[User]
I'm looking to create a 3D printable chain that's flexible and customizable, similar to the 2D chain I've already got, but with the ability to fold and snake through 3D space. I need it to be parametric so I can easily adjust the dimensions and layout.

Here's what I'm aiming for:

*   **Chain Link Design:** The basic link should be a torus-like shape, perhaps constructed using a series of small cylinders, as shown in the example code. It should be parameterized for diameter, link radius, and twist (vertical elevation).
*   **2D Layout:** I'd like to retain the capability to create a 2D chain like my current setup, with controls for the number of links in the x and y dimensions. In this scenario, all the links would be oriented so that the chain sits flat along the XY plane.
*   **3D Layout:** This is the crucial part. I need to control the overall path of the chain in 3D space. Ideally, I could specify a series of points (x, y, z) and the chain will snake through those points. I want to be able to control the number of points as well.
*  **Link Rotation and Twist:** When creating the 3D path, I would need to be able to control the rotation of the links. For example, I would like to have the ability to specify an amount of twist when moving from one control point to the next.
*   **Parametric Control:**
    *   Number of links in x and y for 2D
    *   Link diameter, link radius, and twist elevation.
    *   Number and location of control points for the 3D path.
    *   Rotation parameters for links, especially around the direction the chain is flowing, as it passes between control points.
*  **Color Support:** It would be nice to retain the ability to specify link colors as in the provided code.

I'm envisioning the ability to define control points for the 3D path and also, optionally, to use a 2D x/y grid layout.

The core chain link geometry can be adapted from the 'kg' module in the original code, but the logic to position and orient it in 3D space based on the defined points is essential.

I'm not using any specific libraries currently, but if any are helpful for achieving this, I'm happy to consider them.

[Assistant]
kette-bd-8-nz.scad:
```
// [7:361] facettes as in $fn
fn=63;  // [7:361]
$fn=fn; // here it is, the magical fn

// kettenglieder in X
nx=5; // [1:40]
// kettenglieder in Y
ny=4; // [1:40]

ax=16-0 ;  // [16] x achse eines kettengliedes
ay=10-0 ;  // [10] y achse eines kettengliedes

// die Kette
k(nx,ny);

module k(knX=9, knY=5)
    {
    x=0; y=0; xs=0; ys=0;
        {
        for (ys=[0:knY]){ y=ys*(2*(ay+3)+1);
            for (xs=[0:knX]){ x=xs*(22);
                    translate([x/1.65,y/1.9, 0])
                        rotate([ 90, 90, 0])
                            kg();
            } // for (xs=
//            ra=+360*$t; echo(ra);
            xx=knX*(22);          // x maximum
            yx=knY*(2*(ay+3)+1);  // y maximum

            if ((ys % 2 == 0) && (y < yx)){
                color("lightblue")
                    translate([(x-22)/1.65 +1,y/1.9 +7, 02])
                        rotate([180, 130, 80]) kg();
                }

            if ((ys % 2 == 1) && (y < yx)){
//              ra=+360*$t; echo(ra);
                color("magenta")    // walze  y  z
                    translate([(xx+22)/1.65 -1,y/1.9 +7, 1])
                        rotate([180, 50, 80])
                            kg();
                } // if (y % 2 == 1)
            } // for ys
        } // mirror
    } // module

// KettenGlied
module kg(){
    eps=.00001;     // I name it epsilon
    d=  6 ; // the diameter of the draht
    R=  3 ; // radius des rings
    hz= 4 ; // elevation of the twist

    for (w=[0:360/fn:360])
        {
        t0=sin(w*2);
        u0=30*-cos(w*2);
        v=w+360/fn;
        t1=sin(v*2);
        u1=30*-cos(v*2);

        hull()
            {
            translate([ax*sin(w), ay*cos(w), hz*t0])
                rotate([0,90,0])
                    rotate([w,0,0])
                        cylinder(d=d, h=eps);

            translate([ax*sin(v), ay*cos(v), hz*t1])
                rotate([0,90,0])
                    rotate([v,0,0])
                        cylinder(d=d, h=eps);
            } // hull
        } // for (w=[0:360/fn:360])
    } // module
```


[User]
I need a parametric design for a snuff box, along with molds for casting it. It should be a cylindrical box with a lid that attaches with a gasket. I want to be able to customize the dimensions, wall thickness, and add a logo to the lid. The design should also include parts for creating a silicone mold.

Here are the details:

**Overall Box:**

*   **Shape:** Cylindrical
*   **Parts:** Bottom, Top (Lid), Gasket, and optionally a logo inlay.
*   **Customization:**
    *   Outer radius of the box.
    *   Outer height of the box.
    *   Height of the top part (lid).
    *   Gap between the bottom and top parts for easy opening.
    *   Rotation steps for box (smoothness of the cylinder).
    *   Wall thickness of the box.
    *   Chamfers on outer edges, lid/box gap, and top of the bottom part.
    *   Option to fill the bottom part's insides (for larger storage space or easier molding).
    *   Depth of a notch inside the lid to control how tightly the lid fits along the Z-axis.

**Lid Logo:**

*   **Source:** Import a 2D DXF file. I should be able to specify the file name and layer to use.
*   **Positioning:** The design in the DXF is assumed to be centered around [0, 0].
*   **Customization:**
    *   Scale of the imported logo.
    *   Offset for the logo's perimeter (enlarges the cutout in the lid).
    *   Depth of the logo cutout.
    *   Gap between the logo and the lid (shrinks the inlay part).

**Gasket:**

*   **Shape:** A circular cross-section that fits into a groove in the box and lid.
*   **Customization:**
    *   Height of the gasket.
    *   Shrinkage of the gasket's cross-section (to adjust fit).
    *   Shrinkage of the gasket's outer radius (to adjust fit).
    *   Amount to extend the gasket outwards, towards the lid (to adjust lid tightness).
    *   Option to rotate the gasket's cross-section by 45 degrees.

**Mold:**

*   **Parts:** Bottom and Top molds
*   **Customization:**
    *   Wall thickness of the silicone molds.

**Additional considerations:**

*   The design should be parametric, using variables for all customizable values so I can adjust them easily.
*   The code needs to handle invalid parameter inputs and ensure the parts are printable.
*   I would like to be able to render each part separately: box bottom, box top, gasket, logo inlay, bottom shell, and top shell, and a test render as well.
*   For debugging purposes, I should be able to disable the lathe (rotation-extrude) operation.

I would like to have all of these parts generated in a single SCAD file. Please use comments to organize and describe the code. I am not concerned with whether the parts are assembled into a final assembly design.

Thanks!

[Assistant]
snuffbox.scad:
```
/* [Box] */

// Part to render.
part = "box_bot";// [box_bot:"Box bottom", box_top:"Box top", gasket:"Gasket", logo:"Logo inlay", shell_bot:"Shell bottom", shell_top:"Shell top", test:"Test (not for printing)"]

// Outer radius of box.
box_radius = 35; // [20:0.5:50]

// Outer height of box.
box_height = 25; // [20:0.5:50]

// Height of top part.
top_height = 10; // [7:0.5:30]

// Gap between bottom and top parts.
box_play = .3; // [.1:.05:1]

// Rotation steps for box. Higher is smoother but slower.
box_fn = 256; // [8, 12, 16, 24, 32, 64, 128, 256, 512]

// Wall thickness.
box_wt = 3; // [2:.05:4]

// Chamfer on outer edges.
chamfer = 2; //[0:.1:3]

// Chamfer on gap between lid and box.
chamf_mid = 1; // [0:.1:2]

// Chamfer at the top of bottom part, where the lid slides onto the box.
chamf_top = 1; // [0:.1:1]

// Fill out the bottom insides. Set to true for larger storage space, false for easier molding.
bot_fill = true; // [true, false]

// Depth of notch inside lid. Decrease if the lid slides on fine, but wiggles too much along Z.
top_notch_depth = .25; // [0:.05:.5]

/* [Lid logo] */
// 2D DXF file to import as a lid logo. Assumes the design is centered around [0, 0].
logo_file = ""; // ["", "aperture.dxf", "ring.dxf", "ring_short.dxf", "biohazard.dxf", "rad.dxf", "dontpanic.dxf", "dontpanic2.dxf", "skull.dxf"]

// Name of layer in the DXF to import.
logo_layer = "0";

// Logo scale
logo_scale = 1; // [.1:.01:5]

// Offset for logo perimeter. Enlarges the logo cutout of lid.
logo_ofs = .2;  // [-5:.1:5]

// Cutout depth for logo
logo_depth = 1.2; // [.2: .2: 3]

// Gap between logo and lid. Higher shrinks the inlay part.
logo_gap = .1; // [0:.1:1]

/* [Gasket] */

// Height of gasket.
gasket_h = 3.2; // [1:.1:4]

// Shrinkage of gasket cross section. Increase if the gasket doesn't fit in the slot.
gasket_ofs = .05; //[0:.05:.5]

// Shrinkage of gasket outer radius. Increase if the fit is too loose.
gasket_ins = 1.4; // [0:.05:3]

// Amount to extend gasket outwards, towards top part. Higher value means a tighter fit for the lid.
gasket_ext = .6; // [.1:.05:1.6]

// Rotate the cross section 45 degrees for easier printing.
gasket_twist = true; // [true, false]

/* [Mold] */

// Wall thickness of silicone mold.
mold_wt = 8; // [1:.5:15]

/* [Hidden] */
// Set to false to debug cross sections.
lathe_enabled = true;
lathe_angle = part == "test" ? 270 : 360;

// Adjust gasket to wall thickness.
gasket_r_min = box_wt-.6;
gasket_r = min(gasket_r_min, gasket_h/2);

// Check that box radius isn't too small. Adjust if it is.
box_r_min = box_wt*2+box_play+1;
box_r = max(box_r_min, box_radius);

// Check that height isn't too small. Adjust if it is.
box_h_min = box_wt + chamf_mid + gasket_h + chamf_mid + box_play + box_wt;
box_h = max(box_h_min, box_height);

// Height of bottom/top split
mid_h_min = chamfer+chamf_mid;
mid_h_max = box_h-box_wt-box_play-chamf_mid-gasket_h-1;
mid_h = min(mid_h_max, max(mid_h_min, box_h-top_height));

// Z position of gasket
gasket_z = ((box_h-box_wt-chamf_top-box_play) + mid_h )/2;

// Widen inner space of bottom part. Or not, if box height doesn't allow it.
wide_bot = mid_h>box_wt*2.5 ? bot_fill : false;

//////////////////////////////////////////////////

if(part=="box_bot")
	box_bot();

else if(part=="box_top")
	translate([0, 0, !lathe_enabled?0:box_h])
	rotate(180, [1, 0, 0])
	box_top();

else if(part=="gasket")
	translate([0, 0, !lathe_enabled?0:-gasket_z+(gasket_r)/sqrt(2)-gasket_ofs])
	gasket(ofs=gasket_ofs, rot=gasket_twist?45:0,
		ins=gasket_ins, cutout=false);

else if(part=="logo") {
	translate([0, 0, logo_depth])
	rotate(180, [0, 1, 0])
	logo();
}

else if(part=="shell_bot")
	rotate(180, [1, 0, 0])
	shell_bot();

else if(part=="shell_top")
	shell_top();

else if(part=="test") {
	lathe_angle = 270;
	color([.2, .2, .2])
	gasket(ofs=gasket_ofs, rot=0, ins=0, cutout=false);
	//gasket(ofs=gasket_ofs, rot=0, ins=gasket_ins, cutout=false);

	color([0, .5, .5])
	translate([0, 0, -.01])
	box_bot();

	color([0, 0, 1])
	box_top();
}

module box_bot2D(notch=true, hollow=true, lid_shelf=true) {
	inside_y = hollow ? box_wt : box_h-box_wt-box_play;
	gasket_ins = notch ? gasket_r : 0;

	polygon(points=concat(
		[
			[0, 0],
			[box_r-chamfer, 0],
			[box_r, chamfer],
			[box_r, mid_h-chamf_mid],
		], !lid_shelf ? [] : [
			[box_r-chamf_mid, mid_h],
			[box_r-box_wt-box_play, mid_h],
			[box_r-box_wt-box_play, gasket_z-gasket_r], // Gasket bot
			[box_r-box_wt-box_play-gasket_ins, gasket_z],// Gasket mid
		], [
			[box_r-box_wt-box_play, gasket_z+gasket_r], // Gasket top
			[box_r-box_wt-box_play, box_h-box_wt-box_play-chamf_top],
			[box_r-box_wt-box_play-chamf_top, box_h-box_wt-box_play],
			[box_r-box_wt*2-box_play, box_h-box_wt-box_play],
		], !wide_bot ? [] : [
			[box_r-box_wt*2-box_play, inside_y+mid_h-box_wt*2+box_wt/2],
			[box_r-box_wt*2-box_play+box_wt-0, inside_y+mid_h-box_wt*3+box_wt/2],
			[box_r-box_wt*2-box_play+box_wt, inside_y],
		], [
			[box_r-box_wt*2-box_play, inside_y],
			[0, inside_y]
		]
	));
}

module box_bot() {
	lathe()
	box_bot2D(notch=true, hollow=true, lid_shelf=true);
}

module box_top2D(notch=true, hollow=true) {
	inside_y = hollow ? box_h-box_wt : mid_h;
	chamf = .6; // Lid chamfer

	notch_sh_x = !notch ? 0 :
		min(top_notch_depth, gasket_ext);
	notch_sh_y = !notch ? 0 :
		(gasket_h + notch_sh_x*gasket_h/gasket_ext)/2;

	difference() {
		polygon(points = [
			[0, box_h],
			[box_r-chamfer, box_h],
			[box_r, box_h-chamfer],
			[box_r, mid_h],
			[box_r-box_wt+chamf, mid_h],
			[box_r-box_wt, mid_h+chamf],
			[box_r-box_wt, gasket_z-gasket_r+notch_sh_y], // Gasket bot
			if(notch)
				[box_r-box_wt+notch_sh_x, gasket_z], // Gasket mid
			[box_r-box_wt, gasket_z+gasket_r-notch_sh_y], // Gasket top
			[box_r-box_wt, inside_y],
			[0, inside_y],
		]);
	}
}

module box_top() {
	difference() {
		lathe()
		box_top2D(notch=true, hollow=true);

		if(logo_file!="") {
			translate([0, 0, box_h-logo_depth])
			linear_extrude(box_wt)
			offset(delta=logo_ofs)
			scale(logo_scale)
			import(file = logo_file, layer = logo_layer);
		}
	}
}

module logo() {
	if(logo_file!="") {
		linear_extrude(logo_depth-logo_gap)
		offset(delta=logo_ofs-logo_gap)
		scale(logo_scale)
		import(file = logo_file, layer = logo_layer);
	}
}

module gasket2D(ofs=0, cutout=false, rot=0, ins=0) {
	translate([box_r-box_wt-box_play-ins, gasket_z]) {
		rotate(rot)
		offset(delta=-ofs, chamfer=false)

		polygon([
			if(cutout)
			[0, 0],
			[0, -gasket_r],
			//[-gasket_r, -gasket_r],
			[-gasket_r, 0],
			[0, gasket_r],
			[gasket_ext, 0]
		]);
	}
}

module gasket(ofs=0, cutout=false, rot=0, ins=0) {
	lathe()
	gasket2D(ofs, cutout, rot, ins);
}

module shell_bot() {
	out_r = box_r + mold_wt;
	h = box_h - box_wt + mold_wt;

	lathe()
	square([out_r, h]);
}

module shell_top() {
	out_r = box_r + mold_wt;
	h = top_height + mold_wt;

	lathe()
	square([out_r, h]);
}

module lathe() {
	if(lathe_enabled) {
		rotate_extrude($fn=box_fn, angle=lathe_angle)
		children();
	}
	else
		children();
}

```


[User]
Okay, so I'm looking to design a little adapter for vacuum sealing freezer bags by mouth. Basically, you'd insert the oval-shaped end into a partially closed bag, press the bag around it, then suck the air out using the tube part. I need this to be easily customizable, so parametric design is important.

Here's a breakdown of what I have in mind:

*   **Shape:** The main part will have a sort of flattened eye shape or a rounded, elongated oval where the bag is sealed around it. This oval will transition smoothly into a cylindrical tube or straw that you would use to suck out the air.
*   **Dimensions:** I'd like to control several dimensions:
    *   `tubeID`: The inner diameter of the tube.
    *   `tubeWall`: The thickness of the tube wall.
    *   `tubeHeight`: The length of the tube/straw section.
    *   `baseHeight`: The height of the oval base part.
    *   `baseWidth`: The width of the oval base part.
    *   `holeAspectRatio`: Controls the 'flattening' of the oval end – a value less than 1 will make it more eye-shaped, closer to 1 would make it a more circular profile.
    *   `minimumWidth`: The smallest width of the rounded base shape, to avoid very thin sections.
    *   `tensionFactor1` and `tensionFactor2`: These control how the curved sides of the oval shape transition into the main body.
*   **Construction:**
    *   The base shape should use a Bezier curve for the oval profile to give smooth transitions.
    *   The base shape should be extruded to the specified baseHeight, and the tube should be a cylinder extruded from this base shape.
    *   A cylindrical hole should cut out the interior of both the tube and the base.
    *   I'd like to be able to easily adjust all of these parameters as variables at the top of the file, so I can tweak the design to my liking.
*   **Libraries:** This design would rely heavily on Bezier curves, so I'd need to use a bezier.scad library that can handle Bezier curves to produce the desired shape, if that's doable. I don't have a specific library in mind but I found one online; I can include the code from the one I was looking at if that helps but I'd rather not have to bundle a library.

Ultimately, I'm aiming for a clean and functional design that is simple to print. I'll be printing this in plastic with 100% infill, so the focus is on a well-formed solid model that doesn't have too thin of a profile.

Could you generate an OpenSCAD file or files for this based on these requirements? Thanks!

[Assistant]
vacuumer-standalone.scad:
```
tubeID = 10;
tubeWall = 1.5;
tubeHeight = 30;
baseHeight = 13;
baseWidth = 27;
holeAspectRatio = 0.65;
minimumWidth = 0.6;
tensionFactor1 = 0.2;
tensionFactor2 = 0.25;

module end_of_parameters_dummy() {}

//BEGIN: use <bezier.scad>;
/*
Copyright (c) 2017 Alexander R. Pruss.

Licensed under any Creative Commons Attribution license you like or under the
following MIT License.

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

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

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

*/

// Public domain Bezier stuff from www.thingiverse.com/thing:8443
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+BEZ13(u)*p1+BEZ23(u)*p2+BEZ33(u)*p3;
// End public domain Bezier stuff
function d2BEZ03(u) = 6*(1-u);
function d2BEZ13(u) = 18*u-12;
function d2BEZ23(u) = -18*u+6;
function d2BEZ33(u) = 6*u;

function worstCase2ndDerivative(p0, p1, p2, p3, u1, u2)
    = norm([
        for(i=[0:len(p0)-1])
            max([for(u=[u1,u2])
                d2BEZ03(u)*p0[i]+d2BEZ13(u)*p1[i]+
                d2BEZ23(u)*p2[i]+d2BEZ33(u)*p3[i]]) ]);

function neededIntervalLength(p0,p1,p2,p3,u1,u2,tolerance)
    = let(d2=worstCase2ndDerivative(p0,p1,p2,p3,u1,u2))
        d2==0 ? u2-u1+1 : sqrt(2*tolerance/d2);

function REPEAT_MIRRORED(v,angleStart=0,angleEnd=360) = ["m",v,angleStart,angleEnd];
function SMOOTH_REL(x) = ["r",x];
function SMOOTH_ABS(x) = ["a",x];
function SYMMETRIC() = ["r",1];
function OFFSET(v) = ["o",v];
function SHARP() = OFFSET([0,0,0]);
function LINE() = ["l",0];
function POLAR(r,angle) = OFFSET(r*[cos(angle),sin(angle)]);
function POINT_IS_SPECIAL(v) = (v[0]=="r" || v[0]=="a" || v[0]=="o" || v[0]=="l");

// this does NOT handle offset type points; to handle those, use DecodeBezierOffsets()
function getControlPoint(cp,node,otherCP,otherNode,nextNode) =
    let(v=node-otherCP) (
    cp[0]=="r" ? node+cp[1]*v:
    cp[0]=="a" ? (
        norm(v)<1e-9 ? node+cp[1]*(node-otherNode)/norm(node-otherNode) : node+cp[1]*v/norm(v) ) :
    cp[0]=="l" ? (2*node+nextNode)/3 :
        cp );

function onLine2(a,b,c,eps=1e-4) =
    norm(c-a) <= eps ? true
        : norm(b-a) <= eps ? false /* to be safe */
            : abs((c[1]-a[1])*(b[0]-a[0]) - (b[1]-a[1])*(c[0]-a[0])) <= eps * eps && norm(c-a) <= eps + norm(b-a);

function isStraight2(p1,c1,c2,p2,eps=1e-4) =
    len(p1) == 2 &&
    onLine2(p1,p2,c1,eps=eps) && onLine2(p2,p1,c2,eps=eps);

function Bezier2(p,index=0,precision=0.05,rightEndPoint=true,optimize=true) = let(nPoints=
        max(1, precision < 0 ?
                    ceil(1/
                        neededIntervalLength(p[index],p[index+1],p[index+2],p[index+3],0,1,-precision))
                    : ceil(1/precision)) )
    optimize && isStraight2(p[index],p[index+1],p[index+2],p[index+3]) ? (rightEndPoint?[p[index+0],p[index+3]]:[p[index+0]] ) :
    [for (i=[0:nPoints-(rightEndPoint?0:1)]) PointAlongBez4(p[index+0],p[index+1],p[index+2],p[index+3],i/nPoints)];

function flatten(listOfLists) = [ for(list = listOfLists) for(item = list) item ];

// p is a list of points, in the format:
// [node1,control1,control2,node2,control3, control4,node3, ...]
// You can replace inner control points with:
//   SYMMETRIC: uses a reflection of the control point on the other side of the node
//   SMOOTH_REL(x): like SYMMETRIC, but the distance of the control point to the node is x times the distance of the other control point to the node
//   SMOOTH_ABS(x): like SYMMETRIC, but the distance of the control point to the node is exactly x
// You can also replace any control point with:
//   OFFSET(v): puts the control point at the corresponding node plus the vector v
//   SHARP(): equivalent to OFFSET([0,0])
//   LINE(): when used for both control points between two nodes, generates a straight line
//   POLAR(r,angle): like OFFSET, except the offset is specified in polar coordinates

function DecodeBezierOffset(control,node) = control[0] == "o" ? node+control[1] : control;

function _mirrorMatrix(normalVector) = let(v = normalVector/norm(normalVector)) len(v)<3 ? [[1-2*v[0]*v[0],-2*v[0]*v[1]],[-2*v[0]*v[1],1-2*v[1]*v[1]]] : [[1-2*v[0]*v[0],-2*v[0]*v[1],-2*v[0]*v[2]],[-2*v[0]*v[1],1-2*v[1]*v[1],-2*v[1]*v[2]],[-2*v[0]*v[2],-2*v[1]*v[2],1-2*v[2]*v[2]]];

function _correctLength(p,start=0) =
    start >= len(p) || p[start][0] == "m" ? 3*floor(start/3)+1 : _correctLength(p,start=start+1);

function _trimArray(a, n) = [for (i=[0:n-1]) a[i]];

function _transformPoint(matrix,a) =
    let(n=len(a))
        len(matrix[0])==n+1 ?
            _trimArray(matrix * concat(a,[1]), n)
            : matrix * a;

function _transformPath(matrix,path) =
    [for (a=path) _transformPoint(matrix,a)];

function _reverseArray(array) = let(n=len(array)) [for (i=[0:n-1]) array[n-1-i]];

function _stitchPaths(a,b) = let(na=len(a)) [for (i=[0:na+len(b)-2]) i<na? a[i] : b[i-na+1]-b[0]+a[na-1]];

// replace all OFFSET/SHARP/POLAR points with coordinates
function DecodeBezierOffsets(p) = [for (i=[0:_correctLength(p)-1]) i%3==0?p[i]:(i%3==1?DecodeBezierOffset(p[i],p[i-1]):DecodeBezierOffset(p[i],p[i+1]))];

function _mirrorPaths(basePath, control, start) =
    control[start][0] == "m" ? _mirrorPaths(_stitchPaths(basePath,_reverseArray(_transformPath(_mirrorMatrix( control[start][1] ),basePath))), control, start+1) : basePath;

function DecodeSpecialBezierPoints(p0) =
    let(
        l = _correctLength(p0),
        doMirror = len(p0)>l && p0[l][0] == "m",
        p=DecodeBezierOffsets(p0),
        basePath = [for (i=[0:l-1]) i%3==0?p[i]:(i%3==1?getControlPoint(p[i],p[i-1],p[i-2],p[i-4],p[i+2]):getControlPoint(p[i],p[i+1],p[i+2],p[i+4],p[i-2]))])
        doMirror ? _mirrorPaths(basePath, p0, l) : basePath;

function Distance2D(a,b) = sqrt((a[0]-b[0])*(a[0]-b[0])+(a[1]-b[1])*(a[1]-b[1]));

function RemoveDuplicates(p,eps=0.00001) = let(safeEps = eps/len(p)) [for (i=[0:len(p)-1]) if(i==0 || i==len(p)-1 || Distance2D(p[i-1],p[i]) >= safeEps) p[i]];

function Bezier(p,precision=0.05,eps=0.00001,optimize=true) = let(q=DecodeSpecialBezierPoints(p), nodes=(len(q)-1)/3) RemoveDuplicates(flatten([for (i=[0:nodes-1]) Bezier2(q,optimize=optimize,index=i*3,precision=precision,rightEndPoint=(i==nodes-1))]),eps=eps);

function GetSplineAngle(a,b,c) =
    a==c && b==a ? 0 :
    a==c ? let(ba=b-a) atan2(ba[1],ba[0]) :
    let(ca=c-a) atan2(ca[1],ca[0]);

/*    let(ba=norm(b-a),cb=norm(c-b))
        ba == 0 && cb == 0 ? 0 :
    let(v = ba == 0 ? c-b :
            cb == 0 ? b-a :
            (c-b)*norm(b-a)/norm(c-b)+(b-a))
    atan2(v[1],v[0]); */

// do a spline around b
function SplineAroundPoint(a,b,c,tension=0.5,includeLeftCP=true,includeRightCP=true) =
    includeLeftCP && includeRightCP ?
        [POLAR(tension*norm(a-b),GetSplineAngle(c,b,a)),b,POLAR(tension*norm(c-b),GetSplineAngle(a,b,c))] :
    includeLeftCP ?
        [POLAR(tension*norm(a-b),GetSplineAngle(c,b,a)),b] :
    includeRightCP ?
        [b,POLAR(tension*norm(c-b),GetSplineAngle(a,b,c))] :
        [b];

function BezierSmoothPoints(points,tension=0.5,closed=false)
    = let (n=len(points))
        flatten(
        closed ? [ for (i=[0:n]) SplineAroundPoint(points[(n+i-1)%n],points[i%n],points[(i+1)%n],tension=tension,includeLeftCP=i>0,includeRightCP=i<n) ] :
        [ for (i=[0:n-1])
            SplineAroundPoint(
            i==0 ? 2*points[0]-points[1] : points[(n+i-1)%n],
            points[i],
            i==n-1 ? 2*points[n-1]-points[n-2] : points[(i+1)%n],tension=tension,includeLeftCP=i>0,includeRightCP=i<n-1  ) ]);

module BezierVisualize(p,precision=0.05,eps=0.00001,lineThickness=0.25,controlLineThickness=0.125,nodeSize=1) {
    $fn = 16;
    dim = len(p[0]);
    module point(size) {
        if (dim==2)
            circle(d=size);
        else
            sphere(d=size);
    }
    p1 = DecodeSpecialBezierPoints(p);
    l = Bezier(p1,precision=precision,eps=eps);
    for (i=[0:len(l)-2]) {
        hull() {
            translate(l[i]) point(lineThickness);
            translate(l[i+1]) point(lineThickness);
        }
    }
    for (i=[0:len(p1)-1]) {
        if (i%3 == 0) {
            color("black") translate(p1[i]) point(nodeSize);
        }
        else {
            node = i%3 == 1 ? i-1 : i+1;
            color("red") translate(p1[i]) point(nodeSize);
            color("red") hull() {
                translate(p1[node]) point(controlLineThickness);
                translate(p1[i]) point(controlLineThickness);
            }
        }
    }
}

//END: use <bezier.scad>;

module dummy() {}
$fn = 36;

tubeH = tubeID * holeAspectRatio + tubeWall*2;
tubeW = tubeID + tubeWall*2;

module base() {
    polygon(Bezier([[-baseWidth/2,0],
    POLAR(minimumWidth/4,90),POLAR(minimumWidth/4,180),[-baseWidth/2+minimumWidth/2,minimumWidth/2],
    POLAR(baseWidth*tensionFactor1,0),POLAR(baseWidth*tensionFactor2,180),[0,tubeH/2],REPEAT_MIRRORED([1,0]),REPEAT_MIRRORED([0,-1])]));
}

difference() {
    union() {
        linear_extrude(height=baseHeight)
        base();
        scale([1,tubeH/tubeW,1])
        cylinder(d=tubeW,h=tubeHeight+baseHeight);
    }
    scale([1,holeAspectRatio,1])
    cylinder(d=tubeID,h=4*(tubeHeight+baseHeight),center=true);
}

```


[User]
I'd like to create a design for a cube that can be split into three interlocking pieces via a spiral cut. It's based on a design called "Cubic Trisection" by Robert Reid and Oskar van Deventer, and there's an existing OpenSCAD implementation by Erikjuh on Thingiverse (thing:629887). I've provided the code for this existing implementation below, which you can use as reference.

```
// Side length of cube
size=35;
tolerance=.4;
// Controls the fineness of the cube
slices=1000;
// How much the spiral should twist. Values < 180 will not hold together!
twist=240;
// How much to initially rotate the spiral
offset=-60;
part="single"; // [cube:Assembled Cube,single:Single Piece]

/* [Hidden] */
t=twist;
o=offset;
tol=tolerance;

rotate([-45,0,0])
	rotate([0, -atan(1/sqrt(2)), 0])
		difference(){
			rotate([45, atan(1/sqrt(2)), 0])
				cube(size, center=true);

			linear_extrude(
				height=size*sqrt(3),
				twist=t,
				convexity=10,
				center=true,
				slices=slices
			){
				for(i=[0:360/3:359])
					rotate(i+o+t/2)
						translate([-tol/2, 0, 0])
							square([tol, 100*size]);
				if(part=="single")
					for(i=[0,360/3])
						rotate(i)
							polygon([
								[0, 0],
								[0, -100*size],
								100*size*[sin(60),cos(60)]
							]);
			}
}
```

The design should be parametric, so I can easily change the cube's size (`size`), the tolerance between the pieces (`tolerance`), the smoothness of the spiral cut (`slices`), the amount of twist in the spiral (`twist`), and an initial rotation of the spiral (`offset`).  The `part` variable allows you to specify whether to render a single piece or the assembled cube. I'd like the generated code to also have this functionality, using a string variable to control what's displayed; specifically, if the string is "single", display only one of the interlocking pieces, and if it's "cube", display the full assembled cube. The default values for the parameters should match those in the provided example code.

I don't need any specific libraries, just a clean OpenSCAD implementation. Can you generate that?

[Assistant]
CubeTrisection.scad:
```
// Side length of cube
size=35;
tolerance=.4;
// Controls the fineness of the cube
slices=1000;
// How much the spiral should twist. Values < 180 will not hold together!
twist=240;
// How much to initially rotate the spiral
offset=-60;
part="single"; // [cube:Assembled Cube,single:Single Piece]

/* [Hidden] */
t=twist;
o=offset;
tol=tolerance;

rotate([-45,0,0])
	rotate([0, -atan(1/sqrt(2)), 0])
		difference(){
			rotate([45, atan(1/sqrt(2)), 0])
				cube(size, center=true);

			linear_extrude(
				height=size*sqrt(3),
				twist=t,
				convexity=10,
				center=true,
				slices=slices
			){
				for(i=[0:360/3:359])
					rotate(i+o+t/2)
						translate([-tol/2, 0, 0])
							square([tol, 100*size]);
				if(part=="single")
					for(i=[0,360/3])
						rotate(i)
							polygon([
								[0, 0],
								[0, -100*size],
								100*size*[sin(60),cos(60)]
							]);
			}
}
```


[User]
Hey, I'd like to design a custom planter drip tray, and I'm hoping you can help me out with the OpenSCAD code. Basically, I want it to be a shallow cylinder with an optional set of risers underneath. Here's what I'm looking for:

*   **Overall Shape:** The tray itself should be a frustum (a truncated cone), so the top rim is a bit wider than the base.
*   **Customizable Dimensions:** I need to be able to set the overall height of the tray, as well as the diameter of both the base and the top rim. Also, I'd like to be able to control the thickness of both the tray walls and the base.
*   **Optional Risers:** It should have an option to add risers to the bottom, creating some space beneath the tray. If I choose to add risers, I'd need to be able to specify their height, the outer diameter, the inner diameter, and the width of the gaps between the risers.
*   **Vase Mode Option:** I need to be able to generate a version of just the tray (no base, no risers) that can be printed in vase mode.
*   **Separate STL Files:** The ideal outcome would be code that generates three STL files: one with the full tray and risers, one of just the vase mode tray, and one of just the risers.
*   **Simple Design:** I don't need anything fancy, just a clean, functional design.

I don't have any existing SCAD code to give you. I'd prefer you not rely on any external libraries beyond the built-in OpenSCAD functions.

[Assistant]
drip-tray.scad:
```
// STL to view
part = "all"; // [all:Tray with risers,trayvase:Tray vase mode,riser:Risers only]

// Total height of the tray (mm)
height = 26;

// Diameter of the base (mm)
base_diameter = 100;

// Diameter of the top rim (mm). This should be greater than base_diameter but not so large that it requires support.
top_diameter = 117;

// Width of the tray wall (mm). Ignored in vase mode.
wall_width = 1.3;

// Width of the tray base (mm). Ignored in vase mode.
base_width = 1.2;

// Add risers to give space for water under the pot
add_risers = 1; // [0:false,1:true]

// Height of the risers (mm)
riser_height = 10;

// Diameter of the risers (outer edge to outer edge) (mm). This should be less than base_diameter.
riser_diameter = 70;

// Inner diameter of the risers (inner edge to inner edge) (mm). This should be between riser_diameter/2 and riser_diameter.
riser_inner_diameter = 60;

// Space between the riser segments (mm). Decrease as the riser diameter decreases.
riser_cut_width = 20;

base_radius = base_diameter/2;
top_radius = top_diameter/2;
riser_cut_height = riser_height*2+1;
riser_radius = riser_diameter/2;
riser_inner_radius = riser_inner_diameter/2;

if (part == "all") {
  everything();
}
else if (part == "trayvase") {
  trayVaseMode();
}
else if (part == "riser") {
  risers();
}

module everything() {
  $fa=1;
  union() {
    // wall
    difference() {
      cylinder(h=height, r1=base_radius, r2=top_radius);
      translate([0,0,-0.01])
      cylinder(h=height+0.02, r1=base_radius-wall_width, r2=top_radius-wall_width);
    }

    // base
    color("gray")
    cylinder(h=base_width, r=base_diameter/2);

    // risers
    if (add_risers == 1) {
      translate([0,0,base_width-0.01])
      risers();
    }
  }
}

module trayVaseMode() {
  $fa=1;
  cylinder(h=height, r1=base_radius, r2=top_radius);
}

module risers() {
  $fa=1;
  difference() {
    cylinder(h=riser_height, r=riser_radius);
    cylinder(h=riser_cut_height, r=riser_inner_radius, center=true);

    for (a = [0:90:270]) {
      rotate([0,0,a])
      translate([riser_inner_radius, 0, 0])
      cube(size=[riser_radius, riser_cut_width, riser_cut_height], center=true);
    }
  }
}

```


[User]
I'd like to design a customizable drawer system, based on the "Ultimate Drawer System" concept.  I've looked at a couple of existing implementations and I want to create my own version with a few key features.

Here's what I'm thinking:

**Core Concept**

The system should use a modular approach based on "U" units, like the existing designs. A 1U drawer should be around 120mm x 120mm x 19mm (internal dimensions), with a 131mm x 130mm footprint, designed to fit within a complementary shelf unit, and the heights will be determined by 20mm increments. I want to be able to control the width, depth and height of the drawers in these "U" increments. I'd like this to be parametrically controlled, of course. So, I'd like a `U_wide`, `U_deep`, and `U_high` variable to adjust these dimensions.

**Drawer Features**

*   **Label Slots:** I want to include label slots on the front of the drawers. These should be optional and not included for the 0.5U-wide drawers. These should be a cut-out and should have a small lip to hold labels in place, or could have a window and backplate, or some other way to hold the label. I want to use two label slots on wide drawers, one on each side.
*   **Drawer Pulls:** I want to allow for a few different drawer pull styles. I'd like to implement at least "original" (a simple rectangular extrusion) and "ergonomic" (a curved, finger-friendly pull) options. It would be great if the pull itself was parametric enough that new pulls could be defined.
*  **Flanges:** The drawer should have flanges that run on the sides to keep it in the shelf. I would like three options:
    *   "normal": A standard flange that holds the drawer in the shelf, but doesn't 'catch'
    *   "catch": A flange with a bump to provide a locking mechanism with the shelf
    *   "none": No flange on the side to allow other mounting options.
*   **Rear Locking Mechanism**: I also want an option to include a rear locking slot cut-out on the back of the drawers. This would likely need to be implemented as a negative space, or cut-out, on the back of the drawer, for integration with a corresponding lock feature on the shelf.

**Dimensions and Parameters**

I want a set of internal variables that define the overall size of the system. Specifically:

*   `drawerUnit`: The size of a 1U drawer: \[120, 120, 19] (x, y, z).
*   `shelfPadding`: The padding around the drawer in the shelf: \[11, 10, 1] (x, y, z).
*   `wallThickness`: The wall thickness of the drawer (1mm).
*   `shelfUnit`: The size of a 1U shelf unit: \[131, 130, 30] (x, y, z).

Based on these core dimensions, I want to use calculated values for the dimensions of the drawer itself such as `shelf` and `drawer`. In other words, I want to determine `shelf` as a multiple of `shelfUnit`, adjusted by wall thickness as appropriate, and `drawer` derived from `shelf` and `shelfPadding`. This should help ensure compatibility with shelf units made with similar dimensions.

Other dimensions:
*   `cornerR`: Radius of rounded corners (4)
*   `flange`: Dimensions of the flange (3, d\_to\_y(U\_deep)-shelfPadding.y, 1). The second dimension here is dynamic.
*   `pullD`: Diameter of the circular part of the pull (24.38)
*   `pull`: Pull dimensions: \[2, pullD/2 + 2.8, 16]
*   `label`: Dimensions of the label (51, 2, 16)
*   `labelSlot`: Dimensions of the label slot (49, 1, 15)
*   `labelWindow`: Dimensions of the label window (46, 1, 14)
*   `catch`: Dimensions of the catch flange (3, 4, 1)
*   `rearLockSlot`: Dimensions of the rear lock slot (26, 3.5, 8)

I will also need some utility functions:

*  `u_to_z(u)`: Converts a U height to a z-dimension
*  `w_to_x(w)`: Converts a U width to an x-dimension
*  `d_to_y(d)`: Converts a U depth to a y-dimension

**Modules**

I would like separate modules for each major component:
* `drawer()`: The main module, which includes `add()` and `subtract()` modules, that construct the drawer using positive and negative spaces and has a boolean `includeLabels`.
*   `labels()`: Creates the label slots. Should have an `add()` and `subtract()` method.
*   `pull()`: Creates the drawer pull based on the specified style.
*   `rearLockSlot()`: Creates the rear lock slot, also with an `add()` module.
*   `roundtangle()`: Creates a rectangle with rounded corners using the minkowski() operation.
*   `reflect()`: Used to make symmetrical features, using a mirror() operation.

**Parameters**

All of these parameters should be customizable through variables at the top of the file. Specifically, the design should be controlled by the following variables:
*  `U_wide` (0.5, 1, 1.5)
*  `U_deep` (0.5, 1, 1.5)
*  `U_high` (1-15)
*  `labels` (yes, no)
*  `pull_style` (original, ergonomic, ring)
*  `flange_style` (normal, catch, none)
*  `rear_lock_slot` (yes, no)

Could you generate this for me? I think this will require at least one file, potentially more if that makes sense. I also would prefer not to rely on any external libraries, such as BOSL.

[Assistant]
drawer.scad:
```
// Customizable Ultimate Drawer System Drawer
// Remixed from MarcElbichon's Ultimate Drawer System https://www.thingiverse.com/thing:2302575 (CC-BY 4.0)
// Copyright (C) 2019 by Brian Alano (and possibly others)
// Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC-BY-NC-SA 4.0)

/* Release Notes
 * Version 1.1
 * Made label slots optional, and removed them entirely for 0.5U wide drawers.
 * Added 0.5U wide and 0.5U deep options
 */

/* Design notes
// width is x dimension, across the face of the drawer
// depth is y dimension, front to back of the drawer
// height is z dimension
*/

/* Coding Style Guide
 * User parameters and modules use underscores between words.
 * Other variable names use camel case.
 * Separate features into their own modules if they are more than a couple lines long.
 * All dimensions should be assigned to variables, usually global ones so they can be found easily.
 * Keep local modules local.
 * Keep local variables local.
 * Maintain Thingiverse Customizer compatibility.
 * Maintain backwards compatibility with MarcElbichon's Ultimate Drawer System
   (https://www.thingiverse.com/thing:2302575). This means a 1Ux1Ux1U drawer
   made with this program will work in MarcElbichon's shelf.
*/

/* [Size] */
// units wide (actual drawer width is 131*U_wide - 10)
U_wide=1; // [0.5, 1, 1.5]
// units deep (actual drawer depth is 130*U_deep - 10)
U_deep=1; // [0.5, 1, 1.5]
// units high (actual drawer height is 20*U_high - 1)
U_high=3; // [1:15]

/* [Features] */
// Include slots for labels?
labels = "yes"; //[yes, no]
// What kind of drawer pull?
pull_style = "original"; // [original, ergonomic, ring]
// the flange is what keeps the drawer in the slot. "catch" leaves a bump for holding the drawer in the a shelf with snaps.
flange_style = "normal"; // [normal, catch, none]
// include slots on the back of the drawer for the locking mechanism
rear_lock_slot = "no"; // [yes, no]

/* [Hidden] */
// utility variables
epsilon = 0.01;
$fs=1;
$fa=5;

drawerUnit=[120, 120, 19];
shelfPadding=[11, 10, 1];

wallThickness = 1;
shelfUnit = [131, 130, 30];
shelf = [shelfUnit.x * U_wide, shelfUnit.y * U_deep, (shelfUnit.z - wallThickness*2) * U_high - wallThickness*2]; // reference dimension from shelf .scad file.
echo("shelf dimensions", shelf);
drawer = [shelf.x - shelfPadding.x, shelf.y - shelfPadding.y, shelf.z - shelfPadding.z];
echo("drawer dimensions", drawer);

cornerR = 4;
cornerD = cornerR * 2;
flange = [flange_style == "catch"
    ? 3*0.6
    : flange_style == "none"
        ? 0
        : 3, d_to_y(U_deep)-shelfPadding.y, 1];
flangeR = flange.x - epsilon;
flangeD = flangeR * 2;
catchFlange = 10;
pullD = 24.38;
pull = [2, pullD/2 + 2.8, 16];
label = [51, 2, 16];
labelSlot = [49, 1, 15];
labelWindow = [46, 1, 14];
catch = [3, 4, flange.z];
rearLockSlot = [26, 3.5, 8];
includeLabels = labels == "yes" && U_wide > 0.5;

// the spacing between drawings is 20, or drawerUnit.z + 1. so a 1U drawer is 19, a 2U drawer is 39, etc.
//FIXME replace with drawer[]
//FIXME put lock on bottom, not top.
function u_to_z(u) = (drawerUnit.z + shelfPadding.z) * u - shelfPadding.z;
function w_to_x(w) = (drawerUnit.x + shelfPadding.x) * w - shelfPadding.x;
function d_to_y(d) = (drawerUnit.y + shelfPadding.y) * d - shelfPadding.y;

module drawer(U_wide = U_wide, U_deep = U_deep, U_high = U_high, includeLabels = includeLabels) {
    module add() {
        // main body
        linear_extrude(u_to_z(U_high))
            roundtangle(width=w_to_x(U_wide), length=d_to_y(U_deep), radius=cornerR);
        // flanges
        reflect([1, 0, 0]) {
            linear_extrude(flange.z)
            translate([w_to_x(U_wide)/2, -(d_to_y(U_deep) - flange.y)/2]) {
                roundtangle(flange.x*2, flange.y, flangeR);
            }
            translate([w_to_x(U_wide)/2, -(d_to_y(U_deep) - catch.y)/2, 0]) {
                linear_extrude(flange.z) roundtangle(catch.x*2, catch.y, flangeR);
            }
        }

        // pull
        translate([0, d_to_y(U_deep)/2, pull.z/2]) pull(style=pull_style);

        // label holders (positive part)
        if (includeLabels) labels("add");

        // rear lock pockets
        if (rear_lock_slot == "yes")
            for(j = [1:U_high])
                translate([0, -d_to_y(U_deep)/2, u_to_z(j)])
                    rearLockSlot();
    }

    module subtract() {
        // main cut, minus fillets
        cut = [w_to_x(U_wide) - wallThickness*2, d_to_y(U_deep) - wallThickness*2, u_to_z(U_high) - wallThickness - cornerR];
        translate([0, 0, u_to_z(U_high) - cut.z + epsilon])
            linear_extrude(cut.z + epsilon) roundtangle(cut.x, cut.y, cornerR);
        // fillet cut
       translate([0, 0, u_to_z(U_high) - cut.z])
            minkowski() {
                cube([cut.x - cornerD, cut.y - cornerD, epsilon], center=true);
                sphere(d=cornerD);
            }
        // label holders (positive part)
        if (includeLabels) labels("subtract");

    }

    difference() {
        add();
        subtract();
    }
}

module labels(mode="add") {
    module add() {
        for (i = [1, -1]) {
            translate([w_to_x(U_wide)/4*i, (d_to_y(U_deep) + label.y)/2 - epsilon, label.z/2]) cube([label.x, label.y + epsilon, label.z], center=true);
        }
    }

    module subtract() {
        for (i=[1, -1]) {
            // label cuts
            translate([w_to_x(U_wide)/4*i, d_to_y(U_deep)/2 + labelSlot.y/2, labelSlot.z/2 + (label.z - labelSlot.z) + epsilon])
                cube(labelSlot, center=true);
            translate([w_to_x(U_wide)/4*i, d_to_y(U_deep)/2 + label.y - wallThickness/2, labelWindow.z/2 + (label.z - labelWindow.z) + epsilon])
                cube(labelWindow, center=true);
        }
    }

    if (mode=="add") add(); else subtract();
}

module pull(style) {
    // drawer pull
    module original() {
        intersection() {
           translate([0, pull.y/2 - epsilon]) cube([pull.x, pull.y + epsilon, pull.z], center = true);
           translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) cylinder(d=pullD, h=pull.x, center = true);
        }
    }

    module ergonomic() {
        difference() {
            original();
            translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) {
                intersection() {
                    cylinder(d=pullD/2, h=pull.x+epsilon*4, center = true);
                    translate([0, pullD/3]) cylinder(d=pullD/2, h=pull.x+epsilon*4, center = true);
                }
            }
        }
        scale([3, 1, 1]) difference() {
            original();
            translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) cylinder(d=pullD-pull.x*2, h=pull.x+epsilon*2, center = true);
        }
    }

    if (style == "original") original();
    if (style == "ergonomic") ergonomic();
}

module rearLockSlot() {
    module half() {
        translate([rearLockSlot.x/2, -rearLockSlot.y, -drawerUnit.z + rearLockSlot.z/2])
        {
            cube([wallThickness, rearLockSlot.y, rearLockSlot.z/2]);
            rotate([0, 90, 0])
                linear_extrude(wallThickness)
                polygon([[0, 0], [rearLockSlot.y, rearLockSlot.y], [0, rearLockSlot.y]]);
        }
        translate([0, -rearLockSlot.y, -drawerUnit.z + rearLockSlot.z/2])
            cube([rearLockSlot.x/2, wallThickness, rearLockSlot.z/2]);
    }

    module add() {
        for(i=[0, 1])
            mirror([i, 0, 0]) half();
    }
    add();
//    half();
}

/* render both the child object and its mirror
    usage: otherwise operates just like mirror()
*/
module reflect(v) {
    children();
    mirror(v) children();
}

module roundtangle(width, length, radius) {
    minkowski() {
                square([width - radius*2, length - radius*2], center=true);
                circle(r=radius);
            }
}

drawer();
//pull(style="ergonomic");
//rear_lock();
```
Customizable_Ultimate_Drawer_System_Drawer_v1.0.scad:
```
// Customizable Ultimate Drawer System Drawer
// Remixed from MarcElbichon's Ultimate Drawer System https://www.thingiverse.com/thing:2302575 (CC-BY 4.0)
// Copyright (C) 2019 by Brian Alano (and possibly others)
// Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC-BY-NC-SA 4.0)

/* Design notes
// width is x dimension, across the face of the drawer
// depth is y dimension, front to back of the drawer
// height is z dimension
*/

/* Coding Style Guide
 * User parameters and modules use underscores between words.
 * Other variable names use camel case.
 * Separate features into their own modules if they are more than a couple lines long.
 * All dimensions should be assigned to variables, usually global ones so they can be found easily.
 * Keep local modules local.
 * Keep local variables local.
 * Maintain Thingiverse Customizer compatibility.
 * Maintain backwards compatibility with MarcElbichon's Ultimate Drawer System
   (https://www.thingiverse.com/thing:2302575). This means a 1Ux1Ux1U drawer
   made with this program will work in MarcElbichon's shelf.
*/

/* [Size] */
// units wide (actual drawer width is 131*U_wide - 10)
U_wide=1; // [1, 1.5]
// units deep (actual drawer depth is 130*U_deep - 10)
U_deep=1; // [1, 1.5]
// units high (actual drawer height is 20*U_high - 1)
U_high=3; // [1:15]

/* [Features] */
// What kind of drawer pull?
pull_style = "original"; // [original, ergonomic]
// modify the flange to allow for the drawer catch on the shelf?
drawer_catch = "no"; // [yes, no]
// include slots on the back of the drawer for the locking mechanism
rear_lock_slot = "no"; // [yes, no]

/* [Hidden] */
drawerUnit=[120, 120, 19];
shelfPadding=[11, 10, 1];

wallThickness = 1;
shelfUnit = [131, 130, 30];
shelf = [shelfUnit.x * U_wide, shelfUnit.y * U_deep, (shelfUnit.z - wallThickness*2) * U_high - wallThickness*2]; // reference dimension from shelf .scad file.
drawer = [shelf.x - shelfPadding.x, shelf.y - shelfPadding.y, shelf.z - shelfPadding.z];

cornerR = 4;
cornerD = cornerR * 2;
flangeR = 3;
flangeD = flangeR * 2;
flange = [3, d_to_y(U_deep)-10, 1];
pullD = 24.38;
pull = [2, pullD/2 + 2.8, 16];
label = [51, 2, 16];
labelSlot = [49, 1, 15];
labelWindow = [46, 1, 14];
catch = [flange.x * 0.4, d_to_y(U_deep) - 4, flange.z];
rearLockSlot = [26, 3.5, 8];

// utility variables
epsilon = 0.01;

// the spacing between drawings is 20, or drawerUnit.z + 1. so a 1U drawer is 19, a 2U drawer is 39, etc.
//FIXME replace with drawer[]
//FIXME put lock on bottom, not top.
function u_to_z(u) = (drawerUnit.z + shelfPadding.z) * u - shelfPadding.z;
function w_to_x(w) = (drawerUnit.x + shelfPadding.x) * w - shelfPadding.x;
function d_to_y(d) = (drawerUnit.y + shelfPadding.y) * d - shelfPadding.y;

module drawer() {
    module add() {
        // main body
        linear_extrude(u_to_z(U_high))
            roundtangle(width=w_to_x(U_wide), length=d_to_y(U_deep), radius=cornerR);
        // flanges
        linear_extrude(flange.z)
            for (i = [1, -1]) {
                translate([w_to_x(U_wide)/2*i, -d_to_y(U_deep)/2] ) {
                    translate([-flange.x, 0]) square([flange.x*2, flange.y - flangeR]);
                    translate([0, flange.y - flangeR]) circle(r=flangeR);
                }
            }
        // pull
        translate([0, d_to_y(U_deep)/2, pull.z/2]) pull(style=pull_style);
        // label holders (positive part)
        for (i = [1, -1]) {
            translate([w_to_x(U_wide)/4*i, (d_to_y(U_deep) + label.y)/2 - epsilon, label.z/2]) cube([label.x, label.y + epsilon, label.z], center=true);
        }
        // rear lock pockets
        if (rear_lock_slot == "yes")
            for(j = [1:U_high])
                translate([0, -d_to_y(U_deep)/2, u_to_z(j)])
                    rearLockSlot();
    }

    module subtract() {
        // main cut, minus fillets
        cut = [w_to_x(U_wide) - wallThickness*2, d_to_y(U_deep) - wallThickness*2, u_to_z(U_high) - wallThickness - cornerR];
        translate([0, 0, u_to_z(U_high) - cut.z + epsilon])
            linear_extrude(cut.z + epsilon) roundtangle(cut.x, cut.y, cornerR);
        // fillet cut
       translate([0, 0, u_to_z(U_high) - cut.z])
            minkowski() {
                cube([cut.x - cornerD, cut.y - cornerD, epsilon], center=true);
                sphere(d=cornerD);
            }
        for (i=[1, -1]) {
            // label cuts
            translate([w_to_x(U_wide)/4*i, d_to_y(U_deep)/2 + labelSlot.y/2, labelSlot.z/2 + (label.z - labelSlot.z) + epsilon])
                cube(labelSlot, center=true);
            translate([w_to_x(U_wide)/4*i, d_to_y(U_deep)/2 + label.y - wallThickness/2, labelWindow.z/2 + (label.z - labelWindow.z) + epsilon])
                cube(labelWindow, center=true);
            // drawer catch cutout
            if (drawer_catch == "yes") {
               translate([(w_to_x(U_wide)/2 + flange.x - catch.x/2 + epsilon)*i,
                d_to_y(U_deep)/2 - catch.y/2,
                catch.z/2 - epsilon])
                    cube([catch.x + epsilon, catch.y, catch.z + 2*epsilon], center=true);
            }
        }
    }

    difference() {
        add();
        subtract();
    }
}

module pull(style) {
    // drawer pull
    module original() {
        intersection() {
           translate([0, pull.y/2 - epsilon]) cube([pull.x, pull.y + epsilon, pull.z], center = true);
           translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) cylinder(d=pullD, h=pull.x, center = true);
        }
    }

    module ergonomic() {
        difference() {
            original();
            translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) {
                intersection() {
                    cylinder(d=pullD/2, h=pull.x+epsilon*4, center = true);
                    translate([0, pullD/3]) cylinder(d=pullD/2, h=pull.x+epsilon*4, center = true);
                }
            }
        }
        scale([3, 1, 1]) difference() {
            original();
            translate([0, pull.y - pullD/2]) rotate([0, 90, 0]) cylinder(d=pullD-pull.x*2, h=pull.x+epsilon*2, center = true);
        }
    }

    if (style == "original") original();
    if (style == "ergonomic") ergonomic();
}

module rearLockSlot() {
    module half() {
        translate([rearLockSlot.x/2, -rearLockSlot.y, -drawerUnit.z + rearLockSlot.z/2])
        {
            cube([wallThickness, rearLockSlot.y, rearLockSlot.z/2]);
            rotate([0, 90, 0])
                linear_extrude(wallThickness)
                polygon([[0, 0], [rearLockSlot.y, rearLockSlot.y], [0, rearLockSlot.y]]);
        }
        translate([0, -rearLockSlot.y, -drawerUnit.z + rearLockSlot.z/2])
            cube([rearLockSlot.x/2, wallThickness, rearLockSlot.z/2]);
    }

    module add() {
        for(i=[0, 1])
            mirror([i, 0, 0]) half();
    }
    add();
//    half();
}

module roundtangle(width, length, radius) {
    minkowski() {
                square([width - radius*2, length - radius*2], center=true);
                circle(r=radius);
            }
}
drawer();
//pull(style="ergonomic");
//rear_lock();
```


[User]
I'd like to create a sink strainer using OpenSCAD. I'm looking for a parametric design that lets me customize the strainer's dimensions and features.

Specifically, I need to be able to define the following parameters:

*   **Sink Diameter:** The diameter of the sink opening the strainer will fit into.
*   **Sink Depth:** The depth of the sink where the strainer will sit.
*   **Border Width:**  The width of the flat rim around the strainer.
*   **Thickness:** The overall thickness of the material used for the strainer, especially the main plate and the dome.
*  **Hole Diameter:** The diameter of the individual holes in the strainer's mesh.
*   **Handle:** A toggle to add or remove a handle on the side of the strainer.
*   **Retaining Tabs:** A toggle to add or remove retaining tabs on the strainer sides to hold it in place better.

The main body of the strainer should be a geodesic dome shape, with a flat rim surrounding it. The holes should be arranged in a regular pattern across the dome, and also perforate the flat rim, though the grid pattern might need to transition between the flat and curved portions. The flat rim should have the retaining tabs (if enabled) positioned around the circumference, and the handle (if enabled) should be on the side.

I'm aiming for a single-piece design, so it should be printable without supports. It would be great if the code was well-commented, and it would be perfect if the structure was reasonably robust so I don't have to worry about it falling apart. I'm not looking for any specific libraries - just a single .scad file that can handle all of this.

Could you please generate the code for me?

[Assistant]
Geodesic_Sink_Grid.scad:
```
/*
*Author: Eduardo Foltran
*Desing by Eduardo Foltran
*Date: 2019-08-08
*Revision 2.1 - 20200510 - Including handel
*Revision 2.2 - 20200518 - Including retaining tabs
*Version: 2.3 - 20200530 - Correcting bug when trying to make a strainer too deep
*License: Creative Commons CC-BY (Attribution)
*Thingiverse: https://www.thingiverse.com/thing:3797754
*Visit my portifolio at
*https://www.thingiverse.com/EduardoFoltran/designs
*/

//Sink Diameter
SinkDiameter=50;
//Deepth
Sink_Depth=16;
//Border width
BorderWidth=15;
//Thikness
Thikness=1.5;
//Diameter of the holes
HoleDiameter=4;//[0.1:0.1:10]
//Add handle
AddHandle="no"; // [yes,no]
//Add retaing tab
AddTab="no"; // [yes,no]

/* [Hidden] */
//Calculating sink radius
SkR=SinkDiameter/2;
//For the geometry to work, SinkDepth must be less or equal to the sink radius
SinkDepth = min(Sink_Depth,SkR);
//Calculating the sphere radius to generate the dome
SR=(pow(SkR,2)+pow(SinkDepth,2))/(2*SinkDepth);
//Calculating the dome angle
DA=atan(SkR/(SR-SinkDepth));
//Calculating the radius of the holes
HR=HoleDiameter/2;
//Calculating the heigth of the rods that generate the holes on the dome
HH=SR+Thikness;
//Calculating the center height of the pentagonal hole on the top of the dome
PeH=HR*cos(36)/(2*sin(36));
//Calculating the center height of the hexagonal holes
HeH=HR*cos(30);
//Calculating the overall diameter
FD=SinkDiameter+2*BorderWidth;
//Calculating the lenght of the arc covered by the dome
ArcLenght=SR*PI*DA/180;
//Calculating how many layers of holes fit on the ark
Layers=floor((ArcLenght-PeH)/(2*HeH+Thikness));
//Calculating the number of rings of holes on the border
Rings=floor((BorderWidth-2*Thikness)/(2*HeH+Thikness));

$fa=2;
$fs=1;

union(){

	translate([0,0,-SR*cos(DA)+Thikness])
	//This part generates the side plate
	difference(){
		union(){
		translate([0,0,+SR*cos(DA)-Thikness]){
			difference(){
				union(){
					cylinder(d1=FD-4*Thikness,h=Thikness,d2=FD);
					//This part generates the retaining tabs
					//Inspired on the design by Simon Kong Win Chang
					//https://www.thingiverse.com/SkullKill/about
					if (AddTab=="yes"){
						TabHeigth = 2*SinkDepth/3+Thikness;
						TabCarv=SinkDiameter*sin(22.5);
						difference(){
							cylinder(d=SinkDiameter, h=TabHeigth);
							translate([0,0,TabHeigth/2])
							union(){
								cylinder(d=SinkDiameter-2*Thikness, h=TabHeigth+2,center=true);
								cube([TabCarv,SinkDiameter+1,TabHeigth+2],center=true);
								cube([SinkDiameter+1,TabCarv,TabHeigth+2],center=true);
							}
						}
					}
				}
				for (k=[0:4])
					rotate([0,0,k*72])
						for (j=[1:Rings])
							for (i=[0:Layers])
								rotate([0,0,(i+(j-1)/2)*72/(Layers+1)])
									translate([0,-SkR-(j-1)*(2*HeH+Thikness)-HeH-Thikness,0])
										rotate([0,0,-j*30])
											cylinder(r=HR,h=3*Thikness,center=true,$fn=6);
			}
		}

		//This part generates the dome
		difference(){
			sphere(r=SR);
			union(){
				rotate([0,0,18]){
					cylinder(r=HR/(2*sin(36)),h=HH,$fn=5);}
				for (k=[0:4]){
					rotate([0,0,k*72])
					for (i=[0:Layers]){
						LayerArc=72/(i+1);
						for (j=[0:i]){
							SkRr=(j!=0)? HeH*sin(36):0;
							rotate([((((i+1)*(2*HeH+Thikness)+PeH-HeH-SkRr))/SR)*180/PI,0,j*LayerArc])
								rotate([0,0,-j*60/(i+1)])
									cylinder(r=HR,h=HH,$fn=6);
						}
					}
				}
			}
		}
	}
	//This part makes the sphere holow and cuts it
	sphere(r=SR-Thikness);
	translate([0,0,-SR*(1-cos(DA))-Thikness])
		cube(2*SR,center=true);
	}
	//This part generates the handel
	if (AddHandle=="yes"){
		difference(){
			intersection(){
				translate([-SinkDiameter/2,-Thikness/2,0])
					cube([SinkDiameter,Thikness,SinkDepth+Thikness]);
				translate([0,0,-SR*cos(DA)+Thikness])
					sphere(r=SR);
			}
			translate([0,0,(SR-Thikness)+Thikness])
			sphere(r=SR-Thikness);
		}
	}
}

//			for (k=[0:4])
//				rotate([0,0,k*72])
//					for (j=[1:Rings])
//						for (i=[0:Layers+j])
//							rotate([0,0,i*72/(Layers+j+1)])
//								translate([0,-SR-j*(2*HeH+Thikness)+RBL,0])
//									rotate([0,0,-i*60/(Layers+j+1)])
//										cylinder(r=HR,h=3*Thikness,center=true,$fn=6);}

```


[User]
Hi there, I'm looking to create a customizable drawer insert system based on the Ultimate Drawer System concept, but I need it to be entirely parametric and generate the SCAD files from scratch. I've included the existing code as a reference, but please don't just modify it; I'd like a fresh implementation.

Here's what I need:

**Core Functionality:**

*   **Parametric Inserts:** The core function should create a basic tray-like insert with customizable width, depth, and height. These are the outer dimensions of the insert.
*   **Tolerance:**  I need a tolerance parameter that subtracts from all sides (x,y, and z) of the insert, allowing for printing wiggle room.
*   **Wall Thickness and Corner Radius:** The insert should have a specified wall thickness and corner radius. These values should be adjustable.
*   **Rounded Rectangles:** The primary shape should be a rounded rectangle (or "roundtangle" as it's called in the reference). This means both the interior and exterior should have rounded corners.

**Advanced Features:**

*   **Island Feature:** I'd like to have a central "island" insert within the main insert. This island should be able to take on three forms: "none" (disabled), "round", or "square". The size of the island, and the offset (position) should be parameters.
*   **Pliers Holder:** The ability to add dividers shaped like plier handles would be incredibly useful. It would require parameters for plier width, height, and offset. The handle shape is defined by a math function in the reference code, and should be copied in the new implementation.
*   **Backwards Compatibility:** Although I want to generate all new code, the insert *must* be compatible with MarcElbichon's Ultimate Drawer System. So, a 1Ux1Ux1U insert in this system should work in MarcElbichon's shelf system.
*   **Use of Libraries**: Use appropriate OpenSCAD libraries to help make this process easier. I'm not picky, so use whatever you think makes sense. You don't need to provide the library files, just the file using the library. I am assuming you know how to obtain the libraries.

**OpenSCAD Specifics**

*   **Parameters:** All relevant dimensions (width, depth, height, tolerance, wall thickness, corner radius, island size, island offset, plier width, plier height, plier offset) should be accessible as user-defined parameters at the top of the SCAD file.
*   **Modularity:**  The code should be modular, with features implemented in separate modules (e.g., the main insert, the island feature, the plier holder).
*   **Clear Comments:** I need clear comments throughout the code to make it easy to understand and modify later.
*   **Function Naming:** Variable, module, and function names should follow the coding conventions described in the comments of the attached `insert.scad`. Camel case for variables/functions, underscore separation for module parameters.

Essentially, I need a robust, parametric system that allows me to create a variety of drawer inserts, optimized for the Ultimate Drawer System, but built from the ground up with better structure and flexibility. Let me know if you have questions!

[Assistant]
insert.scad:
```
// Customizable Ultimate Drawer System Inserts
// Remixed from MarcElbichon's Ultimate Drawer System https://www.thingiverse.com/thing:2302575 (CC-BY 4.0)
// Copyright (C) 2019 by Brian Alano (and possibly others)
// Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC-BY-NC-SA 4.0)

/* Design notes
// width is x dimension, across the face of the drawer
// depth is y dimension, front to back of the drawer
// height is z dimension
*/

/* Coding Style Guide
 * User parameters and modules use underscores between words.
 * Other variable names use camel case.
 * Separate features into their own modules if they are more than a couple lines long.
 * All dimensions should be assigned to variables, usually global ones so they can be found easily.
 * Keep local modules local.
 * Keep local variables local.
 * Maintain Thingiverse Customizer compatibility.
 * Maintain backwards compatibility with MarcElbichon's Ultimate Drawer System
   (https://www.thingiverse.com/thing:2302575). This means a 1Ux1Ux1U drawer
   made with this program will work in MarcElbichon's shelf.

   See README.md for more.
*/

/* [Size] */
// Outside width in mm (1U drawer is 118 mm inside, 1.5U is 182.5 mm, 2U is 249 mm)
Width=59; // [8:0.1:249]
// Outside depth in mm (1U drawer is 118 mm inside, 1.5U is 182 mm, 2U is 248 mm)
Depth=59; // [8:0.1:248]
// Outside height in mm (1U drawer is 18 mm inside, 2U is 38 mm, 3U is 58 mm, etc.)
Height= 18; // [8:398]
// This amount is subtracted from each of the six sides to provide some wiggle room. Half your nozzle diameter is a safe place to start if you're not sure.
Tolerance=0.2; // [0.00:0.02:1.00]

/* [Island] */
Island_Shape="none"; //[none,round,square]
// Size of center insert-within-insert. Must be smaller than depth
Island = 27;
Island_Offset = 0;

/* [Pliers] */
// Set the outside width of a divider conforming to a general plier handle. 0 to disable.
Plier_Width=0;
// Set the outside height of a divider conforming to a general plier handle.
Plier_Height=0;
Plier_Offset=0;

/* [Hidden] */
drawerWallThickness = 1; // assumed
drawerCornerRadius = 4; // assumed
insertWallThickness = 1;
insertCornerRadius = drawerCornerRadius;
insertSize = [Width - Tolerance*2, Depth - Tolerance*2, Height - Tolerance*2];
X=[1, 0, 0];
Y=[0, 1, 0];
Z=[0, 0, 1];

// utility variables
epsilon = 0.01;
$fa=4;
$fs=0.5;

module double_fillet_profile(thickness, r) {
    module add() {
        translate([0, +r/2]) square([thickness+2*r, r], center=true);
    }

    module subtract() {
        reflect(X) translate([r+thickness/2, r]) circle(r);
    }

    difference() {
        add();
        subtract();
    }
}

module insert(size) {
    module add() {
        // main body
       translate([0, 0, insertCornerRadius])
            linear_extrude(size.z - insertCornerRadius)
            roundtangle([size.x, size.y], radius=insertCornerRadius);
        // filleted bottom
       translate([0, 0, insertCornerRadius])
            roundtangle3d([size.x, size.y], insertCornerRadius);
    }

    module subtract() {
        insideRadius = insertCornerRadius - insertWallThickness;
        // main cut, minus fillets
        cut = [size.x - insertWallThickness*2,
            size.y - insertWallThickness*2,
            size.z - insertWallThickness];
        translate([0, 0, insideRadius + insertWallThickness - epsilon])
            linear_extrude(cut.z - insideRadius + epsilon * 2)
            roundtangle([cut.x, cut.y], insideRadius );
        // fillet cut
       translate([0, 0, insideRadius + insertWallThickness])
            roundtangle3d([cut.x, cut.y], insideRadius);
    }

    difference() {
        add();
        subtract();
    }
}

module island(size) {
    maxSize=min(size, Depth-insertCornerRadius*2-insertWallThickness);
    island=[maxSize*Width/Depth, maxSize];

    module side() {
        side=[island.x-insertCornerRadius*2, island.y-insertCornerRadius*2];
        reflect(X)
            translate([(island.x-insertWallThickness)/2, 0]) rotate(X*90)
            linear_extrude(side.y, center=true)
            double_fillet_profile(insertWallThickness, insertCornerRadius);
        reflect(Y)
            translate([0, (island.y-insertWallThickness)/2]) rotate([90, 0, 90])
            linear_extrude(side.x, center=true)
            double_fillet_profile(insertWallThickness, insertCornerRadius);
    }

    module round() {
        scale([Width/Depth, 1])
            rotate_extrude()
            translate([(island.y-insertWallThickness)/2, 0])
            double_fillet_profile(insertWallThickness, insertCornerRadius);
    }

    module add() {
        // corners
        reflect(X) reflect(Y)
            translate([island.x/2 - insertCornerRadius, island.y/2 - insertCornerRadius])
            rotate_extrude(angle=90)
            intersection() {
            translate([(insertCornerRadius-insertWallThickness/2), 0, 0]) double_fillet_profile(insertWallThickness, insertCornerRadius);
            square(insertCornerRadius*2);
        }

        // sides
        side();
    }

    translate([0, Island_Offset, insertWallThickness])
        if (Island_Shape=="round") {
            round();
        } else {
            add();
        }

}

module pliers(width, height, offset) {
    step=width/20;
    yFactor= height/y(0);
//    Height=19;

    function y(x) = -(pow(x/(width/2)-0.5,2))+2.25;

    module add() {
        translate([0, offset]) for(x=[-width/2:step:0]) {
            x0=x-step; // used to get angle0
            y0=y(x0)*yFactor; // used to get angle0
            y=y(x)*yFactor; // equation is normalized to -1<x<1, 0<y<1
            x2=x+step;
            y2=y(x2)*yFactor;
            angle0=atan((y-y0)/(x-x0));
            angle1=atan((y2-y)/(x2-x));
            echo("x,y,x2,y2, angle", x, y, x2, y2,angle1);
            hull()
            {
                translate([x, y, Height/4]) rotate([0, 0, 90+angle0]) cube([insertWallThickness, epsilon, Height/2], center=true); //double_fillet_profile();
                translate([x2, y2, Height/4]) rotate([0, 0, 90+angle1]) cube([insertWallThickness, epsilon,  Height/2], center=true);// double_fillet_profile();
            }
        }
    }

    reflect(X) intersection() {
        add();
        translate([-width/2, offset]) cube([width/2, height, Height]);
    }

}

module reflect(vector) {
    children();
    mirror(vector) children();
}

module roundtangle(size, radius) {
    minkowski() {
        square([max(size.x - radius*2, epsilon), max(size.y - radius*2, epsilon)], center=true);
        circle(r=radius);
    }
}

module roundtangle3d(size, r) {
    minkowski() {
        cube([max(size.x - r*2, epsilon), max(size.y - r*2, epsilon), epsilon], center=true);
        sphere(r=r );
    }
}

//difference() {
    union() {
        insert(insertSize);
        if (Island_Shape != "none") island(Island);
        if (Plier_Width != 0) pliers(Plier_Width, Plier_Height, Plier_Offset);
    }
//    cube(100);
//}

```
Customizable_Ultimate_Drawer_System_Insert_v1.0.scad:
```
// Customizable Ultimate Drawer System Inserts
// Remixed from MarcElbichon's Ultimate Drawer System https://www.thingiverse.com/thing:2302575 (CC-BY 4.0)
// Copyright (C) 2019 by Brian Alano (and possibly others)
// Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 (CC-BY-NC-SA 4.0)

/* Design notes
// width is x dimension, across the face of the drawer
// depth is y dimension, front to back of the drawer
// height is z dimension
*/

/* Coding Style Guide
 * User parameters and modules use underscores between words.
 * Other variable names use camel case.
 * Separate features into their own modules if they are more than a couple lines long.
 * All dimensions should be assigned to variables, usually global ones so they can be found easily.
 * Keep local modules local.
 * Keep local variables local.
 * Maintain Thingiverse Customizer compatibility.
 * Maintain backwards compatibility with MarcElbichon's Ultimate Drawer System
   (https://www.thingiverse.com/thing:2302575). This means a 1Ux1Ux1U drawer
   made with this program will work in MarcElbichon's shelf.

   See README.md for more.
*/

/* [Size] */
// Outside width in mm (1U drawer is 118 mm inside, 1.5U is 182.5 mm, 2U is 249 mm)
Width=59; // [8:0.5:249]
// Outside depth in mm (1U drawer is 118 mm inside, 1.5U is 182 mm, 2U is 248 mm)
Depth=59; // [8:248]
// Outside height in mm (1U drawer is 18 mm inside, 2U is 38 mm, 3U is 58 mm, etc.)
Height= 18; // [8:398]
// This amount is subtracted from each of the six sides to provide some wiggle room. Half your nozzle diameter is a good place to start if you're not sure.
Tolerance=0.2; // [0.00:0.02:1.00]

/* [Hidden] */
drawerWallThickness = 1; // assumed
drawerCornerRadius = 4; // assumed
insertWallThickness = 1;
insertCornerRadius = drawerCornerRadius;
insertSize = [Width - Tolerance*2, Depth - Tolerance*2, Height - Tolerance*2];

// utility variables
epsilon = 0.01;
$fn=24;

module insert() {
    module add() {
        // main body
       translate([0, 0, insertCornerRadius])
            linear_extrude(insertSize.z - insertCornerRadius)
            roundtangle([insertSize.x, insertSize.y], radius=insertCornerRadius);
        // filleted bottom
       translate([0, 0, insertCornerRadius])
            roundtangle3d([insertSize.x, insertSize.y], insertCornerRadius);
    }

    module subtract() {
        insideRadius = insertCornerRadius - insertWallThickness;
        // main cut, minus fillets
        cut = [insertSize.x - insertWallThickness*2,
            insertSize.y - insertWallThickness*2,
            insertSize.z - insertWallThickness];
        translate([0, 0, insideRadius + insertWallThickness - epsilon])
            linear_extrude(cut.z - insideRadius + epsilon * 2)
            roundtangle([cut.x, cut.y], insideRadius );
        // fillet cut
       translate([0, 0, insideRadius + insertWallThickness])
            roundtangle3d([cut.x, cut.y], insideRadius);
    }

    difference() {
        add();
        subtract();
    }
}

module roundtangle(size, radius) {
    minkowski() {
        square([max(size.x - radius*2, epsilon), max(size.y - radius*2, epsilon)], center=true);
        circle(r=radius);
    }
}

module roundtangle3d(size, r) {
    minkowski() {
        cube([max(size.x - r*2, epsilon), max(size.y - r*2, epsilon), epsilon], center=true);
        sphere(r=r );
    }
}

insert();

```


[User]
Okay, so I'm looking to create a fully parametric OpenSCAD design for a 3D printer enclosure, specifically based on the popular IKEA Lack design, but I need to be able to customize it for different printer models like Ender 3 and Prusa i3. I want to incorporate magnet mounts for the doors and have parameters to adjust the magnet size, padding around the magnet cutout, and the part being designed. I've already got a bunch of STL files for the various parts, and a ton of documentation on what's out there already, and I've included what I've written so far. Here's the breakdown:

**Core Requirements:**

*   **Parametric Design:** The design should be driven by variables like `magnet_length`, `magnet_width`, `magnet_depth`, and padding values like `border_length`, `border_width`, `border_depth`.
*   **Part Selection:** I want to be able to select which part I'm generating the magnet cutout for using a string variable, such as `part = "OpenTab1"`. This should be a dropdown menu, probably.
*   **Magnet Cutout:** The design should generate a magnet cutout within an existing STL file. It should handle the appropriate rotation and translation based on the selected part and orient the cube to the correct side of the piece.
*   **Multiple STL Support:** I need to support a bunch of different STL files, including `OpenTab1.stl`, `OpenTabBR.stl`, `Front_Spacer2.stl`, `Front_Spacer.stl`, `Front_Spacer_TL.stl`, `Front_Spacer_TR.stl`, `Hinge1.stl`, `HingeBR.stl`, `HingeTL.stl`, `HingeTR.stl`, and `DoorStop.stl`.
*   **Color Indication:** The magnet cutout should be colored "lime" to make it stand out.

**Specific Part Details:**
Here's how the magnet cutout should be positioned in each part:

*   **OpenTab1:** Rotate the `OpenTab1.stl` by 90 degrees around the Y axis.  The cutout should be on the same side as the lip, with an offset of `[-11.15, 7.5, -10]` plus a translation to center on the cube. The depth parameter `sub_depth` should be added to the X axis.
*   **OpenTabBR:** Rotate the `OpenTabBR.stl` by -90 degrees around the Y axis. The cutout should be on the same side as the lip, with an offset of `[11.15, 7.5, 50]`, plus a translation to center the cube. The depth parameter `sub_depth` should be subtracted from the X axis.
*   **Front_Spacer2:** Rotate the `Front_Spacer2.stl` by 90 degrees around the X axis. The cutout should be on the inside face, with an offset of `[19.16, -27, -33]` plus a translation to center the cube.  The depth parameter `sub_depth` should be added to the X axis, and the width parameter `sub_width` should be added to the Z axis.
*   **Front_Spacer:** Rotate the `Front_Spacer.stl` by 90 degrees around the X axis.  The cutout should be on the inside face, with an offset of `[19.16, -27, -33]` plus a translation to center the cube. The depth parameter `sub_depth` should be subtracted from the X axis, and the width parameter `sub_width` should be added to the Z axis.
*   **Front_Spacer_TL:** Rotate the `Front_Spacer_TL.stl` by -90 degrees around the X axis. The cutout should be on the inside face, with an offset of `[19.16, 27, 14]` plus a translation to center the cube. The depth parameter `sub_depth` should be subtracted from the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **Front_Spacer_TR:** Rotate the `Front_Spacer_TR.stl` by -90 degrees around the X axis. The cutout should be on the inside face, with an offset of `[29.16, 27, 14]` plus a translation to center the cube.  The depth parameter `sub_depth` should be added to the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **Hinge1:** Rotate the `Hinge1.stl` by -90 degrees around the X axis. The cutout should be on the outside face, with an offset of `[9.5, 22, 33]` plus a translation to center the cube. The depth parameter `sub_depth` should be added to the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **HingeBR:** Rotate the `HingeBR.stl` by -90 degrees around the X axis. The cutout should be on the outside face, with an offset of `[39.51, 22, 33]` plus a translation to center the cube.  The depth parameter `sub_depth` should be subtracted from the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **HingeTL:** Rotate the `HingeTL.stl` by -90 degrees around the X axis.  The cutout should be on the outside face, with an offset of `[9.5, 22, 13]` plus a translation to center the cube.  The depth parameter `sub_depth` should be added to the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **HingeTR:** Rotate the `HingeTR.stl` by -90 degrees around the X axis.  The cutout should be on the outside face, with an offset of `[39.5, 22, 13]` plus a translation to center the cube. The depth parameter `sub_depth` should be subtracted from the X axis, and the width parameter `sub_width` should be subtracted from the Z axis.
*   **DoorStop:** Rotate the `DoorStop.stl` by 90 degrees around the X axis. Two magnet cutouts should be created, one on each face. They should have an offset of `[20, 0, 7.5]` and `[-20, 0, 7.5]`, and a translation to center the cubes, respectively. The depth parameter `sub_depth` should be added to the Y axis.

I think the easiest way to implement this would be to have each piece in a module, then a single top level `if` statement to control which piece is rendered, just like I've set it up so far. I'm not including the STL files, but they should all be in the same folder as the scad file. I also don't need any special libraries, so you can ignore the libraries request part.

[Assistant]
magnets.scad:
```
/* [Magnet] */

part = "OpenTab1"; // [OpenTab1, OpenTabBR, Front_Spacer2, Front_Spacer, Front_Spacer_TL, Front_Spacer_TR, Hinge1, HingeBR, HingeTL, HingeTR, DoorStop]

magnet_length=20; // [1:30]
magnet_width=5; // [1:10]
magnet_depth=2;   // [1:5]

/* [Padding] */
border_length=0.15;
border_width=0.15;
border_depth=0.15;

/* [Hidden] */
sub_length=magnet_length + (2*border_length);
sub_width=magnet_width + (2*border_width);
sub_depth=magnet_depth + border_depth;

if (part == "OpenTab1") {
  OpenTab1();
} else if (part == "OpenTabBR") {
  OpenTabBR();
} else if (part == "Front_Spacer2") {
  Front_Spacer2();
} else if (part == "Front_Spacer") {
  Front_Spacer();
} else if (part == "Front_Spacer_TL") {
  Front_Spacer_TL();
} else if (part == "Front_Spacer_TR") {
  Front_Spacer_TR();
} else if (part == "Hinge1") {
  Hinge1();
} else if (part == "HingeBR") {
  HingeBR();
} else if (part == "HingeTL") {
  HingeTL();
} else if (part == "HingeTR") {
  HingeTR();
} else if (part == "DoorStop") {
  DoorStop();
}

module OpenTab1() {
  difference() {
    rotate([0, 90, 0])
      import("OpenTab1.stl");
    translate([-11.15, 7.5, -10]) {
      translate([sub_depth/2, 0, 0]) {
        color("lime") cube([sub_depth, sub_width, sub_length], center=true);
      }
    }
  }
}

module OpenTabBR() {
  difference() {
    rotate([0, -90, 0])
      import("OpenTabBR.stl");
    translate([11.15, 7.5, 50]) {
      translate([-sub_depth/2, 0, 0]) {
        color("lime") cube([sub_depth, sub_width, sub_length], center=true);
      }
    }
  }
}

module Front_Spacer2() {
  difference() {
    rotate([90, 0, 0])
      import("Front_Spacer2.stl");
    translate([19.16, -27, -33]) {
      translate([sub_depth/2, 0, sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module Front_Spacer() {
  difference() {
    rotate([90, 0, 0])
      import("Front_Spacer.stl");
    translate([19.16, -27, -33]) {
      translate([-sub_depth/2, 0, sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module Front_Spacer_TL() {
  difference() {
    rotate([-90, 0, 0])
      import("Front_Spacer_TL.stl");
    translate([19.16, 27, 14]) {
      translate([-sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module Front_Spacer_TR() {
  difference() {
    rotate([-90, 0, 0])
      import("Front_Spacer_TR.stl");
    translate([29.16, 27, 14]) {
      translate([sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module Hinge1() {
  difference() {
    rotate([-90, 0, 0])
      import("Hinge1.stl");
    translate([9.5, 22, 33]) {
      translate([sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module HingeBR() {
  difference() {
    rotate([-90, 0, 0])
      import("HingeBR.stl");
    translate([39.51, 22, 33]) {
      translate([-sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module HingeTL() {
  difference() {
    rotate([-90, 0, 0])
      import("HingeTL.stl");
    translate([9.5, 22, 13]) {
      translate([sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module HingeTR() {
  difference() {
    rotate([-90, 0, 0])
      import("HingeTR.stl");
    translate([39.5, 22, 13]) {
      translate([-sub_depth/2, 0, -sub_width/2]) {
        color("lime") cube([sub_depth, sub_length, sub_width], center=true);
      }
    }
  }
}

module DoorStop() {
  difference() {
    rotate([90, 0, 0])
      import("DoorStop.stl");
    translate([20, 0, 7.5]) {
      translate([0, sub_depth/2, 0]) {
        color("lime") cube([sub_length, sub_depth, sub_width], center=true);
      }
    }
    translate([-20, 0, 7.5]) {
      translate([0, sub_depth/2, 0]) {
        color("lime") cube([sub_length, sub_depth, sub_width], center=true);
      }
    }
  }
}

```


[User]
Hey, I'm looking to create a set of radius gauges, and I've got a pretty clear idea of what I need. I'd like the gauges to be designed parametrically in OpenSCAD so I can easily adjust things if I need to.

Here's the breakdown:

**Gauges:**

*   Each gauge will have a straight body with a convex radius on one end and a concave radius on the other.
*   The gauge's length will be determined by the radius size, plus an extra amount, so the larger the radius, the longer the gauge.
*   Each gauge needs to have its radius size printed on it.
*   I need to be able to specify the radius sizes I want to create (e.g. 1, 2, 3, 4... or 2, 4, 6, 8...). So the script needs to work with a list of radius values, not just a range.
*   The thickness of the gauges should be a variable I can change.
*   I need the text depth and font type (and style like bold, italic, etc) to be configurable as well.

**Holder Box:**

*   The gauges need to be stored in a box, with a dedicated slot for each gauge, with the gauge sliding in the slot.
*   The slot should be sized according to the gauge dimensions, including a tolerance so that the gauges fit in without being too tight or loose.
*   I need the ability to add a small nub or bump in each slot to add a bit more friction.
*   The box itself should be parametrically determined by the gauges. It needs to be tall enough so that the gauges don't move around too much, but not waste material either.
*   I'd like the slots to be slightly beveled on the top edges for better aesthetics.
*   The wall thickness of the box should also be configurable.
*   I'm happy for the box to be on one side (not surrounding) the gauges in the print preview.

**Parameters:**

I need to be able to adjust these values:
* `thickness`: The thickness of the gauges and the box's wall thickness (default 2.2mm)
* `extra_length`: Extra length added to each gauge (default 0)
* `sizes`: List of radius sizes to generate (e.g. `[1,2,3,4,5,6,7,8,9,10]`)
* `tolerance`: How much larger the box slot should be than the gauge (default 0.1mm)
* `friction_fit`: How thick the friction fit bump should be in each slot (default 0, meaning no bump)
* `font_family`: Font family to use for the text (default "Arimo")
* `font_weight`: Font style for the text (default "Bold")
* `font_size`: Font size of the text (default 6)
* `text_depth`: The depth that the text is recessed (default 0.4mm)

I think that covers everything. Can you generate the OpenSCAD code for this? I'd prefer a single file, but if you think it's better to split it, go for it! I'm not using any extra libraries at the moment, so just stick to the standard OpenSCAD functions.

[Assistant]
radius_gauge.scad:
```
// preview[view:south, tilt:top]

// Gauge thickness
thickness = 2.2;
// Extra length to add to each gauge
extra_length = 0;
// Radius size list
sizes = [1,2,3,4,5,6,7,8,9,10];
// Box slot tolerance
tolerance = 0.1;
// Thickness of nub in each slot to increase friction on gauge
friction_fit = 0;

// You can use any of these - https://fonts.google.com/
font_family = "Arimo";
font_weight = "Bold";
font_size = 6;

font = str(font_family, ":style=", font_weight);

text_depth = 0.4;

/* [hidden] */
_fudge = 0.1;
_length = max(sizes) * 2 + font_size + 3 + extra_length;
_minBoxExposedGauge = 9;

// Keep inside curve of largest gauge slightly inside box, but at least 12 mm exposed
_boxHeight = _length - max(max(sizes), 12) + 4;

module drawGauge(radius, width) {
  _l = _length - radius;

  union() {
    difference() {
      union() {
        cube([_l, width, thickness]);
        // convex radius
        translate([_l, width/2, 0]) {
          difference() {
            cylinder(h=thickness, r=radius, $fa = 4, $fs = 0.5);
            translate([-radius, -radius, -_fudge]) {
              cube([radius, radius * 2, thickness+_fudge*2]);
            }
          }
        }
      }
      // draw text
      translate([0, width/2, thickness-text_depth]) {
        translate([radius+2, 0, 0]) {
          linear_extrude(height=text_depth+_fudge){
            text(text=str(radius), size=font_size, font=font, halign="left", valign="center");
          }
        }
      }

      // concave radius
      translate([0, width - radius - 2, -_fudge]) {
        cylinder(h=thickness + _fudge*2, r=radius, $fa = 4, $fs = 0.5);
      }

      // concave radius offset
      translate([-_fudge, -_fudge, -_fudge]) {
        cube([radius+_fudge, width-radius-2+_fudge, thickness + _fudge * 2], center=false);
      }
    }
  }
}

function gaugeWidth(radius) = max(radius * 2, font_size + 2);

module nextGauge(i) {
  if (i < len(sizes)) {
    radius = sizes[i];
    width = gaugeWidth(radius);
    drawGauge(radius, width);
    translate([0, width + 3, 0]) {
      nextGauge(i+ 1);
    }
  }
}

module createBox() {
  wall_thickness = thickness;
  bevel = 1;

  // put box off to the side
  translate([-(gaugeWidth(max(sizes))/2 + wall_thickness + 10), 0, 0]) {
    difference() {
      union() {
        for(i=[0:len(sizes)-2]) {
          current_width = gaugeWidth(sizes[i]);
          next_width = gaugeWidth(sizes[i+1]);
          hull() {
            translate([0, 2 + i * (thickness + 2), 0]) {
              // draw box around current slot
              translate([0, 0, _boxHeight/2]) {
                cube([current_width + wall_thickness/2  + tolerance + 4, wall_thickness * 3 + tolerance, _boxHeight], center=true);
              }

              // draw shorter, larger box around current slot for bevel
              translate([0, 0, (_boxHeight-bevel)/2]) {
                cube([current_width + wall_thickness/2  + tolerance + 4 + bevel * 2, wall_thickness * 3 + tolerance + bevel * 2, _boxHeight-bevel], center=true);
              }
            }

            translate([0,  2 + (i + 1) * (thickness+2), 0]) {
              // draw box around next slot
              translate([0, 0, _boxHeight/2]) {
                cube([next_width + wall_thickness/2 + tolerance + 4, wall_thickness * 3 + tolerance, _boxHeight], center=true);
              }

              // draw shorter, larger box around next slot for bevel
              translate([0, 0, (_boxHeight-bevel)/2]) {
                cube([next_width + wall_thickness/2 + tolerance + 4 + bevel * 2, wall_thickness * 3 + tolerance + bevel * 2, _boxHeight-bevel], center=true);
              }
            }
          }
        }
      }

      // cut out slots for gauges
      for(i=[0:len(sizes)-1]) {
        width = gaugeWidth(sizes[i]);
        slot_y = 2 + i * (thickness + 2) - (thickness + tolerance) / 2;

        difference() {
          translate([-(width/2 + tolerance), slot_y, 4]) {
            cube([width + 2 * tolerance, thickness + 2 * tolerance, _boxHeight], center=false);
          }

          if(friction_fit > 0) {
            translate([-1, slot_y, 4]) {
              cube([2, friction_fit, _boxHeight], center=false);
            }
          }
        }
      }
    }
  }
}

nextGauge(0);
createBox();

```


[User]
Okay, I'm looking to create a customizable, spiraling sphere tube design in OpenSCAD, and I'd like your help building the code from the ground up. I have some specific features in mind, along with parameters to control them.

The basic idea is to generate a tube made up of spheres arranged in an upward spiral. Here's a breakdown of what I want:

*   **Core Structure:** The tube is built from a series of spheres, each incremented in height and rotated slightly to create the spiral effect.
*   **Customizable Parameters:**
    *   `inc`:  This will control the number of spheres (or "increments") along the tube.
    *   `ball_r`: This sets the base radius of the individual spheres.
    *   `tweak_ball_r`: This should allow the sphere radius to be adjusted *without* affecting the spacing of the spheres along the tube, allowing for slight fattening or thinning. This should be a percentage based change in radius.
    *  `tweak_spac`: This allows adjustments to the distance between balls along the tube circumference. It should affect horizontal spacing and is specified as a percentage adjustment.
    *   `shell_off`: A simple toggle (0 or 1) to disable the outer shell.
    *   `shell`: This should determine the radius of the outer "shell" of the design, using the primary `ball_r` as a base value, again specified as a percentage value.
    *   `tube_r`:  This parameter should control the distance of the sphere centers from the center of the tube, effectively controlling the tube's radius.
     *  `inner_edge`: Allows the inside edge to be adjusted, again using a percentage. 0 would result in no inside edge, where 100% would create the largest inside edge.
    *   `tweak_h`: This is similar to `tweak_spac` but it should allow a percentage based adjustment to the spacing in the vertical or 'height' direction.
    *   `flat_bottom`: This should be a toggle to add or remove a flat bottom to the tube (1 for flat, 0 for not).
    *   `add_base`:  This should also be a toggle. If set to 1, and `flat_bottom` is also 1, it should add a base to the tube.

*   **Functional Details**
    *   The spacing between the spheres should be dynamically calculated, so adjusting `ball_r` changes the spacing. I need to adjust the spacing a little, so a percentage adjustment to the distance between balls along the tube circumference is desired via the `tweak_spac` variable.
    *   There should be some degree of ability to adjust the vertical spacing of the balls, independent of the horizontal, via the `tweak_h` variable, again as a percentage.
    * The 'shell' should form a solid outer layer that can be toggled on and off, and its size is specified as a percentage.
    *   If flat_bottom is enabled, I need a way to create that flat bottom, and if `add_base` is enabled, it should add a solid disk at the base as well.

I'm looking for the code to be well-commented for readability. I don't need any specific library functions for this. Let me know if you have any questions.

[Assistant]
Sphere_tube_03_customizer.scad:
```
$fn         = 30; //smooth global
inc         = 80; //inraments i.e number of balls
tube_r      = 31; //distance of ball from center
ball_r      = 10; //ball radius, change will auto update ball spacing
tweak_ball_r= 4; //changes ball radius without altering spacing
tweak_spac  = 65;//0-100%
shell_off   = 0;//0=off 1=on (set to off to speed up preview)
shell       = 75; //0-100%
inner_edge  = 50;//0-100%. 0=no hard inner edge
tweak_h     = 64;//-(ball_r/2);
flat_bottom = 1;//gives tube a flat bottom
add_base    = 1;//0=dont add base, 1=add base. flat_bottom must also =1.

/************* Publication Notes **************/{/*

Customizable Sphere Tube/Cup   by  SavageRodent
Original at: https:www.thingiverse.com/thing:3802943
Last updated: 10/08/2019
Published under: the Creative Commons CC - BY 3.0 licence
Licence details here: https://creativecommons.org/licenses/by/3.0/
OpenSCAD version 2019.05
*/}

/******************* Other ********************/{
/*/Derivative Variable:*/{
ball_d  = ball_r*2;
tube_d  = tube_r*2;

//distance between balls along tube cecomfrance
spacing_c   = (ball_d*.4)+ per(ball_d*1, 0, con(1, 100, tweak_spac));
spacing_h   = (ball_d*.3)+ per(ball_d*.7, 0, con(1, 100, tweak_h));
b_rad       = ball_r + per(ball_r, 0, con(1, 100, tweak_ball_r));

rot_ball    = angle_A(spacing_c,tube_r);
base_thick  = 2;
}
//echo("b_rad = ",b_rad);
//echo("spacing_c = ",spacing_c);
//echo("spacing_h = ",spacing_h);
//echo("Angle of rotation per inc = ",angle_A(ball_r,tube_r));
}

/******************* Render *******************/{

ball_spiral_pluss(inc,b_rad);

}
/****************** Modules *******************/{
module ball_spiral_pluss(incraments,b_rad){
//shell
difference(){
//cut inner edge
difference(){
//flat bottom y or n
if(flat_bottom==1){
    difference(){
    ball_spiral(incraments,b_rad);
    bottom(base_thick, sub_add=0);//crop bottom
    }
    }
    else{
    ball_spiral(incraments,b_rad);
    }
cylinder(r=(tube_r-(b_rad))+per((b_rad*2),1,con(0,2000,inner_edge)), h=200, $fn=80);
}
if(shell>0 && shell_off==1){
ball_spiral(incraments,per(b_rad, 0, con(0,95,shell)));
}
}

//add_base y or n
if(add_base==1&&flat_bottom==1){
    bottom(base_thick, sub_add=1);
    }
}
/*
#translate([0,0,-1000])
    cylinder(r=(tube_r-(b_rad))+per((b_rad*2),1,con(0,2000,inner_edge)), h=200, $fn=80);
*/

module ball_spiral(incraments,ball_rad){
for(i=[0:incraments]){
    //height
    translate([0,0,((spacing_h)/(360/rot_ball))*i])
    rotate([0,0,rot_ball*i])
    translate([tube_r,0,0])
    sphere(r=ball_rad);
    }
}

//sub_add=0 (creates shape to cut from bottom.  sub_add=1 (creates base plate)
module bottom(base_thick, sub_add){
//remove bottom
if(sub_add==0){
translate([0,0,-b_rad])
cylinder(r=tube_d, h=b_rad*2);
}
else
//create base
intersection(){
union(){
translate([0,0,b_rad])
cylinder(r=tube_r*1.01, h=base_thick, $fn=80);
ball_spiral(720/rot_ball,b_rad);
}
translate([0,0,b_rad])
cylinder(r=tube_d, h=base_thick);
}
}

/*Modules End*/}

/***************** Functions ******************/{
function per(val,inv,input)=
inv==0 || inv==undef ? (val/100)*input :
    val-((val/100)*input);

function con(mi, mx, input)=
input > mi && input < mx ? input :
    input < mi ? mi : mx;

function c(a,b)=//side c
sqrt(pow(a,2)+pow(b,2));

function angle_A(a,b)=//this is the angle the ball will rotate each inc.

acos(((b*b)+(c(a,b)*c(a,b))-(a*a))/(2*b*c(a,b)));

}
```
Sphere_tube_03_pub.scad:
```
/************* Publication Notes **************/{/*

Customizable Sphere Tube/Cup   by  SavageRodent
Original at: https:www.thingiverse.com/thing:3802943
Last updated: 10/08/2019
Published under: the Creative Commons CC - BY 3.0 licence
Licence details here: https://creativecommons.org/licenses/by/3.0/
OpenSCAD version 2019.05
*/}

/********** CUSTAMIZABLE PERAMITORS ***********/{
$fn         = 30; //smooth global
inc         = 120; //inraments i.e number of balls
ball_r      = 10; //ball radius, change will auto update ball spacing
tweak_ball_r= 0; //changes ball radius without altering spacing
tweak_spac  = 79;//0-100%
shell_off   = 1;//0=off 1=on (set to off to speed up preview)
shell       = 70; //0-100%
tube_r      = 35; //distance of ball from center
inner_edge  = 50;//0-100%. 0=no hard inner edge
tweak_h     = 55;//-(ball_r/2);
flat_bottom = 1;//gives tube a flat bottom
add_base    = 1;//0=dont add base, 1=add base. flat_bottom must also =1.
}
/******************* Other ********************/{
/*/Derivative Variable:*/{
ball_d  = ball_r*2;
tube_d  = tube_r*2;

//distance between balls along tube cecomfrance
spacing_c   = (ball_d*.4)+ per(ball_d*.6, 0, con(1, 100, tweak_spac));
spacing_h   = (ball_d*.3)+ per(ball_d*.7, 0, con(1, 100, tweak_h));
b_rad       = ball_r + per(ball_r, 0, con(1, 100, tweak_ball_r));

rot_ball    = angle_A(spacing_c,tube_r);
base_thick  = 2;
}
//echo("b_rad = ",b_rad);
//echo("spacing_c = ",spacing_c);
//echo("spacing_h = ",spacing_h);
//echo("Angle of rotation per inc = ",angle_A(ball_r,tube_r));
}

/******************* Render *******************/{

ball_spiral_pluss(inc,b_rad);

}
/****************** Modules *******************/{
module ball_spiral_pluss(incraments,b_rad){
//shell
difference(){
//cut inner edge
difference(){
//flat bottom y or n
if(flat_bottom==1){
    difference(){
    ball_spiral(incraments,b_rad);
    bottom(base_thick, sub_add=0);//crop bottom
    }
    }
    else{
    ball_spiral(incraments,b_rad);
    }
cylinder(r=(tube_r-(b_rad))+per((b_rad*2),1,con(0,2000,inner_edge)), h=200, $fn=80);
}
if(shell>0 && shell_off==1){
ball_spiral(incraments,per(b_rad, 0, con(0,95,shell)));
}
}

//add_base y or n
if(add_base==1&&flat_bottom==1){
    bottom(base_thick, sub_add=1);
    }
}
/*
#translate([0,0,-1000])
    cylinder(r=(tube_r-(b_rad))+per((b_rad*2),1,con(0,2000,inner_edge)), h=200, $fn=80);
*/

module ball_spiral(incraments,ball_rad){
for(i=[0:incraments]){
    //height
    translate([0,0,((spacing_h)/(360/rot_ball))*i])
    rotate([0,0,rot_ball*i])
    translate([tube_r,0,0])
    sphere(r=ball_rad);
    }
}

//sub_add=0 (creates shape to cut from bottom.  sub_add=1 (creates base plate)
module bottom(base_thick, sub_add){
//remove bottom
if(sub_add==0){
translate([0,0,-b_rad])
cylinder(r=tube_d, h=b_rad*2);
}
else
//create base
intersection(){
union(){
translate([0,0,b_rad])
cylinder(r=tube_r*1.01, h=base_thick, $fn=80);
ball_spiral(720/rot_ball,b_rad);
}
translate([0,0,b_rad])
cylinder(r=tube_d, h=base_thick);
}
}

/*Modules End*/}

/***************** Functions ******************/{
function per(val,inv,input)=
inv==0 || inv==undef ? (val/100)*input :
    val-((val/100)*input);

function con(mi, mx, input)=
input > mi && input < mx ? input :
    input < mi ? mi : mx;

function c(a,b)=//side c
sqrt(pow(a,2)+pow(b,2));

function angle_A(a,b)=//this is the angle the ball will rotate each inc.

acos(((b*b)+(c(a,b)*c(a,b))-(a*a))/(2*b*c(a,b)));

}
```