of that notch at its deepest point.**
*   **The width of the tips at the ends of the shuttle.**
*   I'd also like an **option to engrave or etch some text** on the shuttle, so I would need a parameter for that text string, as well as one for the text's height, and one for the depth of the etching. It would be nice if the text height could be set to "automatic", so it scaled appropriately with the other dimensions, but I'd also need manual control over it.

Additionally, it'd be great to have these advanced features available:

*   An option to **round the edges of the shuttle.** I need to be able to control the radius of that rounding. I realize that this might impact the rendering time, so it could be good to have a warning about that.
*   It would be super helpful if I could have an option to add **thin pads to the ends of the shuttle.** This would help prevent warping or curling while 3D printing the object. I should be able to specify the height of those pads, and if possible, it would be great if there was an option to cut off the corners at 45 degrees.
*   I should also be able to **rotate the entire model** around the Z axis for printing.
*   Finally, it'd be nice to have a **build plate preview** to see how the model fits on different printers, like a Makerbot Replicator 2, Makerbot Replicator, Makerbot Thingomatic, or an M3D Micro.

The output should be in OpenSCAD format. I don't have any preference on external libraries, though if the build plate preview or any other features rely on them, please let me know what library you're using. I also need to specify some default values for the parameters in the scad file, and need the user to be able to specify the units of each of the dimensions.

[Assistant]
Customizable_Hand-Weaving_Straight_Shuttle.scad:
```
// Customizable Hand-Weaving Straight Shuttle
// Author: Alexander Smith
// License: CC BY-SA <https://creativecommons.org/licenses/by-sa/4.0/>

// This OpenSCAD file is formatted for use by the Makerbot Customizer.

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

use <utils/build_plate.scad>;

/* [Basic] */
shuttle_length = 127;   // [0:0.1:200]
shuttle_width = 12;     // [0:0.1:50]
shuttle_height = 3;    // [0:0.1:20]
notch_length = 31.75; // [0:0.1:100]

// The width of the notch at its deepest point.
notch_width = 3;   // [0:0.1:30]

// The width of the tips at the ends of the shuttle.
tip_width = 3; // [0:0.1:25]

// If you make multiple of these, you might want to label the sizes.
etch_text = "5 in";

// The radius used to round the edges of the shuttle. CAUTION: setting this to a value greater than zero will greatly slow down the rendering time. You should set this to zero and adjust all the other parameters first. When you are happy with the size and shape of the shuttle, then set this value for your final output. Values in the range 0.5-1.0 mm produce good results.
rounding = 0;   // [0:0.1:2]

/* [Advanced] */
// Approximate text height from baseline to ascender. 0 = automatic.
text_height = 0;    // [0:0.1:50]

// How deeply to etch the text.
etch_depth = 1;     // [0:0.1:20]

/* [Printing Assistance] */
// Because the shuttle is long and thin, the edges may curl off the print bed. This option will generate thin pads attached to the ends of the shuttle which you can snap off after printing. You should set this to a value that will equal about two layers after slicing. Alternatively, print with a raft or brim.
pad_height = 0;     // [0:0.05:1]

// This cuts the pads off at 45 degrees. This makes them less effective. However, if you're printing a large version close to the limits of your printable area, this might help you fit the model on your print bed.
cut_pad_corners = 0;    // [0:No, 1:Yes]

rotate_model = 0;   // [-180:1:180]

build_plate_preview = -1; //[-1: None, 0:Makerbot Replicator 2, 1: Makerbot Replicator, 2:Makerbot Thingomatic, 3: M3D Micro]

/* [Hidden] */
// Some lengths are enforced to be > 0. They are set to this minimum size.
eps = 0.001;

// Shorter aliases, used for calculations. Some basic input sanitization.
input_L = max(0, shuttle_length);
input_W = max(0, shuttle_width);
input_H = max(0, shuttle_height);
input_Wt = max(0, tip_width);
input_Ls = max(0, notch_length);
input_Ws = max(0, notch_width);
input_r = max(0, rounding);
input_He = max(0, etch_depth);
input_Htext = max(0, text_height);
input_pad_height = max(0, pad_height);

// Render the word "ERROR" to show the user something went wrong.
// This is rendered in debug mode (%) so that it doesn't affect the actual model.
module renderError()
{
    translate([0, 0, 25])
        %linear_extrude(0.5)
        text(text="ERROR", size=10, halign="center", valign="center");
}

// This creates the shuttle. The result is centered in and sitting on the xy plane.
module shuttle(L, W, H, Ls, Ws, Wt)
{
    if ((L == undef) || (W == undef) || (H == undef) || (Ls == undef) || (Ws == undef) || (Wt == undef)) {
        echo("Error: One or more of the input paramaeters is invalid or undefined.");
        renderError();

    } else if ((L < 0) || (W < 0) || (H < 0) || (Ls < 0) || (Ws < 0) || (Wt < 0)) {
        // Clamp all lengths to be >= 0. L, W, and H must be > 0.
        shuttle(max(L,eps), max(W,eps), max(H, eps), max(Ls,0), max(Ws,0), max(Wt,0));

    } else if (Wt > W/2) {
        echo("tip_width must be <= shuttle_width/2");
        shuttle(L, W, H, Ls, Ws, W/2);

    } else if (Ls > L/2) {
        echo("notch_length must be <= shuttle_length/2");
        shuttle(L, W, H, L/2, Ws, Wt);

    } else if (Ws > W - 2*Wt) {
        echo("notch_width must be <= shuttle_width - 2*tip_width");
        shuttle(L, W, H, Ls, W - 2*Wt, Wt);

    } else {
        // Parameters are ok.

        // We mostly need the input values each divided by 2.
        l = L/2;
        w = W/2;
        ls = Ls/2;
        ws = Ws/2;

        P1 = [l-Ls, ws];
        P2 = [l, w-Wt];
        P3 = [l, w];

        linear_extrude(H)
        polygon([
            P1,
            P2,
            P3,
            [-P3[0], P3[1]],
            [-P2[0], P2[1]],
            [-P1[0], P1[1]],
            -P1,
            -P2,
            -P3,
            [P3[0], -P3[1]],
            [P2[0], -P2[1]],
            [P1[0], -P1[1]]
        ]);
    }
}

// For rounded corners, we  take a Minkowski sum of the shuttle with a sphere. Doing so makes the output larger by the diameter of the sphere. Therefore, in order to get the correct size output, we must shrink the dimensions of the shuttle. This function calls shuttle() with suitable values for use with a sphere of radius 'r'.
module shuttle_minkowski_base(r, L, W, H, Ls, Ws, Wt)
{
    if (r == undef) {
        echo("rounding is undefined");
        renderError();

    } else {
        shuttle(L - 2*r, W - 2*r, H - 2*r, Ls + r, Ws + 2*r, Wt - 2*r);
    }
}

// This returns a text object that can be subtracted from the shuttle to etch text into it. If Htext is zero, then a default height will be calcualted.
module shuttle_etch_text(text, H, W, Ws, He, Htext = 0)
{
    if ((H == undef) || (W == undef) || (Ws == undef) || (He == undef)) {
            echo("Error: One or more of the input arguments is invalid or undefined.");
            renderError();

    } else if ((Htext == 0) || (Htext == undef)) {
        shuttle_etch_text(text, H, W, Ws, He, 0.75*Ws + 0.25*W);

    } else {
        translate([0, 0, H - He])
            linear_extrude(2*He)
                text(text=text, font="Helvetica:style=Bold", size=Htext, halign="center", valign="center");
    }
}

// Because the shuttle is long and thin, there is a risk of the ends curling off the print bed when 3D printing it. This generates thin, flat pads attached to the ends of the shuttle which should be easy to snap off. You should set padH to be the height of 2 or 3 layers.
module pads(L, W, r, padH = 0.4, padR = 15, padSep = 5)
{
    if ((L == undef) || (W == undef) || (r == undef) || (padH == undef) || (padR == undef) || (padSep == undef)) {
        echo("Error: One or more of the input paramaeters is invalid or undefined.");
        renderError();

    } else {
        l = L/2;
        w = W/2;

        for (sx = [-1:2:1]) {
            for (sy = [-1:2:1]) {
                scale([sx, sy, 1])
                difference() {
                    union() {
                        translate([l - padR - r, w + padSep, 0])
                            cylinder(padH, padR, padR);
                        translate([l - 2*padR - r, w - r, 0])
                            cube([2*padR, padSep + r, padH]);
                    }

                    translate([l - 2*padR - r, -padR-1, -1])
                        cube([2*padR, padR + 1 + w-r, padH+2]);

                    if ((cut_pad_corners != 0) && (cut_pad_corners != false)) {
                        // Cut off the pads at 45 degrees.
                        D = padSep + 2*padR;
                        translate([-r, 0, -1])
                            linear_extrude(padH+2)
                            polygon([
                                [l, padSep/2 + w],
                                [l, padSep/2 + w + D],
                                [l - D, padSep/2 + w + D]
                            ]);
                    }
                }
            }
        }
    }
}

rotate([0, 0, rotate_model])
if (input_r == undef) {
    echo("rounding is invalid or undefined.");
    renderError();

} else {
        $fs = max(0.01, min(1, input_r/10));
        $fa = 1;

    // Render the shuttle and optionally round edges.
    difference() {
        if (input_r > 0) {
            minkowski() {
                // Use a sphere to round out all corners and edges.
                // We translate it to sit on the xy plane, so that the result also stays sitting on the xy plane. (This is already the case for the shuttle base.)
                translate([0, 0, input_r])
                    sphere(input_r);

                shuttle_minkowski_base(input_r, input_L, input_W, input_H, input_Ls, input_Ws, input_Wt);
            }

        } else {
            // No rounding. Just render the shuttle.
            shuttle(input_L, input_W, input_H, input_Ls, input_Ws, input_Wt);
        }

        // Optionally etch text into the shuttle.
        if (len(etch_text) > 0) {
            shuttle_etch_text(etch_text, input_H, input_W, input_Ws, input_He, input_Htext);
        }
    }

    // Optionally add pads to prevent the ends from curling.
    if (input_pad_height > 0) {
        pads(input_L, input_W, input_r, input_pad_height);
    }
}

// Show the build plate. This only appears in the preview, not in the final model. 109x113 are the M3D micro's specs. The last two parameters are only used if the first parameters is 3 (manual).
build_plate(build_plate_preview, 109, 113);

```


[User]
I need an OpenSCAD design for a customizable hand-weaving shuttle. It should be curved, kind of like a boat. I've got some parameters in mind.

First off, the basic dimensions: I need to be able to set the overall length of the shuttle, the width, and the height. I also want to specify the length and width of the notch in the middle where the yarn goes. There should also be a parameter for the gap between the tips of the shuttle at the ends of that notch.

I need to be able to round the edges of the shuttle using a radius. I'd like to be able to etch text into the top of the shuttle as well - so I'll need parameters for the text itself, its height, and how deep it should be etched into the shuttle.

The shape of the tips is important too. I want to be able to control how sharply they curve inwards, with a "tip_scaling" parameter - a larger value should give gentler curves. And also, for the curve of the top edge of the shuttle, I need a parameter that controls the location of a control point for the curve, kind of as a fraction of the distance between the notch and the edge. I guess you can call that parameter "top_cpt_fraction".

For printing assistance, I want to add small pads to the ends of the shuttle. These should be easy to snap off after printing.  I need to be able to specify the height of those pads. I might want to cut the corners of the pads off at 45 degrees too. Finally, I need to be able to rotate the whole model before printing and also to preview the model with a build plate.

I think that covers it. Can you generate a parametric OpenSCAD design with these features? Please include a bezier curve library; I know they're in the public domain so I don't think there's an existing library in OpenSCAD I can use.

[Assistant]
Customizable_Hand-Weaving_Curved_Shuttle.scad:
```
// Customizable Hand-Weaving Curved Shuttle
// Author: Alexander Smith
// License: CC BY-SA <https://creativecommons.org/licenses/by-sa/4.0/>
//
// This file incorporates a Bezier library, below, which is from the public domain. (The Makerbot Customizer does not support include files.)

// This OpenSCAD file is formatted for use by the Makerbot Customizer.

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

use <utils/build_plate.scad>;

/* [Basic] */

shuttle_length = 127;   // [0:0.1:200]
shuttle_width = 18;     // [0:0.1:50]
shuttle_height = 3.5;    // [0:0.1:20]
notch_length = 31.75; // [0:0.1:100]
notch_width = 5.5;   // [0:0.1:30]

// The gap between the tips at the ends of the shuttle.
tip_gap = 3; // [0:0.1:25]

// If you make multiple of these, you might want to label the sizes.
etch_text = "5 in";

// The radius used to round the edges of the shuttle. CAUTION: setting this to a value greater than zero will take SEVERAL MINUTES to render! You should set this to zero and adjust all the other parameters first. When you are happy with the size and shape of the shuttle, then set this value for your final output. Values in the range 0.5-1.0 mm produce good results.
rounding = 0;   // [0:0.1:2]

/* [Advanced] */
// Approximate text height from baseline to ascender. 0 = automatic.
text_height = 0;    // [0:0.1:50]

// How deeply to etch the text.
etch_depth = 1;     // [0:0.1:20]

// This determines how sharply the tips close. Larger values give gentler curves.
tip_scaling = 0.75;  // [0:0.1:1]

/* [Printing Assistance] */
// Because the shuttle is long and thin, the edges may curl off the print bed. This option will generate thin pads attached to the ends of the shuttle which you can snap off after printing. You should set this to a value that will equal about two layers after slicing. Alternatively, print with a raft or brim.
pad_height = 0;     // [0:0.05:1]

// This cuts the pads off at 45 degrees. This makes them less effective. However, if you're printing a large version close to the limits of your printable area, this might help you fit the model on your print bed.
cut_pad_corners = 0;    // [0:No, 1:Yes]

rotate_model = 0;   // [-180:1:180]

build_plate_preview = -1; //[-1: None, 0:Makerbot Replicator 2, 1: Makerbot Replicator, 2:Makerbot Thingomatic, 3: M3D Micro]

/* [Hidden] */
// The fraction of the vertical distance from the notch to the edge at which to put one of the control points determing the curve of the top.
top_cpt_fraction = 1/3;

// Shorter aliases, used for calculations. Some basic input sanitization.
input_L = max(0, shuttle_length);
input_W = max(0, shuttle_width);
input_H = max(0, shuttle_height);
input_Wg = max(0, tip_gap);
input_Ls = max(0, notch_length);
input_Ws = max(0, notch_width);
input_ts = max(0, min(1, tip_scaling)); // clamp to [0, 1]
input_f_top = max(0, min(1, top_cpt_fraction));
input_r = max(0, rounding);
input_He = max(0, etch_depth);
input_Htext = max(0, text_height);
eps = min(0.01, input_ts*min(input_W, input_W - input_Ws)/3);
input_pad_height = max(0, pad_height);

//=======================================
// Begin Bezier library
//=======================================
// This is from the Bezier library at <http://www.thingiverse.com/thing:8443>, which is created by William Adams and palced by him in the public domain.
gSteps = 10;
gHeight = 4;

function BEZ03(u) = pow((1-u), 3);
function BEZ13(u) = 3*u*(pow((1-u),2));
function BEZ23(u) = 3*(pow(u,2))*(1-u);
function BEZ33(u) = pow(u,3);

function PointAlongBez4(p0, p1, p2, p3, u) = [
	BEZ03(u)*p0[0]+BEZ13(u)*p1[0]+BEZ23(u)*p2[0]+BEZ33(u)*p3[0],
	BEZ03(u)*p0[1]+BEZ13(u)*p1[1]+BEZ23(u)*p2[1]+BEZ33(u)*p3[1]];

module BezQuadCurve(c, focalPoint, steps=gSteps, height=gHeight)
{
	for(step = [steps:-1:1])
	{
		linear_extrude(height = height, convexity = 10)
		polygon(
			points=[
				focalPoint,
				PointAlongBez4(c[0], c[1], c[2],c[3], step/steps),
				PointAlongBez4(c[0], c[1], c[2],c[3], (step-1)/steps)],
			paths=[[0,1,2,0]]
		);
	}
}
//=======================================
// End Bezier library
//=======================================

// Render the word "ERROR" to show the user something went wrong.
// This is rendered in debug mode (%) so that it doesn't affect the actual model.
module renderError()
{
    translate([0, 0, 25])
        %linear_extrude(0.5)
        text(text="ERROR", size=10, halign="center", valign="center");
}

// Performing a Minkowski sum on large, complex objects is very expensive. When possible, it is faster to perform the sum on smaller sub-objects and then union them together.
module smooth_all(r)
{
    if (r > 0.0) {
        for ( i= [0:1:$children-1]) {
            minkowski() {
                children(i);
                sphere(r, $fn=min(50, 20*r));
            }
        }
    } else {
        // no rounding; do nothing
        children();
    }
}

// The part of the tip that closes at the tip of the notch.
module tip_bottom(H, Ls, Ws, Wg, D, r)
{
    ws = Ws/2;
    wg = Wg/2;

    P1 = [0 + r, ws + r];
    P2 = [D + r, ws + r];
    P3 = [D + r, wg + r];
    P4 = [2*D, wg + r];
    P5 = [3*D - r, wg + r];
    P6 = [3*D - r, ws + r];

    smooth_all(r) {
        BezQuadCurve([P1, P2, P3, P4], [2*D + eps, ws + r + eps], 20, H - 2*r);
        BezQuadCurve([P4, P5, P5, P6], [2*D - eps, ws + r + eps], 15, H - 2*r);
    }
}

// The rest of the tip.
module shuttle_head_top(W, H, Ls, Ws, D, f_top, r)
{
    w = W/2;
    ws = Ws/2;

    k = 4*(sqrt(2)-1)/3; // for approximating circles with Bezier control points

    P1 = [0 - r, 0];
    P2 = [0 - r, k*ws + r];
    P3 = [(1-k)*(ws) - r, ws + r];
    P4 = [ws + r, ws + r];
    P5 = [Ls - r, ws + r];
    P6 = [Ls - r, ws + f_top*(w - ws) - r];
    P7 = [max(Ls - 3*D - r, D - r + ws), w - r];
    P8 = [D - r, w - r];

    smooth_all(r) {
        BezQuadCurve([P1, P2, P3, P4], [0 - r - eps, ws + r], 15, H - 2*r);
        BezQuadCurve([P5, P6, P7, P8], [0 - r - eps, ws + r], 30, H - 2*r);
        translate([0 - r - eps, ws + r, 0]) cube([D + r + eps, w - ws - 2*r, H - 2*r]);
    }
}

// Both parts of the tip. Two of these, mirrored over the x axis, form the notch.
module shuttle_head(L, W, H, Ls, Ws, Wg, D, f_top, r)
{
    w = W/2;
    ws = Ws/2;

    shuttle_head_top(W, H, Ls, Ws, D, f_top, r);
    translate([Ls - 3*D, 0]) tip_bottom(H, Ls, Ws, Wg, D, r);
}

// The entire shuttle.
module shuttle(L, W, H, Ls, Ws, Wg, ts, f_top, r)
{
    D = ts*min(Ws, (W-Ws));

    if ((L == undef) || (W == undef) || (H == undef) || (Ls == undef) || (Ws == undef) || (Wg == undef) || (ts == undef) || (f_top == undef) || (r == undef)) {
        echo("Error: One or more of the input paramaeters is invalid or undefined.");
        renderError();

    } else if (ts < 0) {
        echo("Error: tip_scaling must be >= 0.");
        shuttle(L, W, H, Ls, Ws, Wg, 0, f_top, r);

    } else if (ts > 1) {
        echo("Error: tip_scaling must be < 1.");
        shuttle(L, W, H, Ls, Ws, Wg, 1, f_top, r);

    } else if (f_top < 0) {
        echo("Error: top_cpt_fraction must be >= 0.")
        shuttle(L, W, H, Ls, Ws, Wg, ts, 0, r);

    } else if (f_top > 1) {
        echo("Error: top_cpt_fraction must be <= 1.")
        shuttle(L, W, H, Ls, Ws, Wg, ts, 1, r);

    } else if (W < 2*r) {
        echo("Error: shuttle_width must be >= 2*rounding.");
        shuttle(L, 2*r, H, Ls, Ws, Wg, ts, f_top, r);

    } else if (H < 2*r) {
        echo("Error: shuttle_height must be >= 2*rounding.");
        shuttle(L, W, 2*r, Ls, Ws, Wg, ts, f_top, r);

    } else if (Ws < 2*r) {
        echo("Error: notch_width must be >= 2*rounding.");
        shuttle(L, W, H, Ls, 2*r, Wg, ts, f_top, r);

    } else if (Ws > W - 2*r) {
        echo("Error: notch_width must be < shuttle_width - 2*rounding.");
        shuttle(L, W, H, Ls, W - 2*r, Wg, ts, f_top, r);

    } else if (Wg < 0) {
        echo("Error: tip_gap must be >= 0.");
        shuttle(L, W, H, Ls, Ws, 0, ts, f_top, r);

    } else if (Wg > Ws) {
        echo("Error: tip_gap must be <= notch_width.");
        shuttle(L, W, H, Ls, Ws, Ws, ts, f_top, r);

    } else if (Ls < r + Ws/2 + 3*D) {
        if (W < W-Ws) {
            echo("Error: notch_length must be >= rounding + notch_width/2 + 1.5*tip_scaling*shuttle_width.");
        } else {
            echo("Error: notch_length must be >= rounding + notch_width/2 + 1.5*tip_scaling*(shuttle_width - notch_width).");
        }
        shuttle(L, W, H, r + Ws/2 + 3*D, Ws, Wg, ts, f_top, r);

    } else if (L < 2*Ls + 2*r) {
        echo("Error: shuttle_length must be >= 2*notch_length + 2*rounding.");
        shuttle(2*Ls + 2*r, W, H, Ls, Ws, Wg, ts, f_top, r);

    } else {
        union() {
            for (sx = [-1:2:1]) {
                for (sy = [-1:2:1]) {
                    scale([sx, sy, 1])
                        translate([L/2 - Ls, 0, 0]) shuttle_head(L, W, H, Ls, Ws, Wg, D, f_top, r);
                }
            }

            smooth_all(r) {
                translate([-(L - 2*Ls)/2 + r, -W/2 + r, 0])
                cube([L - 2*Ls - 2*r, W - 2*r, H - 2*r]);
            }
        }
    }
}

// This returns a text object that can be subtracted from the shuttle to etch text into it. If Htext is zero, then a default height will be calcualted.
module shuttle_etch_text(text, H, W, Ws, He, Htext = 0)
{
    if ((H == undef) || (W == undef) || (Ws == undef) || (He == undef)) {
            echo("Error: One or more of the input arguments is invalid or undefined.");
            renderError();

    } else if ((Htext == 0) || (Htext == undef)) {
        shuttle_etch_text(text, H, W, Ws, He, 0.75*Ws + 0.25*W);

    } else {
        translate([0, 0, H - He])
            linear_extrude(2*He)
                text(text=text, font="Helvetica:style=Bold", size=Htext, halign="center", valign="center");
    }
}

// Because the shuttle is long and thin, there is a risk of the ends curling off the print bed when 3D printing it. This generates thin, flat pads attached to the ends of the shuttle which should be easy to snap off. You should set padH to be the height of 2 or 3 layers.
module pads(L, W, Ls, Ws, r, padH)
{
    if ((L == undef) || (W == undef) || (Ls == undef) || (Ws == undef) || (r == undef) || (padH == undef)) {
        echo("Error: One or more of the input paramaeters is invalid or undefined.");
        renderError();

    } else {
        l = L/2;
        w = W/2;
        ws = Ws/2;

        padR = W - Ws;

        P1 = [l - Ls - r, w];
        P2 = [l - r, ws + r];
        P3 = 0.5*(P1 + P2);
        alpha = atan2(P2[1]-P1[1], P2[0]-P1[0]);
        sep = (w - ws)/2;

        for (sx = [-1:2:1]) {
            for (sy = [-1:2:1]) {
                scale([sx, sy, 1])
                difference() {
                    translate(P2)
                    rotate([0, 0, alpha])
                    translate([-padR, 0, 0]) {
                        translate([-padR, 0, 0]) cube([2*padR, sep, padH]);
                        difference() {
                                translate([0, sep, 0]) cylinder(padH, padR, padR);
                                translate([-padR-1, 0, -1]) scale([1, -1, 1]) cube([2*padR+2, padR, padH+2]);
                        }
                    }

                    if ((cut_pad_corners != 0) && (cut_pad_corners != false)) {
                        // Cut off the pads at 45 degrees.
                        translate([l, ws + sep, -1])
                        rotate([0, 0, 45])
                        translate([0, -padR, 0])
                        cube([3*padR, 4*padR, padH+2]);
                    }
                }
            }
        }
    }
}

rotate([0, 0, rotate_model]) {
    difference() {
        translate([0, 0, input_r]) shuttle(input_L, input_W, input_H, input_Ls, input_Ws, input_Wg, input_ts, input_f_top, input_r);

        // Optionally etch text into the shuttle.
        if (len(etch_text) > 0) {
            shuttle_etch_text(etch_text, input_H, input_W, input_Ws, input_He, input_Htext);
        }
    }

    // Optionally add pads to prevent the ends from curling.
    if (input_pad_height > 0) {
        pads(input_L, input_W, input_Ls, input_Ws, input_r, input_pad_height);
    }
}

// Show the build plate. This only appears in the preview, not in the final model. 109x113 are the M3D micro's specs. The last two parameters are only used if the first parameters is 3 (manual).
build_plate(build_plate_preview, 109, 113);

```


[User]
I want to design a phone mount that connects to standard GoPro mounts. I'd like it to be parametric so I can adjust it for different phone sizes and cases. The main things I need to be able to customize are:

1.  **Phone Edge Diameter:** The diameter of the rounded edge of the phone I'm using. It's usually between 6 and 15mm, but I'd like the flexibility to go beyond that if necessary.
2.  **Clamp Width:** The width of the area where the phone is clamped. I'd like to be able to change this from 20mm to 100mm.
3.  **Minimum Clamp Height:** The minimal height of the clamping area, which should be a little less than the height of the phone, say from 20mm to 100mm.
4. **Clamp Range**: The travel distance of the clamp, that is how much the clamp opens. Values from 10mm to 50mm should work.
5.  **Clamp Sides:** Whether the clamp is enclosed on both sides of the phone (0 for false, 1 for true).
6.  **Minimal Wall Thickness:** The minimum thickness of the walls of the mount (1 to 5mm is fine).
7.  **Spring Wire Diameter:** The diameter of the wire used for the spring mechanism (0.5 to 5mm).
8. **Lock Spring Wire Diameter:** The diameter of the wire used for the locking spring mechanism (0.5 to 2mm).
9.  **Spring Box Size:** The dimensions of the square spring box (10 to 20mm).
10. **Tube Tolerance**: The tolerance between the two moving tubes in the design, from 0 to 3mm.
11. **GoPro Connector Type:** Whether to use a double or triple-arm GoPro connector (like the ones described in the included code).

The design should have two main parts: a top piece that holds the top part of the phone edge, and a bottom piece that slides up to clamp the phone into place. The top part should include the GoPro mount and the clamping mechanism. The bottom part should be able to move and clamp the phone into place with the spring mechanism. The top piece should be designed to accommodate the spring and lock.

The design can use a difference function of a circular extrusion to create the curved phone edge hold. A hull function should be used to join the phone hold, the gopro connector, and spring box.

For the gopro connector, please use the included gopro\_connector module and use all of the variables described, i.e. gopro\_nut\_d, gopro\_nut\_h, gopro\_holed\_two, gopro\_holed\_three, gopro\_connector\_th3\_middle, gopro\_connector\_th3\_side, gopro\_connector\_th2, gopro\_connector\_gap, gopro\_connector\_roundness, gopro\_wall\_th, gopro\_connector\_wall\_tol, and gopro\_tol.

Please generate the OpenSCAD code from scratch for the phone mount and the gopro\_connector. I don't need any external libraries for this design.

[Assistant]
iphone_gopro.scad:
```

// part to render
part = "assembly"; // [bottom:Bottom,top:Top,print:For printing,assembly:Whole assembly]

// quality
$fn = 50;

// GoPro connector
goproConnector = "triple"; // [double,triple]

// diameter of edge of phone (6 to 15mm are good values)
edgeDiameter = 9;

// width of clamping area of phone
clampWidth = 50; // [20:100]

// minimal clamp height; a few millimeters less than the height of the phone
minClampHeight = 67; // [20:100]

// clamp range
clampRange = 20; // [10:50]

// clamp sides of phone; if true, clamp is enclosed on both sides
clampSides = 0; // [0:false,1:true]

// minimal wall thickness
thickness = 2.5; // [1:0.1:5]

// width of spring wire (0.5 to 5mm are good values)
springWireDiameter = 3;

// diameter of lock spring wire (0.5 to 2mm)
lockSpringWireDiameter = 1.5;

// spring box dimension (width and height)
springBoxSquareDimension = 12; // [10:20]

// tolerance between tubes (0 to 3mm are good values)
tubeTolerance = 1.2;

/* [Hidden] */

// internal variables
__minClampDim = minClampHeight - edgeDiameter;
__realClampWidth = (clampSides == 1) ? (clampWidth + 2*thickness) : clampWidth;

module phoneEdge() {
  translate ([0, __realClampWidth/2, 0])
  rotate ([90,0,0])
  linear_extrude (height=__realClampWidth, convexity=3)
  difference() {
    circle (d=edgeDiameter + thickness, center=true);
    translate ([-edgeDiameter/2-thickness/2, 0]) square (size=edgeDiameter + thickness, center=true);
    circle (d=edgeDiameter, center=true);
  }
}

module tube (height, dimension) {
  difference() {
    cube ([dimension + 2*thickness, dimension + 2*thickness, height], center=true);
    translate([0,0,-0.05]) cube ([dimension - 0.1, dimension - 0.1, height + 0.2], center=true);
  }
}

module topCover() {
  bOffset = -springBoxSquareDimension/2 - edgeDiameter/2 - thickness;

  difference() {
    union() {
      phoneEdge();
      translate([-thickness/2, 0, bOffset]) rotate([0,90,0]) {
        // cover
        union() {
          rotate([0,0,90]) difference() {
            pom = thickness * 2 + lockSpringWireDiameter;
            cube ([springBoxSquareDimension - 0.2, springBoxSquareDimension - 0.2, pom], center=true);
            cube ([springWireDiameter, 100, pom + 0.1], center=true);
          }
          translate ([0,0,thickness-0.1]) cube ([springBoxSquareDimension + 2*thickness, springBoxSquareDimension + 2*thickness, thickness], center=true);
        }
      }

      // gopro connector
      translate([10 + 4 * thickness, 0, -springBoxSquareDimension+edgeDiameter/2]) rotate([0, 90, 90]) gopro_connector (goproConnector);

      // hull connection between elements
      difference() {
        hull() {
          translate([4 * thickness,0,-springBoxSquareDimension+edgeDiameter/2]) rotate([0,90,0]) cylinder (d=springBoxSquareDimension + 2*thickness + edgeDiameter/2, h=1);
          translate([thickness,0,bOffset]) cube ([2*thickness, springBoxSquareDimension + 2*thickness, springBoxSquareDimension + 2*thickness], center=true);
          phoneEdge();
        }
        translate ([0, clampWidth/2 + 0.05, 0]) rotate ([90,0,0]) linear_extrude (height=clampWidth + 0.1, convexity=3) circle (d=edgeDiameter, center=true);
      }

      translate([-__minClampDim/2, 0, bOffset]) rotate([0,90,0]) difference() {
        tube (__minClampDim, springBoxSquareDimension);
        translate ([-springBoxSquareDimension/2-thickness/2-0.2,0,0]) cube ([thickness, springBoxSquareDimension/2, __minClampDim+0.1], center=true);
      }
    }
    // hole for lock wire
    translate([-thickness/2,0,bOffset]) rotate([90,0,0]) cylinder (d = lockSpringWireDiameter, h = springBoxSquareDimension * 2, center=true);
  }
}

module bottomCover() {
  pom2 = springBoxSquareDimension - 2*thickness - tubeTolerance;
  pom = thickness * 2 + lockSpringWireDiameter;

  difference() {
    rotate([0,90,0]) union() {
      rotate([0,0,90]) difference() {
        cube ([pom2, pom2, pom], center=true);
        cube ([springWireDiameter, 100, pom + 0.1], center=true);
      }
      translate ([0,0,thickness-0.1]) cube ([springBoxSquareDimension + 2*thickness, springBoxSquareDimension + 2*thickness, thickness], center=true);
      translate ([0,0,-clampRange/2+thickness/2]) tube (clampRange, pom2);
    }
    rotate([90,0,0]) cylinder (d = lockSpringWireDiameter, h = springBoxSquareDimension * 2, center=true);
  }

  translate([thickness/2,0,-springBoxSquareDimension/2-edgeDiameter/2-thickness]) phoneEdge();

  difference() {
    hull() {
      edgePos = -springBoxSquareDimension/2-edgeDiameter/2-thickness;
      botDia = springBoxSquareDimension + edgeDiameter;

      translate([thickness+0.1,0,0]) rotate([0,90,0])cube ([springBoxSquareDimension + 2*thickness, springBoxSquareDimension + 2*thickness, thickness], center=true);
      translate([thickness/2,0,edgePos]) phoneEdge();
      translate([4 * thickness + edgeDiameter/6, 0, edgePos+botDia/2-edgeDiameter/2-thickness/2]) rotate([0,90,0]) cylinder (d=botDia, h=1);
    }
    translate([thickness/2, clampWidth/2 + 0.05, -springBoxSquareDimension/2-edgeDiameter/2-thickness]) rotate ([90,0,0]) linear_extrude (height=clampWidth + 0.1, convexity=3) circle (d=edgeDiameter, center=true);
  }
}

module assembly() {
  translate([-minClampHeight-clampRange/2-edgeDiameter,0,-springBoxSquareDimension - tubeTolerance/2 - edgeDiameter/2 + thickness + tubeTolerance/2]) rotate([0,180,0]) bottomCover();
  topCover();
}

module forPrint() {
  translate([0,0,springBoxSquareDimension+edgeDiameter+thickness/2]) topCover();
  translate([-25, 60, springBoxSquareDimension]) rotate([0,90,0]) bottomCover();
}

module print_part() {
	if (part == "top") {
		topCover();
	} else if (part == "bottom") {
		rotate([0,90,0]) bottomCover();
  } else if (part == "print") {
    forPrint();
	} else {
		assembly();
	}
}

print_part();

/** End of my code */

/**
 * This is part of http://www.thingiverse.com/thing:62800. I'am copy this there to make thing
 * compact for Thingiverse Customizer.
*/

// The locking nut on the gopro mount triple arm mount (keep it tight)
gopro_nut_d= 9.2;
// How deep is this nut embossing (keep it small to avoid over-overhangs)
gopro_nut_h= 2;
// Hole diameter for the two-arm mount part
gopro_holed_two= 5;
// Hole diameter for the three-arm mount part
gopro_holed_three= 5.5;
// Thickness of the internal arm in the 3-arm mount part
gopro_connector_th3_middle= 3.1;
// Thickness of the side arms in the 3-arm mount part
gopro_connector_th3_side= 2.7;
// Thickness of the arms in the 2-arm mount part
gopro_connector_th2= 3.04;
// The gap in the 3-arm mount part for the two-arm
gopro_connector_gap= 3.1;
// How round are the 2 and 3-arm parts
gopro_connector_roundness= 1;
// How thick are the mount walls
gopro_wall_th= 3;

gopro_connector_wall_tol=0.5+0;
gopro_tol=0.04+0;

// Can be queried from the outside
gopro_connector_z= 2*gopro_connector_th3_side+gopro_connector_th3_middle+2*gopro_connector_gap;
gopro_connector_x= gopro_connector_z;
gopro_connector_y= gopro_connector_z/2+gopro_wall_th;

module gopro_torus(r,rnd) {
	translate([0,0,rnd/2])
		rotate_extrude(convexity= 10)
			translate([r-rnd/2, 0, 0])
				circle(r= rnd/2, $fs=0.2);
}

module gopro_connector(version="double", withnut=true, captive_nut_th=0, captive_nut_od=0, captive_rod_id=0, captive_nut_angle=0) {
	module gopro_profile(th) {
		hull() {
			gopro_torus(r=gopro_connector_z/2, rnd=gopro_connector_roundness);
			translate([0,0,th-gopro_connector_roundness])
				gopro_torus(r=gopro_connector_z/2, rnd=gopro_connector_roundness);
			translate([-gopro_connector_z/2,gopro_connector_z/2,0])
				cube([gopro_connector_z,gopro_wall_th,th]);
		}
	}
	difference() {
		union()	{
			if(version=="double") {
				for(mz=[-1:2:+1]) scale([1,1,mz])
						translate([0,0,gopro_connector_th3_middle/2 + (gopro_connector_gap-gopro_connector_th2)/2]) gopro_profile(gopro_connector_th2);
			}
			if(version=="triple") {
				translate([0,0,-gopro_connector_th3_middle/2]) gopro_profile(gopro_connector_th3_middle);
				for(mz=[-1:2:+1]) scale([1,1,mz])
					translate([0,0,gopro_connector_th3_middle/2 + gopro_connector_gap]) gopro_profile(gopro_connector_th3_side);
			}

			// add the common wall
			translate([0,gopro_connector_z/2+gopro_wall_th/2+gopro_connector_wall_tol,0])
				cube([gopro_connector_z,gopro_wall_th,gopro_connector_z], center=true);

			// add the optional nut emboss
			if(version=="triple" && withnut) {
				translate([0,0,gopro_connector_z/2-gopro_tol])
				difference() {
					cylinder(r1=gopro_connector_z/2-gopro_connector_roundness/2, r2=11.5/2, h=gopro_nut_h+gopro_tol);
					cylinder(r=gopro_nut_d/2, h=gopro_connector_z/2+3.5+gopro_tol, $fn=6);
				}
			}
		}
		// remove the axis
		translate([0,0,-gopro_tol])
			cylinder(r=(version=="double" ? gopro_holed_two : gopro_holed_three)/2, h=gopro_connector_z+4*gopro_tol, center=true, $fs=1);
	}
}

```