[User]
I'd like to create a configurable game board similar to the Cublino board, but with some important differences in how the grid is created and how the frame interacts with it.

Here's a breakdown of what I need:

**Core Game Board:**

*   **Grid:** I need a grid of squares, where both the number of squares in the X direction and the number of squares in the Y direction are configurable.
*   **Square Size:** The side length of each individual square in the grid needs to be configurable.
*   **Dividers:** There should be dividers between each square in the grid, with a configurable width and height.
*   **Base:** The game board should have a solid base beneath the grid and dividers, with a configurable thickness.
*   **Overall Size:** The overall size of the board should be determined by the number of spaces, their size, and the width of the dividers.
*   **Grid Generation:** Instead of using `translate` for each square in a nested loop, I'd like you to generate the spaces and the grid itself as a 2D array of cubes (and corresponding dividers) using `linear_extrude`.

**Frame:**

*   **Frame Option:** I need an option to include a frame around the outer edge of the game board.
*   **Frame Width & Height:** Both the width and height of the frame need to be configurable.
*   **Frame Construction:** The frame must be generated using linear extrusion. The corners of the frame should be *rounded* using a union with cylinders, not just using a box.

**Parametric Design:**

*   I need all of the above properties to be configurable using OpenSCAD variables. I'd like to be able to change the number of squares in each direction, the size of the squares, the dimensions of the dividers, the thickness of the base, whether to include a frame, and the dimensions of the frame.
*   I want everything to be parameterized. Specifically, all calculations should be done based on a user-supplied parameters for space size, divider size, board thickness and frame size as described in this query. You should be generating the complete size of the grid from these values.

**Libraries:**

*   I'd prefer the design to not use any external libraries if possible.
*   If using an external library for some simple operations makes the code more readable, consider using BOSL2 but please let me know which features are used.

**Output:**

*   I'd like a single .scad file containing all of this design. Please ensure it includes clear comments explaining what is happening and which variables control what aspect of the design.

[Assistant]
Cublino_Board_Creator_V2.scad:
```
/* [Gameboard Creator (all measurments are in millimeters)] */

// How many spaces on the board?
spaces_x = 4; // [1:100]
spaces_y = 4; // [1:100]

// The size of the spaces
spaces_size = 13; // [0.1:0.05:100]

// Dividers
// The width of the Dividers
divider_width = 1; // [0.1:0.05:100]
// Height of the Dividers
divider_height = 1.5; // [0.1:0.05:100]

// Height of the gameboard
board_bottom_thickness = 1; // [0.1:0.05:100]

// Frame
// Only grid or a frame as well?
frame = true; // [true,false]
frame_width = 2;  // [0.1:0.05:100]
frame_height = 2;  // [0.1:0.05:100]

/* [hidden] */
spaces_complete = spaces_size + divider_width;

// Size of the board
board_size_w =
    spaces_x * ( spaces_size + divider_width ) + divider_width;
board_size_l =
    spaces_y * ( spaces_size + divider_width ) + divider_width;

union() {
    difference() {
        // Board base
        color("orange")
        cube(
            [
                1 + board_size_w,
                1 + board_size_l,
                divider_height
            ],
            true );

        // Spaces
        for( y = [ 0 : spaces_y - 1 ] ) {
            for( x = [ 0 : spaces_x - 1 ] ) {
                // Create one space
                color("blue")
                translate(
                    [
                        ( -( spaces_x / 2 ) + x ) *
                          spaces_complete + spaces_complete / 2,

                        ( -( spaces_y / 2 ) + y ) *
                          spaces_complete + spaces_complete / 2,

                        0
                    ])
                    {
                        cube(
                            [
                                spaces_size,
                                spaces_size,
                                divider_height + .01
                            ],
                            true);
                    }
            }
        }
    }

    // Bottom
    color("red")
    translate(
        [
            0,
            0,
            -( board_bottom_thickness + divider_height ) / 2
        ]
    )
    cube(
        [
            1 + board_size_w,
            1 + board_size_l,
            board_bottom_thickness
        ],
        center=true );

    // Frame
    if(frame) {
        translate( [
            0,
            0,
            -( board_bottom_thickness + divider_height ) / 2 - board_bottom_thickness / 2 + frame_height / 2
        ] )
        union() {
            // Edges
            translate(
                [
                    board_size_w / 2 + frame_width / 2,
                    0,
                    0
                ]
            )
            cube(
                [
                    frame_width,
                    board_size_l + frame_width,
                    frame_height,
                ],
                true );

            translate(
                [
                    -board_size_w / 2 - frame_width / 2,
                    0,
                    0
                ]
            )
            cube(
                [
                    frame_width,
                    board_size_l + frame_width,
                    frame_height,
                ],
                true );

            translate(
                [
                    0,
                    board_size_l / 2 + frame_width / 2,
                    0
                ]
            )
            cube(
                [
                    board_size_w + frame_width,
                    frame_width,
                    frame_height,
                ],
                center=true );

            translate(
                [
                    0,
                    -board_size_l / 2 - frame_width / 2,
                    0
                ]
            )
            cube(
                [
                    board_size_w + frame_width,
                    frame_width,
                    frame_height,
                ],
                center=true );

            // Corners
            translate(
                [
                    board_size_w / 2 + frame_width / 2,
                    board_size_l / 2 + frame_width / 2,
                    0
                ]
            )
            cylinder(
                    h = frame_height,
                    r1 = frame_width / 2,
                    r2 = frame_width / 2,
                    center = true,
                    $fn = 100);

            translate(
                [
                    -board_size_w / 2 - frame_width / 2,
                    board_size_l / 2 + frame_width / 2,
                    0
                ]
            )
            cylinder(
                    h = frame_height,
                    r1 = frame_width / 2,
                    r2 = frame_width / 2,
                    center = true,
                    $fn = 100);

            translate(
                [
                    board_size_w / 2 + frame_width / 2,
                    -board_size_l / 2 - frame_width / 2,
                    0
                ]
            )
            cylinder(
                    h = frame_height,
                    r1 = frame_width / 2,
                    r2 = frame_width / 2,
                    center = true,
                    $fn = 100);

            translate(
                [
                    -board_size_w / 2 - frame_width / 2,
                    -board_size_l / 2 - frame_width / 2,
                    0
                ]
            )
            cylinder(
                    h = frame_height,
                    r1 = frame_width / 2,
                    r2 = frame_width / 2,
                    center = true,
                    $fn = 100);
        }
    }
}
```


[User]
Hey, I'm working on designing custom center caps for my wheels, and I'm trying to get the base shape right. I've got some initial dimensions I've been playing with, but I'd really like a flexible OpenSCAD design that I can easily tweak.

Here's what I'm after:

The cap will have a main face that's a frustum (a cone with the top cut off) shape. I'll need to define the top radius (`capfaceradtop`), the bottom radius (`capfaceradbot`), and the thickness (`capfacethick`).

Then, there's a cylindrical "leg" that fits into the wheel. This needs a radius (`caplegrad`) and height (`caplegthick`). It should be attached to the bottom of the frustum.

Finally, I need a simple clip at the top and bottom of the "leg".  The top clip should have a small overhang inwards, and the bottom clip should have an overhang outwards. I don't need specific variables for the clip dimensions, just something simple, maybe with a small chamfer.

I'd like to have the ability to remove three "slicers" that can help prevent printing issues with bridging on the bottom. These would be three rectangular cuts going from the inside of the leg, extending through the outside of the leg and the frustrum. They should be evenly distributed, so 120 degrees from each other. The size of these should be able to be set using a length (`slicerlength`), width (`slicerwidth`), and height (`slicerheight`).

I'd like all these values to be easily changeable variables at the top of the file.

Could you create an OpenSCAD file that does all of that? I don't have any special requirements about which libraries to use, so just use what makes sense to you for this design.

[Assistant]
center_cap.scad:
```
// @pabile 20190514
// Cover wheel center cap - Parametric
// comments, questions, suggestions and tips may be sent to pabile@gmail.com

capfaceradtop = 30; // cap face radius. radius of top most cover
capfaceradbot = 34; // cap face radius. radius of top most cover

capfacethick = 5; // cap face thickness
caplegrad = 31; // cap leg radius. radius of wheel center where the cap will placed
caplegthick = 10; // cap leg thickness/height
// clip radius = caplegrad + 1

slicerlength = caplegrad*3;
slicerwidth = 5;
slicerheight = caplegthick*2;

difference() {
    union() {
        // face
        cylinder(h=capfacethick, r1=capfaceradtop, r2=capfaceradbot, center=false, $fn=64);

        // leg
        translate ([0,0,capfacethick]) cylinder(h=caplegthick, r=caplegrad, center=false, $fn=64);

        // clip top
        translate ([0,0,caplegthick+capfacethick+2])
        cylinder(h=3, r1=caplegrad+1.5, r2=caplegrad-2, center=false);
        //clip bottom
        translate ([0,0,caplegthick+capfacethick])
        cylinder(h=2, r1=caplegrad, r2=caplegrad+1.5, center=false);

    }
    // inner cylinder
    translate ([0,0,capfacethick])
    cylinder(h=caplegthick*.75, r1=caplegrad-4, r2=caplegrad-1.5, center=false);
    translate ([0,0,capfacethick+caplegthick*.75])
    cylinder(h=caplegthick, r=caplegrad-1.5, center=false);

    //slicers
    translate ([-slicerlength/2,-slicerwidth/2,capfacethick])
    cube (size = [slicerlength,slicerwidth,slicerheight]);

    rotate(120) translate ([-slicerlength/2,-slicerwidth/2,capfacethick])
    cube (size = [slicerlength,slicerwidth,slicerheight]);

    rotate(-120) translate ([-slicerlength/2,-slicerwidth/2,capfacethick])
    cube (size = [slicerlength,slicerwidth,slicerheight]);

}

```


[User]
Hey, I'm looking to get a custom pen holder designed. I've seen a few online, but I'd really like one that fits my finger and a specific pen size, and I want to make sure it prints without needing supports.

Basically, it needs to be a vertical pen holder that you can slide onto your finger. The design should have a hole for a finger and another for the pen, with a connecting piece between them. I'd like to be able to specify the exact diameter of the finger hole and the pen hole. For the finger hole, I'm thinking that it would be a partial circle, missing a segment on one side, and similar for the pen hole. I think having a "fillet" or a smooth curve connection the two holes would help with structural stability.

Also, the height of the pen-holding part should be shorter than the finger-holding section, with a sloped or angled connection between the two. It should have a flat base for printing. I'd like the ability to adjust the overall height, too. Finally, I'd like the design to have a sort of vertical cutout on the sides, like a rectangular block with some material removed to give it a more unique shape, and also to remove weight and material.

I'm planning on using a 3D printer so I need it to be a solid model. Is that something you can help with? I have OpenSCAD, and I know that it is a parametric design language so it would be great if the dimensions could be customized by changing variables at the top of the file. Let me know what you think, thanks! I don't think I'd need any special libraries or anything.

[Assistant]
Parametric_Finger_Pen_Holder_Vertical-No_Support.scad:
```
// parametric finger pen holder, remix for MMC
// of their https://www.thingiverse.com/thing:2802074
// modified for no support - prints quicker on Prusa
// scruss - 2019-05
// update 2020-03 to remove warnings in code
// *** All dimensions millimetres because of course they are ***

//CUSTOMIZER VARIABLES

// Measured finger diameter, mm
finger_d = 17.0; // [6.0:0.5:25.0]
// Measured pen diameter, mm
pen_d = 11.0; // [6.0:0.5:25.0]

// CUSTOMIZER VARIABLES END

module naff() { }       // to make Customizer look no further

// fixed design parameters
$fn = 64;	            // OpenSCAD arc smoothness: fairly high
finger_wall = 2.0;		// wall thickness, finger side
pen_wall = 1.5;			// wall thickness, pen side
overall_height = 18;	// total height of holder
pen_height = 10;		// height of (shorter) pen holder
bar = 0.75 * pen_d;		// length of separator between finger and pen
pen_centre_x = bar + (pen_d + finger_d) / 2; // x-coord of centre of pen
finger_cut_angle = 50;	// angle cut out from finger side, degrees
pen_cut_angle = 60;		// angle cut out from pen side

// length - which we need for the side details - depends on
//  the segments we left out of the finger and pen side
overall_length = ((finger_d / 2) + finger_wall) * cos(finger_cut_angle / 2) + pen_centre_x + ((pen_d / 2) + pen_wall) * cos(pen_cut_angle / 2);
// model isn't symmetrical, so we need to calculate minimum
//  coord for correct placement
min_x = 0 - ((finger_d / 2) + finger_wall) * cos(finger_cut_angle / 2);

/*  sine rule fillet - scruss 2018-06
    circle radius r1, centre at origin
    circle radius r2, centre at [x, 0]
  requires
    fillet radius (x - r1)
    centre *polar* coords [ x, 2 * asin((r2 + x - r1) / (2 * x)) ]
*/
module sine_fillet(r1 = 20, r2 = 10, x = 40) {
    angle = 2 * asin((r2 + x - r1) / (2 * x));
    difference() {
        polygon([
            [0, 0],
            [x * cos(-angle), x * sin(-angle)],
            [x, 0],
            [x * cos(angle), x * sin(angle)]
        ]);
        union() {
            translate([x * cos(angle), x * sin(angle)]) {
                circle(r = x - r1);
            }
            translate([x * cos(-angle), x * sin(-angle)]) {
                circle(r = x - r1);
            }
        }
    }
}

// generate two circles with fillet web between them
module filleted_circles(r1 = 20, r2 = 10, x = 40) {
    union() {
        sine_fillet(r1, r2, x);
        circle(r = r1);
        translate([x, 0])circle(r = r2);
    }
}

// cut a triangular segment out of a circle origin 0,0
module segment(start_angle  = -30,
               end_angle    =  30,
               radius       =  10) {
    scale(radius)polygon([
                   [0,                 0],
                   [cos(start_angle),  sin(start_angle)],
                   [cos(end_angle),    sin(end_angle)]
    ]);
}

// 2D model of the finger and pen holes, XY plane
module plan_outline() {
    // positive then negative offset results in smoothed corners
    offset(r=0.5)offset(r=-0.5)difference() {
        filleted_circles((finger_d / 2) + finger_wall, (pen_d / 2) + pen_wall, pen_centre_x);
        // this union is the finger and pen holes
        union() {
            circle(d=finger_d);
            segment(180 - finger_cut_angle / 2, 180 + finger_cut_angle / 2, finger_d);
            translate([pen_centre_x, 0]) {
                circle(d=pen_d);
                segment(-pen_cut_angle / 2, pen_cut_angle / 2, pen_d);
            }
        }
    }
}

// 2D model of the vertical profile, XZ plane
module elevation_outline() {
    // again with the offset ... offset smoothing
    offset(r=2)offset(r=-2)translate([min_x, -overall_height / 2]) {
        difference() {
            // side profile is basically a rectangle ...
            square([overall_length, overall_height]);
            union() {
                // ... less a rounded relief out the TR corner for pen
                translate([finger_d + 2 * finger_wall + overall_height - pen_height, overall_height])hull() {
                    circle(r=overall_height - pen_height);
                    translate([finger_d, 0])circle(r=overall_height - pen_height);
                }
                // ... also less a rounded gap in the finger grip
                // translate([-finger_d / 6, overall_height / 3])offset(r=1)offset(r=-1)square([finger_d, overall_height / 3]);
            }
        }
    }
}

// intersect extrusions of the 2D profiles at 90 degrees to make model
intersection() {
    linear_extrude(height=overall_height, center=true)plan_outline();
    rotate([90, 0, 0]) {
        linear_extrude(height=2 * overall_height, center=true)elevation_outline();
    }
}

```


[User]
Hi there! I'm looking for help creating a parametric Braille generator in OpenSCAD. I've been trying to make something similar to what's already out there, but I'd like a more flexible and robust solution. I want to be able to input a text string, and have it generate a 3D printable model where each letter is represented in braille with raised dots.

Here’s the basic idea:

*   **Input:** A text string (e.g., "Hello World").
*   **Output:** A 3D model of a series of braille cells, each representing a character in the input string, arranged horizontally.
*   **Braille Representation:**  Each character should be translated into its corresponding braille pattern using a standard 6-dot braille cell. The dot positions should be based on standard braille configurations.
*   **Layout:** The cells should be arranged left-to-right with a configurable gap between them.
*   **Base Plate:** I would like a base plate behind the braille cells, for structural integrity. This base plate will also have configurable dimensions.
*   **Dimensions:** All dimensions (cell width, height, depth, dot radius, gaps, plate thickness, etc.) should be configurable as parameters.
*   **Character Support:**  I’d like to support at least basic alphabet (A-Z, a-z), numbers (0-9), and common punctuation marks (!, ., space, -).

I'd also like these specific parameters:

*   `cell_width`: Width of a single braille cell.
*   `cell_height`: Height of a single braille cell.
*   `cell_depth`: Depth of a single braille cell.
*   `dot_radius`: Radius of a single braille dot.
*   `row_margin`: Margin between the top/bottom of the braille dots within the cell and the cell's edges.
*   `column_margin`: Margin between the sides of the braille dots within the cell and the cell's edges.
*   `row_spacing`: Space between the two rows of dots within the cell.
*    `column_spacing`: Space between the three columns of dots within the cell.
*   `cell_gap`: Gap between braille cells
*   `plate_height`: Height of base plate behind the braille cells.
*    `plate_depth`: Depth of base plate behind the braille cells.
*   `base_color`: Color of the base plate
*   `cell_color`: Color of the braille cell
*   `dot_color`: Color of the braille dots.

I'd like to specify the `BRAILLE_ALPHABET` as a lookup table within the design. This table would map characters to the 6-dot braille array (true for raised dots). I think I can handle this part in OpenSCAD if needed, or we can go over it.

I'd prefer if the design used no external libraries if possible, but I'm okay with it if you think something like BOSL is necessary to make things more organized and less cluttered. I'm comfortable with either approach, but I'd like to try the least dependent approach first.

Let me know if you have any questions, and thank you in advance for your help!

[Assistant]
BrailleGenerator.scad:
```
// =======================================================
// AUTHOR        : Jose Lopez, JoLoCity, LLC
// DATE          : 20190515
// DESCRIPTION   : Braille generator for 3d printing
// VERSION       : 1.0
// =======================================================
// word to display
PHRASE = "ABCDE";

/* [Dimensions] */
// tablet height
biHeight = 25;
// tablet width
biWidth = 15;
// tablet depth
biDepth = 5;

// tablet gap
tbtGap = 2;

// button radius
biRadius = 2;

// row margin
biSpaceA = 4;
// row spacing
biSpaceB = biWidth - (biSpaceA*2);

// column margin
biSpaceX = 4;
// column spacing;
biSpaceY = (biHeight - (biSpaceX*2))/2;
/* [Colors] */
//back base color
baseColor = [0,0,0]; //[0:0.1:1]

//tablet color
tbtColor = [1.0,1.0,1.0]; //[0:0.1:1]

// Item color
biColor = [0.5,1.0,0.5]; //[0:0.1:1]

/* [Other] */
//braille alphabet
BRAILLE_ALPHABET = [
    [false, false, false, false, true, false] //A
    , [false, false, true, false, true, false] //B
    , [false, false, false, false, true, true] //C
    , [false, false, false, true, true, true] //D
    , [false, false, false, true, true, false] //E
    , [false, false, true, false, true, true] //F
    , [false, false, true, true, true, true] //G
    , [false, false, true, true, true, false] //H
    , [false, false, true, false, false, true] //I
    , [false, false, true, true, false, true] //J
    , [true, false, false, false, true, false] //K
    , [true, false, true, false, true, false] //L
    , [true, false, false, false, true, true] //M
    , [true, false, false, true, true, true] //N
    , [true, false, false, true, true, false] //O
    , [true, false, true, false, true, true] //P
    , [true, false, true, true, true, true] //Q
    , [true, false, true, true, true, false] //R
    , [true, false, true, false, false, true] //S
    , [true, false, true, true, false, true] //T
    , [true, true, false, false, true, false] //U
    , [true, true, true, false, true, false] //V
    , [false, true, true, true, false, true] //W
    , [true, true, false, false, true, true] //X
    , [true, true, false, true, true, true] //Y
    , [true, true, false, true, true, false] //Z
    , [false, false, false, false, true, false] //Accent
    , [true, false, false, false, false, false] //Apostrophe
    , [false, false, false, false, false, false] //Space
    , [true, true, false, false, false, false] //-
    , [false, false, true, false, false, false] //,
    , [true, false, true, false, false, false] //;
    , [false, false, false, true, true, false] //:
    , [false, true, true, true, false, false] //.
    , [true, true, true, false, false, false] //?
    , [true, false, true, true, false, false] //!
    , [true, true, true, true, false, false] //()
    , [true, true, false, true, false, true] //Number
    , [false, true, false, false, false, false] //Capital
    , [false, true, false, true, false, false] //Letter
    , [false, false, true, true, false, true] //0
    , [false, false, false, false, true, false] //1
    , [false, false, true, false, true, false] //2
    , [false, false, false, false, true, true] //3
    , [false, false, false, true, true, true] //4
    , [false, false, false, true, true, false] //5
    , [false, false, true, false, true, true] //6
    , [false, false, true, true, true, true] //7
    , [false, false, true, true, true, false] //8
    , [false, false, true, false, false, true] //9
];

showBackPiece();
showWord(PHRASE);

module showBackPiece() {
    translate([0,3,0])
        color(baseColor)
            cube([((biWidth+tbtGap)*len(PHRASE))-tbtGap,biDepth,biHeight],false);
}
module showWord(word) {
    for(pos = [0:len(word)-1]){
        echo(ord(word[pos]));
        // translate character to braille alphabet
        charValue = ord(word[pos]);

        // 0-9 < TODO must prefix
        if((charValue>=48)&&(charValue<=57)) {
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[charValue-8]);
        }
        // A-Z
        if((charValue>=65)&&(charValue<=90)) {
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[charValue-65]);
        }
        // a-z
        if((charValue>=97)&&(charValue<=122)) {
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[charValue-97]);
        }
        // space
        if(charValue==32){
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[28]);
        }
        // -
        if(charValue==45){
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[29]);
        }
        // .
        if(charValue==46){
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[33]);
        }
        // !
        if(charValue==33){
            translate([pos*(biWidth+tbtGap), 0, 0])
                showBrailleItem(BRAILLE_ALPHABET[35]);
        }
    }
}

module showBrailleItem(letterArray) {
    // back plate
    color(tbtColor)
        cube([biWidth,biDepth,biHeight],false);

    translate([biSpaceA,0,biSpaceX])
    for (rowId = [0:1:1]){
        // column from bottom to top
        for (colId = [0:1:2]){
            if(letterArray[((colId*2)+rowId)]==true) {
                translate([rowId*biSpaceB,0,biSpaceY*colId])
                    color(biColor)
                        sphere(biRadius, $fn=32);
            }
        }
        translate([biSpaceB,0,0]);
    }
}

```


[User]
Okay, I'm looking to generate a mobile design, something that can be 3D printed or laser cut. I have some specific ideas about the structure and how it should be built, and I'm hoping you can help me create an OpenSCAD file to do it parametrically.

Basically, I need to generate a series of beams that are connected by wires, with objects of different weights hanging from the lower levels. The whole thing needs to be balanced, of course.

Here's how I envision the structure:
*   **Beams:** The beams are rectangular with rounded ends, and each beam has three holes drilled through it; one at each end and one in the middle.
*   **Hierarchy:** Beams are arranged in a hierarchical structure, with longer beams at the top and shorter ones below, branching out to accommodate the hanging weights. Each level down uses beams that are a percentage shorter than the beam above.
*   **Weights:** I will define a list of weights and their labels, and the program needs to calculate the appropriate fulcrum points of each beam based on these weights (and the weight of the beams themselves) to achieve balance. The fulcrum will be the center wire of each beam.
*   **Params:** I need to control the following parameters:
    *   Length of the longest beam
    *   Width of beams
    *   Thickness of beams
    *   Diameter of the wire holes
    *   The percentage of reduction in beam length for child beams
    *   The density of the material the beams are made from
    *   The mass of the connecting wires, which is assumed to be the same for every connection
    *   The weights and names of the objects to be hung from the mobile
*   **Output:** Ideally, the program should output two things:
    *   A 3D model of just the beams for printing
    *   Assembly instructions that can be printed and used for the assembly by including the names of the hanging objects and a tree structure.

The calculation for the fulcrum point on a beam should take into account the weight of objects hanging from either side, the weight of the beam itself, and the weight of the wires connecting it. The formula for the fulcrum (as a fraction of beam length from the left) will be: (wire\_mass+b+m/2)/(2\*wire\_mass+a+b+m), where 'a' is the total weight of the beam on the left, 'b' is the total weight of the beam on the right, and 'm' is the weight of this beam.

The calculations should recurse down the tree. That is, the weight of a left child is the sum of its weights, beam, and wires. The base case for that recurrence would be individual objects.

I'm not sure which OpenSCAD libraries are best to use for this, but I'd like to keep it pretty simple and avoid using anything too complicated. I expect that all of the code will have to be generated from scratch. Could you provide me with the complete OpenSCAD code, including any modules, functions, and global parameters needed to generate this mobile?

[Assistant]
MobileBeamGenerator.scad:
```
// Mobile Beam Generator
//   by Michael Van Biesbrouck, (c) 2019.
//   License: Attribution 4.0 International
//            https://creativecommons.org/licenses/by/4.0/
//
// First published 17 May 2019 in honour of my niece Daria's birth.

// preview[view:south, tilt:top]
/* [Global] */
// You probably want to print BeamsOnly and look at AssemblyInstructions on a computer.
part = "AssemblyInstructions"; // [AssemblyInstructions, BeamsOnly]
/* [General Configuration] */
// Length of largest beam in mm.
beam_length = 100;      // [50:300]
// Width of beams in mm.
beam_width = 5;         // [3:25]
// Thickness of beams in mm.
beam_thickness = 2;     // [1:0.5:10]
// Diameter of wire holes in mm.
hole_diameter = 2;      // [1:0.5:10]
// Percentage length of child beams.
beam_length_decay = 80; // [50:100]
// Density in g/cm^3.  Default is for PLA with 100% infill.
filament_density = 1.25;// [0:0.01:10]
// Mass of each connecting wire in g; use 0 for light wire or thread.
wire_mass = 0;          // [0:0.1:10]
/* [Weights (with labels) for hanging objects] */
// Weight in g of first object.
weight_1 = 10; // [0:0.1:100]
// Name used for first object in assembly instructions.
weight_1_name = "1";
weight_2 = 20; // [0:0.1:100]
weight_2_name = "2";
weight_3 = 0; // [0:0.1:100]
weight_3_name = "3";
weight_4 = 0; // [0:0.1:100]
weight_4_name = "4";
weight_5 = 0; // [0:0.1:100]
weight_5_name = "5";
weight_6 = 0; // [0:0.1:100]
weight_6_name = "6";
weight_7 = 0; // [0:0.1:100]
weight_7_name = "7";
weight_8 = 0; // [0:0.1:100]
weight_8_name = "8";
weight_9 = 0; // [0:0.1:100]
weight_9_name = "9";
weights = [
[weight_1_name, weight_1],
[weight_2_name, weight_2],
[weight_3_name, weight_3],
[weight_4_name, weight_4],
[weight_5_name, weight_5],
[weight_6_name, weight_6],
[weight_7_name, weight_7],
[weight_8_name, weight_8],
[weight_9_name, weight_9],
];

eps = 0 + 0.000001;
pi = 3.14159265358979323846 + 0;
row_delta = beam_width + 5;
$fn = 75 + 0;

beam_separation = beam_length - beam_width;
beam_mass = 0.001 * filament_density * beam_thickness * (beam_separation*beam_width + pi/4 * (pow(beam_width, 2) - 3*pow(hole_diameter, 2)));

module beam (separation, fulcrum, description) {
    difference () {
        union () {
            cube ([separation, beam_width, beam_thickness], center=true);
            translate ([separation/2, 0, 0]) cylinder (h=beam_thickness, d=beam_width, center=true);
            translate ([-separation/2, 0, 0]) cylinder (h=beam_thickness, d=beam_width, center=true);
        }
        translate ([separation/2, 0, 0]) cylinder (h=beam_thickness+1, d=hole_diameter, center=true);
        translate ([-separation/2, 0, 0]) cylinder (h=beam_thickness+1, d=hole_diameter, center=true);
        translate ([separation*(fulcrum-0.5), 0, 0]) cylinder (h=beam_thickness+1, d=hole_diameter, center=true);
    }
    if (part == "AssemblyInstructions" && len(description) > 0) translate ([separation/2+beam_width+5, 0, -beam_thickness/2]) linear_extrude(height=1) text(text=description, size=beam_width, halign="left", valign="center");
}

function find_fulcrum(a, b, m) = (wire_mass+b+m/2)/(2*wire_mass+a+b+m);

function build_node_int(label, a, b, separation, beam_mass) =
    [label, a[1]+b[1]+beam_mass+wire_mass*2, a, b, separation, find_fulcrum(a[1], b[1], beam_mass), str(label,"=",a[0],"+",b[0])];

function build_node(label, cur_length, a, b) =
    build_node_int(label, a, b, cur_length-beam_width, 0.001 * filament_density * beam_thickness * ((cur_length-beam_width)*beam_width + pi/4 * (pow(beam_width, 2) - 3*pow(hole_diameter, 2))));

function sublist(list, start, end) = [for (i = [start:end]) list[i]];

function rec_combine(node_list, split, cur_length, new_length, label) =
    build_node (label, cur_length,
        combiner(sublist(node_list, 0, split-1), new_length, str(label, "L")),
        combiner(sublist(node_list, split, len(node_list)-1), new_length, str(label, "R")));

function combiner (node_list, cur_length, label) =
    len(node_list) == 1 ? node_list[0] :
        rec_combine(node_list, floor(len(node_list)/2), cur_length, cur_length*beam_length_decay/100, label);

function count_beams (subtree) = len(subtree) == 2 ? 0 : 1+count_beams(subtree[2])+count_beams(subtree[3]);

module render_tree(subtree) {
    if (len(subtree) > 2) {
        beam (subtree[4], subtree[5], subtree[6]);
        translate ([0, row_delta, 0]) render_tree (subtree[2]);
        translate ([0, (count_beams(subtree[2])+1)*row_delta, 0]) render_tree (subtree[3]);
    }
}

render_tree(combiner ([for (w=weights) if (w[1] > 0) w], beam_length, "T"));

```


[User]
I'm looking to generate a vase shape using OpenSCAD, and I'd like it to be parametric based on a superformula for the cross-section and a Bézier curve for the overall profile. I've seen examples using the dotSCAD library that do this, so I'd like to achieve a similar result.

Specifically, I need the vase's cross-section to be defined by a superformula, with parameters for `m`, `n`, and `n3`, as well as a `phi_step` to control the resolution. I'd also like an offset parameter `d` to create an outer shell for the vase. This offset should be a uniform distance away from the inner shape. The final shape should have both the original and offset superformula curves.

The vertical profile of the vase should be determined by a Bézier curve. I want to control the curve with a set of control points, at least 6, and including the control points for both the inner and outer curves (where the offset curve is offset along x and y with respect to the original curve). I'd also like parameters for `r1`, `r2`, `h1`, `h2` to have some specific points along the vertical profile. The curve should have a `t_step` for resolution and a `twist` parameter to twist the profile as it goes up.

So, to recap, I would need the following:

*   **Superformula parameters:** `phi_step`, `m`, `n`, `n3`, `d` (offset).
*   **Bézier curve parameters:**  `r1`, `r2`, `h1`, `h2`, `t_step`, `twist`.
*   **Library**: dotSCAD for the superformula, Bézier curves, and other helper functions
*   The final output should be a vase-like shape formed by sweeping the superformula profile along the Bézier curve and applying the twist.

I expect the generated code will require a `superformula_vase` module and will need to use `polysections` to generate the 3D mesh. It should also use the `bezier_curve`, `shape_superformula`, `bijection_offset`, `path_scaling_sections` and `rotate_p` functions, which are provided in the dotSCAD library.

I don't need an interactive GUI or anything fancy, just the OpenSCAD code that produces the parametric vase shape. I also expect the code to be modular and easy to read.

[Assistant]
superformula_vase.scad:
```
/* [Superformula] */
phi_step = 0.025;
m = 16;
n = 5;
n3 = 8;

/* [Offset] */
d = 0.025;

/* [Curve] */
r1 = 1;
r2 = 2;
h1 = 4;
h2 = 8;
t_step = 0.05;
twist = 90;

module superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist) {

    shape_pts = shape_superformula(phi_step, m, m, n, n, n3);
    outer_shape_pts = bijection_offset(shape_pts, d);

    all = concat(outer_shape_pts, shape_pts);

    offset_v = outer_shape_pts[0] - shape_pts[0];

    ctrl_pts = [
        [1, 0, 0],
        [4, 0, 2],
        [2, 0, 3],
        [r1, 0, h1],
        [1, 0, 5],
        [r2, 0, h2],
    ];
    ctrl_pts2 = [for(p = ctrl_pts) p + [offset_v[0], offset_v[1], 0]];

    path = bezier_curve(t_step, ctrl_pts2);

    leng = len(path);
    twist_step = twist / leng;

    sections = path_scaling_sections(all, path);
    twisted_sections = [
        for(i = [0:leng - 1])
            [for(p = sections[i]) rotate_p(p, twist_step * i)]
    ];

    polysections(twisted_sections, "HOLLOW");
    rotate(-twist_step) linear_extrude(d) offset(d) polygon(shape_pts);
}

superformula_vase(phi_step, m, n, n3, d, r1, r2, h1, h2, t_step, twist);

/**
 * The dotSCAD library
 * @copyright Justin Lin, 2017
 * @license https://opensource.org/licenses/lgpl-3.0.html
 *
 * @see https://github.com/JustinSDK/dotSCAD
*/

/**
* shape_superformula.scad
*
* @copyright Justin Lin, 2017
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_superformula.html
*
**/

function _superformula_r(angle, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) =
    pow(
        pow(abs(cos(m1 * angle / 4) / a), n2) +
        pow(abs(sin(m2 * angle / 4) / b), n3),
        - 1 / n1
    );

function shape_superformula(phi_step, m1, m2, n1, n2 = 1, n3 = 1, a = 1, b = 1) =
   [
        for(phi = [0:phi_step:6.28318])
            let(
                angle = __to_degree(phi),
                r = _superformula_r(angle, m1, m2, n1, n2, n3, a, b)

            )
            __ra_to_xy(r, angle)
   ];

function _bijection_edges_from(pts) =
    let(leng = len(pts))
    concat(
        [for(i = [0:leng - 2]) [pts[i], pts[i + 1]]],
        [[pts[len(pts) - 1], pts[0]]]
    );

function _bijection_inward_edge_normal(edge) =
    let(
        pt1 = edge[0],
        pt2 = edge[1],
        dx = pt2[0] - pt1[0],
        dy = pt2[1] - pt1[1],
        edge_leng = norm([dx, dy])
    )
    [-dy / edge_leng, dx / edge_leng];

function _bijection_outward_edge_normal(edge) = -1 * _bijection_inward_edge_normal(edge);

function _bijection_offset_edge(edge, dx, dy) =
    let(
        pt1 = edge[0],
        pt2 = edge[1],
        dxy = [dx, dy]
    )
    [pt1 + dxy, pt2 + dxy];

function _bijection__bijection_offset_edges(edges, d) =
    [
        for(edge = edges)
        let(
            ow_normal = _bijection_outward_edge_normal(edge),
            dx = ow_normal[0] * d,
            dy = ow_normal[1] * d
        )
        _bijection_offset_edge(edge, dx, dy)
    ];

function _bijection__bijection__bijection_offset_edges_intersection(edge1, edge2) =
    let(
        den = (edge2[1][1] - edge2[0][1]) * (edge1[1][0] - edge1[0][0]) - (edge2[1][0] - edge2[0][0]) * (edge1[1][1] - edge1[0][1])
    )
    // when den is 0, they are parallel or conincident edges
    den == 0 ? [] : _bijection_offset__bijection__bijection__bijection_offset_edges_intersection_sub(edge1, edge2, den);

function _bijection_offset__bijection__bijection__bijection_offset_edges_intersection_sub(edge1, edge2, den) =
    let(
        ua = ((edge2[1][0] - edge2[0][0]) * (edge1[0][1] - edge2[0][1]) - (edge2[1][1] - edge2[0][1]) * (edge1[0][0] - edge2[0][0])) / den
    )
    [
        edge1[0][0] + ua * (edge1[1][0] - edge1[0][0]),
        edge1[0][1] + ua * (edge1[1][1] - edge1[0][1])
    ];

function bijection_offset(pts, d) =
    let(
        es = _bijection_edges_from(pts),
        offset_es = _bijection__bijection_offset_edges(es, d),
        leng = len(offset_es),
        last_p = _bijection__bijection__bijection_offset_edges_intersection(offset_es[leng - 1], offset_es[0])
    )
    concat(
        [
            for(i = [0:leng - 2])
            let(
                this_edge = offset_es[i],
                next_edge = offset_es[i + 1],
                p = _bijection__bijection__bijection_offset_edges_intersection(this_edge, next_edge)
            )
            // p == p to avoid [nan, nan], because [nan, nan] != [nan, nan]
            if(p != [] && p == p) p
        ],
        last_p != [] && last_p == last_p ? [last_p] : []
    );

function path_scaling_sections(shape_pts, edge_path) =
    let(
        start_point = edge_path[0],
        base_leng = norm(start_point),
        scaling_matrice = [
            for(p = edge_path)
            let(s = norm([p[0], p[1], 0]) / base_leng)
            m_scaling([s, s, 1])
        ]
    )
    __reverse([
        for(i = [0:len(edge_path) - 1])
        [
            for(p = shape_pts)
            let(scaled_p = scaling_matrice[i] * [p[0], p[1], edge_path[i][2], 1])
            [scaled_p[0], scaled_p[1], scaled_p[2]]
        ]
    ]);

/**
* rotate_p.scad
*
* @copyright Justin Lin, 2017
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-rotate_p.html
*
**/

function _q_rotate_p_3d(p, a, v) =
    let(
        half_a = a / 2,
        axis = v / norm(v),
        s = sin(half_a),
        x = s * axis[0],
        y = s * axis[1],
        z = s * axis[2],
        w = cos(half_a),

        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

        xx = x * x2,
        yx = y * x2,
        yy = y * y2,
        zx = z * x2,
        zy = z * y2,
        zz = z * z2,
        wx = w * x2,
        wy = w * y2,
        wz = w * z2
    )
    [
        [1 - yy - zz, yx - wz, zx + wy] * p,
        [yx + wz, 1 - xx - zz, zy - wx] * p,
        [zx - wy, zy + wx, 1 - xx - yy] * p
    ];

function _rotx(pt, a) =
    let(cosa = cos(a), sina = sin(a))
    [
        pt[0],
        pt[1] * cosa - pt[2] * sina,
        pt[1] * sina + pt[2] * cosa
    ];

function _roty(pt, a) =
    let(cosa = cos(a), sina = sin(a))
    [
        pt[0] * cosa + pt[2] * sina,
        pt[1],
        -pt[0] * sina + pt[2] * cosa,
    ];

function _rotz(pt, a) =
    let(cosa = cos(a), sina = sin(a))
    [
        pt[0] * cosa - pt[1] * sina,
        pt[0] * sina + pt[1] * cosa,
        pt[2]
    ];

function _rotate_p_3d(point, a) =
    _rotz(_roty(_rotx(point, a[0]), a[1]), a[2]);

function _rotate_p(p, a) =
    let(angle = __to_ang_vect(a))
    len(p) == 3 ?
        _rotate_p_3d(p, angle) :
        __to2d(
            _rotate_p_3d(__to3d(p), angle)
        );

function _q_rotate_p(p, a, v) =
    len(p) == 3 ?
        _q_rotate_p_3d(p, a, v) :
        __to2d(
            _q_rotate_p_3d(__to3d(p), a, v)
        );

function rotate_p(point, a, v) =
    v == undef ? _rotate_p(point, a) : _q_rotate_p(point, a, v);

function __to2d(p) = [p[0], p[1]];

function __to_3_elems_ang_vect(a) =
     let(leng = len(a))
     leng == 3 ? a : (
         leng == 2 ? [a[0], a[1], 0] :  [a[0], 0, 0]
     );

function __to_ang_vect(a) = __is_float(a) ? [0, 0, a] : __to_3_elems_ang_vect(a);

function __ra_to_xy(r, a) = [r * cos(a), r * sin(a)];

function __reverse(vt) =
    let(leng = len(vt))
    [
        for(i = [0:leng - 1])
            vt[leng - 1 - i]
    ];

/**
* m_scaling.scad
*
* @copyright Justin Lin, 2019
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-m_scaling.html
*
**/

function _to_3_elems_scaling_vect(s) =
     let(leng = len(s))
     leng == 3 ? s : (
         leng == 2 ? [s[0], s[1], 1] : [s[0], 1, 1]
     );

function _to_scaling_vect(s) = __is_float(s) ? [s, s, s] : _to_3_elems_scaling_vect(s);

function m_scaling(s) =
    let(v = _to_scaling_vect(s))
    [
        [v[0], 0, 0, 0],
        [0, v[1], 0, 0],
        [0, 0, v[2], 0],
        [0, 0, 0, 1]
    ];

function __to3d(p) = [p[0], p[1], 0];

function __to_degree(phi) = 180 / 3.14159 * phi;

/**
* polysections.scad
*
* @copyright Justin Lin, 2017
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-polysections.html
*
**/

module polysections(sections, triangles = "SOLID") {

    function side_indexes(sects, begin_idx = 0) =
        let(
            leng_sects = len(sects),
            leng_pts_sect = len(sects[0])
        )
        concat(
            [
                for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect])
                    for(i = [0:leng_pts_sect - 1])
                        [
                            j + i,
                            j + (i + 1) % leng_pts_sect,
                            j + (i + 1) % leng_pts_sect + leng_pts_sect
                        ]
            ],
            [
                for(j = [begin_idx:leng_pts_sect:begin_idx + (leng_sects - 2) * leng_pts_sect])
                    for(i = [0:leng_pts_sect - 1])
                        [
                            j + i,
                            j + (i + 1) % leng_pts_sect + leng_pts_sect ,
                            j + i + leng_pts_sect
                        ]
            ]
        );

    function search_at(f_sect, p, leng_pts_sect, i = 0) =
        i < leng_pts_sect ?
            (p == f_sect[i] ? i : search_at(f_sect, p, leng_pts_sect, i + 1)) : -1;

    function the_same_after_twisting(f_sect, l_sect, leng_pts_sect) =
        let(
            found_at_i = search_at(f_sect, l_sect[0], leng_pts_sect)
        )
        found_at_i <= 0 ? false :
            l_sect == concat(
                [for(i = [found_at_i:leng_pts_sect-1]) f_sect[i]],
                [for(i = [0:found_at_i - 1]) f_sect[i]]
            );

    function to_v_pts(sects) =
            [
            for(sect = sects)
                for(pt = sect)
                    pt
            ];

    module solid_sections(sects) {

        leng_sects = len(sects);
        leng_pts_sect = len(sects[0]);
        first_sect = sects[0];
        last_sect = sects[leng_sects - 1];

        v_pts = [
            for(sect = sects)
                for(pt = sect)
                    pt
        ];

        function begin_end_the_same() =
            first_sect == last_sect ||
            the_same_after_twisting(first_sect, last_sect, leng_pts_sect);

        if(begin_end_the_same()) {
            f_idxes = side_indexes(sects);

            polyhedron(
                v_pts,
                f_idxes
            );

            // hook for testing
            test_polysections_solid(v_pts, f_idxes);
        } else {
            first_idxes = [for(i = [0:leng_pts_sect - 1]) leng_pts_sect - 1 - i];
            last_idxes = [
                for(i = [0:leng_pts_sect - 1])
                    i + leng_pts_sect * (leng_sects - 1)
            ];

            f_idxes = concat([first_idxes], side_indexes(sects), [last_idxes]);

            polyhedron(
                v_pts,
                f_idxes
            );

            // hook for testing
            test_polysections_solid(v_pts, f_idxes);
        }
    }

    module hollow_sections(sects) {
        leng_sects = len(sects);
        leng_sect = len(sects[0]);
        half_leng_sect = leng_sect / 2;
        half_leng_v_pts = leng_sects * half_leng_sect;

        function strip_sects(begin_idx, end_idx) =
            [
                for(i = [0:leng_sects - 1])
                    [
                        for(j = [begin_idx:end_idx])
                            sects[i][j]
                    ]
            ];

        function first_idxes() =
            [
                for(i =  [0:half_leng_sect - 1])
                    [
                       i,
                       i + half_leng_v_pts,
                       (i + 1) % half_leng_sect + half_leng_v_pts,
                       (i + 1) % half_leng_sect
                    ]
            ];

        function last_idxes(begin_idx) =
            [
                for(i =  [0:half_leng_sect - 1])
                    [
                       begin_idx + i,
                       begin_idx + (i + 1) % half_leng_sect,
                       begin_idx + (i + 1) % half_leng_sect + half_leng_v_pts,
                       begin_idx + i + half_leng_v_pts
                    ]
            ];

        outer_sects = strip_sects(0, half_leng_sect - 1);
        inner_sects = strip_sects(half_leng_sect, leng_sect - 1);

        outer_v_pts =  to_v_pts(outer_sects);
        inner_v_pts = to_v_pts(inner_sects);

        outer_idxes = side_indexes(outer_sects);
        inner_idxes = [
            for(idxes = side_indexes(inner_sects, half_leng_v_pts))
                __reverse(idxes)
        ];

        first_outer_sect = outer_sects[0];
        last_outer_sect = outer_sects[leng_sects - 1];
        first_inner_sect = inner_sects[0];
        last_inner_sect = inner_sects[leng_sects - 1];

        leng_pts_sect = len(first_outer_sect);

        function begin_end_the_same() =
           (first_outer_sect == last_outer_sect && first_inner_sect == last_inner_sect) ||
           (
               the_same_after_twisting(first_outer_sect, last_outer_sect, leng_pts_sect) &&
               the_same_after_twisting(first_inner_sect, last_inner_sect, leng_pts_sect)
           );

        v_pts = concat(outer_v_pts, inner_v_pts);

        if(begin_end_the_same()) {
            f_idxes = concat(outer_idxes, inner_idxes);

            polyhedron(
                v_pts,
                f_idxes
            );

            // hook for testing
            test_polysections_solid(v_pts, f_idxes);
        } else {
            first_idxes = first_idxes();
            last_idxes = last_idxes(half_leng_v_pts - half_leng_sect);

            f_idxes = concat(first_idxes, outer_idxes, inner_idxes, last_idxes);

            polyhedron(
                v_pts,
                f_idxes
            );

            // hook for testing
            test_polysections_solid(v_pts, f_idxes);
        }
    }

    module triangles_defined_sections() {
        module tri_sections(tri1, tri2) {
            hull() polyhedron(
                points = concat(tri1, tri2),
                faces = [
                    [0, 1, 2],
                    [3, 5, 4],
                    [1, 3, 4], [2, 1, 4], [2, 3, 0],
                    [0, 3, 1], [2, 4, 5], [2, 5, 3]
                ]
            );
        }

        module two_sections(section1, section2) {
            for(idx = triangles) {
               tri_sections(
                    [
                        section1[idx[0]],
                        section1[idx[1]],
                        section1[idx[2]]
                    ],
                    [
                        section2[idx[0]],
                        section2[idx[1]],
                        section2[idx[2]]
                    ]
                );
            }
        }

        for(i = [0:len(sections) - 2]) {
             two_sections(
                 sections[i],
                 sections[i + 1]
             );
        }
    }

    if(triangles == "SOLID") {
        solid_sections(sections);
    } else if(triangles == "HOLLOW") {
        hollow_sections(sections);
    }
    else {
        triangles_defined_sections();
    }
}

// override it to test

module test_polysections_solid(points, faces) {

}

function __is_float(value) = value + 0 != undef;

/**
* bezier_curve.scad
*
* @copyright Justin Lin, 2017
* @license https://opensource.org/licenses/lgpl-3.0.html
*
* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html
*
**/

function _combi(n, k) =
    let(
        bi_coef = [
               [1],     // n = 0: for padding
              [1,1],    // n = 1: for Linear curves, how about drawing a line directly?
             [1,2,1],   // n = 2: for Quadratic curves
            [1,3,3,1]   // n = 3: for Cubic Bézier curves
        ]
    )
    n < len(bi_coef) ? bi_coef[n][k] : (
        k == 0 ? 1 : (_combi(n, k - 1) * (n - k + 1) / k)
    );

function bezier_curve_coordinate(t, pn, n, i = 0) =
    i == n + 1 ? 0 :
        (_combi(n, i) * pn[i] * pow(1 - t, n - i) * pow(t, i) +
            bezier_curve_coordinate(t, pn, n, i + 1));

function _bezier_curve_point(t, points) =
    let(n = len(points) - 1)
    [
        bezier_curve_coordinate(
            t,
            [for(p = points) p[0]],
            n
        ),
        bezier_curve_coordinate(
            t,
            [for(p = points) p[1]],
            n
        ),
        bezier_curve_coordinate(
            t,
            [for(p = points) p[2]],
            n
        )
    ];

function bezier_curve(t_step, points) =
    let(
        pts = concat([
            for(t = [0: ceil(1 / t_step) - 1])
                _bezier_curve_point(t * t_step, points)
        ], [_bezier_curve_point(1, points)])
    )
    len(points[0]) == 3 ? pts : [for(pt = pts) __to2d(pt)];

```


[User]
Hey, I'm looking to create a customizable threaded pipe coupler for a project, and I'd love some help generating the OpenSCAD code. I've seen some designs out there, but I need it to be parametric, so I can adjust it easily for different projects.

Essentially, I need a cylindrical part with male threads on one end and female threads on the other, and the dimensions should all be adjustable. Here are the parameters I think I'll need:

*   **`Length`**: The overall length of the coupler.
*   **`OD`**: The outside diameter of the non-threaded section of the coupler.
*   **`ID`**: The inside diameter of the coupler (the bore).
*   **`num_sides`**: The number of sides for the non-threaded section; this can be set to 3 to create a triangular shape, 4 for a square, 9 for a nonagon, etc. This will determine if the non-threaded section is round or a polygon for grip.
*   **`Thread_Dia`**: The outer diameter of the threads.
*   **`Thread_Depth`**: The depth (or height) of the threads.
*   **`Thread_Len`**: The length of the threaded sections at each end.
*   **`Thread_Pitch`**: The pitch of the threads.

I'd also need to specify if the threads are internal or external threads. I would like to use the [BOSL library](https://github.com/revarbat/BOSL) for making the threads, particularly `threading.scad`. Can you make sure that the code will work with this library included? Also I think a small epsilon variable will be useful to make sure the solid bodies are well formed.

I'd also want some helper functions for making the shapes and doing the subtractions, just so the code is easy to read. It would be great if this design was fully parametric.

I think that's it. Thanks!

[Assistant]
Flashlight_Extender.scad:
```
/* Customizable threaded pipe coupler
** I built this to make an extension on a dollar-store
** flashlight. It used 3xAA batteries, and I wanted to use
** an 18650 instead. While adapters are readily available to
** fit around the 18650 cell to make it a larger diameter
** to fit where the 3 AA cells were, the particular
** flashlight body I had was too short to contain a 65mm cell.
** Its cell holder was only 52.5mm long leaving me in need
** of an additional 65-52.5 = 12.5mm
** My flashlight body is 22.7 mm ID and
** male thread OD is 25 mm with 2 mm pitch, 1 start, about 0.5mm thread height.
** Appear to be metric trapezoidal threads, with shallow threads.
** I need 5.5mm of female threads
** and 5.5mm of male threads + my 12.5 mm of length.
** so overall 5.5+5.5+12.5=23.5mm.
** Wall thickness varies between 1.0 to 1.4mm on the
** existing cap (9 corrugations for grip).
** I'm just going to use a 9-gon shape to make it match the tail cap somewhat and grip easily.
** For version 1 of this, I'm going to make it solve my problem
** but design it for folks on Thingiverse to adapt it easily to
** other purposes.
** V1.0
** Uses the excellent BOSL library for creating the threads
** (Which means it won't work in Customizer, but just get the development version of OpenSCAD)
*/

/*[sizing]*/
Length   = 20.0; //overall length of coupler
OD       = 29.0; //Outside diameter of non-threaded section
ID       = 22.7; //Inside diameter of coupler
num_sides= 9;    //Number of sides

/*[Threads]*/
Thread_Dia      = 26.0;
Thread_Depth    = 0.5;
Thread_Len      = 5.5;
Thread_Pitch    = 2.0;

/*[Hidden]*/
eps=0.001; //used carefully below to ensure solid meshes when overlapping solids

include <BOSL/constants.scad>
use <BOSL/threading.scad>   //an easy to use threading library

flashlight_coupler(Length=Length, r1=OD/2, r2=ID/2, Thread_Len=Thread_Len, Thread_Pitch=Thread_Pitch,
                    Thread_Dia=Thread_Dia, Thread_Depth=Thread_Depth, num_sides=num_sides);

module flashlight_coupler(  Length=23.5,    //overall length
                            r1=14.15,       //outside radius
                            r2=11.35,       //inside radius
                            Thread_Len=5.5, //length of threaded ends
                            Thread_Pitch=2, //pitch of threads
                            Thread_Dia=25,
                            Thread_Depth=0.5,
                            num_sides=9,    //outer cylinder n-ogon "n"
                            smooth=96       //number of sides for a "smooth" cylinder
                            )
    {  difference(){
           union()                              //build from bottom up
           {                                    cylinder(r=r1, h=Thread_Len,$fn=smooth);
            translate([0,0,Thread_Len-eps])     cylinder(r=r1, h=2*eps+Length-2*Thread_Len,$fn=num_sides);
            translate([0,0,Length-Thread_Len])
            trapezoidal_threaded_rod(d=Thread_Dia, l=Thread_Len, pitch=Thread_Pitch,
                                     thread_depth=Thread_Depth, thread_angle=15, center=false, $fn=32);
           }
            translate([0,0,-eps])
            cylinder(r=r2, h=Length+2*eps, $fn=smooth); //bore the inside out smooth
            translate([0,0,-eps]) // bore out the female threads
            trapezoidal_threaded_rod(d=Thread_Dia, l=Thread_Len+eps, pitch=Thread_Pitch, center=false, slop=.3,
                                     thread_depth=Thread_Depth, thread_angle=15, internal=true, $fn=32);
           for(a=[0:360/num_sides:(num_sides-1)*360/num_sides])
           {
               rotate([0,0,a])
               translate([r1,0,0])
               cylinder(r=(OD-Thread_Dia)/4,h=Length-Thread_Len+eps);
           }
       }
    }

```
Flashlight_Extender.scad:
```
/* Customizable threaded pipe coupler
** I built this to make an extension on a dollar-store
** flashlight. It used 3xAA batteries, and I wanted to use
** an 18650 instead. While adapters are readily available to
** fit around the 18650 cell to make it a larger diameter
** to fit where the 3 AA cells were, the particular
** flashlight body I had was too short to contain a 65mm cell.
** Its cell holder was only 52.5mm long leaving me in need
** of an additional 65-52.5 = 12.5mm
** My flashlight body is 22.7 mm ID and
** male thread OD is 25 mm with 2 mm pitch, 1 start, about 0.5mm thread height.
** Appear to be metric trapezoidal threads, with shallow threads.
** I need 5.5mm of female threads
** and 5.5mm of male threads + my 12.5 mm of length.
** so overall 5.5+5.5+12.5=23.5mm.
** Wall thickness varies between 1.0 to 1.4mm on the
** existing cap (9 corrugations for grip).
** I'm just going to use a 9-gon shape to make it match the tail cap somewhat and grip easily.
** For version 1 of this, I'm going to make it solve my problem
** but design it for folks on Thingiverse to adapt it easily to
** other purposes.
** V1.0
** Uses the excellent BOSL library for creating the threads
** (Which means it won't work in Customizer, but just get the latest version of OpenSCAD)
*/

/*[sizing]*/
Length   = 20.0; //overall length of coupler
OD       = 29.0; //Outside diameter of non-threaded section
ID       = 22.7; //Inside diameter of coupler
num_sides= 9;    //Number of sides

/*[Threads]*/
Thread_Dia      = 26.0;
Thread_Depth    = 0.5;
Thread_Len      = 5.5;
Thread_Pitch    = 2.0;

/*[Hidden]*/
eps=0.001; //used carefully below to ensure solid meshes when overlapping solids

include <BOSL/constants.scad>
use <BOSL/threading.scad>   //an easy to use threading library

flashlight_coupler(Length=Length, r1=OD/2, r2=ID/2, Thread_Len=Thread_Len, Thread_Pitch=Thread_Pitch,
                    Thread_Dia=Thread_Dia, Thread_Depth=Thread_Depth, num_sides=num_sides);

module flashlight_coupler(  Length=23.5,    //overall length
                            r1=14.15,       //outside radius
                            r2=11.35,       //inside radius
                            Thread_Len=5.5, //length of threaded ends
                            Thread_Pitch=2, //pitch of threads
                            Thread_Dia=25,
                            Thread_Depth=0.5,
                            num_sides=9,    //outer cylinder n-ogon "n"
                            smooth=96       //number of sides for a "smooth" cylinder
                            )
    {  difference(){
           union()                              //build from bottom up
           {                                    cylinder(r=r1, h=Thread_Len,$fn=smooth);
            translate([0,0,Thread_Len-eps])     cylinder(r=r1, h=2*eps+Length-2*Thread_Len,$fn=num_sides);
            translate([0,0,Length-Thread_Len])
            trapezoidal_threaded_rod(d=Thread_Dia, l=Thread_Len, pitch=Thread_Pitch,
                                     thread_depth=Thread_Depth, thread_angle=15, center=false, $fn=32);
           }
            translate([0,0,-eps])
            cylinder(r=r2, h=Length+2*eps, $fn=smooth); //bore the inside out smooth
            translate([0,0,-eps]) // bore out the female threads
            trapezoidal_threaded_rod(d=Thread_Dia, l=Thread_Len+eps, pitch=Thread_Pitch, center=false, slop=.3,
                                     thread_depth=Thread_Depth, thread_angle=15, internal=true, $fn=32);
           for(a=[0:360/num_sides:(num_sides-1)*360/num_sides])
           {
               rotate([0,0,a])
               translate([r1,0,0])
               cylinder(r=(OD-Thread_Dia)/4,h=Length-Thread_Len+eps);
           }
       }
    }

```


[User]
Hey, I'm looking to design a parametric nuc disc for beekeeping, and I'd love some help with the OpenSCAD code. I want it to be configurable for different nuc sizes and hole sizes, and also have different modes: fully open, fully closed, queen excluder mode (so workers can pass through but the queen can't), and a ventilation mode.

Here are the basic parameters I'm thinking of:

*   **`hole_size`**: The diameter of the central hole.
*   **`disc_radius`**: The overall radius of the disc.
*   **`Thickness`**:  The thickness of the disc itself.
*   **`knob_height`**: The height of the small knobs that help with rotation. I'd like it if setting this to less than the thickness removed them entirely.
*   **`queen_excluder_width`**: The width of the gaps for the queen excluder mode.

The basic design is a circular disc with a central hole. Around the central hole, there should be four smaller holes spaced evenly, kind of like the corners of a square. These smaller holes should have a diameter equal to the `hole_size` parameter.

Then, there needs to be a mechanism to rotate the disc for different modes - the main disc should have small, shallow knobs to make it easier to spin, maybe like short cylinders.

The "queen excluder" mode will use a series of bars that are a small amount more narrow than `queen_excluder_width` set inside the four holes, they should not overlap with the central hole. I imagine this will be accomplished by having a second disc on top that has the bar-like shapes cut out. When the top disc is rotated over the base disc, the bars will either allow the holes to be fully open or they will be covered. I want to have the gaps in the excluder to be about 1.2mm wider than the `queen_excluder_width`, if you can manage that. The `dist` variable in my code is doing the math for how far from the center these holes are.

Finally, I'd like to include a small ventilation hole that is always open. This could just be a small circular hole on one side of the main disc. I want this hole to be slightly smaller than the ones that make up the queen excluder, and placed somewhere other than the center and the holes used for the excluder. I added a 1.9mm hole in my example code, but that can be changed if necessary.

I'd like a single file if possible, I don't think I need multiple files for this. I think I'd like a module called `disc()` that generates the entire disc.

[Assistant]
nucdisc.scad:
```
/* [Main Dimensions] */

// Hole Size
hole_size = 28;
// Disc Size
disc_radius = 78;
// Disc Thickness
Thickness = 1.2;
// Knob height (make smaller than thickness to remove)
knob_height = 5;
// Width between queen excluder bars
queen_excluder_width = 4.1;

/* [Hidden] */
width = queen_excluder_width+1.2;
dist = (disc_radius/2+hole_size/2)/(1+sqrt(2));

//echo(dist);
//echo(disc_radius/4);

module check(in)
{
    if(dist > in/4)
    {
        return(dist*4+2);
    }
    else
    {
        return(in);
    }
}

outside_rad = disc_radius;
//disc_radius = check(disc_radius);

module spoke(Lengtht,widd=wid)
{
    cube([.8,Lengtht,Thickness],center=true);
    cube([1.2,Lengtht,Thickness-.6],center=true);
}

module spokes(lengt,wid=width)
{
    steps = floor(hole_size / wid);
    centerr = steps/2*wid;
    intersection()
    {
        for(j=[0:steps])
        {
            translate([j*wid-centerr,0,Thickness/2])
                spoke(lengt);
        }
        cylinder(r=hole_size/2,h=Thickness);
    }
}

module disc()
{

    difference()
    {
        cylinder(r=outside_rad/2,h=Thickness,$fn=120);
        for(i=[0:3])
        {
            if(i != 3)
                translate([cos(i*90)*dist,sin(i*90)*dist,0])
                    cylinder(r=hole_size/2,h=Thickness);
        }
        cylinder(r=1.9,h=Thickness,$fn=30);
    }
    difference()
    {
        cylinder(r=4+.8,h=Thickness*2);
        cylinder(r=4,h=Thickness*2);
    }

    for(i=[0:3])
    {
        if(i == 3)
            translate([cos(i*90)*dist,sin(i*90)*dist,0])
                cylinder(r=5,h=knob_height,$fn=30);
    }

    translate([dist,0,0])
        spokes(hole_size,width);

    translate([-dist,0,0])
        spokes(hole_size,3);
}

rotate(180,[0,0,1])
    disc();
```


[User]
I need an OpenSCAD design for a parametric square spiral. It's going to be used to check the bed level on a 3D printer, so it should print very quickly (single layer, single width).

The spiral should start with a small square and then grow outward in a spiral pattern. Each line segment should be a single extrusion width. I'll need to be able to control the following parameters:

*   `gapWidth`: The distance between the center of adjacent spiral lines. I'd like to set this in the range of 3 to 10 units.
*   `lineWidth`: The width of each line segment. I expect this to be fairly thin, like 0.2 to 1.2 units
*   `lineHeight`: The height of each line segment (since it's single layer, this should be the layer height). I'd like to specify this in the range of 0.1 to 1.0 units, and would prefer this to increment by 0.01 units.
*   `steps`: The number of line segments in the spiral. I'd like to control this directly in the range 1-50.

I think it will require a loop to generate the segments, using translate and rotate.  I do not want a separate module per line. The first line should be at zero and the second should start immediately after.

[Assistant]
square_spiral.scad:
```
gapWidth = 5; // [3:10]
lineWidth = 0.4; // [0.2,0.4,0.8,1.0,1.2]
lineHeight = 0.2; // [0.1:0.01:1]
//number of lines
steps = 20; // [1:1:50]

//builds a single layer high single extrusion width "square sprial" for checking bed level;

translate([ 0*gapWidth, 0*gapWidth,0]) rotate(  0) cube([gapWidth*1,lineWidth,lineHeight]);
for(i=[1:steps]){
x = (1-2*(1-(ceil(i/2)%2)))*ceil(i/2);
y = (1-2*(ceil((i+1)/2)%2))*(2*ceil((i-1)/4));
translate([ x *gapWidth, y*gapWidth,0]) rotate(90*(i%4)) cube([gapWidth*(i+1),lineWidth,lineHeight]);
}
```


[User]
I'd like to design a customizable mesh box, and I need some help creating the OpenSCAD files.

Here's what I'm looking for:

The box should be defined by three main dimensions: length, width, and height. These should all be customizable parameters. I'd also like to be able to specify the thickness of the bars that make up the mesh.

The mesh itself should be constructed with a diagonal pattern on the walls. The density of the mesh on the walls should be adjustable using a 'wall bar multiplier'. So, a higher multiplier will create a denser mesh.

The floor of the box should also be a mesh, but it should have its own adjustable angle and density. I'd like to control the angle of the floor bars and the density with a separate 'floor multiplier'. The bars should run in two directions for stability.

Finally, I would like the option to chamfer the vertical corner posts. This should be a simple boolean parameter.

I need the OpenSCAD code to handle all of these parameters, allowing the user to modify each dimension, the bar thickness, and the various density and angle options, as well as toggling the corner chamfering.

I'm not looking for code that uses any libraries. I think the design is simple enough that everything can be done without them.

[Assistant]
customizable_mesh_box_chamfered_corners.scad:
```
/*
 * by Luke Crevier
 * version v0.1
 * This work is licensed under the Creative Commons - Attribution - Non-Commercial ShareAlike license.
 * https://creativecommons.org/licenses/by-nc-sa/3.0/
 */

 // Parameter Section //
//-------------------//

// Length
l = 80;

// Width
w = 80;

// Height
h = 40;

// Thickness of bars
barDiam = 2;

// Wall bar multiplier
wallCoef = 1;

// Angle of the floor bars
floorAngle = 45;

// Floor multiplier
floorCoef = 2.5;

// Boolean to chamfer the corner posts
chamferCorners = false;

/* [Hidden] */

module cross(basewid, h_) {
    rotate([0,30,0])
    cube([barDiam,barDiam, (h_ / sin(60))]);
}

module wall(length, wid, h_, wallCoef = 1) {
    segment = tan(30) * h_;
    segMult = segment * 5;
    wallSegments = [ for(i = [0 - segMult : segment / wallCoef  : length]) i];
    for(i = [0, wid - barDiam]){
        for(j = wallSegments) {
            translate([j,i,])
            cross(segment, h_);
        }
    }
    oppSegments = [ for(i = [length + segMult : -segment / wallCoef : 0]) i];
    for(i = [0, wid - barDiam]){
        for(j = oppSegments) {
            translate([j,i,])
            mirror([180,0,0])
            cross(segment, h_);
        }
    }
}
module floor(ang = 30, scaler = 2) {
    segment = tan(ang) * w ;
    seg3 = 2 * segment;
    floorSegments = [ for(i = [0 - seg3 : segment / scaler : l]) i];
    oppSegments = [ for(i = [l + seg3: -segment / scaler : 0]) i];
    for(i = floorSegments) {
        translate([i,0,0]){
            rotate([0,0,-ang])
            cube([barDiam, segment / sin(ang), barDiam/1.5]);
        }
    }

    for(i = oppSegments) {
        translate([i,0,0]){
            rotate([0,0,ang])
            cube([barDiam, segment / sin(ang), barDiam/1.5]);
        }
    }
}

module skeleton() {
    wall(l,w, h, wallCoef);
    rotate([0,0,90])
    mirror([0,180,0])
    wall(w,l, h, wallCoef);
}

module edges(length, width, height){
    difference() {
        cube([l,w,h]);
        union() {
            translate([-l/2,barDiam,barDiam/1.5])
            cube([l* 2, w-barDiam*2, h-barDiam*1.5]);
            translate([barDiam, -w/2, barDiam/1.5])
            cube([l-barDiam*2, w*2, h-barDiam*1.5]);
            translate([barDiam, barDiam, -1/2 * h])
            cube([l-barDiam*2, w-barDiam*2, h*2]);

        }
    }
}

difference(){
    union() {
        edges();
        intersection() {
            skeleton();
            cube([l,w,h]);
        }
        intersection() {
            cube([l,w,h]);
            floor(floorAngle, floorCoef);

        }
    }
    if (chamferCorners == true) {
        chamferEdges();
    }
}

module chamferEdges () {
    for(i = [0, l + barDiam*1.8]){
        for(j = [0,w + barDiam*1.8]){
            echo(i);
            echo(j);
            translate([i-barDiam,j-barDiam,-1]){
                rotate([0,0,45])
                translate([-barDiam*2,-barDiam*2,0])
                cube([barDiam*4,barDiam*4,h+2]);
            }
        }
    }
}
```


[User]
Hey, I'm looking to design a bottle opener that I can customize with text. I've got a pretty good idea of the basic shape, inspired by a design I saw online, but I'd like a parametric version that's easier to adjust and customize.

Specifically, I envision a roughly circular opener with a keyhole-shaped cutout for grabbing the bottle cap. The main body should be a cylinder with an outer diameter that I can control, and a certain thickness or height as well. The keyhole cutout should be created by subtracting a shape from the cylinder. This shape will have a smaller diameter hole and a rectangle with a few extra cuts to create the keyhole form, that will grab the cap. I also want to place a small cylinder in the middle of each of the two main circular curves.

I'd like to be able to add text on both sides of the opener. This text should be centered on the flat faces and can be either one or two lines. I also want to be able to set the font size, the actual text strings for each side, and to be able to turn the text on and off.

I'd also like to be able to control the angle between the "keyhole" cutout, and the body. The text should rotate with this angle.

Could you help me design this in OpenSCAD? I'm thinking a single `.scad` file for everything would be ideal, with parameters to control all the dimensions, text, and rotations. I'm not using any particular libraries, so just plain OpenSCAD is good. Thanks!

[Assistant]
Flaschenoeffner.scad:
```
// -----------------------------------------------------
// Flaschenoeffner
//
//  Detlev Ahlgrimm, 25.05.2019
// -----------------------------------------------------

include_text=0;  // [0:False, 1:True]

strg1="info@dg-cybersicherheit.de";
size1=7;

strg2="www.cyberscan.io";
size2=7;

$fn=100;

/* [Hidden] */
r=300;
a=24;
hgt=20;
ws=3;

$vpt=[128, 109, -73];
$vpr=[62, 0, 330];
$vpd=446;

xp=r*sin(a);
yp=r*cos(a);
translate([1.5, -r+yp+ws/2, 0]) {
  difference() {
    translate([0, -yp, 0]) difference() {
      cylinder(r=r, h=hgt);
      translate([0, 0, -0.1]) cylinder(r=r-ws, h=hgt+0.2);
    }
    translate([-r-0.1, -r-yp-0.1, -0.1]) cube([r+0.1, 2*r+0.2, hgt+0.2]);
    translate([-0.1, -r-yp-0.1, -0.1]) cube([r+0.2, r+0.1, hgt+0.2]);
    translate([0, -yp, -0.1]) rotate([0, 0, -a]) cube([r+0.1, r+0.1, hgt+0.2]);
  }
  translate([(r-ws/2)*sin(a), (r-ws/2)*cos(a)-yp, 0]) cylinder(d=ws, h=hgt);
  translate([(r-ws/2)*sin(0), (r-ws/2)*cos(0)-yp, 0]) cylinder(d=ws, h=hgt);
}

difference() {
  intersection() {
    translate([25, 0, 0]) scale([1, 0.6, 1]) cylinder(r=25, h=hgt);
    translate([1.5, -yp-r+yp+ws/2, 0]) cylinder(r=r, h=hgt);
  }
  rotate([0, 0, -6]) {
    translate([10, -19, -0.1]) linear_extrude(hgt+0.2) polygon([ [0,0], [0,17], [20,17], [20,10.5], [18,10.5], [18,9.5], [35,0] ]);
    translate([30, -19+17-6.5/2, -0.1]) cylinder(d=6.5, h=hgt+0.2);
  }
  translate([27, -30, hgt/2]) rotate([-90, 0, -2*a]) cylinder(d=hgt-4, h=50);
  translate([13, -8, hgt/2]) rotate([90, 0, 0]) intersection() {
    cylinder(d=32, h=10);
    translate([10, -16, -0.2]) cube([17, 32, 10.2]);
  }
}

if(include_text && len(strg1)>0) render() difference() {
  intersection() {
    translate([60, -23, hgt/2]) rotate([-90, 0, -a/2]) linear_extrude(32) text(strg1, size=size1, halign="center", valign="center");
    translate([1.5, -yp-r+yp+ws/2, 0]) cylinder(r=r+1, h=hgt);
  }
  translate([1.5, -yp-r+yp+ws/2, 0]) cylinder(r=r-1, h=hgt);
}

if(include_text && len(strg2)>0) render() difference() {
  intersection() {
    translate([85, 0, hgt/2]) rotate([90, 0, -a/2]) linear_extrude(25) text(strg2, size=size2, halign="center", valign="center");
    translate([1.5, -yp-r+yp+ws/2, 0]) cylinder(r=r, h=hgt);
  }
  translate([1.5, -yp-r+yp+ws/2, 0]) cylinder(r=r-ws-1, h=hgt);
}

```


[User]
I need an OpenSCAD design for a drill bit case that can be customized. I want to specify the drill bit sizes (diameter and length) and have the case automatically adjust to fit. Here are the specifics:

1.  **Drill Bit Array:** The design should take an array of drill bit specifications, where each element in the array is itself an array containing the diameter and length of a bit. For example `[[1.5, 50], [2, 55], [2.5, 60]]`. The case should generate holes to fit these bits.

2.  **Blade Width:** The case will use a utility knife blade as a spring, so I need to specify the blade width as a parameter.

3.  **Text:** I would like the option to add text indicating the size of the drill bit next to each hole. This should be customizable (height of the text, whether it is raised or engraved, or no text at all). I'd prefer the text to be automatically oriented to face out of the case when closed, and to be near the opening when the case is open.

4.  **Case Parts:** The case should consist of two parts that are hinged together, with a place for the blade to act as a spring between the two parts. I need an option to export the entire assembly, or just either one of the two parts independently. I'd also like a preview mode where the two parts are shown open next to each other, and a mode to export just the text.

5.  **Customizable Case Parameters:** The case should have customizable parameters for the side wall thickness, overall wall thickness, top thickness, hinge radius, hinge hole diameter, and gap between the two case halves when closed. I'd also like control over whether the holes are square or round.

6.  **Hinges:** The hinges should be simple cylindrical pivots on each of the two halves of the case, with matching holes to allow a pin (like a cut paperclip) to pass through.

7.  **Spring:** The spring should be a cut-out area to hold a utility knife blade, with an additional area for the spring to press on a flat area of the opposite part of the case.

8. **Text Font Size:** The font size should be adjusted so that the text size is close to the drill diameter but not smaller than a minimum or bigger than a maximum font size. The text for each drill size should be in the range of, for example, `minFont=3` and `maxFont=5`.

I'm not sure exactly how best to structure all of this, so feel free to organize it in a way that makes sense.

[Assistant]
drill_bits_case_w_spring_v1.2.scad:
```
//Holes for drill bits. Format: [diameter1, length1],[diameter2, length2],... Use bigger length then bits really have
drills = [
			[1.5, 50 ],
			[2,   55 ],
			[2.5, 60 ],
			[3,   65],
			[3.2, 75],
			[3.5, 75],
			[4,   80],
			[4.5, 85],
			[5,   90],
			[5.5, 100],
			[6,   100],
];
//blade width
blade = 19;//[9:9mm,18:18mm,19:19mm,25:25mm]
//Text height: positive - humps, negative - hollows, 0 - no text
textHeight = 0.4;
mode = 0; //[0:Both parts, 1:Part 1, 2:Part 2, 3:Preview, 4:Text Only]

/*[Advanced]*/
side = 2;
wall = 2;
top = 1.5;
hingeR = 2;
hingeHoleD = 1;
gap = 0.5;
minfont = 3;
maxfont = 5;
holesShape = 1; //[0:Square, 1:Round]

/*[Hidden]*/
//dont edit this, dude
springThin = 1;
n = len(drills);
bot = 2*hingeR;;
width = sumw()+(n-1)*wall+side*2;
springWidth = blade+0.5;
hingeW = (width-springWidth)/2;
maxD = maxDia();
partLen = (maxLen()+side*2)/2;
height = maxDia() + bot + top+gap;
echo(width=width, length=(partLen*2), sumw());

module part1(){
	difference(){
		union(){
			cube([width, partLen - hingeR, height]);
			translate([0, partLen, height - hingeR]) hinge();
			translate([width-hingeW, partLen, height - hingeR]) hinge();
			if(textHeight > 0) translate([0,0,-textHeight])extrudedText();
		}
		union(){
			for(i = [0:1:n-1]){
				translate([side+sumw(i)+wall*i-drills[i][0]/2 , partLen, (height-top-hingeR*2)/2+top])
				if(holesShape == 0){
					cube([drills[i][0]+gap, partLen, drills[i][0]+gap], center = true);
				}else{
					rotate([-90,0,0]) cylinder(d = drills[i][0]+gap, h = drills[i][1], center = true, $fn = 32);
				}
			}
			if(textHeight < 0) extrudedText();
		}
	}
}
module extrudedText(){
	#for(i = [0:1:n-1]){
		linear_extrude(abs(textHeight))
			translate([side+ sumw(i) - drills[i][0] + i*wall, partLen/3*(1+(i+1)%2), 0])
				rotate([180,0,90]) text(str(drills[i][0]), size = min(maxfont,max(minfont,drills[i][0]+wall)));
	}
}
module part2(){
	difference(){
		union(){
			translate([0,hingeR,0]) cube([width, partLen - hingeR, height]);
			translate([hingeW, 0, height - hingeR]) scale([-1,-1,1]) hinge();
			translate([width, 0, height - hingeR]) scale([-1,-1,1]) hinge();
		}
		union(){
//			for(i = [0:1:n-1]){
			for(i = [0:1:n-1]){
				translate([side + sumw(i) - drills[i][0]/2+ i*wall, 0, -50+top+gap+maxD/2+drills[i][0]/2]) cube([drills[i][0]+wall+0.05, drills[i][1],100], center = true);
			}
		}
	}
}
module hinge(w = 16){
	difference(){
		union(){
			translate([0,-hingeR*2,-hingeR])cube([hingeW/4,hingeR*2,hingeR*2]);
			translate([0,0,0])rotate([0,90,0])cylinder(r = hingeR, h = hingeW/4, $fn=32);
			translate([hingeW/2,-hingeR*2,-hingeR])cube([hingeW/4,hingeR*2,hingeR*2]);
			translate([hingeW/2,0,0])rotate([0,90,0])cylinder(r = hingeR, h = hingeW/4, $fn=32);
		}
		translate([0,0,0])rotate([0,90,0])cylinder(d = hingeHoleD, h = w, $fn=32);
	}
}
module springHole(){
	translate([width/2, 0, height-hingeR]) union(){
		#translate([0,0,hingeHoleD/2+springThin/2])cube([width - 2*hingeW,partLen*2*2/3,springThin], center = true);
		translate([0,0,hingeHoleD/2+hingeR/2]) cube([width - 2*hingeW,partLen*2/3,hingeR], center = true);
	}
}
function sumw(n = -66) = (n==-66)?sumw(len(drills)-1):((n>0)?drills[n][0]+sumw(n-1):drills[0][0]);
function maxDia(n = -66) = (n==-66)?maxDia(len(drills)-1):((n>0)?max(drills[n][0], maxDia(n-1)):drills[0][0]);
function maxLen(n = -66) = (n==-66)?maxLen(len(drills)-1):((n>0)?max(drills[n][1], maxLen(n-1)):drills[0][1]);
module run(){
	if(mode == 0){
		union(){
			difference(){
				translate([0,-partLen,0])part1();
				springHole();
			}
			translate([0,2*hingeR+1,0])
				difference(){
					part2();
					springHole();
				}
		}
	}else if(mode == 1){
		difference(){
			translate([0,-partLen,0])part1();
			springHole();
		}
	}else if(mode == 2){
		difference(){
			part2();
			springHole();
		}
	}else if(mode == 3){
		difference(){
			union(){
				translate([0,-partLen,0])part1();
				part2();
			}
			springHole();
		}
	}else if(mode == 4){
		translate([0,-partLen,0])
			if(textHeight > 0) translate([0,0,-textHeight]) extrudedText();
			else extrudedText();
	}
}
rotate([0,180,0]) run();
```


[User]
Hey, I'm looking to have a parametric OpenSCAD design created for an acrylic window grip. I've seen some designs online, but I'd like one that's highly customizable and can handle different situations.

Here's what I'm envisioning:

*   **Basic Structure:** The grip should have a base that rests against a frame and a grip section that holds an acrylic sheet.
*   **Parametric Length:** I need to be able to set the overall length of the grip.
*   **Material Thickness:** It should have a parameter for the overall thickness of the material used to print it.
*   **Acrylic Thickness:** There should be an adjustable setting for the thickness of the acrylic sheet.
*   **Grip Type:** I need an option for either a double grip (grips the acrylic on both sides) or a single grip (for door seals), where a flat portion exists where an acrylic sheet would usually sit.
*   **Grip Depth:** I'd like to control the depth of the grip area to accommodate different acrylic sheet insertion depths.

*   **Tapered Ends:** It needs parameters to set taper angles at both the left and right ends.
*   **Screw Holes:** There should be a parametric way to set a number of screw holes, screw hole diameters, and screw head diameters.
*   **Countersinking:** I need an option to enable or disable countersinking for the screw holes, and a parameter to set the countersink angle.
*    **Counterbore:** There should be a parameter to set the depth to counterbore screws, and how far down the screw head is allowed to sit below the material (above hole bore depth)
*   **Screw Plate Width:** It should have a parameter for setting the width of the screw plate where the screw holes are located.
*   **Bevels:** I also want options to bevel both the grip and the base edges.

I'd prefer that the OpenSCAD file use only basic OpenSCAD commands, without any external libraries, at least for the base design. I'm looking for a single .scad file that contains a single module that allows for customization based on these parameters. I also need some comments in the file to help me understand what each part of the code is doing.

I think that should cover it all. Thanks in advance!

[Assistant]
codeandmake.com_Acrylic_Window_Grip_v2.0.scad:
```
/*
 * Copyright 2019-2020 Code and Make (codeandmake.com)
 *
 * 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.
 */

/*
 * Acrylic Window Grip by Code and Make (https://codeandmake.com/)
 *
 * https://www.thingiverse.com/thing:3661247
 *
 * v2.0 (29 January 2020)
 */

/* [General] */

// length of strip (in mm)
length = 200; // 0.01

// overall thickness of the material (in mm)
materialThickness = 3; // 0.01

// thickness of your acrylic (in mm) - oversize slightly
acrylicThickness = 3.05; // 0.01

// single or double grip - use single for door seals
gripType = "double"; // [double:Double, single:Single]

// depth of the grip groove (in mm)
gripDepth = 5; // 0.01

/* [Taper] */

// taper angle of left end (> -90 and < 90)
leftEndTaperAngle = 0; // [-89:0.01:89.9]

// taper angle of right end (> -90 and < 90)
rightEndTaperAngle = 0; // [-89.9:0.01:89.9]

/* [Screws] */

// the total number of screw holes
numberOfScrewHoles = 3;

// diameter of the screw holes (in mm)
screwHoleDiameter = 4; // 0.01

// diameter of the screw head (in mm)
screwHeadDiameter = 8; // 0.01

// countersink screw holes
countersinkScrews = 1; // [0:No, 1:Yes]

// countersink angle (82 and 90 are common)
countersinkAngle = 90; // [0.0:0.01:180.0]

// depth to counterbore screws (in mm)
counterboreDepth = 0; // 0.01

// width of the screw plate (in mm)
screwPlateWidth = 12; // 0.01

/* [Bevel] */

// bevel the grip
bevelGrip = 1; // [0:No, 1:Yes]

// bevel the base
bevelBase = 1; // [0:No, 1:Yes]

module acrylicWindowGrip(
length = length,
materialThickness = materialThickness,
acrylicThickness = acrylicThickness,
gripType = gripType,
gripDepth = gripDepth,

leftEndTaperAngle = leftEndTaperAngle,
rightEndTaperAngle = rightEndTaperAngle,

numberOfScrewHoles = numberOfScrewHoles,
screwHoleDiameter = screwHoleDiameter,
screwHeadDiameter = screwHeadDiameter,
countersinkScrews = countersinkScrews,
countersinkAngle = countersinkAngle,
counterboreDepth = counterboreDepth,
screwPlateWidth = screwPlateWidth,

bevelGrip = bevelGrip,
bevelBase = bevelBase) {

  // clamp values
  lengthClamped = max(length, 0);
  materialThicknessClamped = max(materialThickness, 0);
  acrylicThicknessClamped = max(acrylicThickness, 0);
  gripDepthClamped = max(gripDepth, 0);
  screwHoleDiameterClamped = max(screwHoleDiameter, 0);
  screwHeadDiameterClamped = max(screwHeadDiameter, 0);
  countersinkAngleClamped = max(countersinkAngle, 0);
  counterboreDepthClamped = max(counterboreDepth, 0);
  screwPlateWidthClamped = max(screwPlateWidth, 0);

  numberOfScrewHolesClamped = floor(max(min(numberOfScrewHoles, lengthClamped / (max(screwHoleDiameterClamped, screwHeadDiameterClamped) + 0.5)), 0));

  $fn = 100;

  gripWidth = acrylicThicknessClamped + (materialThicknessClamped * 2);

  totalWidth = screwPlateWidthClamped + gripWidth;
  totalHeight = materialThicknessClamped + gripDepthClamped;

  module plate(length, minWidth, width, thickness, vertical, flip) {
    bevelWidth = min(width - minWidth, thickness);
    plateWidth = width - bevelWidth;

    rotate([(vertical ? 90 : 0), 0, 0]) {
      translate([0, 0, (vertical ? -thickness : 0)]) {
        cube([length, plateWidth, thickness]);
        if (bevelWidth) {
          translate([0, plateWidth, 0]) {
            mirror([0, 0, (flip ? 1 : 0)]) {
              translate ([0, 0, (flip ? -thickness : 0)]) {
                resize([0, bevelWidth, thickness]) {
                  intersection() {
                    cube([length, 1, 1]);
                    rotate([0, 90, 0]) {
                      cylinder(length, 1, 1);
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }

  module taper(angle, width, height) {
    hypotenuse = height / cos(abs(angle));
    opposite = hypotenuse * sin(abs(angle));
    translate([(angle < 0 ? opposite : 0), -1, 0]) {
      rotate([0, angle, 0]) {
        translate([-height, 0, 0]) {
          cube([height, width, hypotenuse]);
        }
      }
    }
  }

  module screwHole(holeDepth, holeDiameter, headDiameter, boreDepth, aboveHoleBoreDepth, sinkAngle) {
    boreDiameter = (holeDiameter > 0 ? max(holeDiameter, headDiameter) : 0);
    countersinkAdjacent = (boreDiameter / 2) / tan(sinkAngle / 2);

    translate([0, 0, -0.001]) {
      // screw hole
      cylinder(holeDepth + 0.002, holeDiameter / 2, holeDiameter / 2, false);

      // countersink
      if (sinkAngle > 0) {
        translate([0, 0, holeDepth - countersinkAdjacent - boreDepth]) {
          cylinder(countersinkAdjacent + 0.002, 0, (boreDiameter / 2), false);
        }

        // above hole and bore
        translate([0, 0, holeDepth - boreDepth]) {
          cylinder(boreDepth + aboveHoleBoreDepth + 0.002, boreDiameter / 2, boreDiameter / 2, false);
        }
      } else {
        // full bore
        cylinder(holeDepth + aboveHoleBoreDepth + 0.002, boreDiameter / 2, boreDiameter / 2, false);
      }
    }
  }

  difference() {
    union() {
      // base plate
      if (gripType == "single") {
        basePlateWidth = screwPlateWidthClamped + materialThicknessClamped;
        translate([0, materialThicknessClamped + acrylicThicknessClamped, 0]) {
          plate(lengthClamped, (bevelBase ? materialThicknessClamped : basePlateWidth), basePlateWidth, materialThicknessClamped);
        }
      } else {
        plate(lengthClamped, (bevelBase ? gripWidth : totalWidth), totalWidth, materialThicknessClamped);
      }

      // inside grip
      translate([0, materialThicknessClamped + acrylicThicknessClamped, 0]) {
        plate(lengthClamped, (bevelGrip ? materialThicknessClamped : totalHeight), totalHeight, materialThicknessClamped, true, true);
      }

      // outside grip
      if (gripType != "single") {
        plate(lengthClamped, (bevelGrip ? materialThicknessClamped : totalHeight), totalHeight, materialThicknessClamped, true);
      }
    }

    // screw holes
    if(numberOfScrewHolesClamped > 0 && screwPlateWidthClamped >= max(screwHoleDiameterClamped, screwHeadDiameterClamped)) {
      holeSpacing = (length / floor(numberOfScrewHolesClamped));

      for (i = [1:numberOfScrewHolesClamped]) {
        translate([(holeSpacing * i) - (holeSpacing / 2), (materialThicknessClamped * 2) + acrylicThicknessClamped + ((screwPlateWidthClamped - (bevelBase ? materialThicknessClamped : 0)) / 2), 0]) {
          screwHole(materialThicknessClamped, screwHoleDiameterClamped, screwHeadDiameterClamped, counterboreDepthClamped, gripDepthClamped + 0.1, (countersinkScrews ? countersinkAngleClamped : 180));
        }
      }
    }

    // left end taper
    if (leftEndTaperAngle != 0) {
      taper(leftEndTaperAngle, totalWidth + 2, totalHeight);
    }

    // right end taper
    if (rightEndTaperAngle != 0) {
      translate([lengthClamped, 0, 0]) {
        mirror([0, 1, 0,]) {
          rotate([0, 0, 180]) {
            taper(rightEndTaperAngle, totalWidth + 2, totalHeight);
          }
        }
      }
    }
  }
}

acrylicWindowGrip();
```


[User]
I need an OpenSCAD design for a custom label that will fit onto Harbor Freight Apache cases. I'm planning to 3D print these labels, so the design needs to be suitable for that.

Here's what I'm looking for:

*   **Base Shape:** The base of the label should have the same overall dimensions and shape as the label in the provided `Apache_Case_Label_Maker_customizer.scad` file. This includes the angled cuts on the bottom and the sides as well as the dimensions of the main body. So it's a rectangle, but with cut outs. It should be parametrically designed using variables.
*   **Text:** I need to be able to add embossed text to the label. This text should be customizable in terms of the actual text string, the font, the font size, and how much it protrudes (the emboss height). I'd like to use Google Fonts, if possible.
*   **Parameters:** The whole thing should be controlled by parameters at the top of the file so it's easy to adjust in the Customizer UI or manually in the scad file, much like the original file I referenced.. I'll need parameters for:
    *   `text_` (string)
    *   `font_` (string, including an optional style specifier like "Orbitron:Bold 700")
    *   `font_size` (number)
    *   `emboss_height` (number)
*   **Orientation:** The label needs to be designed with the correct orientation for 3D printing, so it should have a flat base and the text should be raised up on the face of the label. I want it to come out of openscad oriented like the original scad file.

Basically, I'm looking for a completely new version of the same thing, using parameters and the correct dimensions, but not relying on the original code. It needs to work with the Customizer.

[Assistant]
Apache_Case_Label_Maker_customizer.scad:
```
// Custom Label Maker for Harbor Freight Apache Cases

// Created by Aaron Collier (astroaaron on Thingiverse)
// 5.29.19 // Modified 11.17.19

////////////////////////////////////////////////////
//Customizer Parameters

// what do you want the label to say?
text_ = "TEXT HERE";

// enter a supported Google font name followed by optional style parameter separated by colon, example: "Orbitron:Bold 700" (default = Cutive)
font_ = "Cutive";

// size of text (default = 11)
font_size = 11;

// amount that text will protrude from surface (default = 1)
emboss_height = 1;

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

//base
rotate(180){
    translate([-121/2,-24.5/2,0]){
        difference(){
            cube([121,24.5,3.5]);     //main body

            translate([0,24.5,0]){
                rotate([30,0,0]){
                    cube([121,5,5]);  //bottom cut
                }
            }

            rotate([-2,30,-3]){
                translate([-5,-1,0]){
                    cube([5,30,6]);     //right cut
                }
            }

            translate([121,-1,0]){
                rotate([-2,-30,3]){
                    cube([5,30,6]);     //left cut
                }
            }
        }
    }
}

//embossed text
translate([0,1,3.5]){
    linear_extrude(emboss_height){
        text(text_, font = font_, font_size, halign = "center", valign = "center");
    }
}
```