[User]
I'm looking to create a parametric design for flexible chainmail that I can 3D print. I've been experimenting with a couple of different approaches, but I'd like something more modular and easier to adjust. I'd like to be able to control various aspects of the design using parameters.

Specifically, I'd like two main SCAD files, perhaps with some common modules or functions in a separate file. One file should generate a single chainmail link, and the other should take that link design and generate various repeating patterns.

For the link design, I need to be able to control:

*   The overall scale of the link.
*   The angle of the initial arc segment. This will control how much of a hexagon versus a circle the base of the link is, similar to the 'ang1' parameter.
*   The tilt angle of the initial arc segment, which controls how much the link curves in the Z direction, like the 'tilt' parameter.
*   The offset of the main arc, 'arc1_offset', and the radius of that arc, 'arc1_radius' which are related to the overall link size and shape.
*   The wire diameter.
*   The overall flattened Z thickness of the link, like the 'thickness' parameter.
*   A small overlap parameter for ensuring the arcs connect properly, as well as a small clearance parameter to prevent links sticking to one another.

The links are constructed from three identical but rotated main arcs, with each arc made of three different arc segments. The link design is described in detail in the 'chain_mail_tri-mesh_smooth6f_triangles_Rev5_half_size.scad' file. The single link generation SCAD file will not be used on its own, but rather be imported and patterned by the other main SCAD file.

The second SCAD file should be able to take the generated link from the first file, and use that to make different patterns, similar to what is done in 'fast_pattern_2.scad'. I would like to be able to control:

*   The link file to import.
*   The offset spacing for links in the pattern.
*   The shape of the pattern, choosing between square, triangle, trapezoid, or hex patterns.
*   The number of "rings" or repeats in the X and Y directions, with X_rings controlling the size of a pattern in the x direction and Y_rings controlling the size in the y. The X_rings parameter will also control the length of the side of a triangle or hexagon pattern.
*   It'd be nice if the console would print the total spacing for rectangular patterns, as is done in the provided `fast_pattern_2.scad` file. This is important for joining printed pieces together.

I'm not attached to any specific design for generating the arcs, but it should be as performant as possible. The math that was used to create the link is detailed in 'chain_mail_tri-mesh_smooth6f_triangles_Rev5_half_size.scad'.

Essentially, I want a flexible, parametric approach to generating this style of chainmail that is easy to adjust and customize with different patterns.

[Assistant]
fast_pattern_2.scad:
```
//Choose the link file to import by changing "file_name".  The "offset" variable sets the spacing for the links.  The best value for this is ECHOed in the link generating program

//Avoid rendering patterns larger that 150 links.  Make smaller patterns that can be joined later in the slicer.  The console will ECHO the x and y spacing so they can accuratly be joined.  Note this works with "square" patterns only.

file_name="56 percent link dec.stl";
file_dir="";
offset=5.88;

X_rings= 3;
//number of exposed rings in Y direction (square pattern only) (default=3)
Y_rings= 10;
//shape of ring pattern
shape="square"; //["square", "triange","trapezoid, hex"]
//  preview[view:south, tilt:top]

//ink_file=str(file_dir,file_name);

module triangle(size){
    for(nloop=[0:size-1]){
        xstart=nloop*offset*cos(30);
        ystart=nloop*offset*1.5;
        xinc=2*offset*cos(30);
        for(nh=[0:size-nloop-1]){
          if(ystart!=0)translate([xstart+xinc*nh,ystart,0])rotate([0,0,90])flat_loop();
         if(ystart==0) translate([xstart+xinc*nh,ystart,0])rotate([0,0,90])flat_loop();
        }
        if(size-nloop>=2)for(nh=[0:size-nloop-2]){
           translate([xstart+xinc/2+xinc*nh,ystart+offset*cos(60),0])rotate([0,0,-90])flat_loop();
        }
    }
}

module triangle2(size){
   translate([(((size-1)*2)+1)*cos(30)*offset,offset*(sin(30)),0])
        rotate([0,0,60]) triangle(size);
}

module sixth_hex(size){
    translate([-offset*cos(30)*(size-1),-offset*(1+1.5*(size-1)),0])triangle(size);
}

module hex(size){
  sixth_hex(size);
  rotate([0,0,60]) sixth_hex(size);
  rotate([0,0,120]) sixth_hex(size);
  rotate([0,0,180]) sixth_hex(size);
  rotate([0,0,240])  sixth_hex(size);
  rotate([0,0,300])  sixth_hex(size);
}

//create 4 rings for square pattern
module four_loop(){
    rotate([0,0,90]) flat_loop();
    translate([offset*cos(30),offset*sin(30),0]) rotate([0,0,30])flat_loop();
    translate([offset*cos(30),offset*(1+sin(30)),0]) rotate([0,0,90]) flat_loop();
    translate([0,offset*2,0]) rotate([0,0,30])flat_loop();
}

y_step= 2*offset+2*offset*cos(60);
x_step = 2*offset*sin(60);

 module make_shape(){

     if (shape=="square"){
         echo("total X spacing", x_step*X_rings);
         echo("total Y spacing",y_step*Y_rings);
              for(nx=[0:X_rings-1]){
                    for(ny=[0:Y_rings-1]){
                        translate([nx*x_step,ny*y_step,0]) four_loop();
                    }
              }
          }
            if(shape=="hex")hex(X_rings);
          if(shape=="triangle")triangle(X_rings);

            if (shape=="trapezoid")rotate([0,0,15]){
                triangle(X_rings);
                triangle2(X_rings);
            }
    }
make_shape();

module flat_loop(){
    rotate([0,0,0])
import(file=str(file_dir,file_name));
}

```
chain_mail_tri-mesh_smooth6f_triangles_Rev5_half_size.scad:
```

//Chain Mail Tri-mesh Improved
// Licenced under the Creative Commons - Attribution - Share Alike license
//2017 Don Fyler
// Rev 1 Nov 11,2017  Cleaned up and made revisable
//Rev 2 Sept 22,2018  Modified to print triangular pattern
//Rev 3 Nov 18, 2018  General  updates
//Rev 4 Dec 2, 2018  Modified to print hex pattern also
//Rev 5 May 28 2021 Fixed extra 0 in rotation matrices
//-----------------------------------------------------------------------------------------
//Brief description of model
//Each ring is made from 3 sections that are the same except rotated.  Each of the sections is made of 3 arcs.
//The first arc (arc1) defines the general size of the ring, the shape of the ring, and how far the ring goes up and down in the z direction.
//Arc2 and arc3 are the larger up and down loops.  Arc3 is the same as arc2 except flipped 180 degrees.
//After arc1 is defined, there is only one (if any) solutions for arc2 and arc3.  This means you dont get any options for adjusting them except what you can do to arc1.  This makes for some unexpected behavior and it will take some practice to get what you want.
//Set "overlap" to -5 if you want to see what the individual arcs look like.
//Set "shape" to the pattern type you want to see.  Avoid rendering large patterns because OpenSCAD will crash.  It is better to render a single link, decimate it in Blender to create a low-poly version, and then import that into the "fast_pattern" OpenSCAD program.
//--------------------------------------------------------------------------------------

//resolution, needs to be high for clean joints(default=20)
Res=30;
//overall scale of everything to simply scale mesh(default=1.02)
scalar=.56;

//angle sweep of initial arc.  ang1=0 will make hexagon rings. (default=20)
ang1=30; //[0:45]
 //From 0 deg to 90 deg (flat to full wave in rings)(default=65)
tilt=70;//[0:90]

// the max radius of a ring at the center of the wire will usually be arc1_offset+arc1_radius
//mm offset from center for arc1(default=5mm)
arc1_offset = 5;
//mm radius of arc1 (default=3mm)
arc1_radius = 3;
//mm diameter of ring wire(default=3.6mm)
wire_dia=3.5;
//mm total Z thickness after flat is cut. A reasonable size flat is necessary to stick to the bed (default=3.4mm)
thickness=3.5;
// degrees of arc overlap to make sure OpenSCAD joins the arcs(default=1 )
overlap=1.;
//mm clearance offset so rings do not touch during printing.  Leave about 2 layers gap  between rings to be sure they dont stick to each other. (default=.9)
clearance=2;
//number of exposed rings in X direction (or  per side of triangle)(default=3)

X_rings= 3;
//number of exposed rings in Y direction (square pattern only) (default=3)
Y_rings= 2;
//overall mesh profile
shape="one"; // [square, triangle,trapezoid,hex,one]

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

// this module is here to force Customizer from interpreting any more variables
module hide_variables(){
}

$fn=Res;

bendoffset1=arc1_offset*scalar;//arc1 offset -scaled
bendrad1=arc1_radius*scalar;//arc1 bend radius -scaled
dia=wire_dia*scalar;  // diameter of spagetti -scaled
thick=thickness*scalar;  //flattened thickness (cropped)

offset=2*(bendoffset1+bendrad1)-dia-clearance*scalar;// spacing of rings as printed, adjust to make sure rings do not touch
echo("offset=",offset);

p1=[bendrad1,0,0];  //point at end for arc1 (unrotated)
n1=[bendrad1,1,0];  //unit normal at end of  arc1

R1=[[cos(ang1/2),sin(ang1/2),0],[-sin(ang1/2),cos(ang1/2),0],[0,0,1]]; //rotation matrix 1 (1/2 of ang1 about z)
T1=[bendoffset1,0,0];  //translate 1

R2=[[1,0,0],[0,cos(tilt),sin(tilt)],[0,sin(tilt),cos(tilt)]]; //rotation matrix about x (tilt ang about x)

R3=[[cos(60),-sin(60),0],[sin(60),cos(60),0],[0,0,1]]; // rotation matrix about z(-60deg about z)
p1a=(p1*R1+T1)*R2*R3; //point at end of arc 1
n1a=(n1*R1+T1)*R2*R3; //normal point
V2=n1a-p1a; //normal vector
P1v=V2*p1a;  // plane equation is V2[0]*x+V2[1]*y+V2[2]*z = P1v
//echo ("P1v=",P1v);
//echo("p1a=",p1a);
//echo("n1a=",n1a);
//echo("V2=",V2);

//Note: arc1 has been rotated -60deg about z so arc2 ends on x axis

xpos=[P1v/V2[0],0,0];  //get point were plane goes through the x axis.
//echo("xpos=",xpos);

ap2=[norm(xpos-p1a)+xpos[0],0,0]; // get point on x axis were new arc ends.
//echo("ap2=",ap2);

coord_mid=(p1a+ap2)/2;
angx=atan(p1a[2]/p1a[1]);  // x axis rotation
Rx=[[1,0,0],[0,cos(angx),-sin(angx)],[0,sin(angx),cos(angx)]];
Rxn=[[1,0,0],[0,cos(angx),sin(angx)],[0,-sin(angx),cos(angx)]];
p1ax=p1a*Rx;
n1ax=n1a*Rx;
coord_midx=coord_mid*Rx;
ap2x=ap2*Rx;

angz=-atan((p1ax[0]-ap2x[0])/(p1ax[1]-ap2x[1]));
Rz=[[cos(angz),-sin(angz),0],[sin(angz),cos(angz),0],[0,0,1]];
Rzn=[[cos(angz),sin(angz),0],[-sin(angz),cos(angz),0],[0,0,1]];
p1az=p1ax*Rz;
n1az=n1ax*Rz;
coord_midz=coord_midx*Rz;
ap2z=ap2x*Rz;
V2z=n1az-p1az;
//echo("V2z=",V2z);

angy=atan(V2z[0]/V2z[2]);
Ry=[[cos(angy),0,sin(angy)],[0,1,0],[-sin(angy),0,cos(angy)]];
Ryn=[[cos(angy),0,-sin(angy)],[0,1,0],[sin(angy),0,cos(angy)]];
p1ay=p1az*Ry;
n1ay=n1az*Ry;
coord_midy=coord_midz*Ry;
ap2y=ap2z*Ry;
V2y=n1ay-p1ay;
//echo("V2y=",V2y);

thet=atan(V2y[2]/V2y[1]);
//echo("thet=",thet);
pivotz =coord_midy[2] - (coord_midy[1]-p1ay[1])/tan(thet);
pivot=[coord_midy[0],coord_midy[1],pivotz];
radvec=p1ay-pivot;
rad2=norm(radvec);
//echo("rad2=",rad2);

//routine to draw an arc segment
module arc_seg(big_rad, little_rad,angle){
    intersection(){
        rotate_extrude(convexity=10)
            translate([big_rad,0,0])
                circle(little_rad);
        linear_extrude(bendrad1*2,center=true)
        polygon([[0,0],[(big_rad+little_rad*2)*cos(angle/2),-(big_rad+little_rad*2)*sin(angle/2)],
                    [(big_rad+little_rad*2),0],
                    [(big_rad+little_rad*2)*cos(angle/2),(big_rad+little_rad*2)*sin(angle/2)]]);
    }
}

//arc_seg(10,2,120);

//first arc
module arc1(){
    rotate([tilt,0,0])
    translate([bendoffset1,0,0])
    arc_seg(bendrad1,dia/2,ang1);
}

//second arc
module arc2(){
    rotate([angx,0,0])
    rotate([0,0,angz])
    rotate([0,angy,0])
    translate(pivot)
    rotate([0,-90,0])
    arc_seg(rad2,dia/2,thet*2+overlap);

}

//arc2 and arc3
module arc22(){
   arc2();
   rotate([180,0,0]) arc2();
}

//one entire ring
module loop(){
    union(){
    rotate([0,0,-60]) arc1();
    rotate([0,0,60]) arc1();
    rotate([0,0,180]) arc1();
    arc22();
    rotate([0,0,120]) arc22();
    rotate([0,0,240]) arc22();
    }
}
loop_size=(bendoffset1+bendrad1+dia)*2;//size of loop plus extra

//create flats on extremities of the ring
module flat_loop(){
      intersection(){
         loop();
         translate([0,0,0])cube([loop_size,loop_size,thick*2],center=true);
     }
 }

module triangle(size){
    for(nloop=[0:size-1]){
        xstart=nloop*offset*cos(30);
        ystart=nloop*offset*1.5;
        xinc=2*offset*cos(30);
        for(nh=[0:size-nloop-1]){
            translate([xstart+xinc*nh,ystart,0])rotate([0,0,90])flat_loop();
        }
        if(size-nloop>=2)for(nh=[0:size-nloop-2]){
           translate([xstart+xinc/2+xinc*nh,ystart+offset*cos(60),0])rotate([0,0,-90])flat_loop();
        }
    }
}

//two joined triangles
module triangle2(size){
   translate([(((size-1)*2)+1)*cos(30)*offset,offset*(sin(30)),0])
        rotate([0,0,60]) triangle(size);
}

// 1/6th of a hex shape
module sixth_hex(size){
    translate([-offset*cos(30)*(size-1),-offset*(1+1.5*(size-1)),0])triangle(size);
}

module hex(size){
  sixth_hex(size);
  rotate([0,0,60]) sixth_hex(size);
  rotate([0,0,120]) sixth_hex(size);
  rotate([0,0,180]) sixth_hex(size);
  rotate([0,0,240])  sixth_hex(size);
  rotate([0,0,300])  sixth_hex(size);
}

//create 4 rings for square pattern
module four_loop(){
    rotate([0,0,90]) flat_loop();
    translate([offset*cos(30),offset*sin(30),0]) rotate([0,0,30])flat_loop();
    translate([offset*cos(30),offset*(1+sin(30)),0]) rotate([0,0,90]) flat_loop();
    translate([0,offset*2,0]) rotate([0,0,30])flat_loop();
}

//x and y spacing of the group of four loops  so it can be patterned with another program (use only with rectangular pattern)
y_step= 2*offset+2*offset*cos(60);
x_step = 2*offset*sin(60);

//create entire mesh
 module make_shape(){

     if (shape=="square"){
                echo("total x-ring spacing",x_step*X_rings);
                echo("total y-ring spacing",y_step*Y_rings);
              for(nx=[0:X_rings-1]){
                    for(ny=[0:Y_rings-1]){
                        translate([nx*x_step,ny*y_step,0]) four_loop();
                    }
              }
          }
          if(shape=="hex")hex(X_rings);
          if(shape=="triangle")triangle(X_rings);

            if (shape=="trapezoid")rotate([0,0,15]){
                triangle(X_rings);
                triangle2(X_rings);
            }
             if(shape=="one")flat_loop();

    }

make_shape();

//debugging stuff
//*/
//arc1();
//rotate([0,0,60])arc22();
//loop();

/*
translate(p1a) sphere(1/2);
translate(n1a) sphere(1/2);
translate([xpos[0],0,0]) sphere(1/2);
translate([ap2[0],0,0]) sphere(1/2);
translate(coord_mid) sphere(1/2);

translate(p1az) sphere(1/2);
translate(n1az) sphere(1/2);
translate(ap2z) sphere(1/2);
translate(coord_midz) sphere(1/2);

translate(p1ay) sphere(1/2);
translate(n1ay) sphere(1/2);
translate(ap2y) sphere(1/2);
translate(coord_midy) sphere(1/2);
*/

```


[User]
Hey, I'm looking to create a maker coin in OpenSCAD. I've got some specific design parameters in mind, and I'd like the code to be parametric so I can easily adjust things later.

Here’s what I need:

The coin should be based on a rotated extrusion profile. The basic shape is a sort of flat cylinder with a rounded edge and a recessed area in the center, creating a sort of two-tiered effect on its edge.

**Coin Dimensions:**

*   I'd like to control the overall radius of the coin, let’s call this `coin_radius`.
*   There will be an outer thickness or height, `outer_thickness`.
*   There's a recessed section, so there will also be an inner height, `inner_thickness`.
*   Finally there's a circular torus in the center with a specified diameter, `torus_diameter`.

The edge of the coin is not a simple cylinder - there should be a smooth, curved transition between the outer height, the inner height, and the recessed area. The inner height should be slightly offset, so it is not a simple subtraction of a cylinder from the outer edge. The center torus is to be a simple torus.

**Notches:**

*   I want to be able to add notches around the outer edge. I need to control the `notches` (number of notches).
*   Each notch is a cylindrical cutout; I need a `notches_radius` and `notches_offset` from the edge.

**Text Logo:**

*   I need to be able to add text to the center of the coin on the top face. There should be three lines of text: an upper line, a center line, and a lower line.
*   The content of the text should be configurable using `text_upper`, `text_center`, and `text_lower` parameters.
*   I need control over `font_face`, `font_style` (e.g. Bold), and the individual font sizes for each line of text: `font_upper_size`, `font_center_size`, and `font_lower_size`.

So, all these values should be easily changed in the SCAD file. I think that should cover it, if you have any questions, please let me know!

[Assistant]
coin.scad:
```
// A maker coin
// 2019 - Christian Muehlhaeuser <muesli@gmail.com>
// Inspired by https://www.thingiverse.com/thing:1897796

/* [Coin Dimensions] */

// radius of the coin
coin_radius=24; //[10:1:30]
// outer height/thickness
outer_thickness=9; //[4:1:20]
// inner height/thickness
inner_thickness=4; //[2:1:20]
// diameter of internal torus
torus_diameter=7; //[4:1:12]

/* [Notches] */

// how many notches
notches=8; //[0:1:16]
// radius of notches
notches_radius=20; //[1:1:36]
// offset for notches
notches_offset=18; //[1:1:34]

/* [Logo] */

// upper text
text_upper="mueslix";
// center text
text_center="@";
// lower text
text_lower="twitter.com";

// font face
font_face="Roboto";
// font style
font_style="Bold";
// size of upper text
font_upper_size=4; //[0:1:10]
// size of center text
font_center_size=3; //[0:1:10]
// size of lower text
font_lower_size=4; //[0:1:10]

/* [Hidden] */
$fn = 64;

r1=outer_thickness/2;
r1_dist=coin_radius-r1;
diff=r1-inner_thickness;
r2=(pow(r1_dist,2)-(pow(r1,2)-pow(diff,2)))/((2*r1)+(2*diff));
r2_dist=r2+inner_thickness;
r3=torus_diameter/2;

module coin() {
	rotate_extrude(convexity = 10) {
		difference() {
			union() {
				polygon(points=[[0,0],[r1_dist,0],[r1_dist,r1,],[0,r2_dist]]);
				translate([r1_dist,r1,0])
					circle(r1);
			}
			// add an extra .01 to ensure they touch
			translate([0,r2_dist,0])
				circle(r2+.01);
		}
	}
}

module torus() {
	rotate_extrude(convexity = 10) {
		translate([r1_dist,r1,0])
			circle(r3);
	}
}

module logo() {
	translate([0,(font_upper_size+font_center_size/2),1])
		linear_extrude(r1*2)
			text(text_upper,font=str(font_face, ":style=", font_style),size=font_upper_size,valign="center",halign="center");

	translate([0,0,1])
		linear_extrude(r1*2)
			text(text_center,font=str(font_face, ":style=", font_style),size=font_center_size,valign="center",halign="center");

	translate([0,-(font_lower_size+font_center_size/2),1])
		linear_extrude(r1*2)
			text(text_lower,font=str(font_face, ":style=", font_style),size=font_lower_size,valign="center",halign="center");
}

module notches() {
	if (notches > 0) {
		for (a=[0:360/notches:359]) {
			rotate([0,0,a])
				translate([coin_radius+notches_offset,0,0])
					cylinder(r=notches_radius,h=outer_thickness);
		}
	}
}

difference() {
	difference() {
		union() {
			coin();
			torus();
		}
		logo();
	}
	notches();
}

```


[User]
I'm looking to create a parametric strainer for isopropyl alcohol (IPA), similar to the one described in the Thingiverse link you sent. I need it to be customizable in size and handle design, which is why I wanted to make it parametric.

Here are the specific parameters I’d like to control in the OpenSCAD file:

**Overall Dimensions:**

*   `length`: The overall length of the strainer (in mm).
*   `width`: The overall width of the strainer (in mm).
*   `height`: The total height of the strainer from top to bottom (in mm).
*   `handles_count`: The number of handles (should allow 1 to 4 handles).

**Strainer Grid:**

*   `bt_thick`: The thickness of the strainer's grid (mm).
*   `bt_rad`: The radius of the rounded corners of the grid (mm).
*   `hexa_size`: The size (distance between centers) of the hexagons in the grid (mm).
*   `brd_thick`: The thickness of the borders and handles (mm).
*   `hexa_thick`: The thickness of the hexagons in the grid (mm).
*   `brd_height`: The height of the border above the grid (mm).

**Handles:**

*   `handle_top_size`: The size of the handles at the top (mm).
*   `handle_bottom_size`: The size of the handles at the bottom (mm).
*   `handle_corner_radius`: The radius of the rounded corners of the handles (mm).
*   `handle_hole`: A boolean (0 for no, 1 for yes) to enable or disable a split in the handle.
*   `handle_border_size_top`: The size of the split handle's arms at the top (mm). This only applies when `handle_hole` is set to 1
*   `handle_border_size_bottom`: The size of the split handle's arms at the bottom (mm). This only applies when `handle_hole` is set to 1.

I would also like some internal variables to be set like this:
```
$fn=64;
COS_60 = 1/2;
SIN_60 = sqrt(3)/2;

brd_height2 = bt_thick + brd_height;
handle_thinning = handle_top_size / handle_bottom_size;
arm_length = height - brd_thick;
```
I’d also like to be sure that it uses the `minkowski()` function to create rounded edges, like in the example. Additionally, please use `linear_extrude` and `offset` to make the pseudo pyramid, and `cylinder` to make the hex prism. Can the main components like the ground, the arm, and the handles be done as separate modules?

Could you generate the OpenSCAD code based on these specifications? Thanks!

[Assistant]
parametric_ipa_strainer.scad:
```
// all units in mm

/* [Dimensions] */
// the length of the strainer (mm)
length = 110;
// the width of the strainer (mm)
width = 110;
// the total height (mm - from top to bottom)
height = 85;

// the number of handles
handles_count = 2; // [1,2,3,4]

/* [Strainer] */

// the thickness of the strainer's grid (mm)
bt_thick = 2;

// the radius of the rounded corners of the grid (mm)
bt_rad = 15;

// the size (distance between centers) of the hexagons (mm)
hexa_size = 6;

// The thickness of the borders and handles (mm)
brd_thick = 2;

// the thickness of the hexagons (mm)
hexa_thick = 0.8;

// The height of the border above the grid (mm)
brd_height = 10;

/* [Handles] */
// the size of the handles (mm - at top)
handle_top_size = 20;

// the size of the handles (mm - at bottom)
handle_bottom_size = 30;

// the radius of the handle rounded corners (mm)
handle_corner_radius = 10;

// Are the handle split ?
handle_hole = 1; // [0: No; 1: Yes]

// the size of the split handle's arms (mm - at the top)
handle_border_size_top = 10;

// the size of the split handle's arms (mm - at the bottom)
handle_border_size_bottom = 15;

/* [hidden] */
$fn=64;
COS_60 = 1/2;
SIN_60 = sqrt(3)/2;

brd_height2 = bt_thick + brd_height;
handle_thinning = handle_top_size / handle_bottom_size;

arm_length = height - brd_thick;

union() {
  ground();
  for(i = [0 : handles_count - 1])
    intersection() {
      scale([(abs(1.5-i)-1)*2,(i%2)*2-1,1])
        arm();
    }
}

module arm() {
  *translate([0,0,arm_length/2]) cube([length, width, arm_length], center=true);

  difference() {
    intersection() {
     hollow_rounded();

     translate([length, width, 0]/2)
       difference() {
       pseudo_pyramid(arm_length+brd_thick,
          handle_top_size,
          handle_bottom_size,
          handle_corner_radius);
         scale(handle_hole)
         pseudo_pyramid(arm_length+brd_thick,
          handle_top_size - handle_border_size_top,
          handle_bottom_size - handle_border_size_bottom,
          handle_corner_radius);
       }
    }
    translate([0,0, brd_height2/2-1])
      cube([length, width, brd_height2+1],center=true);
  }
}

module hollow_rounded() {
  size = [length, width, arm_length+brd_thick+bt_rad];
  translate([0,0,-brd_thick - bt_rad])
    difference() {
      rounded_cube(size, bt_rad, bt_rad);
      translate([0,0,brd_thick])
        rounded_cube(size-[2,2,2]*brd_thick, bt_rad, bt_rad);
    }
}

module ground() {
  difference() {
    rounded_cube([length-brd_thick*2, width-brd_thick*2, bt_thick], bt_rad-brd_thick, 0);
    hexa_ground();
  }

  L = (bt_rad * 2 + brd_height2);
  intersection() {
    translate([0,0, brd_height2/2]) cube([length, width, brd_height2],center=true);

    translate([0,0,-L]) difference() {
      rounded_cube([length, width, L * 2], bt_rad, bt_rad);
      translate([0,0,brd_thick])
        rounded_cube([length, width, L * 2]-[2,2,2]*brd_thick, bt_rad, bt_rad);
    }
  }
*  difference() {
    rounded_cube([length, width, brd_height2], bt_rad, 0);
    translate([0,0,-0.5])
    rounded_cube([length-brd_thick*2, brd_height2-brd_thick*2, brd_height2+1], bt_rad-brd_thick, 0);
  }
}

module hexa_ground() {
  DX = (COS_60+1) * hexa_size;
  DY = SIN_60 * hexa_size;

  translate([-length/2, -width/2, 0])
    for( x = [0 : ceil(length / DX)] )
      for( y = [0 : ceil(width / DY)] ) {
        translate([x * DX, y * DY, -0.5])
          hexa_prism(hexa_size - hexa_thick / sin(60), bt_thick + 1);

        translate([(x + 0.5) * DX, (y + 0.5) * DY, -0.5])
          hexa_prism(hexa_size - hexa_thick / sin(60), bt_thick + 1);
      }
}

module hexa_prism(size, height) {
    cylinder(d=size, h=height, $fn=6);
}

module rounded_cube(size, radiusXY, radiusZ) {
    radii = [radiusXY, radiusXY, radiusZ];
    translate(radii-[size[0], size[1], 0] / 2)
      minkowski() {
        cube(size - radii * 2);
        scale(radii) sphere(r=1);
      }
}

module pseudo_pyramid(height, top_size, bottom_size, radius) {
    rotate([0,0,45]) translate([1,0,0]*-top_size/2)
      linear_extrude(height=height, scale=top_size/bottom_size)
        offset(radius)
          square(bottom_size*sqrt(2)-radius*2,center=true);
}

function lerp(x,a,b) = (1-x) * a + x * b;
```


[User]
Hey! I'm looking to design a port extender for my Glowforge laser cutter. The existing exhaust port is kind of short, making it a pain to attach and detach the exhaust hose. I've got a decent idea of what I need, and I'd like you to help me generate some OpenSCAD files to create a parametric design for 3D printing. I'm planning on printing this with a semi-flex filament like TPU.

Essentially, I need a cylindrical extender that fits snugly over the existing 95.5mm diameter exhaust port (this is an interference fit, but semi flex filament should handle that) and extends it outwards by a bit. It should have a bit of a "lip" or recess for the exhaust hose to sit against so it helps with the connection. The port is about 12.5mm long, and I'd like the extender to add another 12mm of length.

Here are the specifics, I guess:

*   **Inner Diameter:** The inner diameter of the main section of the extender needs to be 95.5mm to tightly fit the Glowforge exhaust port.
*   **Main Body Length:** The main cylindrical portion needs to extend 12mm beyond the 12.5mm port, so 24.5mm in total.
*   **Extender Wall Thickness:** The wall thickness should be around 4mm.
*   **Lip Recess:** There needs to be a lip or recess inside the main body for the hose to connect to.
     *   This lip should start around 10mm from the end of the extender that interfaces with the GF.
     *  The lip itself should have a length of about 6mm.
     *  The inner diameter of the lip should be 1mm smaller than the outer diameter, so that the lip acts as a recess.
*   **Outer Diameter:** I'd like the outer diameter to follow from the inner diameter and wall thickness.
*   **Filament:** I'll be printing with a flexible material, such as Sainsmart TPU, so the tolerances can be tighter. But if you need to add parameters to allow for stiffer filaments, that's fine by me!
*   **Parametric:** I'd like this to be fully parametric, so if I need to tweak any dimensions I can do that easily.

I think that covers everything. Let me know if you need any more details. Thanks!

[Assistant]
GF-PortExtender.scad:
```

/* Glowforge port extender v1
 * Designed by Techyg
 *
 * Purpose: Extend the back 4" port on the glowforge and allow for
 * an easier time making the connection.
 * If using the default settings below, you will have an additional 12mm extension
 * There is also a recess (lip) that your connector is meant to sit on to help secure it
 *
 * Print with a semi flex filament, such as Sainsmart TPU.
 * It is designed to be stretched over the exhaust port and should be very snug.
 *
 */

//Settings for thickness and diameter below.
//All measurements are milimeters
//Only change if you know what you're doing

$fn=100;
port_od = 95.5; //glowforge outer diameter of exhaust port measured around 97 mm. Minus 1.5mm for tight tolerance
port_depth = 12.5; //length of the port on the GF
extender_depth = port_depth + 12;
extender_thickness = 4; //thickness of the extender
extender_od = port_od + extender_thickness;
extender_connect_lip_depth = 10; //where we want the connection to start (measured from bottom)
extender_connect_lip_length = 6; //length of the lip
extender_connect_recess = extender_od-1; //recess of lip

difference()
{
    cylinder(r=extender_od/2, h=extender_depth); //build outer diameter of extender
    cylinder(r=port_od/2, h=extender_depth+1); //subtract inner diameter of extender
    translate([0,0,extender_connect_lip_depth])
    difference() //subtract the "lip"
    {
        cylinder(r=105/2, h=extender_connect_lip_length); //outside lip
        cylinder(r=extender_connect_recess/2, h=extender_connect_lip_length); //inside lip
    }
}

```


[User]
Okay, I'm looking to design a parametric flange for ACME leadscrews, and I'd like the OpenSCAD code to be flexible enough to work with different imperial sizes and configurations. I've seen some examples online but I would prefer that you generate them rather than modifying what is available.

Here's what I need the design to handle:

**Core Dimensions:**
*   **Stem Diameter (STEM\_D):** This is the diameter of the cylindrical part that will fit onto the leadscrew.
*   **Base Diameter (BASE\_D):** The overall diameter of the flange's base.
*   **Base Thickness (BASE\_THICK):** The thickness of the flange's base.
*   **Stem Height (STEM\_HEIGHT):** The height of the cylindrical stem.

**Hole Pattern:**
*   **Hole Circle Diameter (F):** The diameter of the circle on which the screw holes are located.
*   **Hole Diameter (F2):** The diameter of the screw holes.
*   **Number of Holes (HOLES):** The number of screw holes, which should be evenly spaced.
*   **Open Holes (OPEN):** A boolean option (1 or 0) to make the screw holes connect to the edge of the base (like slots) or not.

**Thread Parameters:**
*   **Major Diameter of Thread (DMAJ):** The outside diameter of the ACME thread.
*   **Threads Per Inch (TPI):** The thread pitch, specified as threads per inch.
*  **Number of Starts (STARTS):** Number of thread starts.

**Other Parameters:**
*   **Bevel (BEVEL):** A small amount to bevel the corners of the flange.
*   **Outside Diameter Compensation ($OD\_COMP):** An adjustment to the thread's outside diameter, in mm.
*   **Inside Diameter Compensation ($ID\_COMP):** An adjustment to the thread's inside diameter, in mm.
*   **Leadscrew Thickness Offset ($PE):** A small adjustment for leadscrew thickness.

I'd like the code to be written so that all these parameters are easily customizable. Also, I expect this to be done in inches, and I don't want to have to define the scaling factors manually, or the unit conversions manually. I also need it to handle the ACME thread generation, not just a cylinder. I'd like for this to be a single OpenSCAD file if possible, but if it would be better to break it up into multiple files, that would be fine too. I would like to include all the necessary libraries. I don't think this should require anything special, just OpenSCAD and whatever standard mathematical operations are required, but include any such libraries in the output.

[Assistant]
flange-imperial.scad:
```
// Parametric ACME Flange in OpenSCAD, for Thingiverse customizer, Tyler Montbriand, 2019

// Diameter of stem, in inches
STEM_D=0.85;
// Diameter of base, in inches
BASE_D=1.606;
// Thickness of base, in inches
BASE_THICK=0.41;
// Height of stem, in inches
STEM_HEIGHT=0.62;
// Hole pattern diameter, in inches
F=1.25;
// Hole diameter, in inches
F2=.266;
// How much to bevel corners.
BEVEL=1/16;
// Outside diameter of thread.
DMAJ=3/8;
// Pitch of thread, in threads-per-inch
TPI=10; // [5:1:30]
STARTS=1; // [0:1:6]

// Number of screw holes
HOLES=4;    // [0:1:8]

// Whether screw holes connect to edges.
OPEN=1; // [0:1]

// Added to outside thread diameters, in mm.
$OD_COMP=-0.25;
// Added to inside thread diameters, in mm.
$ID_COMP=1;
// Thickness offset for leadscrews, in mm
$PE=0.35;

$fs=1;
$fa=3;

imperial() difference() {
    taper(d=DMAJ,h=BASE_THICK+STEM_HEIGHT, off=BEVEL, in=true)
    flange(B=STEM_HEIGHT, C=STEM_D,G=BASE_THICK,H=BASE_D, F=F, F2=F2, off=BEVEL,
    holes=HOLES?([0:360/HOLES:360-(360/HOLES)]):[],
    open=OPEN);
    comp_thread(DMAJ=DMAJ, L=BASE_THICK+STEM_HEIGHT+1/TPI,
    PITCH=1/TPI, A=29, H1=0.5/2, H2=0.5/2, STARTS=STARTS, in=true);
}

 /**
 * Generates truncated, symmetrical thread profiles like UTS or ACME
 * A is pitch angle
 * MIN is distance below centerline in pitch units
 * MAX is distance above centerline in pitch units
 * TOL makes tooth narrower/wider and deeper/shallower than perfect by TOL amount,
 * again in units of pitch
 *
 * Resuls biased to zero and inverted -- just like tsmthread() likes them.
 */
function prof(A,MIN,MAX)=let(
        M=tan(90-(A/2)), // Slope of tooth
        X1=((M/2)-(MIN*2))/M, // Given a Y of MIN, calculate X
        X2=((M/2)+(MAX*2))/M, // Given a Y of MAX, calculate X
    OFF=-X1*M) [
    [0, OFF + M*X1], // Starting point, always
    [X1+X1,OFF + M*X1],
    [X1+X2,OFF+M*X2],
    [X1+2-X2,OFF+M*X2],
    // Profile wraps here
]/2;

/**
 * Profile Interpolation
 *
 * prof() generates, and tsmthread expects, a profile of [X,Y] values like
 * [ [0,0.25], [0.25, 1], [0.5,0.25] ]
 * The first X must be 0.  The last X cannot be 1.  All values are in pitch units.
 *
 * Get a value out with interpolate(PR, X).
 *      interpolate(PR, 0.25) would return 1,
 *      interpolate(PR, 0) would give 0.25,
 *      interpolate(PR, 0.125) would  give someting between.
 *      interpolate(PR, 0.5) would give 0.25.
 *      interpolate(PR,0.75) would wrap, interpolating between P[2]-p[0].
 *
 * Should wrap cleanly for any positive or negative value.
 */

/**
 * Helper function for interpolate().  Allows
 * a thread profile to repeat cleanly for increasing
 * values of N, with growing X accordingly.
 *
 * P=[ [0,0], [0.5,0.5] ];
 * echo(wrap(P,0)); // should be [0,0]
 * echo(wrap(P,1)); // should be [0.5,0.5]
 * echo(wrap(P,2)); // should be [0,0]+[1,0]
 * echo(wrap(P,3)); // should be [0.5,0.5]+[1,0]
 * echo(wrap(P,4)); // should be [0,0]+[2,0]
 * etc.
 */
function wrap(V, N, ACC=[1,0])=let(M=floor(N/len(V))) V[N%len(V)] + M*ACC;

/* Very basic interpolation.  mix(A,B,0)=A, mix(A,B,1)=B, 0 <= X <= 1 */
function mix(A,B,X)=(A*(1-X)) + B*X;

/**
 * Line-matching.  V1-V2 are a pair of XY coordinates describing a line.
 * Returns [X,Y] along that line for the given X.
 */
function mixv(V1,V2,X)=let(XP=X-V1[0]) mix(V1,V2,XP/(V2[0]-V1[0]));
/* Same, but X for given Y */
function mixvy(V1,V2,Y)=let(OUT=mixv([ V1[1],V1[0] ], [V2[1],V2[0]], Y)) [ OUT[1],OUT[0] ];

/**
 * Returns Y for given X along an interpolated Y.
 * V must be a set of points [ [0,Y1], [X2,Y2], ..., [XN,YN] ] X<1
 * X can be any value, even negative.
 */
function interpolate(V, X, ACC=[1,0], N=0)=
//  Speedup that doesn't help much
    (X>1) ? interpolate(V, (X%1),ACC,N)+floor(X)*ACC[1]:
//      Unneeded case
//    (X<0) ? interpolate(V, 1+(X%1),ACC,N)+floor(X)*ACC[1] :
    (X>wrap(V,N+1)[0]) ?
    interpolate(V,X,ACC,N+1)
:   mixv(wrap(V,N,ACC),wrap(V,N+1,ACC),X)[1];

/**
 *  V = [ [X0,Y0], [X1,Y1], ..., [XN,YN] ] where X0 < X1 < X2 ... < XN
 *
 *  Finds N where XN > X.
 */
function binsearch(PR,X,MIN=0,IMAX=-1)=let(MAX=(IMAX<0)?len(PR):IMAX,
    N=floor((MIN+MAX)/2))
    ((MAX-MIN) <= 1) ? N
    :   X < PR[N][0] ?
        binsearch(PR,X,MIN,ceil((MIN+MAX)/2))
    :   binsearch(PR,X,floor((MIN+MAX)/2),MAX);

/**
 *  V = [ [X0,Y0], [X1,Y1], .., [XN,YN] ] where X0 < X1 < ... < XN and XN < 1
 *
 *  Returns N for given XN like binsearch(), except it wraps X > 1 to 0-1
 *  and returns correspondingly higher N.
 */
function binsearch2(PR,X)=binsearch(PR,X%1)+floor(X)*len(PR);

/**
 * Faster lookup for interpolate().  log(N)
 */
function interpolate2(V,X,ADD=[1,0])=V[binsearch(V,(X%1))][1]+floor(X)*ADD[1];

function interpolaten(V,X,ADD=[1,0])=binsearch(V,(X%1))+floor(X);

module tsmthread(DMAJ=20    // Major diameter
    , L=50,                 // Length of thread in mm.  Accuracy depends on pitch.
    , PITCH=2.5,            // Scale of the thread itself.
    , PR=prof(60,0.8660*(7/16), 0.8660*(3/8)) // Thread profile, i.e. ACME, UTS, other
    , STARTS=1,             // Want a crazy 37-start thread?  You're crazy.  but I'll try.
    , TAPER=0,              // Adds an offset of [1,tan(TAPER)] per thread.
    , STUB=0,               // Extends a cylinder below the thread.  In pitch units.
    , STUB_OFF=0            // Reduces the diameter of stub.  In pitch units.
    ) {

    /* Minimum number of radial points required to match thread profile */
    POINTS_MIN=len(PR)*STARTS*2;

    // OpenSCAD-style fragment generation via $fa and $fs.
    // See https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Other_Language_Features
    function points_r(r)=ceil(max(min(360.0 / $fa, (r*2)*3.14159 / $fs), 5));

    // Rounds X up to a nonzero multiple of Y.
    function roundup(X,Y) = Y*max(1,floor(X/Y) + (((X%Y)>0)?1:0));

    // Points can be forced with $fn
    POINTS=($fn>0) ? $fn :
        // Otherwise, it decides via $fs and $fa, with a minimum of
        // 16, rounded up to POINTS_MIN
        max(roundup(16,POINTS_MIN), roundup(points_r(DMAJ/2),POINTS_MIN));

    if(POINTS % POINTS_MIN )
    {
        echo("WARNING:  DMAJ",DMAJ,"PITCH",PITCH,"STARTS",STARTS, "POINTS", POINTS);
        echo("WARNING:  POINTS should be a multiple of",POINTS_MIN);
        echo("WARNING:  Top and bottom geometry may look ugly");
    }

    ADD=add_npt(TAPER); /* How much radius to add to pitch each rotation */

    // 1*STARTS rows of thread tapper happens which isn't drawn
    // Add this to radius to compensate for it
    TAPER_COMP=STARTS*ADD[1]*PITCH;

    // [X,Y,Z] point along a circle of radius R, angle A, at position Z.
    function traj(R,A,Z)=R*[sin(A),cos(A),0]+[0,0,Z];

    /**
     * The top and bottom are cut off so more height than 0 is needed
     * to generate a thread.
     */
    RING_MIN=(STARTS+1)*len(PR);

    // Find the closest PR[N] for a given X, to estimate thread length
    function minx(PR,X,N=0)=(X>wrap(PR,N+1,ADD)[0])?minx(PR,X,N+1):max(0,N);

    // Calculated number of rings per height.
    RINGS=let(SEG=floor(L/PITCH), X=(L%PITCH)/PITCH) max(RING_MIN+1,
        RING_MIN+SEG*len(PR) + minx(PR,X));

    SHOW=0;     // Debug value.  Offsets top and bottom to highlight any mesh flaws

    /**
     * How this works:  Take PR to be the outside edge of a cylinder of radius DMAJ.
     * Generate points for 360 degrees.  N is angle along this circle, RING is height.
     *
     * Now, to turn this circle into a spiral, a little Z is added for each value of N.
     * The join between the first and last vertex of each circle must jump to meet.
     */
    function zoff(RING,N)=(wrap(PR, RING,ADD)[0] + STARTS*(N/POINTS));
    FLAT_B=zoff(len(PR)*STARTS,0);  // Z coordinates of bottom flat
    FLAT_T=zoff(RINGS-len(PR),0);   // Z coordinates of top flat

    /**
     * Deliminate what spiral coordinates exist between the top and bottom flats.
     * Used for loops, so that only those polygons are joined and nothing outside it.
     */
    // function ringmin(N)=binsearch2(PR,FLAT_B - (N/POINTS)*STARTS)+1;
    // function ringmax(N)=binsearch2(PR,FLAT_T - (N/POINTS)*STARTS);

    // Fast-lookup arrays
    MIN=[for(N=[0:POINTS-1]) binsearch2(PR,FLAT_B - (N/POINTS)*STARTS)+1 ];
    MAX=[for(N=[0:POINTS-1]) binsearch2(PR,FLAT_T - (N/POINTS)*STARTS) ];

    // Array-lookup wrappers which speed up ringmax/ringmin manyfold.
    // binsearch makes them fast enough to be tolerable, but still much better
    function ringmax(N)=MAX[N%POINTS];
    function ringmin(N)=MIN[N%POINTS];

    /**
     * Difficult difficult lemon difficult.
     * Interpolate along the profile to find the points it cuts through
     * the main spiral.
     *
     * Some difficulty is RING coordinates increase P, while N decreases
     * it as it crosses the spiral!
     *
     * Taper must be accounted for as well.
     */
    function radius_flat(RING,N)=
        TAPER_COMP+
        (DMAJ/2)-PITCH*interpolate(PR,wrap(PR,len(PR)*STARTS+RING,ADD)[0] -
            // Modulous because this is all the same taper
            (STARTS*(N/POINTS))%1 - STARTS,ADD)
            // Of course we have to un-taper too, sigh
            -ADD[1]*STARTS*(((N/POINTS)*STARTS)%1);
    /**
     * Radius is generated differently for the top&bottom faces than the spiral because
     * they exist in different coordinate spaces.  Also, the top&bottom faces must be
     * interpolated to fit.
     */
    function cap(RING,ZOFF=0,ROFF=0)=[
        for(N=[0:POINTS-1])
        let(P=N/POINTS, A=-360*P,R=radius_flat(RING,N)+ROFF)
            traj(R,A,zoff(RING,0)+ZOFF)
        ];

    /**
     * Debug function.
     * Draws little outlines at every ring height to compare spiral generation
     * to face generation.
     */
    module test() {
        for(RING=[0:RINGS-1]) {
            POLY=cap(RING, ROFF=0.1);
            LIST=[ [ for(N=[0:POINTS-1]) N ] ];

            polyhedron(POLY,LIST);
        }
    }

    /**
     * Helper array for generating polygon points.
     * DATA[0]+N, N=[0:POINTS-1] for a point on the bottom face
     * DATA[1]+N, N=[0:POINTS-1] for a point on the top face
     * DATA[2]+N + (M*POINTS), N=[0:POINTS-1], M=[0:RINGS-1] for
     * a point on the main spiral.
     */
    DATA=[ 0,                          // 0 = bottom face
           POINTS,                     // 1 = top face
           4*POINTS,                   // 2 = main spiral
           2*POINTS,                   // 3 = stub top
           3*POINTS,                   // 4 = stub bottom
           2*POINTS+POINTS*len(PR),
           2*POINTS+POINTS*len(PR) +
                RINGS*POINTS
        ];

    /**
     * This is it, this is where the magic happens.
     * Given a point in RING,N spiral coordinates, this decides whether it
     * ends up in the top, the spiral, or the bottom so I don't have to.
     *
     * TODO:  Optimize this.  This is a pinch point.
     */
    function point(RING,N)=
        (RING<ringmin(N)) ? DATA[0]+(N%POINTS) // Bottom flat
       :(RING>ringmax(N))? DATA[1]+(N%POINTS)  // Top flat
       :DATA[2]+RING*POINTS + (N%POINTS);       // Inbetween

    // Like above but takes a vector to transform into a triangle
    function pointv(V)=[ for(N=V) point(N[0],N[1]) ];

    /**
     * List of points, organized in sections.
     * 0 - RINGS-1          Bottom cap
     * RINGS - (2*RINGS)-1  Top cap
     * RINGS - (3*RINGS)-1  Stub
     * (2*RINGS) - end      Spiral
     * Do not change this arrangement without updating DATA to match!
     */
    POLY=concat(
        // Bottom cap, top cap
        cap(len(PR)*STARTS,-SHOW),cap(RINGS-len(PR),SHOW),
        // Stub top
        [ for(N=[0:POINTS-1]) let(R=(DMAJ/2)-(STUB_OFF*PITCH)) traj(R,-360*(N/POINTS), 1) ],
        // Stub bottom
        [ for(N=[0:POINTS-1]) let(R=(DMAJ/2)-(STUB_OFF*PITCH)) traj(R,-360*(N/POINTS),
           -STUB) ],
        //cap(len(PR)*STARTS, -STUB),

        // Main spiral
        [ for(RING=[0:RINGS-1], N=[0:POINTS-1])
            let(A=-360*(N/POINTS),
                P1=wrap(PR,RING,ADD),
                P2=wrap(PR,RING+len(PR)*STARTS,ADD),
                UV=mix(P1,P2,N/POINTS),
                R=TAPER_COMP+(DMAJ/2)-PITCH*UV[1], Z=UV[0])
                traj(R, A, Z)
        ]);

    /**
     * Remove redundant points from polygons.
     * collapse([0,1,1,2,3,4,0]) == [0,1,2,3,4]
     */
    function collapse(V)=[ for(N=[0:len(V)-1]) if(V[(N+1)%len(V)] != V[N]) V[N] ];

    // Should we use quads here?  Will fewer loops be faster?
    // Probably shouldn't alter the hard-won mesh maker, but
    // can we do more per loops somehow?
    PLIST=concat(
        // Main spiral A
        [   for(N=[0:POINTS-2], RING=[ringmin(N)-1:ringmax(N)])
            pointv([ [RING,N+1],[RING,N],[RING+1,N] ])
        ],
        // Main spiral B
        [   for(N=[0:POINTS-2], RING=[ringmin(N+1)-1:ringmax(N+1)])
            pointv([[RING+1,N+1],[RING,N+1],[RING+1,N]])
        ],
        // stitch A
        [   for(N=POINTS-1, RING=[ringmin(N)-1:ringmax(0)])
            let(P=pointv([ [RING,N],[RING+1,N],[RING+len(PR)*STARTS,0] ]))
            if((P[0] != P[1]) && (P[0] != P[2]) && (P[1] != P[2])) P
        ],
        // Stitch B
        [
            for(N=0, RING=[ringmin(N)-1:ringmax(N)])
            let(P=pointv([[RING+1,N],[RING,N],[RING+1-len(PR)*STARTS,POINTS-1]]))
            if((P[0] != P[1]) && (P[0] != P[2]) && (P[1] != P[2])) P
        ],

        // Bottom extension
        [ if(STUB) for(WELD=[[0,3],[3,4]], N=[0:POINTS-1])
            [ DATA[WELD[0]]+N, DATA[WELD[0]]+(N+1)%POINTS, DATA[WELD[1]]+(N+1)%POINTS ] ],
        [ if(STUB) for(WELD=[[0,3],[3,4]], N=[0:POINTS-1])
            [ DATA[WELD[1]]+N, DATA[WELD[0]]+N, DATA[WELD[1]]+(N+1)%POINTS ] ],

        // Bottom flat
        [ [ for(N=[0:POINTS-1]) N+DATA[(STUB>0)?4:0] ] ],
        // top flat.  Note reverse direction to mirror the normal.
        [ [ for(N=[0:POINTS-1], N2=POINTS-(N+1)) N2+DATA[1] ] ]
    );

    // Screw it, scale after, PITCH=1 is so much less math
    scale([1,1,PITCH]) translate([0,0,STUB?STUB:-FLAT_B]) polyhedron(POLY, PLIST, convexity=5);
}

// Compensated Threads.
// Threads are thinned by $PE mm.  Diameter is adjusted $OD_COMP/$ID_COMP amount
// depending on whether they're inside or outside threads.
// Only use this with leadscrews.
// A and H values as with prof().
module comp_thread(DMAJ=11, L=20, PITCH=2, A=30, H1=0.5/2, H2=0.5/2, STARTS=1, in=false)
{
    PE2=(in?$PE :-$PE)*(2.0/PITCH)*cos(A);
//    echo("PE",PE2,"$PE",$PE);
    PR=prof(A, H1-PE2, H2+PE2);
//    echo("comp_thread","DMAJ",DMAJ,"L",L,"PITCH",PITCH,"A",A,"H1",H1,"H2",H2,"=",PR);

   tsmthread(DMAJ+(in?$ID_COMP:$OD_COMP), L=L, PITCH=PITCH, STARTS=STARTS, PR=PR);
}

/******************************************************************************/
/********************************NPT THREAD************************************/
/******************************************************************************/

/**
 * Tapering only works without distorting teeth because of the special
 * prof_npt thread profile.
 */
module thread_npt(DMAJ=10, L=10, PITCH=2.5, TAPER=1+(47/60), STUB=0) {
    PR=prof_npt(TAPER);
//    echo(PR);
    echo(add_npt(TAPER));
//    echo(TAPER);
    tsmthread(DMAJ=DMAJ, L=L, PITCH=PITCH, TAPER=TAPER, PR=PR, STUB=STUB);
}

/**
 * Differentiate an array.  delta([0,1,2,3,4,5])=[1,1,1,1]
 * Works on vectors too.
 */
function delta(V)=[ for(N=[0:len(V)-2]) V[N+1]-V[N] ];

// Integrate an array up to element N.
function integ(A, ADD=[ [1,0], [0,1] ], KEEP=[ [0,0], [0,0] ])=[
    for(N=[0:len(A)-2]) integ2(A, N, ADD, KEEP)	];
function integ2(A, N,
    ADD=[ [1,0], [0,1] ],
    KEEP=[ [0,0],[0,0] ])=
        (N<=0)?
            A[0]
        :(A[N]*KEEP) + (A[N]*ADD) + (integ2(A, N-1, ADD, KEEP) * ADD);

function normy(V)=V/V[1];               // Normalize a vector along Y, i.e. [3,0.5] -> [6,1]
function add_npt(TAPER)=[1,tan(TAPER)]; // Why so easy? tan(ANGLE) is the slope of an angle.

/**
 * NPT magic:  Length is added to one specific tooth so the
 * distorted half is bent back up to the correct angle.
 *
 * Only one value needs adding to.  The other fixes itself
 * via adding [1,M] per wraparound.
 */
function prof_npt(TAPER=30, H1=0.8/2, H2=0.8/2) =
    let(M=tan(TAPER), PR2=delta(prof(60,H1,H2)))
    integ([
            [0,0],  // Replace origin deleted by delta()
            PR2[0], // bottom flat, OK
            // This is already a perfect 60 degrees, only scale it.
            // Have to add length of line AND length of flat!  Arrrrgh.
            PR2[1]+M*normy(PR2[1])*(PR2[1][0]+PR2[0][0]),
            PR2[2], // top flat
            PR2[3] ]);

/******************************************************************************/
/******************************MISC UTILITIES**********************************/
/******************************************************************************/

/**
 *  Scales up objects to imperial inches and and alters $fs accordingly, so
 *  imperial() cylinder(d=1, h=1); renders a satisfying number of facets
 *  instead of freaking 5.
 */
module imperial(F=25.4) {
    // modified $... values will be seen by children
    $fs     =$fs     /F;
    $OD_COMP=$OD_COMP/F;
    $ID_COMP=$ID_COMP/F;
    $PE     =$PE     /F;
    $SCALE  =         F;
    scale(F) children();
}

/**
 * A double-pointed cone or pyramid of exactly 45 degrees for tapers.
 * obeys $fn, $fs, $fa, r, d, center=true in a manner like cylinder().
 * example:
 *
 *  // Outside taper
 *  taper(d=10, h=10, off=1) cylinder(d=10, h=10);
 *
 *  // Inside taper
 *  difference() { cylinder(d=10, h=10); taper(in=true, d=5, h=10, off=1) cylinder(d=5, h=10); }
 */
module taper(d=1,h=1,off=0,r=0, center=false, in=false) {
    function points_r(r)=$fn?$fn:(ceil(max(min(360.0 / $fa, (r*2)*3.14159 / $fs), 5)));

    if(r) taper(r*2, h, off, r=0, center=center, in=in);
    else {
        // Calculate number of fragments same way openscad does
        U=points_r(d/2);

        if(in) difference() {
            children();
            translate(center?[0,0,0]:[0,0,h/2]) union() {
                for(M=[[0,0,1],[0,0,0]]) mirror(M)
                translate([0,0,h/2-d/2-off]) cylinder(d1=0, d2=d*2, h=d, $fn=points_r(d/2));
            }
        }
        else intersection() {
            children();
            translate(center?[0,0,0]:[0,0,h/2]) scale(h+d-off) polyhedron(
                concat( [ for(N=[0:U-1]) 0.5*[cos((N*360)/U),sin((N*360)/U),0] ],
                        // Top and bottom of pyramid
                        [ 0.5*[ 0,0,1], -0.5*[0,0,1] ] ),
                concat( [ for(N=[0:U-1]) [ N, U, (N+1)%U]],
                        [ for(N=[0:U-1]) [ (N+1)%U, U+1, N]]
                ));
        }
    }
}

// Flange pattern as described by this URL:
// https://www.helixlinear.com/Product/PowerAC-38-2-RA-wBronze-Nut/
//
//      /---\   <--------
//      |   |           |
// ---> |>>>|           |
// |    |   |           |
// |    |   \---\ <--   |
// |    |       |   |   |
// F*2  |       |   C   H
// |    |       |   |   |
// |    |   /---/ <--   |
// |    |   |           |
// ---> |>>>|           |
//      |   |           |
//      \---/   <--------
//      ^   ^   ^
//      |-G-|-B-|
//
//      B is height of stem
//      C is diameter of stem
//      F is the radius of the screw pattern
//      F2 is the diameter of the screw holes.
//      G is the thickness of the base
//      H is width of base.
//
//      holes is the pattern of holes to drill.  default is 4 holes, 1 every 90 degrees.
//      when open is true, the holes are sots extending to the edge.
//      off is how much to bevel.
module flange(B,C,F,F2,G,off=0,holes=[45:90:360], open=false) {
    taper(d=H,h=G,off=off) linear_extrude(G, convexity=3) offset(off/2) offset(-off/2) difference() {
        circle(d=H);
        for(A=holes) hull() {
            translate(F*[sin(A),cos(A)]/2) circle(d=F2);
            if(open) translate(3*F*[sin(A),cos(A)]/2) circle(d=F2);
        }
    }
    if(B && C) taper(d=C,h=G+B,off=off) cylinder(d=C, h=G+B);
}

// What the hell is this?  I don't know.
module garnet() intersection_for(A=[[0,0,1],[0,1],[1,0]]) rotate(45*A) cube(10*[1,1,1],center=true);

//garnet();
```


[User]
I'm looking to create a parametric flange design for trapezoidal leadscrews, and I've got some specific requirements for my project. I need to be able to adjust the flange dimensions, the thread details, the screw hole pattern, and a few other aspects for precision.

Here’s the basic idea:

*   **Flange Body:**
    *   I need a cylindrical stem section on top of a base.
    *   Both the stem and base diameters should be adjustable.
    *   The thickness of the base should be configurable.
    *   The height of the stem should be adjustable.
*   **Thread:**
    *   It should have a trapezoidal thread on the inside.
    *   I need to be able to set the thread's major diameter (DMAJ).
    *   The thread pitch (PITCH) should be adjustable.
    *   I'd like to specify the number of thread starts.
*   **Screw Holes:**
    *   I need to define a screw hole pattern using a diameter for the circle the holes sit on.
    *   The diameter of each screw hole should be an adjustable parameter.
    *   The number of screw holes needs to be configurable.
    *   I should be able to make the screw holes open to the edge of the flange, or closed.
*   **Beveling:**
    *   I need to be able to add a bevel to the edge of the flange and stem.
*   **Precision:**
    *  I'd like to adjust the outside diameter thread compensation.
    *  I'd like to adjust the inside diameter thread compensation.
    *   There should be a thickness offset for the leadscrew.
*   **Units:**
    *   Everything should be in millimeters.

Could you please generate an OpenSCAD file (or files if necessary) that can handle these adjustments? It should be completely parametric, so I can modify everything as needed. I'm expecting the output to be like the `flange-metric.scad` I have, but I would like a fresh implementation instead of modifying that one.

Also, I would like the design to use the `tsmthread` module, which seems like it may need to be rewritten to be parametric, along with the other functions and modules necessary for it to work, so please create that.

[Assistant]
flange-metric.scad:
```
// Parametric Trapezoidal Flange in OpenSCAD, for Thingiverse customizer, Tyler Montbriand, 2019

// Diameter of stem, in mm
STEM_D=10.2;
// Diameter of base, in mm
BASE_D=22;
// Thickness of base, in mm
BASE_THICK=3.5;
// Height of stem, in mm
STEM_HEIGHT=10;
// Hole pattern diameter, in mm
F=16;
// Hole diameter, in mm
F2=3.5;
// How much to bevel, in mm
BEVEL=1;
// Outside diameter of thread, in mm
DMAJ=8;
// Pitch of thread, in mm
PITCH=2; // [0.5:0.25:10]
STARTS=4; // [0:1:6]
// Number of screw holes
HOLES=4;    // [0:1:8]

// Whether screw holes connect to edges.
OPEN=1; // [0:1]

// Added to outside thread diameters, in mm.
$OD_COMP=-0.25;
// Added to inside thread diameters, in mm.
$ID_COMP=1;
// Thickness offset for leadscrews, in mm
$PE=0.35;
$fs=1;
$fa=3;

difference() {
    taper(d=DMAJ,h=BASE_THICK+STEM_HEIGHT, off=BEVEL, in=true)
    flange(B=STEM_HEIGHT, C=STEM_D,G=BASE_THICK,H=BASE_D, F=F, F2=F2, off=BEVEL,
    holes=HOLES?([0:360/HOLES:360-(360/HOLES)]):[],
    open=OPEN);
    comp_thread(DMAJ=DMAJ, L=BASE_THICK+STEM_HEIGHT+PITCH,
    PITCH=PITCH, A=30, H1=0.5/2, H2=0.5/2, STARTS=STARTS, in=true);
}

 /**
 * Generates truncated, symmetrical thread profiles like UTS or ACME
 * A is pitch angle
 * MIN is distance below centerline in pitch units
 * MAX is distance above centerline in pitch units
 * TOL makes tooth narrower/wider and deeper/shallower than perfect by TOL amount,
 * again in units of pitch
 *
 * Resuls biased to zero and inverted -- just like tsmthread() likes them.
 */
function prof(A,MIN,MAX)=let(
        M=tan(90-(A/2)), // Slope of tooth
        X1=((M/2)-(MIN*2))/M, // Given a Y of MIN, calculate X
        X2=((M/2)+(MAX*2))/M, // Given a Y of MAX, calculate X
    OFF=-X1*M) [
    [0, OFF + M*X1], // Starting point, always
    [X1+X1,OFF + M*X1],
    [X1+X2,OFF+M*X2],
    [X1+2-X2,OFF+M*X2],
    // Profile wraps here
]/2;

/**
 * Profile Interpolation
 *
 * prof() generates, and tsmthread expects, a profile of [X,Y] values like
 * [ [0,0.25], [0.25, 1], [0.5,0.25] ]
 * The first X must be 0.  The last X cannot be 1.  All values are in pitch units.
 *
 * Get a value out with interpolate(PR, X).
 *      interpolate(PR, 0.25) would return 1,
 *      interpolate(PR, 0) would give 0.25,
 *      interpolate(PR, 0.125) would  give someting between.
 *      interpolate(PR, 0.5) would give 0.25.
 *      interpolate(PR,0.75) would wrap, interpolating between P[2]-p[0].
 *
 * Should wrap cleanly for any positive or negative value.
 */

/**
 * Helper function for interpolate().  Allows
 * a thread profile to repeat cleanly for increasing
 * values of N, with growing X accordingly.
 *
 * P=[ [0,0], [0.5,0.5] ];
 * echo(wrap(P,0)); // should be [0,0]
 * echo(wrap(P,1)); // should be [0.5,0.5]
 * echo(wrap(P,2)); // should be [0,0]+[1,0]
 * echo(wrap(P,3)); // should be [0.5,0.5]+[1,0]
 * echo(wrap(P,4)); // should be [0,0]+[2,0]
 * etc.
 */
function wrap(V, N, ACC=[1,0])=let(M=floor(N/len(V))) V[N%len(V)] + M*ACC;

/* Very basic interpolation.  mix(A,B,0)=A, mix(A,B,1)=B, 0 <= X <= 1 */
function mix(A,B,X)=(A*(1-X)) + B*X;

/**
 * Line-matching.  V1-V2 are a pair of XY coordinates describing a line.
 * Returns [X,Y] along that line for the given X.
 */
function mixv(V1,V2,X)=let(XP=X-V1[0]) mix(V1,V2,XP/(V2[0]-V1[0]));
/* Same, but X for given Y */
function mixvy(V1,V2,Y)=let(OUT=mixv([ V1[1],V1[0] ], [V2[1],V2[0]], Y)) [ OUT[1],OUT[0] ];

/**
 * Returns Y for given X along an interpolated Y.
 * V must be a set of points [ [0,Y1], [X2,Y2], ..., [XN,YN] ] X<1
 * X can be any value, even negative.
 */
function interpolate(V, X, ACC=[1,0], N=0)=
//  Speedup that doesn't help much
    (X>1) ? interpolate(V, (X%1),ACC,N)+floor(X)*ACC[1]:
//      Unneeded case
//    (X<0) ? interpolate(V, 1+(X%1),ACC,N)+floor(X)*ACC[1] :
    (X>wrap(V,N+1)[0]) ?
    interpolate(V,X,ACC,N+1)
:   mixv(wrap(V,N,ACC),wrap(V,N+1,ACC),X)[1];

/**
 *  V = [ [X0,Y0], [X1,Y1], ..., [XN,YN] ] where X0 < X1 < X2 ... < XN
 *
 *  Finds N where XN > X.
 */
function binsearch(PR,X,MIN=0,IMAX=-1)=let(MAX=(IMAX<0)?len(PR):IMAX,
    N=floor((MIN+MAX)/2))
    ((MAX-MIN) <= 1) ? N
    :   X < PR[N][0] ?
        binsearch(PR,X,MIN,ceil((MIN+MAX)/2))
    :   binsearch(PR,X,floor((MIN+MAX)/2),MAX);

/**
 *  V = [ [X0,Y0], [X1,Y1], .., [XN,YN] ] where X0 < X1 < ... < XN and XN < 1
 *
 *  Returns N for given XN like binsearch(), except it wraps X > 1 to 0-1
 *  and returns correspondingly higher N.
 */
function binsearch2(PR,X)=binsearch(PR,X%1)+floor(X)*len(PR);

/**
 * Faster lookup for interpolate().  log(N)
 */
function interpolate2(V,X,ADD=[1,0])=V[binsearch(V,(X%1))][1]+floor(X)*ADD[1];

function interpolaten(V,X,ADD=[1,0])=binsearch(V,(X%1))+floor(X);

module tsmthread(DMAJ=20    // Major diameter
    , L=50,                 // Length of thread in mm.  Accuracy depends on pitch.
    , PITCH=2.5,            // Scale of the thread itself.
    , PR=prof(60,0.8660*(7/16), 0.8660*(3/8)) // Thread profile, i.e. ACME, UTS, other
    , STARTS=1,             // Want a crazy 37-start thread?  You're crazy.  but I'll try.
    , TAPER=0,              // Adds an offset of [1,tan(TAPER)] per thread.
    , STUB=0,               // Extends a cylinder below the thread.  In pitch units.
    , STUB_OFF=0            // Reduces the diameter of stub.  In pitch units.
    ) {

    /* Minimum number of radial points required to match thread profile */
    POINTS_MIN=len(PR)*STARTS*2;

    // OpenSCAD-style fragment generation via $fa and $fs.
    // See https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Other_Language_Features
    function points_r(r)=ceil(max(min(360.0 / $fa, (r*2)*3.14159 / $fs), 5));

    // Rounds X up to a nonzero multiple of Y.
    function roundup(X,Y) = Y*max(1,floor(X/Y) + (((X%Y)>0)?1:0));

    // Points can be forced with $fn
    POINTS=($fn>0) ? $fn :
        // Otherwise, it decides via $fs and $fa, with a minimum of
        // 16, rounded up to POINTS_MIN
        max(roundup(16,POINTS_MIN), roundup(points_r(DMAJ/2),POINTS_MIN));

    if(POINTS % POINTS_MIN )
    {
        echo("WARNING:  DMAJ",DMAJ,"PITCH",PITCH,"STARTS",STARTS, "POINTS", POINTS);
        echo("WARNING:  POINTS should be a multiple of",POINTS_MIN);
        echo("WARNING:  Top and bottom geometry may look ugly");
    }

    ADD=add_npt(TAPER); /* How much radius to add to pitch each rotation */

    // 1*STARTS rows of thread tapper happens which isn't drawn
    // Add this to radius to compensate for it
    TAPER_COMP=STARTS*ADD[1]*PITCH;

    // [X,Y,Z] point along a circle of radius R, angle A, at position Z.
    function traj(R,A,Z)=R*[sin(A),cos(A),0]+[0,0,Z];

    /**
     * The top and bottom are cut off so more height than 0 is needed
     * to generate a thread.
     */
    RING_MIN=(STARTS+1)*len(PR);

    // Find the closest PR[N] for a given X, to estimate thread length
    function minx(PR,X,N=0)=(X>wrap(PR,N+1,ADD)[0])?minx(PR,X,N+1):max(0,N);

    // Calculated number of rings per height.
    RINGS=let(SEG=floor(L/PITCH), X=(L%PITCH)/PITCH) max(RING_MIN+1,
        RING_MIN+SEG*len(PR) + minx(PR,X));

    SHOW=0;     // Debug value.  Offsets top and bottom to highlight any mesh flaws

    /**
     * How this works:  Take PR to be the outside edge of a cylinder of radius DMAJ.
     * Generate points for 360 degrees.  N is angle along this circle, RING is height.
     *
     * Now, to turn this circle into a spiral, a little Z is added for each value of N.
     * The join between the first and last vertex of each circle must jump to meet.
     */
    function zoff(RING,N)=(wrap(PR, RING,ADD)[0] + STARTS*(N/POINTS));
    FLAT_B=zoff(len(PR)*STARTS,0);  // Z coordinates of bottom flat
    FLAT_T=zoff(RINGS-len(PR),0);   // Z coordinates of top flat

    /**
     * Deliminate what spiral coordinates exist between the top and bottom flats.
     * Used for loops, so that only those polygons are joined and nothing outside it.
     */
    // function ringmin(N)=binsearch2(PR,FLAT_B - (N/POINTS)*STARTS)+1;
    // function ringmax(N)=binsearch2(PR,FLAT_T - (N/POINTS)*STARTS);

    // Fast-lookup arrays
    MIN=[for(N=[0:POINTS-1]) binsearch2(PR,FLAT_B - (N/POINTS)*STARTS)+1 ];
    MAX=[for(N=[0:POINTS-1]) binsearch2(PR,FLAT_T - (N/POINTS)*STARTS) ];

    // Array-lookup wrappers which speed up ringmax/ringmin manyfold.
    // binsearch makes them fast enough to be tolerable, but still much better
    function ringmax(N)=MAX[N%POINTS];
    function ringmin(N)=MIN[N%POINTS];

    /**
     * Difficult difficult lemon difficult.
     * Interpolate along the profile to find the points it cuts through
     * the main spiral.
     *
     * Some difficulty is RING coordinates increase P, while N decreases
     * it as it crosses the spiral!
     *
     * Taper must be accounted for as well.
     */
    function radius_flat(RING,N)=
        TAPER_COMP+
        (DMAJ/2)-PITCH*interpolate(PR,wrap(PR,len(PR)*STARTS+RING,ADD)[0] -
            // Modulous because this is all the same taper
            (STARTS*(N/POINTS))%1 - STARTS,ADD)
            // Of course we have to un-taper too, sigh
            -ADD[1]*STARTS*(((N/POINTS)*STARTS)%1);
    /**
     * Radius is generated differently for the top&bottom faces than the spiral because
     * they exist in different coordinate spaces.  Also, the top&bottom faces must be
     * interpolated to fit.
     */
    function cap(RING,ZOFF=0,ROFF=0)=[
        for(N=[0:POINTS-1])
        let(P=N/POINTS, A=-360*P,R=radius_flat(RING,N)+ROFF)
            traj(R,A,zoff(RING,0)+ZOFF)
        ];

    /**
     * Debug function.
     * Draws little outlines at every ring height to compare spiral generation
     * to face generation.
     */
    module test() {
        for(RING=[0:RINGS-1]) {
            POLY=cap(RING, ROFF=0.1);
            LIST=[ [ for(N=[0:POINTS-1]) N ] ];

            polyhedron(POLY,LIST);
        }
    }

    /**
     * Helper array for generating polygon points.
     * DATA[0]+N, N=[0:POINTS-1] for a point on the bottom face
     * DATA[1]+N, N=[0:POINTS-1] for a point on the top face
     * DATA[2]+N + (M*POINTS), N=[0:POINTS-1], M=[0:RINGS-1] for
     * a point on the main spiral.
     */
    DATA=[ 0,                          // 0 = bottom face
           POINTS,                     // 1 = top face
           4*POINTS,                   // 2 = main spiral
           2*POINTS,                   // 3 = stub top
           3*POINTS,                   // 4 = stub bottom
           2*POINTS+POINTS*len(PR),
           2*POINTS+POINTS*len(PR) +
                RINGS*POINTS
        ];

    /**
     * This is it, this is where the magic happens.
     * Given a point in RING,N spiral coordinates, this decides whether it
     * ends up in the top, the spiral, or the bottom so I don't have to.
     *
     * TODO:  Optimize this.  This is a pinch point.
     */
    function point(RING,N)=
        (RING<ringmin(N)) ? DATA[0]+(N%POINTS) // Bottom flat
       :(RING>ringmax(N))? DATA[1]+(N%POINTS)  // Top flat
       :DATA[2]+RING*POINTS + (N%POINTS);       // Inbetween

    // Like above but takes a vector to transform into a triangle
    function pointv(V)=[ for(N=V) point(N[0],N[1]) ];

    /**
     * List of points, organized in sections.
     * 0 - RINGS-1          Bottom cap
     * RINGS - (2*RINGS)-1  Top cap
     * RINGS - (3*RINGS)-1  Stub
     * (2*RINGS) - end      Spiral
     * Do not change this arrangement without updating DATA to match!
     */
    POLY=concat(
        // Bottom cap, top cap
        cap(len(PR)*STARTS,-SHOW),cap(RINGS-len(PR),SHOW),
        // Stub top
        [ for(N=[0:POINTS-1]) let(R=(DMAJ/2)-(STUB_OFF*PITCH)) traj(R,-360*(N/POINTS), 1) ],
        // Stub bottom
        [ for(N=[0:POINTS-1]) let(R=(DMAJ/2)-(STUB_OFF*PITCH)) traj(R,-360*(N/POINTS),
           -STUB) ],
        //cap(len(PR)*STARTS, -STUB),

        // Main spiral
        [ for(RING=[0:RINGS-1], N=[0:POINTS-1])
            let(A=-360*(N/POINTS),
                P1=wrap(PR,RING,ADD),
                P2=wrap(PR,RING+len(PR)*STARTS,ADD),
                UV=mix(P1,P2,N/POINTS),
                R=TAPER_COMP+(DMAJ/2)-PITCH*UV[1], Z=UV[0])
                traj(R, A, Z)
        ]);

    /**
     * Remove redundant points from polygons.
     * collapse([0,1,1,2,3,4,0]) == [0,1,2,3,4]
     */
    function collapse(V)=[ for(N=[0:len(V)-1]) if(V[(N+1)%len(V)] != V[N]) V[N] ];

    // Should we use quads here?  Will fewer loops be faster?
    // Probably shouldn't alter the hard-won mesh maker, but
    // can we do more per loops somehow?
    PLIST=concat(
        // Main spiral A
        [   for(N=[0:POINTS-2], RING=[ringmin(N)-1:ringmax(N)])
            pointv([ [RING,N+1],[RING,N],[RING+1,N] ])
        ],
        // Main spiral B
        [   for(N=[0:POINTS-2], RING=[ringmin(N+1)-1:ringmax(N+1)])
            pointv([[RING+1,N+1],[RING,N+1],[RING+1,N]])
        ],
        // stitch A
        [   for(N=POINTS-1, RING=[ringmin(N)-1:ringmax(0)])
            let(P=pointv([ [RING,N],[RING+1,N],[RING+len(PR)*STARTS,0] ]))
            if((P[0] != P[1]) && (P[0] != P[2]) && (P[1] != P[2])) P
        ],
        // Stitch B
        [
            for(N=0, RING=[ringmin(N)-1:ringmax(N)])
            let(P=pointv([[RING+1,N],[RING,N],[RING+1-len(PR)*STARTS,POINTS-1]]))
            if((P[0] != P[1]) && (P[0] != P[2]) && (P[1] != P[2])) P
        ],

        // Bottom extension
        [ if(STUB) for(WELD=[[0,3],[3,4]], N=[0:POINTS-1])
            [ DATA[WELD[0]]+N, DATA[WELD[0]]+(N+1)%POINTS, DATA[WELD[1]]+(N+1)%POINTS ] ],
        [ if(STUB) for(WELD=[[0,3],[3,4]], N=[0:POINTS-1])
            [ DATA[WELD[1]]+N, DATA[WELD[0]]+N, DATA[WELD[1]]+(N+1)%POINTS ] ],

        // Bottom flat
        [ [ for(N=[0:POINTS-1]) N+DATA[(STUB>0)?4:0] ] ],
        // top flat.  Note reverse direction to mirror the normal.
        [ [ for(N=[0:POINTS-1], N2=POINTS-(N+1)) N2+DATA[1] ] ]
    );

    // Screw it, scale after, PITCH=1 is so much less math
    scale([1,1,PITCH]) translate([0,0,STUB?STUB:-FLAT_B]) polyhedron(POLY, PLIST, convexity=5);
}

// Compensated Threads.
// Threads are thinned by $PE mm.  Diameter is adjusted $OD_COMP/$ID_COMP amount
// depending on whether they're inside or outside threads.
// Only use this with leadscrews.
// A and H values as with prof().
module comp_thread(DMAJ=11, L=20, PITCH=2, A=30, H1=0.5/2, H2=0.5/2, STARTS=1, in=false)
{
    PE2=(in?$PE :-$PE)*(2.0/PITCH)*cos(A);
//    echo("PE",PE2,"$PE",$PE);
    PR=prof(A, H1-PE2, H2+PE2);
//    echo("comp_thread","DMAJ",DMAJ,"L",L,"PITCH",PITCH,"A",A,"H1",H1,"H2",H2,"=",PR);

   tsmthread(DMAJ+(in?$ID_COMP:$OD_COMP), L=L, PITCH=PITCH, STARTS=STARTS, PR=PR);
}

/******************************************************************************/
/********************************NPT THREAD************************************/
/******************************************************************************/

/**
 * Tapering only works without distorting teeth because of the special
 * prof_npt thread profile.
 */
module thread_npt(DMAJ=10, L=10, PITCH=2.5, TAPER=1+(47/60), STUB=0) {
    PR=prof_npt(TAPER);
//    echo(PR);
    echo(add_npt(TAPER));
//    echo(TAPER);
    tsmthread(DMAJ=DMAJ, L=L, PITCH=PITCH, TAPER=TAPER, PR=PR, STUB=STUB);
}

/**
 * Differentiate an array.  delta([0,1,2,3,4,5])=[1,1,1,1]
 * Works on vectors too.
 */
function delta(V)=[ for(N=[0:len(V)-2]) V[N+1]-V[N] ];

// Integrate an array up to element N.
function integ(A, ADD=[ [1,0], [0,1] ], KEEP=[ [0,0], [0,0] ])=[
    for(N=[0:len(A)-2]) integ2(A, N, ADD, KEEP)	];
function integ2(A, N,
    ADD=[ [1,0], [0,1] ],
    KEEP=[ [0,0],[0,0] ])=
        (N<=0)?
            A[0]
        :(A[N]*KEEP) + (A[N]*ADD) + (integ2(A, N-1, ADD, KEEP) * ADD);

function normy(V)=V/V[1];               // Normalize a vector along Y, i.e. [3,0.5] -> [6,1]
function add_npt(TAPER)=[1,tan(TAPER)]; // Why so easy? tan(ANGLE) is the slope of an angle.

/**
 * NPT magic:  Length is added to one specific tooth so the
 * distorted half is bent back up to the correct angle.
 *
 * Only one value needs adding to.  The other fixes itself
 * via adding [1,M] per wraparound.
 */
function prof_npt(TAPER=30, H1=0.8/2, H2=0.8/2) =
    let(M=tan(TAPER), PR2=delta(prof(60,H1,H2)))
    integ([
            [0,0],  // Replace origin deleted by delta()
            PR2[0], // bottom flat, OK
            // This is already a perfect 60 degrees, only scale it.
            // Have to add length of line AND length of flat!  Arrrrgh.
            PR2[1]+M*normy(PR2[1])*(PR2[1][0]+PR2[0][0]),
            PR2[2], // top flat
            PR2[3] ]);

/******************************************************************************/
/******************************MISC UTILITIES**********************************/
/******************************************************************************/

/**
 *  Scales up objects to imperial inches and and alters $fs accordingly, so
 *  imperial() cylinder(d=1, h=1); renders a satisfying number of facets
 *  instead of freaking 5.
 */
module imperial(F=25.4) {
    // modified $... values will be seen by children
    $fs     =$fs     /F;
    $OD_COMP=$OD_COMP/F;
    $ID_COMP=$ID_COMP/F;
    $PE     =$PE     /F;
    $SCALE  =         F;
    scale(F) children();
}

/**
 * A double-pointed cone or pyramid of exactly 45 degrees for tapers.
 * obeys $fn, $fs, $fa, r, d, center=true in a manner like cylinder().
 * example:
 *
 *  // Outside taper
 *  taper(d=10, h=10, off=1) cylinder(d=10, h=10);
 *
 *  // Inside taper
 *  difference() { cylinder(d=10, h=10); taper(in=true, d=5, h=10, off=1) cylinder(d=5, h=10); }
 */
module taper(d=1,h=1,off=0,r=0, center=false, in=false) {
    function points_r(r)=$fn?$fn:(ceil(max(min(360.0 / $fa, (r*2)*3.14159 / $fs), 5)));

    if(r) taper(r*2, h, off, r=0, center=center, in=in);
    else {
        // Calculate number of fragments same way openscad does
        U=points_r(d/2);

        if(in) difference() {
            children();
            translate(center?[0,0,0]:[0,0,h/2]) union() {
                for(M=[[0,0,1],[0,0,0]]) mirror(M)
                translate([0,0,h/2-d/2-off]) cylinder(d1=0, d2=d*2, h=d, $fn=points_r(d/2));
            }
        }
        else intersection() {
            children();
            translate(center?[0,0,0]:[0,0,h/2]) scale(h+d-off) polyhedron(
                concat( [ for(N=[0:U-1]) 0.5*[cos((N*360)/U),sin((N*360)/U),0] ],
                        // Top and bottom of pyramid
                        [ 0.5*[ 0,0,1], -0.5*[0,0,1] ] ),
                concat( [ for(N=[0:U-1]) [ N, U, (N+1)%U]],
                        [ for(N=[0:U-1]) [ (N+1)%U, U+1, N]]
                ));
        }
    }
}

// Flange pattern as described by this URL:
// https://www.helixlinear.com/Product/PowerAC-38-2-RA-wBronze-Nut/
//
//      /---\   <--------
//      |   |           |
// ---> |>>>|           |
// |    |   |           |
// |    |   \---\ <--   |
// |    |       |   |   |
// F*2  |       |   C   H
// |    |       |   |   |
// |    |   /---/ <--   |
// |    |   |           |
// ---> |>>>|           |
//      |   |           |
//      \---/   <--------
//      ^   ^   ^
//      |-G-|-B-|
//
//      B is height of stem
//      C is diameter of stem
//      F is the radius of the screw pattern
//      F2 is the diameter of the screw holes.
//      G is the thickness of the base
//      H is width of base.
//
//      holes is the pattern of holes to drill.  default is 4 holes, 1 every 90 degrees.
//      when open is true, the holes are sots extending to the edge.
//      off is how much to bevel.
module flange(B,C,F,F2,G,off=0,holes=[45:90:360], open=false) {
    taper(d=H,h=G,off=off) linear_extrude(G, convexity=3) offset(off/2) offset(-off/2) difference() {
        circle(d=H);
        for(A=holes) hull() {
            translate(F*[sin(A),cos(A)]/2) circle(d=F2);
            if(open) translate(3*F*[sin(A),cos(A)]/2) circle(d=F2);
        }
    }
    if(B && C) taper(d=C,h=G+B,off=off) cylinder(d=C, h=G+B);
}

// What the hell is this?  I don't know.
module garnet() intersection_for(A=[[0,0,1],[0,1],[1,0]]) rotate(45*A) cube(10*[1,1,1],center=true);

//garnet();
```


[User] I'm looking for an OpenSCAD design for a parametric polygon box with a lid. I want to be able to control the number of sides (from 3 to 8), the overall diameter, the depth, the corner radius, and the thickness of the walls. The lid should fit snugly on the box. I would like the lid and the box to be generated separately, but also have an option to output both of them together for visualization purposes. It would also be very helpful if the internal diameter of the lid was large enough to accommodate some "play" so that it fits easily. Can you do that?

[Assistant]
polybox.scad:
```
// trinket_box.scad
// library for parametric Trinket Box, Container, Enclosure, Organizer, Storage
// Author: Tony Z. Tonchev, Michigan (USA)
// last update: February 2019

// PolyBox Number of Sides
PolyBox_Sides = 3; //[3:3-SIDED, 4:4-SIDED, 5:5-SIDED, 6:6-SIDED, 7:7-SIDED, 8:8-SIDED]

// Polybox Diameter (in mm)
PolyBox_Diameter = 100;

// Polybox Depth (in mm)
PolyBox_Depth = 50;

// Box corner radius (in mm)
PolyBox_Corner_Radius = 8; //[4:50]

// Box Thickness
PolyBox_Thickness = 2; //[1:5]

// Group
Build_Group = 1; //[1:BOTH, 2:BOX, 3:LID]

/* [Hidden] */

TZT_S = PolyBox_Sides;
TZT_R = PolyBox_Diameter/2;
TZT_D = PolyBox_Depth;
TZT_C = PolyBox_Corner_Radius;
TZT_T = PolyBox_Thickness;
$fn=100;

//TZT_Box ([sides, radius, depth, corner_radius])

if (Build_Group!=3) translate ([0,TZT_R*1.1,0]) TZT_Box ();
if (Build_Group!=2) translate ([0,-TZT_R*1.1,0]) TZT_Lid ();

module TZT_Lid () {
    translate ([0,0,7])
    difference () {
        hull () {
            TZT_Vol ([TZT_S,TZT_R+TZT_T+.5,10,TZT_C+TZT_T+.5]);
            translate ([0,0,-6]) TZT_Vol ([TZT_S,TZT_R+TZT_T-.5,1,TZT_C+TZT_T-.5]);
        }
        translate ([0,0,TZT_T]) TZT_Vol ([TZT_S,TZT_R+.5,11,TZT_C+.5]);
    }
}

module TZT_Box () {
    translate ([0,0,TZT_D/2])
        difference () {
            TZT_Vol ([TZT_S,TZT_R,TZT_D,TZT_C]);
            translate ([0,0,TZT_T]) TZT_Vol ([TZT_S,TZT_R-TZT_T,TZT_D,TZT_C-TZT_T]);
        }
}

module TZT_Vol (TZT) {
    hull ()
        for (i=[0:360/TZT[0]:359])
        rotate ([0,0,i])
        translate ([TZT[1]-TZT[3], 0, 0])
        cylinder (TZT[2], TZT[3], TZT[3], true);
}
```


[User]
I'm looking to create a customizable coin design using OpenSCAD, similar to a shopping token. I'd like the design to be parametric so I can easily change various aspects.

Specifically, I need a circular coin with the following features:

*   **Front Face:** The main part of the coin will have an icon in the center. This icon should be text-based, drawn from font awesome icons. I need to be able to specify both the icon character and the font to be used via variables. The icon's size should also be parametric.
*   **Back Face:** I want some text on the back face as well, as a kind of watermark. This should also be parametric in terms of text content and size. Additionally, I'd like to be able to choose the font. I think I'd like the text to be centered and have a bold italic style.
*   **Dimensions:** I need to control the coin's overall diameter and height as well as a 'cutout' region in the center. I'd like this to be another cylinder slightly smaller than the coin itself that is indented into the coin's top face.
*   **Font Awesome:** For the icons I plan to use Font Awesome icons. It'd be great if the system was set up to easily use "font awesome 5 brands", "font awesome 5 free" and styles within it.

I'm thinking the way to structure this would be a `coin()` module which takes parameters like icon text, icon size, font, back text, back text size, coin diameter, coin height, and potentially the size of the cutout region. Then, I should be able to call this module to generate various coins with different designs.

I don't think I need any special libraries for this, just the basic OpenSCAD functionality, such as `text`, `linear_extrude`, `cylinder`, and `difference`. It would be great if the output was an .scad file that is well-commented so it's easy for me to understand.

I've included a sample of how it should operate that might make this clearer.

```
icon="";
size=12;
backtext="eLAB";
backtextsize=5;
font="font awesome 5 brands";

module coin(label="", dia=23, height=2.4, siz=10, fnt = "Liberation Sans") {
    $fn=50;
    difference(){
        union(){
                difference(){
                    cylinder(r=dia/2, h=height);
                    translate([0,0,1.6]) cylinder(r=10, h=0.8);
                }
                translate([0,0,1.6,]) linear_extrude(0.8) {
                    text(label, size=siz,
                        halign = "center", valign="center",
                        font = fnt);
                }

        }
        translate([0,0,0.4]) rotate([180,0,0]) linear_extrude(0.4) {
            text(backtext, size=backtextsize,
                halign = "center", valign="center",
                font = "Liberation Sans:style=Bold Italic");
        }
    }
}

coin(label=icon, siz=size, fnt=font);
```

[Assistant]
shopping-coin.scad:
```
icon="";
size=12;
backtext="eLAB";
backtextsize=5;
font="font awesome 5 brands";

module coin(label="", dia=23, height=2.4, siz=10, fnt = "Liberation Sans") {
    $fn=50;
    difference(){
        union(){
                difference(){
                    cylinder(r=dia/2, h=height);
                    translate([0,0,1.6]) cylinder(r=10, h=0.8);
                }
                translate([0,0,1.6,]) linear_extrude(0.8) {
                    text(label, size=siz,
                        halign = "center", valign="center",
                        font = fnt);
                }

        }
        translate([0,0,0.4]) rotate([180,0,0]) linear_extrude(0.4) {
            text(backtext, size=backtextsize,
                halign = "center", valign="center",
                font = "Liberation Sans:style=Bold Italic");
        }
    }
}

coin(label=icon, siz=size, fnt=font);

//coin(label="eLAB", siz=5, fnt = "Liberation Sans:style=Bold Italic");
//coin(label="", siz=16, fnt = "font awesome 5 free"); // smile
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // bitcoin
//coin(label="", siz=16, fnt = "font awesome 5 brands"); // ubuntu
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // apple
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // android
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // linux
//coin(label="", siz=16, fnt = "font awesome 5 brands"); // github
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // html5
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // raspberry pi
//coin(label="", siz=16, fnt = "font awesome 5 brands"); // creative commons
//coin(label="", siz=12, fnt = "font awesome 5 brands"); // amazon
//coin(label="", siz=16, fnt = "font awesome 5 free:style=Solid"); // peace
//coin(label="", siz=16, fnt = "font awesome 5 free:style=Solid"); // yingyang
//coin(label="", siz=12, fnt = "font awesome 5 free:style=Solid"); // podcast
//coin(label="", siz=12, fnt = "font awesome 5 free:style=Solid"); // euro
//coin(label="", siz=12, fnt = "font awesome 5 free:style=Solid"); // recycle
//coin(label="", siz=10, fnt = "font awesome 5 free:style=Solid"); // robot
//coin(label="", siz=10, fnt = "font awesome 5 free:style=Solid"); // skull
//!coin(label="", siz=10, fnt = "font awesome 5 free:style=Solid"); // toxic

```


[User]
I'm looking to create a customizable shelf that sits on top of a TV, kind of like the one I saw on Thingiverse (https://www.thingiverse.com/thing:1277290). But I want it to be fully parametric in OpenSCAD so I can easily adjust it for different set-top box sizes and TV thicknesses.

Specifically, I need the shelf to have these features:

*   **Shelf Dimensions:** The user should be able to specify the width and depth of the shelf. I'll be using this for a Roku Premiere (about 90mm x 90mm), but I want to be able to use other sizes as well. It should also have a specified height, probably 3 mm.
*   **Mounting Tabs:** The shelf needs two tabs that hook onto the top of the TV. These tabs should be configurable in terms of:
    *   **Tab Spacing:** The distance between the tabs should be adjustable to accommodate different TV thicknesses.
    *   **Tab Offset:** The distance of the first tab from the front of the shelf should be configurable. The second tab's location is then relative to the first.
    *  **Tab Depth:** I'd like to specify the depth that the tab extends down from the shelf. Something like 10mm would work here
    *   **Tab Width:** I want the tabs to be a bit narrower than the shelf's width.
    *   **Tab Height:** The vertical height of the tab should be thinner than the shelf, maybe 1/4 the height of the shelf.
*   **Rounded Edges:**  Both the shelf and the tabs should have rounded edges to give a smoother look. I want to be able to control the radius of these rounded edges.
*   **Construction:** The main shelf body should be a rounded cube. The tabs should extend perpendicularly down from the main body of the shelf.
*   **Customizer Interface:** All of the above parameters (shelf width, shelf depth, shelf height, tab spacing, first tab offset, tab depth, tab width, tab height, rounded edge radius for both the shelf and the tabs) should be adjustable through OpenSCAD's customizer.

I think that covers everything. Can you generate the OpenSCAD file(s) for this? I don't have any external libraries in mind that you would need to use, but if you find any useful go ahead and include them.

[Assistant]
RokuShelf.scad:
```
/****************************************************************************
Title: Roku Shelf TV Mount

Description: This script is intended to generate a shelf that can be mounted on top of a TV. The shelf is sized to support a Roku Premiere but can be customized to support other STB sizes.

Author: Ross MacDonald
Created In: 2019-02-09

License: Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
License Link: https://creativecommons.org/licenses/by-nc-sa/4.0/

/***************************************************************************/

// Customizable Settings

// Size of the Set top box.
// 90 x 90 mm works great for the Roku Premiere.
shelf_width = 90;
shelf_depth = 90;

// Tab configuration - this is what clamps onto your TV
// Tab spacing is the thickness of the top of your TV
tab_spacing = 13.5;
// How far offset is the tab from the front of the shelf
first_tab_offset = -25;

// No need to modify anything below here
tab_depth = 10;
shelf_height = 3;
tab_width = 0.8 * shelf_width;
tab_height = shelf_height/4;
second_tab_offset = first_tab_offset + tab_spacing + tab_height;
tab_rounded_edge_radius = 2;
rounded_edge_radius = 10;
rounded_fudge = 1;

rounded_cube([shelf_width,
    shelf_depth,
    shelf_height],
    rounded_edge_radius);

translate([0, first_tab_offset, -((tab_depth + shelf_height)/2)])
{
    rotate([-90,0,0])
    {
        rounded_cube([tab_width,
            tab_depth,
            tab_height],
            tab_rounded_edge_radius);
    }
}

translate([0, first_tab_offset, -(shelf_height / 2)])
{
    rotate([-90,0,0])
    {
        cube([tab_width + tab_rounded_edge_radius,
            tab_depth / 1.5,
            tab_height + rounded_fudge],
            center=true);
    }
}

translate([0, second_tab_offset, -((tab_depth + shelf_height) / 2)])
{
    rotate([-90,0,0])
    {
        rounded_cube([tab_width,
            tab_depth,
            tab_height],
            tab_rounded_edge_radius);
    }
}

translate([0, second_tab_offset, -(shelf_height / 2)])
{
    rotate([-90,0,0])
    {
        cube([tab_width  + tab_rounded_edge_radius,
            tab_depth / 2,
            tab_height + rounded_fudge],
            center=true);
    }
}

// The following code was based heavily on the example here:
// https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/The_OpenSCAD_Language#minkowski
module rounded_cube(size, radius)
{
    $fn=50;
    x = size[0]-radius;
    y = size[1]-radius;
    minkowski()
    {
        cube(size=[x,y,size[2]], center=true);
        cylinder(r=radius, center=true);
    }
}
```