BOSL2/shapes2d.scad

//////////////////////////////////////////////////////////////////////
// LibFile: shapes2d.scad
//   This file includes redefinitions of the core modules to
//   work with attachment, and functional forms of those modules
//   that produce paths.  You can create regular polygons
//   with optional rounded corners and alignment features not
//   available with circle().  The file also provides teardrop2d,
//   which is useful for 3D printable holes.  
//   Many of the commands have module forms that produce geometry and
//   function forms that produce a path. 
// Includes:
//   include <BOSL2/std.scad>
// FileGroup: Basic Modeling
// FileSummary: Attachable circles, squares, polygons, teardrop.  Can make geometry or paths.
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////

use <builtins.scad>


// Section: 2D Primitives

// Function&Module: square()
// Synopsis: Creates a 2D square or rectangle.
// SynTags: Geom, Path, Ext
// Topics: Shapes (2D), Path Generators (2D)
// See Also: rect()
// Usage: As a Module
//   square(size, [center], ...);
// Usage: With Attachments
//   square(size, [center], ...) [ATTACHMENTS];
// Usage: As a Function
//   path = square(size, [center], ...);
// Description:
//   When called as the built-in module, creates a 2D square or rectangle of the given size.
//   When called as a function, returns a 2D path/list of points for a square/rectangle of the given size.
// Arguments:
//   size = The size of the square to create.  If given as a scalar, both X and Y will be the same size.
//   center = If given and true, overrides `anchor` to be `CENTER`.  If given and false, overrides `anchor` to be `FRONT+LEFT`.
//   ---
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Example(2D):
//   square(40);
// Example(2D): Centered
//   square([40,30], center=true);
// Example(2D): Called as Function
//   path = square([40,30], anchor=FRONT, spin=30);
//   stroke(path, closed=true);
//   move_copies(path) color("blue") circle(d=2,$fn=8);
function square(size=1, center, anchor, spin=0) =
    let(
        anchor = get_anchor(anchor, center, [-1,-1], [-1,-1]),
        size = is_num(size)? [size,size] : point2d(size)
    )
    assert(all_positive(size), "All components of size must be positive.")
    let(
        path = [
            [ size.x,-size.y],
            [-size.x,-size.y],
            [-size.x, size.y],
            [ size.x, size.y],
        ] / 2
    ) reorient(anchor,spin, two_d=true, size=size, p=path);


module square(size=1, center, anchor, spin) {
    anchor = get_anchor(anchor, center, [-1,-1], [-1,-1]);
    rsize = is_num(size)? [size,size] : point2d(size);
    size = [for (c = rsize) max(0,c)];
    attachable(anchor,spin, two_d=true, size=size) {
        if (all_positive(size))
            _square(size, center=true);
        children();
    }
}



// Function&Module: rect()
// Synopsis: Creates a 2d rectangle with optional corner rounding.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: square()
// Usage: As Module
//   rect(size, [rounding], [chamfer], ...) [ATTACHMENTS];
// Usage: As Function
//   path = rect(size, [rounding], [chamfer], ...);
// Description:
//   When called as a module, creates a 2D rectangle of the given size, with optional rounding or chamfering.
//   When called as a function, returns a 2D path/list of points for a square/rectangle of the given size.
// Arguments:
//   size = The size of the rectangle to create.  If given as a scalar, both X and Y will be the same size.
//   ---
//   rounding = The rounding radius for the corners.  If negative, produces external roundover spikes on the X axis. If given as a list of four numbers, gives individual radii for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no rounding)
//   chamfer = The chamfer size for the corners.  If negative, produces external chamfer spikes on the X axis. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-].  Default: 0 (no chamfer)
//   corner_flip = Flips the direction of the rouding curve or roudover and chamfer spikes. If true it produces spikes on the Y axis. If false it produces spikes on the X axis. If given as a list of four booleans it flips the direction for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-].  Default: false (no flip)
//   atype = The type of anchoring to use with `anchor=`.  Valid opptions are "box" and "perim".  This lets you choose between putting anchors on the rounded or chamfered perimeter, or on the square bounding box of the shape. Default: "box"
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Anchor Types:
//   box = Anchor is with respect to the rectangular bounding box of the shape.
//   perim = Anchors are placed along the rounded or chamfered perimeter of the shape.
// Example(2D):
//   rect(40);
// Example(2D): Anchored
//   rect([40,30], anchor=FRONT);
// Example(2D): Spun
//   rect([40,30], anchor=FRONT, spin=30);
// Example(2D): Chamferred Rect
//   rect([40,30], chamfer=5);
// Example(2D): Rounded Rect
//   rect([40,30], rounding=5);
// Example(2D): Negative-Chamferred Rect
//   rect([40,30], chamfer=-5);
// Example(2D): Negative-Rounded Rect
//   rect([40,30], rounding=-5);
// Example(2D): Combined Rounded-Chamfered Rect with corner flips
//   rect([1,1], chamfer = 0.25*[0,1,-1,0],
//        rounding=.25*[1,0,0,-1], corner_flip = true, $fn=32);
// Example(2D): Default "box" Anchors
//   color("red") rect([40,30]);
//   rect([40,30], rounding=10)
//       show_anchors();
// Example(2D): "perim" Anchors
//   rect([40,30], rounding=10, atype="perim")
//       show_anchors();
// Example(2D): "perim" Anchors
//   rect([40,30], rounding=[-10,-8,-3,-7], atype="perim")
//       show_anchors();
// Example(2D): Mixed Chamferring and Rounding
//   rect([40,30],rounding=[5,0,10,0],chamfer=[0,8,0,15],$fa=1,$fs=1);
// Example(2D): Called as Function
//   path = rect([40,30], chamfer=5, anchor=FRONT, spin=30);
//   stroke(path, closed=true);
//   move_copies(path) color("blue") circle(d=2,$fn=8);
module rect(size=1, rounding=0, atype="box", chamfer=0, anchor=CENTER, spin=0, corner_flip = false) {
    errchk = assert(in_list(atype, ["box", "perim"]));
    size = [for (c = force_list(size,2)) max(0,c)];
    if (!all_positive(size)) {
        attachable(anchor,spin, two_d=true, size=size) {
            union();
            children();
        }
    } else if (rounding==0 && chamfer==0) {
        attachable(anchor, spin, two_d=true, size=size) {
            square(size, center=true);
            children();
        }
    } else {
        pts_over = rect(size=size, rounding=rounding, chamfer=chamfer, atype=atype, corner_flip = corner_flip, _return_override=true);
        pts = pts_over[0];
        override = pts_over[1];
        attachable(anchor, spin, two_d=true, size=size,override=override) {
            polygon(pts);
            children();
        }
    }
}



function rect(size=1, rounding=0, chamfer=0, atype="box", anchor=CENTER, spin=0, _return_override, corner_flip = false) =
    assert(is_num(size)     || is_vector(size,2))
    assert(is_num(chamfer)  || is_vector(chamfer,4))
    assert(is_num(rounding) || is_vector(rounding,4))
    assert(in_list(atype, ["box", "perim"]))
    let(
        anchor=_force_anchor_2d(anchor),
        size = [for (c = force_list(size,2)) max(0,c)],
        corner_flip = [for (c = force_list(corner_flip,4)) c ? true : false],
        chamfer = force_list(chamfer,4), 
        rounding = force_list(rounding,4)
    )
    assert(all_nonnegative(size), "All components of size must be >=0")
    all_zero(concat(chamfer,rounding),0) ?
        let(
             path = [
                 [ size.x/2, -size.y/2],
                 [-size.x/2, -size.y/2],
                 [-size.x/2,  size.y/2],
                 [ size.x/2,  size.y/2],
             ]
        )
        rot(spin, p=move(-v_mul(anchor,size/2), p=path))
    :
    assert(all_zero(v_mul(chamfer,rounding),0), "Cannot specify chamfer and rounding at the same corner")
    let(
        quadorder = [3,2,1,0],
        quadpos = [[1,1],[-1,1],[-1,-1],[1,-1]],
        eps = 1e-9,
        insets = [for (i=[0:3]) abs(chamfer[i])>=eps? chamfer[i] : abs(rounding[i])>=eps? rounding[i] : 0],
        insets_x = max(insets[0]+insets[1],insets[2]+insets[3]),
        insets_y = max(insets[0]+insets[3],insets[1]+insets[2])
    )
    assert(insets_x <= size.x, "Requested roundings and/or chamfers exceed the rect width.")
    assert(insets_y <= size.y, "Requested roundings and/or chamfers exceed the rect height.")
    let(
        corners = [
            for(i = [0:3])
            let(
                quad = quadorder[i],
                qinset = insets[quad],
                qpos = quadpos[quad],
                qchamf = chamfer[quad],
                qround = rounding[quad],
                cverts = quant(segs(abs(qinset)),4)/4,
                step = 90/cverts,
                cp = v_mul(size/2 + (corner_flip[quad] ? (qinset > 0 ? 0 : 1) : -1)*[qinset,abs(qinset)], qpos),
                qpts = abs(qchamf) >= eps? [[0,abs(qinset)], [qinset,0]] :
                    abs(qround) >= eps? [for (j=[0:1:cverts]) let(a=90-j*step) v_mul(polar_to_xy(abs(qinset),a),[sign(qinset),1])] :
                    [[0,0]],
                qfpts = [for (p=qpts) v_mul(p,corner_flip[quad] ? -qpos : qpos)],
                qrpts =  (corner_flip[quad] && qinset > 0 ? -1 : 1) * qpos.x*qpos.y < 0? reverse(qfpts) : qfpts,
                cornerpt = atype=="box" || (qround==0 && qchamf==0) ? undef
                         : qround<0 || qchamf<0 ? [[0,-qpos.y*min(qround,qchamf)]]
                         : [for(seg=pair(qrpts)) let(isect=line_intersection(seg, [[0,0],qpos],SEGMENT,LINE)) if (is_def(isect) && isect!=seg[0]) isect]
              )
            assert(is_undef(cornerpt) || len(cornerpt)==1,"Cannot find corner point to anchor")
            [move(cp, p=qrpts), is_undef(cornerpt)? undef : move(cp,p=
                         (min(chamfer[quad],rounding[quad])<0 && corner_flip[quad] ? [quadpos[quad].x*quadpos[quad].y*cornerpt[0].y, cornerpt[0].x] : cornerpt[0]))]
        ],
        path = deduplicate(flatten(column(corners,0)),closed=true),
        override = [for(i=[0:3])
                      let(quad=quadorder[i])
                      if (is_def(corners[i][1])) [quadpos[quad], [corners[i][1], min(chamfer[quad],rounding[quad])<0 ? (corner_flip[quad] ? [0, quadpos[quad].y] : [quadpos[quad].x, 0]) : undef]]]
      ) _return_override ? [reorient(anchor,spin, two_d=true, size=size, p=path, override=override), override]
                       : reorient(anchor,spin, two_d=true, size=size, p=path, override=override);


// Function&Module: circle()
// Synopsis: Creates the approximation of a circle.
// SynTags: Geom, Path, Ext
// Topics: Shapes (2D), Path Generators (2D)
// See Also: ellipse(), circle_2tangents(), circle_3points()
// Usage: As a Module
//   circle(r|d=, ...) [ATTACHMENTS];
//   circle(points=) [ATTACHMENTS];
//   circle(r|d=, corner=) [ATTACHMENTS];
// Usage: As a Function
//   path = circle(r|d=, ...);
//   path = circle(points=);
//   path = circle(r|d=, corner=);
// Description:
//   When called as the built-in module, creates a 2D polygon that approximates a circle of the given size.
//   When called as a function, returns a 2D list of points (path) for a polygon that approximates a circle of the given size.
//   If `corner=` is given three 2D points, centers the circle so that it will be tangent to both segments of the path, on the inside corner.
//   If `points=` is given three 2D points, centers and sizes the circle so that it passes through all three points.
// Arguments:
//   r = The radius of the circle to create.
//   d = The diameter of the circle to create.
//   ---
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Example(2D): By Radius
//   circle(r=25);
// Example(2D): By Diameter
//   circle(d=50);
// Example(2D): Fit to Three Points
//   pts = [[50,25], [25,-25], [-10,0]];
//   circle(points=pts);
//   color("red") move_copies(pts) circle();
// Example(2D): Fit Tangent to Inside Corner of Two Segments
//   path = [[50,25], [-10,0], [25,-25]];
//   circle(corner=path, r=15);
//   color("red") stroke(path);
// Example(2D): Called as Function
//   path = circle(d=50, anchor=FRONT, spin=45);
//   stroke(path);
function circle(r, d, points, corner, anchor=CENTER, spin=0) =
    assert(is_undef(corner) || (is_path(corner,[2]) && len(corner) == 3))
    assert(is_undef(points) || is_undef(corner), "Cannot specify both points and corner.")
    let(
        data = is_def(points)?
                assert(is_path(points,[2]) && len(points) == 3)
                assert(is_undef(corner), "Cannot specify corner= when points= is given.")
                assert(is_undef(r) && is_undef(d), "Cannot specify r= or d= when points= is given.")
                let( c = circle_3points(points) )
                assert(!is_undef(c[0]), "Points cannot be collinear.")
                let( cp = c[0], r = c[1]  )
                [cp, r] :
            is_def(corner)?
                assert(is_path(corner,[2]) && len(corner) == 3)
                assert(is_undef(points), "Cannot specify points= when corner= is given.")
                let(
                    r = get_radius(r=r, d=d, dflt=1),
                    c = circle_2tangents(r=r, pt1=corner[0], pt2=corner[1], pt3=corner[2])
                )
                assert(c!=undef, "Corner path cannot be collinear.")
                let( cp = c[0] )
                [cp, r] :
            let(
                cp = [0, 0],
                r = get_radius(r=r, d=d, dflt=1)
            ) [cp, r],
        cp = data[0],
        r = data[1]
    )
    assert(r>0, "Radius/diameter must be positive")
    let(
        sides = segs(r),
        path = [for (i=[0:1:sides-1]) let(a=360-i*360/sides) r*[cos(a),sin(a)]+cp]
    ) reorient(anchor,spin, two_d=true, r=r, p=path);

module circle(r, d, points, corner, anchor=CENTER, spin=0) {
    if (is_path(points)) {
        c = circle_3points(points);
        check = assert(c!=undef && c[0] != undef, "Points must not be collinear.");
        cp = c[0];
        r = c[1];
        translate(cp) {
            attachable(anchor,spin, two_d=true, r=r) {
                if (r>0) _circle(r=r);
                children();
            }
        }
    } else if (is_path(corner)) {
        r = get_radius(r=r, d=d, dflt=1);
        c = circle_2tangents(r=r, pt1=corner[0], pt2=corner[1], pt3=corner[2]);
        check = assert(c != undef && c[0] != undef, "Points must not be collinear.");
        cp = c[0];
        translate(cp) {
            attachable(anchor,spin, two_d=true, r=r) {
                if (r>0) _circle(r=r);
                children();
            }
        }
    } else {
        r = get_radius(r=r, d=d, dflt=1);
        attachable(anchor,spin, two_d=true, r=r) {
            if (r>0) _circle(r=r);
            children();
        }
    }
}



// Function&Module: ellipse()
// Synopsis: Creates the approximation of an ellipse or a circle.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), circle_2tangents(), circle_3points()
// Usage: As a Module
//   ellipse(r|d=, [realign=], [circum=], [uniform=], ...) [ATTACHMENTS];
// Usage: As a Function
//   path = ellipse(r|d=, [realign=], [circum=], [uniform=], ...);
// Description:
//   When called as a module, creates a 2D polygon that approximates a circle or ellipse of the given size.
//   When called as a function, returns a 2D list of points (path) for a polygon that approximates a circle or ellipse of the given size.
//   By default the point list or shape is the same as the one you would get by scaling the output of {{circle()}}, but with this module your
//   attachments to the ellipse will retain their dimensions, whereas scaling a circle with attachments will also scale the attachments.
//   If you set `uniform` to true then you will get a polygon with congruent sides whose vertices lie on the ellipse.  The `circum` option
//   requests a polygon that circumscribes the requested ellipse (so the specified ellipse will fit into the resulting polygon).  Note that
//   you cannot gives `circum=true` and `uniform=true`.  
// Arguments:
//   r = Radius of the circle or pair of semiaxes of ellipse 
//   ---
//   d = Diameter of the circle or a pair giving the full X and Y axis lengths.  
//   realign = If false starts the approximate ellipse with a point on the X+ axis.  If true the midpoint of a side is on the X+ axis and the first point of the polygon is below the X+ axis.  This can result in a very different polygon when $fn is small.  Default: false
//   uniform = If true, the polygon that approximates the circle will have segments of equal length.  Only works if `circum=false`.  Default: false
//   circum = If true, the polygon that approximates the circle will be upsized slightly to circumscribe the theoretical circle.  If false, it inscribes the theoretical circle.  If this is true then `uniform` must be false.  Default: false
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Example(2D): By Radius
//   ellipse(r=25);
// Example(2D): By Diameter
//   ellipse(d=50);
// Example(2D): Anchoring
//   ellipse(d=50, anchor=FRONT);
// Example(2D): Spin
//   ellipse(d=50, anchor=FRONT, spin=45);
// Example(NORENDER): Called as Function
//   path = ellipse(d=50, anchor=FRONT, spin=45);
// Example(2D,NoAxes): Uniformly sampled hexagon at the top, regular non-uniform one at the bottom
//   r=[10,3];
//   ydistribute(7){
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//       stroke([ellipse(r=r, $fn=6)],width=0.1,color="red");
//     }
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//       stroke([ellipse(r=r, $fn=6,uniform=true)],width=0.1,color="red");
//     }
//   }
// Example(2D): The realigned hexagons are even more different
//   r=[10,3];
//   ydistribute(7){
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//       stroke([ellipse(r=r, $fn=6,realign=true)],width=0.1,color="red");
//     }
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//       stroke([ellipse(r=r, $fn=6,realign=true,uniform=true)],width=0.1,color="red");
//     }
//   }
// Example(2D): For odd $fn the result may not look very elliptical:
//    r=[10,3];
//    ydistribute(7){
//      union(){
//        stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//        stroke([ellipse(r=r, $fn=5,realign=false)],width=0.1,color="red");
//      }
//      union(){
//        stroke([ellipse(r=r, $fn=100)],width=0.05,color="blue");
//        stroke([ellipse(r=r, $fn=5,realign=false,uniform=true)],width=0.1,color="red");
//      }
//    }
// Example(2D): The same ellipse, turned 90 deg, gives a very different result:
//   r=[3,10];
//   xdistribute(7){
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.1,color="blue");
//       stroke([ellipse(r=r, $fn=5,realign=false)],width=0.2,color="red");
//     }
//     union(){
//       stroke([ellipse(r=r, $fn=100)],width=0.1,color="blue");
//       stroke([ellipse(r=r, $fn=5,realign=false,uniform=true)],width=0.2,color="red");
//     }
//   }
module ellipse(r, d, realign=false, circum=false, uniform=false, anchor=CENTER, spin=0)
{
    r = force_list(get_radius(r=r, d=d, dflt=1),2);
    dummy = assert(is_vector(r,2) && all_positive(r), "Invalid radius or diameter for ellipse");
    sides = segs(max(r));
    sc = circum? (1 / cos(180/sides)) : 1;
    rx = r.x * sc;
    ry = r.y * sc;
    attachable(anchor,spin, two_d=true, r=[rx,ry]) {
        if (uniform) {
            check = assert(!circum, "Circum option not allowed when \"uniform\" is true");
            polygon(ellipse(r,realign=realign, circum=circum, uniform=true));
        }
        else if (rx < ry) {
            xscale(rx/ry) {
                zrot(realign? 180/sides : 0) {
                    circle(r=ry, $fn=sides);
                }
            }
        } else {
            yscale(ry/rx) {
                zrot(realign? 180/sides : 0) {
                    circle(r=rx, $fn=sides);
                }
            }
        }
        children();
    }
}


// Iterative refinement to produce an inscribed polygon
// in an ellipse whose side lengths are all equal
function _ellipse_refine(a,b,N, _theta=[]) =
   len(_theta)==0? _ellipse_refine(a,b,N,lerpn(0,360,N,endpoint=false))
   :
   let(
       pts = [for(t=_theta) [a*cos(t),b*sin(t)]],
       lenlist= path_segment_lengths(pts,closed=true),
       meanlen = mean(lenlist),
       error = lenlist/meanlen
   )
   all_equal(error,EPSILON) ? pts
   :
   let(
        dtheta = [each deltas(_theta),
                  360-last(_theta)],
        newdtheta = [for(i=idx(dtheta)) dtheta[i]/error[i]],
        adjusted = [0,each cumsum(list_head(newdtheta / sum(newdtheta) * 360))]
   )
   _ellipse_refine(a,b,N,adjusted);




function _ellipse_refine_realign(a,b,N, _theta=[],i=0) =
   len(_theta)==0?
         _ellipse_refine_realign(a,b,N, count(N-1,180/N,360/N))
   :
   let(
       pts = [for(t=_theta) [a*cos(t),b*sin(t)],
              [a*cos(_theta[0]), -b*sin(_theta[0])]],
       lenlist= path_segment_lengths(pts,closed=true),
       meanlen = mean(lenlist),
       error = lenlist/meanlen
   )
   all_equal(error,EPSILON) ? pts
   :
   let(
        dtheta = [each deltas(_theta),
                  360-last(_theta)-_theta[0],
                  2*_theta[0]],
        newdtheta = [for(i=idx(dtheta)) dtheta[i]/error[i]],
        normdtheta = newdtheta / sum(newdtheta) * 360,
        adjusted = cumsum([last(normdtheta)/2, each list_head(normdtheta, -3)])
   )
   _ellipse_refine_realign(a,b,N,adjusted, i+1);



function ellipse(r, d, realign=false, circum=false, uniform=false, anchor=CENTER, spin=0) =
    let(
        r = force_list(get_radius(r=r, d=d, dflt=1),2),
        sides = segs(max(r))
    )
    assert(all_positive(r), "All components of the radius must be positive.")
    uniform
      ? assert(!circum, "Circum option not allowed when \"uniform\" is true")
        reorient(anchor,spin,
            two_d=true, r=[r.x,r.y],
            p=realign
              ? reverse(_ellipse_refine_realign(r.x,r.y,sides))
              : reverse_polygon(_ellipse_refine(r.x,r.y,sides))
        )
      : let(
            offset = realign? 180/sides : 0,
            sc = circum? (1 / cos(180/sides)) : 1,
            rx = r.x * sc,
            ry = r.y * sc,
            pts = [
                for (i=[0:1:sides-1])
                let (a = 360-offset-i*360/sides)
                [rx*cos(a), ry*sin(a)]
            ]
        ) reorient(anchor,spin, two_d=true, r=[rx,ry], p=pts);


// Section: Polygons

// Function&Module: regular_ngon()
// Synopsis: Creates a regular N-sided polygon.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: debug_polygon(), circle(), pentagon(), hexagon(), octagon(), ellipse(), star()
// Usage:
//   regular_ngon(n, r|d=|or=|od=, [realign=]) [ATTACHMENTS];
//   regular_ngon(n, ir=|id=, [realign=]) [ATTACHMENTS];
//   regular_ngon(n, side=, [realign=]) [ATTACHMENTS];
// Description:
//   When called as a function, returns a 2D path for a regular N-sided polygon.
//   When called as a module, creates a 2D regular N-sided polygon.
// Arguments:
//   n = The number of sides.
//   r/or = Outside radius, at points.
//   ---
//   d/od = Outside diameter, at points.
//   ir = Inside radius, at center of sides.
//   id = Inside diameter, at center of sides.
//   side = Length of each side.
//   rounding = Radius of rounding for the tips of the polygon.  Default: 0 (no rounding)
//   realign = If false, vertex 0 will lie on the X+ axis.  If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis.    Default: false
//   align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction.  This occurs before spin.
//   align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction.  This occurs before spin.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "tip0", "tip1", etc. = Each tip has an anchor, pointing outwards.
//   "side0", "side1", etc. = The center of each side has an anchor, pointing outwards.
// Example(2D): by Outer Size
//   regular_ngon(n=5, or=30);
//   regular_ngon(n=5, od=60);
// Example(2D): by Inner Size
//   regular_ngon(n=5, ir=30);
//   regular_ngon(n=5, id=60);
// Example(2D): by Side Length
//   regular_ngon(n=8, side=20);
// Example(2D): Realigned
//   regular_ngon(n=8, side=20, realign=true);
// Example(2D): Alignment by Tip
//   regular_ngon(n=5, r=30, align_tip=BACK+RIGHT)
//       attach("tip0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Alignment by Side
//   regular_ngon(n=5, r=30, align_side=BACK+RIGHT)
//       attach("side0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Rounded
//   regular_ngon(n=5, od=100, rounding=20, $fn=20);
// Example(2D): Called as Function
//   stroke(closed=true, regular_ngon(n=6, or=30));
function regular_ngon(n=6, r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0, _mat, _anchs) =
    assert(is_int(n) && n>=3)
    assert(is_undef(align_tip) || is_vector(align_tip))
    assert(is_undef(align_side) || is_vector(align_side))
    assert(is_undef(align_tip) || is_undef(align_side), "Can only specify one of align_tip and align-side")
    let(
        sc = 1/cos(180/n),
        ir = is_finite(ir)? ir*sc : undef,
        id = is_finite(id)? id*sc : undef,
        side = is_finite(side)? side/2/sin(180/n) : undef,
        r = get_radius(r1=ir, r2=or, r=r, d1=id, d2=od, d=d, dflt=side)
    )
    assert(!is_undef(r), "regular_ngon(): need to specify one of r, d, or, od, ir, id, side.")
    assert(all_positive([r]), "polygon size must be a positive value")
    let(
        inset = opp_ang_to_hyp(rounding, (180-360/n)/2),
        mat = !is_undef(_mat) ? _mat :
            ( realign? zrot(-180/n) : ident(4)) * (
                !is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip)) :
                !is_undef(align_side)? rot(from=RIGHT, to=point2d(align_side)) * zrot(180/n) :
                1
            ),
        path4 = rounding==0? ellipse(r=r, $fn=n) : (
            let(
                steps = floor(segs(r)/n),
                step = 360/n/steps,
                path2 = [
                    for (i = [0:1:n-1]) let(
                        a = 360 - i*360/n,
                        p = polar_to_xy(r-inset, a)
                    )
                    each arc(n=steps, cp=p, r=rounding, start=a+180/n, angle=-360/n)
                ],
                maxx_idx = max_index(column(path2,0)),
                path3 = list_rotate(path2,maxx_idx)
            ) path3
        ),
        path = apply(mat, path4),
        anchors = !is_undef(_anchs) ? _anchs :
            !is_string(anchor)? [] : [
            for (i = [0:1:n-1]) let(
                a1 = 360 - i*360/n,
                a2 = a1 - 360/n,
                p1 = apply(mat, polar_to_xy(r,a1)),
                p2 = apply(mat, polar_to_xy(r,a2)),
                tipp = apply(mat, polar_to_xy(r-inset+rounding,a1)),
                pos = (p1+p2)/2
            ) each [
                named_anchor(str("tip",i), tipp, unit(tipp,BACK), 0),
                named_anchor(str("side",i), pos, unit(pos,BACK), 0),
            ]
        ]
    ) reorient(anchor,spin, two_d=true, path=path, extent=false, p=path, anchors=anchors);


module regular_ngon(n=6, r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) {
    sc = 1/cos(180/n);
    ir = is_finite(ir)? ir*sc : undef;
    id = is_finite(id)? id*sc : undef;
    side = is_finite(side)? side/2/sin(180/n) : undef;
    r = get_radius(r1=ir, r2=or, r=r, d1=id, d2=od, d=d, dflt=side);
    check = assert(!is_undef(r), "regular_ngon(): need to specify one of r, d, or, od, ir, id, side.")
            assert(all_positive([r]), "polygon size must be a positive value");
    mat = ( realign? zrot(-180/n) : ident(4) ) * (
            !is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip)) :
            !is_undef(align_side)? rot(from=RIGHT, to=point2d(align_side)) * zrot(180/n) :
            1
        );
    inset = opp_ang_to_hyp(rounding, (180-360/n)/2);
    anchors = [
        for (i = [0:1:n-1]) let(
            a1 = 360 - i*360/n,
            a2 = a1 - 360/n,
            p1 = apply(mat, polar_to_xy(r,a1)),
            p2 = apply(mat, polar_to_xy(r,a2)),
            tipp = apply(mat, polar_to_xy(r-inset+rounding,a1)),
            pos = (p1+p2)/2
        ) each [
            named_anchor(str("tip",i), tipp, unit(tipp,BACK), 0),
            named_anchor(str("side",i), pos, unit(pos,BACK), 0),
        ]
    ];
    path = regular_ngon(n=n, r=r, rounding=rounding, _mat=mat, _anchs=anchors);
    attachable(anchor,spin, two_d=true, path=path, extent=false, anchors=anchors) {
        polygon(path);
        children();
    }
}


// Function&Module: pentagon()
// Synopsis: Creates a regular pentagon.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), regular_ngon(), hexagon(), octagon(), ellipse(), star()
// Usage:
//   pentagon(or|od=, [realign=], [align_tip=|align_side=]) [ATTACHMENTS];
//   pentagon(ir=|id=, [realign=], [align_tip=|align_side=]) [ATTACHMENTS];
//   pentagon(side=, [realign=], [align_tip=|align_side=]) [ATTACHMENTS];
// Usage: as function
//   path = pentagon(...);
// Description:
//   When called as a function, returns a 2D path for a regular pentagon.
//   When called as a module, creates a 2D regular pentagon.
// Arguments:
//   r/or = Outside radius, at points.
//   ---
//   d/od = Outside diameter, at points.
//   ir = Inside radius, at center of sides.
//   id = Inside diameter, at center of sides.
//   side = Length of each side.
//   rounding = Radius of rounding for the tips of the polygon.  Default: 0 (no rounding)
//   realign = If false, vertex 0 will lie on the X+ axis.  If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis.    Default: false
//   align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction.  This occurs before spin.
//   align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction.  This occurs before spin.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "tip0" ... "tip4" = Each tip has an anchor, pointing outwards.
//   "side0" ... "side4" = The center of each side has an anchor, pointing outwards.
// Example(2D): by Outer Size
//   pentagon(or=30);
//   pentagon(od=60);
// Example(2D): by Inner Size
//   pentagon(ir=30);
//   pentagon(id=60);
// Example(2D): by Side Length
//   pentagon(side=20);
// Example(2D): Realigned
//   pentagon(side=20, realign=true);
// Example(2D): Alignment by Tip
//   pentagon(r=30, align_tip=BACK+RIGHT)
//       attach("tip0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Alignment by Side
//   pentagon(r=30, align_side=BACK+RIGHT)
//       attach("side0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Rounded
//   pentagon(od=100, rounding=20, $fn=20);
// Example(2D): Called as Function
//   stroke(closed=true, pentagon(or=30));
function pentagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
    regular_ngon(n=5, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);


module pentagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
    regular_ngon(n=5, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();


// Function&Module: hexagon()
// Synopsis: Creates a regular hexagon.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), regular_ngon(), pentagon(), octagon(), ellipse(), star()
// Usage: As Module
//   hexagon(r/or, [realign=], <align_tip=|align_side=>, [rounding=], ...) [ATTACHMENTS];
//   hexagon(d=/od=, ...) [ATTACHMENTS];
//   hexagon(ir=/id=, ...) [ATTACHMENTS];
//   hexagon(side=, ...) [ATTACHMENTS];
// Usage: As Function
//   path = hexagon(...);
// Description:
//   When called as a function, returns a 2D path for a regular hexagon.
//   When called as a module, creates a 2D regular hexagon.
// Arguments:
//   r/or = Outside radius, at points.
//   ---
//   d/od = Outside diameter, at points.
//   ir = Inside radius, at center of sides.
//   id = Inside diameter, at center of sides.
//   side = Length of each side.
//   rounding = Radius of rounding for the tips of the polygon.  Default: 0 (no rounding)
//   realign = If false, vertex 0 will lie on the X+ axis.  If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis.    Default: false
//   align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction.  This occurs before spin.
//   align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction.  This occurs before spin.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "tip0" ... "tip5" = Each tip has an anchor, pointing outwards.
//   "side0" ... "side5" = The center of each side has an anchor, pointing outwards.
// Example(2D): by Outer Size
//   hexagon(or=30);
//   hexagon(od=60);
// Example(2D): by Inner Size
//   hexagon(ir=30);
//   hexagon(id=60);
// Example(2D): by Side Length
//   hexagon(side=20);
// Example(2D): Realigned
//   hexagon(side=20, realign=true);
// Example(2D): Alignment by Tip
//   hexagon(r=30, align_tip=BACK+RIGHT)
//       attach("tip0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Alignment by Side
//   hexagon(r=30, align_side=BACK+RIGHT)
//       attach("side0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Rounded
//   hexagon(od=100, rounding=20, $fn=20);
// Example(2D): Called as Function
//   stroke(closed=true, hexagon(or=30));
function hexagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
    regular_ngon(n=6, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);


module hexagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
    regular_ngon(n=6, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();


// Function&Module: octagon()
// Synopsis: Creates a regular octagon.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), regular_ngon(), pentagon(), hexagon(), ellipse(), star()
// Usage: As Module
//   octagon(r/or, [realign=], [align_tip=|align_side=], [rounding=], ...) [ATTACHMENTS];
//   octagon(d=/od=, ...) [ATTACHMENTS];
//   octagon(ir=/id=, ...) [ATTACHMENTS];
//   octagon(side=, ...) [ATTACHMENTS];
// Usage: As Function
//   path = octagon(...);
// Description:
//   When called as a function, returns a 2D path for a regular octagon.
//   When called as a module, creates a 2D regular octagon.
// Arguments:
//   r/or = Outside radius, at points.
//   d/od = Outside diameter, at points.
//   ir = Inside radius, at center of sides.
//   id = Inside diameter, at center of sides.
//   side = Length of each side.
//   rounding = Radius of rounding for the tips of the polygon.  Default: 0 (no rounding)
//   realign = If false, vertex 0 will lie on the X+ axis.  If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis.    Default: false
//   align_tip = If given as a 2D vector, rotates the whole shape so that the first vertex points in that direction.  This occurs before spin.
//   align_side = If given as a 2D vector, rotates the whole shape so that the normal of side0 points in that direction.  This occurs before spin.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "tip0" ... "tip7" = Each tip has an anchor, pointing outwards.
//   "side0" ... "side7" = The center of each side has an anchor, pointing outwards.
// Example(2D): by Outer Size
//   octagon(or=30);
//   octagon(od=60);
// Example(2D): by Inner Size
//   octagon(ir=30);
//   octagon(id=60);
// Example(2D): by Side Length
//   octagon(side=20);
// Example(2D): Realigned
//   octagon(side=20, realign=true);
// Example(2D): Alignment by Tip
//   octagon(r=30, align_tip=BACK+RIGHT)
//       attach("tip0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Alignment by Side
//   octagon(r=30, align_side=BACK+RIGHT)
//       attach("side0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Rounded
//   octagon(od=100, rounding=20, $fn=20);
// Example(2D): Called as Function
//   stroke(closed=true, octagon(or=30));
function octagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0) =
    regular_ngon(n=8, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin);


module octagon(r, d, or, od, ir, id, side, rounding=0, realign=false, align_tip, align_side, anchor=CENTER, spin=0)
    regular_ngon(n=8, r=r, d=d, or=or, od=od, ir=ir, id=id, side=side, rounding=rounding, realign=realign, align_tip=align_tip, align_side=align_side, anchor=anchor, spin=spin) children();


// Function&Module: right_triangle()
// Synopsis: Creates a right triangle.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: square(), rect(), regular_ngon(), pentagon(), hexagon(), octagon(), star()
// Usage: As Module
//   right_triangle(size, [center], ...) [ATTACHMENTS];
// Usage: As Function
//   path = right_triangle(size, [center], ...);
// Description:
//   When called as a module, creates a right triangle with the Hypotenuse in the X+Y+ quadrant.
//   When called as a function, returns a 2D path for a right triangle with the Hypotenuse in the X+Y+ quadrant.
// Arguments:
//   size = The width and length of the right triangle, given as a scalar or an XY vector.
//   center = If true, forces `anchor=CENTER`.  If false, forces `anchor=[-1,-1]`.  Default: undef (use `anchor=`)
//   ---
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "hypot" = Center of angled side, perpendicular to that side.
// Example(2D):
//   right_triangle([40,30]);
// Example(2D): With `center=true`
//   right_triangle([40,30], center=true);
// Example(2D): Standard Anchors
//   right_triangle([80,30], center=true)
//       show_anchors(custom=false);
//   color([0.5,0.5,0.5,0.1])
//       square([80,30], center=true);
// Example(2D): Named Anchors
//   right_triangle([80,30], center=true)
//       show_anchors(std=false);
function right_triangle(size=[1,1], center, anchor, spin=0) =
    let(
        size = is_num(size)? [size,size] : size,
        anchor = get_anchor(anchor, center, [-1,-1], [-1,-1])
    )
    assert(is_vector(size,2))
    assert(min(size)>0, "Must give positive size")
    let(
        path = [ [size.x/2,-size.y/2], [-size.x/2,-size.y/2], [-size.x/2,size.y/2] ],
        anchors = [
            named_anchor("hypot", CTR, unit([size.y,size.x])),
        ]
    ) reorient(anchor,spin, two_d=true, size=[size.x,size.y], anchors=anchors, p=path);

module right_triangle(size=[1,1], center, anchor, spin=0) {
    size = is_num(size)? [size,size] : size;
    anchor = get_anchor(anchor, center, [-1,-1], [-1,-1]);
    check = assert(is_vector(size,2));
    path = right_triangle(size, anchor="origin");
    anchors = [
        named_anchor("hypot", CTR, unit([size.y,size.x])),
    ];
    attachable(anchor,spin, two_d=true, size=[size.x,size.y], anchors=anchors) {
        polygon(path);
        children();
    }
}


// Function&Module: trapezoid()
// Synopsis: Creates a trapezoid with parallel top and bottom sides.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: rect(), square()
// Usage: As Module
//   trapezoid(h, w1, w2, [shift=], [rounding=], [chamfer=], [flip=], ...) [ATTACHMENTS];
//   trapezoid(h, w1, ang=, [rounding=], [chamfer=], [flip=], ...) [ATTACHMENTS];
//   trapezoid(h, w2=, ang=, [rounding=], [chamfer=], [flip=], ...) [ATTACHMENTS];
//   trapezoid(w1=, w2=, ang=, [rounding=], [chamfer=], [flip=], ...) [ATTACHMENTS];
// Usage: As Function
//   path = trapezoid(...);
// Description:
//   When called as a function, returns a 2D path for a trapezoid with parallel front and back (top and bottom) sides. 
//   When called as a module, creates a 2D trapezoid.  You can specify the trapezoid by giving its height and the lengths
//   of its two bases.  Alternatively, you can omit one of those parameters and specify the lower angle(s).
//   The shift parameter, which cannot be combined with ang, shifts the back (top) of the trapezoid to the right.  
// Arguments:
//   h = The Y axis height of the trapezoid.
//   w1 = The X axis width of the front end of the trapezoid.
//   w2 = The X axis width of the back end of the trapezoid.
//   ---
//   ang = Specify the bottom angle(s) of the trapezoid.  Can give a scalar for an isosceles trapezoid or a list of two angles, the left angle and right angle.  You must omit one of `h`, `w1`, or `w2` to allow the freedom to control the angles. 
//   shift = Scalar value to shift the back of the trapezoid along the X axis by.  Cannot be combined with ang.  Default: 0
//   rounding = The rounding radius for the corners.  If given as a list of four numbers, gives individual radii for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no rounding)
//   chamfer = The Length of the chamfer faces at the corners.  If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-].  Default: 0 (no chamfer)
//   flip = If true, negative roundings and chamfers will point forward and back instead of left and right.  Default: `false`.
//   atype = The type of anchoring to use with `anchor=`.  Valid opptions are "box" and "perim".  This lets you choose between putting anchors on the rounded or chamfered perimeter, or on the square bounding box of the shape. Default: "box"
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Anchor Types:
//   box = Anchor is with respect to the rectangular bounding box of the shape.
//   perim = Anchors are placed along the rounded or chamfered perimeter of the shape.
// Examples(2D):
//   trapezoid(h=30, w1=40, w2=20);
//   trapezoid(h=25, w1=20, w2=35);
//   trapezoid(h=20, w1=40, w2=0);
//   trapezoid(h=20, w1=30, ang=60);
//   trapezoid(h=20, w1=20, ang=120);
//   trapezoid(h=20, w2=10, ang=60);
//   trapezoid(h=20, w1=50, ang=[40,60]);
//   trapezoid(w1=30, w2=10, ang=[30,90]);
// Example(2D): Chamfered Trapezoid
//   trapezoid(h=30, w1=60, w2=40, chamfer=5);
// Example(2D): Negative Chamfered Trapezoid
//   trapezoid(h=30, w1=60, w2=40, chamfer=-5);
// Example(2D): Flipped Negative Chamfered Trapezoid
//   trapezoid(h=30, w1=60, w2=40, chamfer=-5, flip=true);
// Example(2D): Rounded Trapezoid
//   trapezoid(h=30, w1=60, w2=40, rounding=5);
// Example(2D): Negative Rounded Trapezoid
//   trapezoid(h=30, w1=60, w2=40, rounding=-5);
// Example(2D): Flipped Negative Rounded Trapezoid
//   trapezoid(h=30, w1=60, w2=40, rounding=-5, flip=true);
// Example(2D): Mixed Chamfering and Rounding
//   trapezoid(h=30, w1=60, w2=40, rounding=[5,0,-10,0],chamfer=[0,8,0,-15],$fa=1,$fs=1);
// Example(2D): default anchors for roundings
//   trapezoid(h=30, w1=100, ang=[66,44],rounding=5) show_anchors();
// Example(2D): default anchors for negative roundings are still at the trapezoid corners
//   trapezoid(h=30, w1=100, ang=[66,44],rounding=-5) show_anchors();
// Example(2D): "perim" anchors are at the tips of negative roundings
//   trapezoid(h=30, w1=100, ang=[66,44],rounding=-5, atype="perim") show_anchors();
// Example(2D): They point the other direction if you flip them
//   trapezoid(h=30, w1=100, ang=[66,44],rounding=-5, atype="perim",flip=true) show_anchors();
// Example(2D): Called as Function
//   stroke(closed=true, trapezoid(h=30, w1=40, w2=20));

function _trapezoid_dims(h,w1,w2,shift,ang) = 
    let(  
        h = is_def(h)? h
          : num_defined([w1,w2,each ang])==4 ? (w1-w2) * sin(ang[0]) * sin(ang[1]) / sin(ang[0]+ang[1])
          : undef
    )
    is_undef(h) ? [h]
  :
    let(
        x1 = is_undef(ang[0]) || ang[0]==90 ? 0 : h/tan(ang[0]),
        x2 = is_undef(ang[1]) || ang[1]==90 ? 0 : h/tan(ang[1]),
        w1 = is_def(w1)? w1
           : is_def(w2) && is_def(ang[0]) ? w2 + x1 + x2
           : undef,
        w2 = is_def(w2)? w2
           : is_def(w1) && is_def(ang[0]) ? w1 - x1 - x2
           : undef,
        shift = first_defined([shift,(x1-x2)/2])
    )
    [h,w1,w2,shift];



function trapezoid(h, w1, w2, ang, shift, chamfer=0, rounding=0, flip=false, anchor=CENTER, spin=0,atype="box", _return_override, angle) =
    assert(is_undef(angle), "The angle parameter has been replaced by ang, which specifies trapezoid interior angle")
    assert(is_undef(h) || is_finite(h))
    assert(is_undef(w1) || is_finite(w1))
    assert(is_undef(w2) || is_finite(w2))
    assert(is_undef(ang) || is_finite(ang) || is_vector(ang,2))
    assert(num_defined([h, w1, w2, ang]) == 3, "Must give exactly 3 of the arguments h, w1, w2, and angle.")
    assert(is_undef(shift) || is_finite(shift))
    assert(num_defined([shift,ang])<2, "Cannot specify shift and ang together")
    assert(is_finite(chamfer)  || is_vector(chamfer,4))
    assert(is_finite(rounding) || is_vector(rounding,4))
    let(
        ang = force_list(ang,2),
        angOK = len(ang)==2 && (ang==[undef,undef] || (all_positive(ang) && ang[0]<180 && ang[1]<180))
    )
    assert(angOK, "trapezoid angles must be scalar or 2-vector, strictly between 0 and 180")
    let(
        h_w1_w2_shift = _trapezoid_dims(h,w1,w2,shift,ang),
        h = h_w1_w2_shift[0],
        w1 = h_w1_w2_shift[1],
        w2 = h_w1_w2_shift[2],
        shift = h_w1_w2_shift[3],
        chamfer = force_list(chamfer,4),
        rounding = force_list(rounding,4)
    )
    assert(all_zero(v_mul(chamfer,rounding),0), "Cannot specify chamfer and rounding at the same corner")
    let(
        srads = chamfer+rounding, 
        rads = v_abs(srads)
    )
    assert(w1>=0 && w2>=0 && h>0, "Degenerate trapezoid geometry.")
    assert(w1+w2>0, "Degenerate trapezoid geometry.")
    let(
        base = [
            [ w2/2+shift, h/2],
            [-w2/2+shift, h/2],
            [-w1/2,-h/2],
            [ w1/2,-h/2],
        ],
        ang1 = v_theta(base[0]-base[3])-90,
        ang2 = v_theta(base[1]-base[2])-90,
        angs = [ang1, ang2, ang2, ang1],
        qdirs = [[1,1], [-1,1], [-1,-1], [1,-1]],
        hyps = [for (i=[0:3]) adj_ang_to_hyp(rads[i],angs[i])],
        offs = [
            for (i=[0:3]) let(
                xoff = adj_ang_to_opp(rads[i],angs[i]),
                a = [xoff, -rads[i]] * qdirs[i].y * (srads[i]<0 && flip? -1 : 1),
                b = a + [hyps[i] * qdirs[i].x * (srads[i]<0 && !flip? 1 : -1), 0]
            ) b
        ],
        corners = [
             (
                let(i = 0)
                rads[i] == 0? [base[i]]
              : srads[i] > 0? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[angs[i], 90], r=rads[i])
              : flip? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[angs[i],-90], r=rads[i])
              : arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[180+angs[i],90], r=rads[i])
            ),
             (
                let(i = 1)
                rads[i] == 0? [base[i]] 
              : srads[i] > 0? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[90,180+angs[i]], r=rads[i]) 
              : flip? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[270,180+angs[i]], r=rads[i]) 
              : arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[90,angs[i]], r=rads[i])
            ),
             (
                let(i = 2)
                rads[i] == 0? [base[i]] 
              : srads[i] > 0? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[180+angs[i],270], r=rads[i]) 
              : flip? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[180+angs[i],90], r=rads[i]) 
              : arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[angs[i],-90], r=rads[i])
            ),
             (
                let(i = 3)
                rads[i] == 0? [base[i]] 
              : srads[i] > 0? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[-90,angs[i]], r=rads[i]) 
              : flip? arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[90,angs[i]], r=rads[i]) 
              : arc(n=rounding[i]?undef:2, cp=base[i]+offs[i], angle=[270,180+angs[i]], r=rads[i])
            ),
        ],
        path = reverse(flatten(corners)),
        override = [for(i=[0:3])
                      if (atype!="box" && srads[i]!=0)
                         srads[i]>0?
                             let(dir = unit(base[i]-select(base,i-1)) + unit(base[i]-select(base,i+1)),
                                pt=[for(seg=pair(corners[i])) let(isect=line_intersection(seg, [base[i],base[i]+dir],SEGMENT,LINE))
                                                             if (is_def(isect) && isect!=seg[0]) isect]
                             )
                             [qdirs[i], [pt[0], undef]]
                        : flip?
                            let(  dir=unit(base[i] - select(base,i+(i%2==0?-1:1))))
                            [qdirs[i], [select(corners[i],i%2==0?0:-1), dir]]
                        : let( dir = [qdirs[i].x,0])
                            [qdirs[i], [select(corners[i],i%2==0?-1:0), dir]]]
    ) _return_override ? [reorient(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, p=path, override=override),override]
                       : reorient(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, p=path, override=override);




module trapezoid(h, w1, w2, ang, shift, chamfer=0, rounding=0, flip=false, anchor=CENTER, spin=0, atype="box", angle) {
    path_over = trapezoid(h=h, w1=w1, w2=w2, ang=ang, shift=shift, chamfer=chamfer, rounding=rounding,
                          flip=flip, angle=angle,atype=atype,anchor="origin",_return_override=true);
    path=path_over[0];
    override = path_over[1];
    ang = force_list(ang,2);
    h_w1_w2_shift = _trapezoid_dims(h,w1,w2,shift,ang);
    h = h_w1_w2_shift[0];
    w1 = h_w1_w2_shift[1];
    w2 = h_w1_w2_shift[2];
    shift = h_w1_w2_shift[3];
    attachable(anchor,spin, two_d=true, size=[w1,h], size2=w2, shift=shift, override=override) {
        polygon(path);
        children();
    }
}



// Function&Module: star()
// Synopsis: Creates a star-shaped polygon or returns a star-shaped region.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse(), regular_ngon()
// Usage: As Module
//   star(n, r/or, ir, [realign=], [align_tip=], [align_pit=], ...) [ATTACHMENTS];
//   star(n, r/or, step=, ...) [ATTACHMENTS];
// Usage: As Function
//   path = star(n, r/or, ir, [realign=], [align_tip=], [align_pit=], ...);
//   path = star(n, r/or, step=, ...);
// Description:
//   When called as a function, returns the path needed to create a star polygon with N points.
//   When called as a module, creates a star polygon with N points.
// Arguments:
//   n = The number of stellate tips on the star.
//   r/or = The radius to the tips of the star.
//   ir = The radius to the inner corners of the star.
//   ---
//   d/od = The diameter to the tips of the star.
//   id = The diameter to the inner corners of the star.
//   step = Calculates the radius of the inner star corners by virtually drawing a straight line `step` tips around the star.  2 <= step < n/2
//   realign = If false, vertex 0 will lie on the X+ axis.  If true then the midpoint of the last edge will lie on the X+ axis, and vertex 0 will be below the X axis.    Default: false
//   align_tip = If given as a 2D vector, rotates the whole shape so that the first star tip points in that direction.  This occurs before spin.
//   align_pit = If given as a 2D vector, rotates the whole shape so that the first inner corner is pointed towards that direction.  This occurs before spin.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   atype = Choose "hull" or "intersect" anchor methods.  Default: "hull"
// Named Anchors:
//   "tip0" ... "tip4" = Each tip has an anchor, pointing outwards.
//   "pit0" ... "pit4" = The inside corner between each tip has an anchor, pointing outwards.
//   "midpt0" ... "midpt4" = The center-point between each pair of tips has an anchor, pointing outwards.
// Examples(2D):
//   star(n=5, r=50, ir=25);
//   star(n=5, r=50, step=2);
//   star(n=7, r=50, step=2);
//   star(n=7, r=50, step=3);
// Example(2D): Realigned
//   star(n=7, r=50, step=3, realign=true);
// Example(2D): Alignment by Tip
//   star(n=5, ir=15, or=30, align_tip=BACK+RIGHT)
//       attach("tip0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Alignment by Pit
//   star(n=5, ir=15, or=30, align_pit=BACK+RIGHT)
//       attach("pit0", FWD) color("blue")
//           stroke([[0,0],[0,7]], endcap2="arrow2");
// Example(2D): Called as Function
//   stroke(closed=true, star(n=5, r=50, ir=25));
function star(n, r, ir, d, or, od, id, step, realign=false, align_tip, align_pit, anchor=CENTER, spin=0, atype="hull", _mat, _anchs) =
    assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"")  
    assert(is_undef(align_tip) || is_vector(align_tip))
    assert(is_undef(align_pit) || is_vector(align_pit))
    assert(is_undef(align_tip) || is_undef(align_pit), "Can only specify one of align_tip and align_pit")
    assert(is_def(n), "Must specify number of points, n")
    let(
        r = get_radius(r1=or, d1=od, r=r, d=d),
        count = num_defined([ir,id,step]),
        stepOK = is_undef(step) || (step>1 && step<n/2)
    )
    assert(count==1, "Must specify exactly one of ir, id, step")
    assert(stepOK,  n==4 ? "Parameter 'step' not allowed for 4 point stars"
                  : n==5 || n==6 ? str("Parameter 'step' must be 2 for ",n," point stars")
                  : str("Parameter 'step' must be between 2 and ",floor(n/2-1/2)," for ",n," point stars"))
    let(
        mat = !is_undef(_mat) ? _mat :
            ( realign? zrot(-180/n) : ident(4) ) * (
                !is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip)) :
                !is_undef(align_pit)? rot(from=RIGHT, to=point2d(align_pit)) * zrot(180/n) :
                1
            ),
        stepr = is_undef(step)? r : r*cos(180*step/n)/cos(180*(step-1)/n),
        ir = get_radius(r=ir, d=id, dflt=stepr),
        offset = realign? 180/n : 0,
        path1 = [for(i=[2*n:-1:1]) let(theta=180*i/n, radius=(i%2)?ir:r) radius*[cos(theta), sin(theta)]],
        path = apply(mat, path1),
        anchors = !is_undef(_anchs) ? _anchs :
            !is_string(anchor)? [] : [
            for (i = [0:1:n-1]) let(
                a1 = 360 - i*360/n,
                a2 = a1 - 180/n,
                a3 = a1 - 360/n,
                p1 = apply(mat, polar_to_xy(r,a1)),
                p2 = apply(mat, polar_to_xy(ir,a2)),
                p3 = apply(mat, polar_to_xy(r,a3)),
                pos = (p1+p3)/2
            ) each [
                named_anchor(str("tip",i), p1, unit(p1,BACK), 0),
                named_anchor(str("pit",i), p2, unit(p2,BACK), 0),
                named_anchor(str("midpt",i), pos, unit(pos,BACK), 0),
            ]
        ]
    ) reorient(anchor,spin, two_d=true, path=path, p=path, extent=atype=="hull", anchors=anchors);


module star(n, r, ir, d, or, od, id, step, realign=false, align_tip, align_pit, anchor=CENTER, spin=0, atype="hull") {
    checks =
        assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"")
        assert(is_undef(align_tip) || is_vector(align_tip))
        assert(is_undef(align_pit) || is_vector(align_pit))
        assert(is_undef(align_tip) || is_undef(align_pit), "Can only specify one of align_tip and align_pit");
    r = get_radius(r1=or, d1=od, r=r, d=d, dflt=undef);
    stepr = is_undef(step)? r : r*cos(180*step/n)/cos(180*(step-1)/n);
    ir = get_radius(r=ir, d=id, dflt=stepr);
    mat = ( realign? zrot(-180/n) : ident(4) ) * (
            !is_undef(align_tip)? rot(from=RIGHT, to=point2d(align_tip)) :
            !is_undef(align_pit)? rot(from=RIGHT, to=point2d(align_pit)) * zrot(180/n) :
            1
        );
    anchors = [
        for (i = [0:1:n-1]) let(
            a1 = 360 - i*360/n - (realign? 180/n : 0),
            a2 = a1 - 180/n,
            a3 = a1 - 360/n,
            p1 = apply(mat, polar_to_xy(r,a1)),
            p2 = apply(mat, polar_to_xy(ir,a2)),
            p3 = apply(mat, polar_to_xy(r,a3)),
            pos = (p1+p3)/2
        ) each [
            named_anchor(str("tip",i), p1, unit(p1,BACK), 0),
            named_anchor(str("pit",i), p2, unit(p2,BACK), 0),
            named_anchor(str("midpt",i), pos, unit(pos,BACK), 0),
        ]
    ];
    path = star(n=n, r=r, ir=ir, realign=realign, _mat=mat, _anchs=anchors);
    attachable(anchor,spin, two_d=true, path=path, extent=atype=="hull", anchors=anchors) {
        polygon(path);
        children();
    }
}



/// Internal Function: _path_add_jitter()
/// Topics: Paths
/// See Also: jittered_poly()
/// Usage:
///   jpath = _path_add_jitter(path, [dist], [closed=]);
/// Description:
///   Adds tiny jitter offsets to collinear points in the given path so that they
///   are no longer collinear.  This is useful for preserving subdivision on long
///   straight segments, when making geometry with `polygon()`, for use with
///   `linear_exrtrude()` with a `twist()`.
/// Arguments:
///   path = The path to add jitter to.
///   dist = The amount to jitter points by.  Default: 1/512 (0.00195)
///   ---
///   closed = If true, treat path like a closed polygon.  Default: true
/// Example(3D):
///   d = 100; h = 75; quadsize = 5;
///   path = pentagon(d=d);
///   spath = subdivide_path(path, maxlen=quadsize, closed=true);
///   jpath = _path_add_jitter(spath, closed=true);
///   linear_extrude(height=h, twist=72, slices=h/quadsize)
///      polygon(jpath);
function _path_add_jitter(path, dist=1/512, closed=true) =
    assert(is_path(path))
    assert(is_finite(dist))
    assert(is_bool(closed))
    [
        path[0],
        for (i=idx(path,s=1,e=closed?-1:-2)) let(
            n = line_normal([path[i-1],path[i]])
        ) path[i] + n * (is_collinear(select(path,i-1,i+1))? (dist * ((i%2)*2-1)) : 0),
        if (!closed) last(path)
    ];



// Module: jittered_poly()
// Synopsis: Creates a polygon with extra points for smoother twisted extrusions.
// SynTags: Geom
// Topics: Extrusions
// See Also: subdivide_path()
// Usage:
//   jittered_poly(path, [dist]);
// Description:
//   Creates a 2D polygon shape from the given path in such a way that any extra
//   collinear points are not stripped out in the way that `polygon()` normally does.
//   This is useful for refining the mesh of a `linear_extrude()` with twist.
// Arguments:
//   path = The path to add jitter to.
//   dist = The amount to jitter points by.  Default: 1/512 (0.00195)
// Example:
//   d = 100; h = 75; quadsize = 5;
//   path = pentagon(d=d);
//   spath = subdivide_path(path, maxlen=quadsize, closed=true);
//   linear_extrude(height=h, twist=72, slices=h/quadsize)
//      jittered_poly(spath);
module jittered_poly(path, dist=1/512) {
    no_children($children);
    polygon(_path_add_jitter(path, dist, closed=true));
}


// Section: Curved 2D Shapes


// Function&Module: teardrop2d()
// Synopsis: Creates a 2D teardrop shape.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: teardrop(), onion(), keyhole()
// Description:
//   When called as a module, makes a 2D teardrop shape. Useful for extruding into 3D printable holes as it limits overhang to 45 degrees.  Uses "intersect" style anchoring.  
//   The cap_h parameter truncates the top of the teardrop.  If cap_h is taller than the untruncated form then
//   the result will be the full, untruncated shape.  The segments of the bottom section of the teardrop are
//   calculated to be the same as a circle or cylinder when rotated 90 degrees.  (Note that this agreement is poor when `$fn=6` or `$fn=7`.  
//   If `$fn` is a multiple of four then the teardrop will reach its extremes on all four axes.  The circum option
//   produces a teardrop that circumscribes the circle; in this case set `realign=true` to get a teardrop that meets its internal extremes
//   on the axes.  
//   When called as a function, returns a 2D path to for a teardrop shape.
//
// Usage: As Module
//   teardrop2d(r/d=, [ang], [cap_h]) [ATTACHMENTS];
// Usage: As Function
//   path = teardrop2d(r|d=, [ang], [cap_h]);
//
// Arguments:
//   r = radius of circular part of teardrop.  (Default: 1)
//   ang = angle of hat walls from the Y axis (half the angle of the peak).  (Default: 45 degrees)
//   cap_h = if given, height above center where the shape will be truncated.
//   ---
//   d = diameter of circular portion of bottom. (Use instead of r)
//   circum = if true, create a circumscribing teardrop.  Default: false
//   realign = if true, change whether bottom of teardrop is a point or a flat.  Default: false
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//
// Example(2D): Typical Shape
//   teardrop2d(r=30, ang=30);
// Example(2D): Crop Cap
//   teardrop2d(r=30, ang=30, cap_h=40);
// Example(2D): Close Crop
//   teardrop2d(r=30, ang=30, cap_h=20);
module teardrop2d(r, ang=45, cap_h, d, circum=false, realign=false, anchor=CENTER, spin=0)
{
    path = teardrop2d(r=r, d=d, ang=ang, circum=circum, realign=realign, cap_h=cap_h);
    attachable(anchor,spin, two_d=true, path=path, extent=false) {
        polygon(path);
        children();
    }
}

// _extrapt = true causes the point to be duplicated so a teardrop with no cap
// has the same point count as one with a cap.  

function teardrop2d(r, ang=45, cap_h, d, circum=false, realign=false, anchor=CENTER, spin=0, _extrapt=false) =
    let(
        r = get_radius(r=r, d=d, dflt=1),
        minheight = r*sin(ang),
        maxheight = r/sin(ang), //cos(90-ang),
        pointycap = is_undef(cap_h) || cap_h>=maxheight
    )
    assert(is_undef(cap_h) || cap_h>=minheight, str("cap_h cannot be less than ",minheight," but it is ",cap_h))
    let(
        cap = [
                pointycap? [0,maxheight] : [(maxheight-cap_h)*tan(ang), cap_h],
                r*[cos(ang),sin(ang)]
              ],
        fullcircle = ellipse(r=r, realign=realign, circum=circum,spin=90),        
        
        // Chose the point on the circle that is lower than the cap but also creates a segment bigger than
        // seglen/skipfactor so we don't have a teeny tiny segment at the end of the cap, except for the hexagoin
        // case which is treated specially
        skipfactor = len(fullcircle)==6 ? 15 : 3,
        path = !circum ?
                  let(seglen = norm(fullcircle[0]-fullcircle[1]))
                  [
                   each cap,
                   for (p=fullcircle)
                          if (
                               p.y<last(cap).y-EPSILON
                                 && norm([abs(p.x)-last(cap).x,p.y-last(cap.y)])>seglen/skipfactor
                             ) p,
                   xflip(cap[1]),
                   if (_extrapt || !pointycap) xflip(cap[0])
                  ]
             : let(
                   isect = [for(i=[0:1:len(fullcircle)/4])
                               let(p = line_intersection(cap, select(fullcircle,[i,i+1]), bounded1=RAY, bounded2=SEGMENT))
                               if (p) [i,p]
                           ],
                   i = last(isect)[0],
                   p = last(isect)[1]
               )
               [
                 cap[0],
                 p,
                 each select(fullcircle,i+1,-i-1-(realign?1:0)),
                 xflip(p),
                 if(_extrapt || !pointycap) xflip(cap[0])
               ]
    )
    reorient(anchor,spin, two_d=true, path=path, p=path, extent=false);



// Function&Module: egg()
// Synopsis: Creates an egg-shaped 2d object.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse(), glued_circles(), keyhole()
// Usage: As Module
//   egg(length, r1|d1=, r2|d2=, R|D=) [ATTACHMENTS];
// Usage: As Function
//   path = egg(length, r1|d1=, r2|d2=, R|D=);
// Description:
//   When called as a module, constructs an egg-shaped object by connecting two circles with convex arcs that are tangent to the circles.
//   You specify the length of the egg, the radii of the two circles, and the desired arc radius.
//   Note that because the side radius, R, is often much larger than the end radii, you may get better
//   results using `$fs` and `$fa` to control the number of semgments rather than using `$fn`.
//   This shape may be useful for creating a cam. 
//   When called as a function, returns a 2D path for an egg-shaped object. 
// Arguments:
//   length = length of the egg
//   r1 = radius of the left-hand circle
//   r2 = radius of the right-hand circle
//   R = radius of the joining arcs
//   ---
//   d1 = diameter of the left-hand circle
//   d2 = diameter of the right-hand circle
//   D = diameter of the joining arcs
// Named Anchors:
//   "left" = center of the left circle
//   "right" = center of the right circle
// Example(2D,NoAxes): This first example shows how the egg is constructed from two circles and two joining arcs.
//   $fn=100;
//   color("red") stroke(egg(78,25,12, 60),closed=true);
//   stroke([left(14,circle(25)),
//           right(27,circle(12))]);
// Example(2D,Anim,VPD=250,VPR=[0,0,0]): Varying length between circles
//   r1 = 25; r2 = 12; R = 65;
//   length = floor(lookup($t, [[0,55], [0.5,90], [1,55]]));
//   egg(length,r1,r2,R,$fn=180);
//   color("black") text(str("length=",length), size=8, halign="center", valign="center");
// Example(2D,Anim,VPD=250,VPR=[0,0,0]): Varying tangent arc radius R
//   length = 78; r1 = 25; r2 = 12;
//   R = floor(lookup($t, [[0,45], [0.5,150], [1,45]]));
//   egg(length,r1,r2,R,$fn=180);
//   color("black") text(str("R=",R), size=8, halign="center", valign="center");
// Example(2D,Anim,VPD=250,VPR=[0,0,0]): Varying circle radius r2
//   length = 78; r1 = 25; R = 65;
//   r2 = floor(lookup($t, [[0,5], [0.5,30], [1,5]]));
//   egg(length,r1,r2,R,$fn=180);
//   color("black") text(str("r2=",r2), size=8, halign="center", valign="center");
function egg(length, r1, r2, R, d1, d2, D, anchor=CENTER, spin=0) =
    let(
        r1 = get_radius(r1=r1,d1=d1),
        r2 = get_radius(r1=r2,d1=d2),
        R = get_radius(r1=R, d1=D)
    )
    assert(length>0)
    assert(R>length/2, "Side radius R must be larger than length/2")
    assert(length>r1+r2, "Length must be longer than 2*(r1+r2)")
    assert(length>2*r2, "Length must be longer than 2*r2")
    assert(length>2*r1, "Length must be longer than 2*r1")  
    let(
        c1 = [-length/2+r1,0],
        c2 = [length/2-r2,0],
        Rmin = (r1+r2+norm(c1-c2))/2,
        Mlist = circle_circle_intersection(R-r1, c1, R-r2, c2),
        arcparms = reverse([for(M=Mlist) [M, c1+r1*unit(c1-M), c2+r2*unit(c2-M)]]),
        path = concat(
                      arc(r=r2, cp=c2, points=[[length/2,0],arcparms[0][2]],endpoint=false),
                      arc(r=R, cp=arcparms[0][0], points=select(arcparms[0],[2,1]),endpoint=false),
                      arc(r=r1, points=[arcparms[0][1], [-length/2,0], arcparms[1][1]],endpoint=false),
                      arc(r=R, cp=arcparms[1][0], points=select(arcparms[1],[1,2]),endpoint=false),
                      arc(r=r2, cp=c2, points=[arcparms[1][2], [length/2,0]],endpoint=false)
        ),
        anchors = [named_anchor("left", c1, BACK, 0),
                   named_anchor("right", c2, BACK, 0)]
    )
    reorient(anchor, spin, two_d=true, path=path, extent=true, p=path, anchors=anchors);

module egg(length,r1,r2,R,d1,d2,D,anchor=CENTER, spin=0)
{
  path = egg(length,r1,r2,R,d1,d2,D);
  r1 = get_radius(r1=r1,d1=d1);
  r2 = get_radius(r1=r2,d1=d2);
  anchors = [named_anchor("left", [-length/2+r1,0], BACK, 0),
             named_anchor("right", [length/2-r2,0], BACK, 0)];
  attachable(anchor, spin, two_d=true, path=path, extent=true, anchors=anchors){
    polygon(path);
    children();
  }
}


// Function&Module: ring()
// Synopsis: Draws a 2D ring or partial ring or returns a region or path
// SynTags: Geom, Region, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Regions, Attachable
// See Also: arc(), circle()
//
// Usage: ring or partial ring from radii/diameters
//   region=ring(n, r1=|d1=, r2=|d2=, [full=], [angle=], [start=]);
// Usage: ring or partial ring from radius and ring width
//   region=ring(n, ring_width, r=|d=, [full=], [angle=], [start=]);
// Usage: ring or partial ring passing through three points
//   region=ring(n, [ring_width], [r=,d=], points=[P0,P1,P2], [full=]);
// Usage: ring or partial ring from tangent point on segment `[P0,P1]` to the tangent point on segment `[P1,P2]`.
//   region=ring(n, [ring_width], corner=[P0,P1,P2], [r=,d=], [r1|d1=], [r2=|d2=], [full=]);
// Usage: ring or partial ring based on setting a width at the X axis and height above the X axis
//   region=ring(n, [ring_width], [r=|d=], width=, thickness=, [full=]);
// Usage: as a module
//   ring(...) [ATTACHMENTS];
// Description:
//   If called as a function returns a region or path for a ring or part of a ring.  If called as a module, creates the corresponding 2D ring or partial ring shape.
//   The geometry of the ring can be specified using any of the methods supported by {{arc()}}.  If `full` is true (the default) the ring will be complete and the
//   returned value a region.  If `full` is false then the return is a path describing a partial ring.  The returned path is always clockwise with the larger radius arc first.
//   A ring has two radii, the inner and outer.  When specifying geometry you must somehow specify one radius, which can be directly with `r=` or `r1=` or by giving a point list with 
//   or without a center point.  You specify the second radius by giving `r=` directly, or `r2=` if you used `r1=` for the first radius, or by giving `ring_width`.  If `ring_width`
//   the second radius will be larger than the first; if `ring_width` is negative the second radius will be smaller. 
// Arguments:
//   n = Number of vertices to use for the inner and outer portions of the ring
//   ring_width = width of the ring.  Can be positive or negative
//   ---
//   r1/d1 = inner radius or diameter of the ring
//   r2/d2 = outer radius or diameter of the ring
//   r/d = second radius or diameter of ring when r1 or d1 are not given
//   full = if true create a full ring, if false create a partial ring.  Default: true unless `angle` is given
//   cp = Centerpoint of ring.
//   points = Points on the ring boundary.
//   corner = A path of two segments to fit the ring tangent to.
//   long = if given with cp and points takes the long arc instead of the default short arc.  Default: false
//   cw = if given with cp and 2 points takes the arc in the clockwise direction.  Default: false
//   ccw = if given with cp and 2 points takes the arc in the counter-clockwise direction.  Default: false
//   width = If given with `thickness`, ring is defined based on an arc with ends on X axis.
//   thickness = If given with `width`, ring is defined based on an arc with ends on X axis, and this height above the X axis. 
//   start = Start angle of ring.  Default: 0
//   angle = If scalar, the end angle in degrees relative to start parameter.  If a vector specifies start and end angles of ring.  
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  (Module only) Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  (Module only) Default: `0`
// Examples(2D):
//   ring(r1=5,r2=7, n=32);
//   ring(r=5,ring_width=-1, n=32);
//   ring(r=7, n=5, ring_width=-4);
//   ring(points=[[0,0],[3,3],[5,2]], ring_width=2, n=32);
//   ring(points=[[0,0],[3,3],[5,2]], r=1, n=32);
//   ring(cp=[3,3], points=[[4,4],[1,3]], ring_width=1);
//   ring(corner=[[0,0],[4,4],[7,3]], r2=2, r1=1.5,n=22,full=false);
//   ring(r1=5,r2=7, angle=[33,110], n=32);
//   ring(r1=5,r2=7, angle=[0,360], n=32);  // full circle
//   ring(r=5, points=[[0,0],[3,3],[5,2]], full=false, n=32);
//   ring(32,-2, cp=[1,1], points=[[4,4],[-3,6]], full=false);
//   ring(r=5,ring_width=-1, n=32);
//   ring(points=[[0,0],[3,3],[5,2]], ring_width=2, n=32);
//   ring(points=[[0,0],[3,3],[5,2]], r=1, n=32);
//   ring(cp=[3,3], points=[[4,4],[1,3]], ring_width=1);
// Example(2D): Using corner, the outer radius is the one tangent to the corner
//   corner = [[0,0],[4,4],[7,3]];
//   ring(corner=corner, r2=3, r1=2,n=22);
//   stroke(corner, width=.1,color="red");
// Example(2D): For inner radius tangent to a corner, specify `r=` and `ring_width`.
//   corner = [[0,0],[4,4],[7,3]];
//   ring(corner=corner, r=3, ring_width=1,n=22,full=false);
//   stroke(corner, width=.1,color="red");
// Example(2D):
//   $fn=128;
//   region = ring(width=5,thickness=1.5,ring_width=2);   
//   path = ring(width=5,thickness=1.5,ring_width=2,full=false);
//   stroke(region,width=.25);
//   color("red") dashed_stroke(path,dashpat=[1.5,1.5],closed=true,width=.25);

module ring(n,ring_width,r,r1,r2,angle,d,d1,d2,cp,points,corner, width,thickness,start, long=false, full=true, cw=false,ccw=false, anchor=CENTER, spin=0)
{
  R = ring(n=n,r=r,ring_width=ring_width,r1=r1,r2=r2,angle=angle,d=d,d1=d1,d2=d2,cp=cp,points=points,corner=corner, width=width,thickness=thickness,start=start,
           long=long, full=full, cw=cw, ccw=ccw);
  attachable(anchor,spin,two_d=true,region=is_region(R)?R:undef,path=is_region(R)?undef:R,extent=false) {
     region(R);
     children();
  }
}  

function ring(n,ring_width,r,r1,r2,angle,d,d1,d2,cp,points,corner, width,thickness,start, long=false, full=true, cw=false,ccw=false) =
    let(
        r1 = is_def(r1) ? assert(is_undef(d),"Cannot define r1 and d1")r1
           : is_def(d1) ? d1/2
           : undef,
        r2 = is_def(r2) ? assert(is_undef(d),"Cannot define r2 and d2")r2
           : is_def(d2) ? d2/2
           : undef,
        r = is_def(r) ? assert(is_undef(d),"Cannot define r and d")r
          : is_def(d) ? d/2
          : undef,
        full = is_def(angle) ? false : full
    )
    assert(is_undef(start) || is_def(angle), "start requires angle")
    assert(is_undef(angle) || !any_defined([thickness,width,points,corner]), "Cannot give angle with points, corner, width or thickness")
    assert(!is_vector(angle,2) || abs(angle[1]-angle[0]) <= 360, "angle gives more than 360 degrees")
    assert(is_undef(points) || is_path(points,2), str("Points must be a 2d vector",points))
    assert(!any_defined([points,thickness,width]) || num_defined([r1,r2])==0, "Cannot give r1, r2, d1, or d2 with points, width or thickness")
    is_def(width) && is_def(thickness)?
       assert(!any_defined([r,cp,points,angle,start]), "Conflicting or invalid parameters to ring")
       assert(all_positive([width,thickness]), "Width and thickness must be positive")
       ring(n=n,r=r,ring_width=ring_width,points=[[width/2,0], [0,thickness], [-width/2,0]],full=full)
  : full && is_undef(cp) && is_def(points) ?
       assert(is_def(points) && len(points)==3, "Without cp given, must provide exactly three points")
       assert(num_defined([r,ring_width]), "Must give r or ring_width with point list")
       let(
            ctr_rad = circle_3points(points),
            dummy=assert(is_def(ctr_rad[0]), "Collinear points given to ring()"),
            part1 = move(ctr_rad[0],circle(r=ctr_rad[1], $fn=is_def(n) ? n : $fn)),
            first_r = norm(part1[0]-ctr_rad[0]),
            r = is_def(r) ? r : first_r+ring_width,
            part2 = move(ctr_rad[0],circle(r=r, $fn=is_def(n) ? n : $fn))
       )
       assert(first_r!=r, "Ring has zero width")
       (first_r>r ? [part1, reverse(part2)] : [part2, reverse(part1)])
  : full && is_def(corner) ?
       assert(is_path(corner,2) && len(corner)==3, "corner must be a list of 3 points")
       assert(!any_defined([thickness,width,points,cp,angle.start]), "Conflicting or invalid parameters to ring")
       let(parmok = (all_positive([r1,r2]) && num_defined([r,ring_width])==0) 
                      || (num_defined([r1,r2])==0 && all_positive([r]) && is_finite(ring_width)))
       assert(parmok, "With corner must give (r1 and r2) or (r and ring_width), but you gave some other combination")
       let(
           newr1 = is_def(r1) ? min(r1,r2) : min(r,r+ring_width),
           newr2 = is_def(r2) ? max(r2,r1) : max(r,r+ring_width),
           data = circle_2tangents(newr2,corner[0],corner[1],corner[2]),
           cp=data[0]
       )
       [move(cp,circle($fn=is_def(n) ? n : $fn, r=newr2)),move(cp, circle( $fn=is_def(n) ? n : $fn, r=newr1))]
  : full && is_def(cp) && is_def(points) ?
       assert(in_list(len(points),[1,2]), "With cp must give a list of one or two points.")
       assert(num_defined([r,ring_width]), "Must give r or ring_width with point list")
       let(
           first_r=norm(points[0]-cp),
           part1 = move(cp,circle(r=first_r, $fn=is_def(n) ? n : $fn)),
           r = is_def(r) ? r : first_r+ring_width,
           part2 = move(cp,circle(r=r, $fn=is_def(n) ? n : $fn))
       )
       assert(first_r!=r, "Ring has zero width")
       first_r>r ? [part1, reverse(part2)] : [part2, reverse(part1)]
  : full || angle==360 || (is_vector(angle,2) && abs(angle[1]-angle[0])==360) ?
      let(parmok = (all_positive([r1,r2]) && num_defined([r,ring_width])==0) 
                     || (num_defined([r1,r2])==0 && all_positive([r]) && is_finite(ring_width)))
      assert(parmok, "Must give (r1 and r2) or (r and ring_width), but you gave some other combination")
      let(
          newr1 = is_def(r1) ? min(r1,r2) : min(r,r+ring_width),
          newr2 = is_def(r2) ? max(r2,r1) : max(r,r+ring_width),
          cp = default(cp,[0,0])
      )
      [move(cp,circle($fn=is_def(n) ? n : $fn, r=newr2)),move(cp, circle( $fn=is_def(n) ? n : $fn, r=newr1))]
  :  let(
         parmRok = (all_positive([r1,r2]) && num_defined([r,ring_width])==0) 
                     || (num_defined([r1,r2])==0 && all_positive([r]) && is_finite(ring_width)),
         pass_r = any_defined([points,thickness]) ? assert(!any_defined([r1,r2]),"Cannot give r1, d1, r2, or d2 with a point list or width & thickness")
                                                    assert(num_defined([ring_width,r])==1, "Must defined exactly one of r and ring_width when using a pointlist or width & thickness")
                                                    undef 
                : assert(num_defined([r,r2])==1,"Cannot give r or d and r1 or d1") first_defined([r,r2]),
         base_arc = clockwise_polygon(arc(r=pass_r,n=n,angle=angle,cp=cp,points=points, corner=corner, width=width, thickness=thickness,start=start, long=long, cw=cw,ccw=ccw,wedge=true)),
         center = base_arc[0],
         arc1 = list_tail(base_arc,1),
         r_actual = norm(center-arc1[0]),
         new_r = is_def(ring_width) ? r_actual+ring_width
               : first_defined([r,r1]),
         pts = [center+new_r*unit(arc1[0]-center), center+new_r*unit(arc1[floor(len(arc1)/2)]-center), center+new_r*unit(last(arc1)-center)],
         second=arc(n=n,points=pts),
         arc2 = is_polygon_clockwise(second) ? second : reverse(second) 
     ) new_r>r_actual ? concat(arc2, reverse(arc1)) : concat(arc1,reverse(arc2));


// Function&Module: glued_circles()
// Synopsis: Creates a shape of two circles joined by a curved waist.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse(), egg(), keyhole()
// Usage: As Module
//   glued_circles(r/d=, [spread], [tangent], ...) [ATTACHMENTS];
// Usage: As Function
//   path = glued_circles(r/d=, [spread], [tangent], ...);
// Description:
//   When called as a function, returns a 2D path forming a shape of two circles joined by curved waist.
//   When called as a module, creates a 2D shape of two circles joined by curved waist.  Uses "hull" style anchoring.  
// Arguments:
//   r = The radius of the end circles.
//   spread = The distance between the centers of the end circles.  Default: 10
//   tangent = The angle in degrees of the tangent point for the joining arcs, measured away from the Y axis.  Default: 30
//   ---
//   d = The diameter of the end circles.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Examples(2D):
//   glued_circles(r=15, spread=40, tangent=45);
//   glued_circles(d=30, spread=30, tangent=30);
//   glued_circles(d=30, spread=30, tangent=15);
//   glued_circles(d=30, spread=30, tangent=-30);
// Example(2D): Called as Function
//   stroke(closed=true, glued_circles(r=15, spread=40, tangent=45));
function glued_circles(r, spread=10, tangent=30, d, anchor=CENTER, spin=0) =
    let(
        r = get_radius(r=r, d=d, dflt=10),
        r2 = (spread/2 / sin(tangent)) - r,
        cp1 = [spread/2, 0],
        cp2 = [0, (r+r2)*cos(tangent)],
        sa1 = 90-tangent,
        ea1 = 270+tangent,
        lobearc = ea1-sa1,
        lobesegs = ceil(segs(r)*lobearc/360),
        sa2 = 270-tangent,
        ea2 = 270+tangent,
        subarc = ea2-sa2,
        arcsegs = ceil(segs(r2)*abs(subarc)/360),
        // In the tangent zero case the inner curves are missing so we need to complete the two
        // outer curves.  In the other case the inner curves are present and endpoint=false
        // prevents point duplication.  
        path = tangent==0 ?
                    concat(arc(n=lobesegs+1, r=r, cp=-cp1, angle=[sa1,ea1]),
                           arc(n=lobesegs+1, r=r, cp=cp1, angle=[sa1+180,ea1+180]))
                :
                    concat(arc(n=lobesegs, r=r, cp=-cp1, angle=[sa1,ea1], endpoint=false),
                           [for(theta=lerpn(ea2+180,ea2-subarc+180,arcsegs,endpoint=false))  r2*[cos(theta),sin(theta)] - cp2],
                           arc(n=lobesegs, r=r, cp=cp1, angle=[sa1+180,ea1+180], endpoint=false),
                           [for(theta=lerpn(ea2,ea2-subarc,arcsegs,endpoint=false))  r2*[cos(theta),sin(theta)] + cp2]),
        maxx_idx = max_index(column(path,0)),
        path2 = reverse_polygon(list_rotate(path,maxx_idx))
    ) reorient(anchor,spin, two_d=true, path=path2, extent=true, p=path2);


module glued_circles(r, spread=10, tangent=30, d, anchor=CENTER, spin=0) {
    path = glued_circles(r=r, d=d, spread=spread, tangent=tangent);
    attachable(anchor,spin, two_d=true, path=path, extent=true) {
        polygon(path);
        children();
    }
}


// Function&Module: squircle()
// Synopsis: Creates a shape between a circle and a square, centered on the origin.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), square(), supershape()
// Usage: As Module
//   squircle(size, [squareness], [style]) [ATTACHMENTS];
// Usage: As Function
//   path = squircle(size, [squareness], [style]);
// Description:
//   A [squircle](https://en.wikipedia.org/wiki/Squircle) is a shape intermediate between a square/rectangle and a circle/ellipse. Squircles are sometimes used to make dinner plates (more area for the same radius as a circle), keyboard buttons, and smartphone icons. Old CRT television screens also resembled elongated squircles.
//   .
//   Multiple definitions exist for the squircle. We support two versions: the superellipse {{supershape()}} Example 3, also known as the Lamé upper squircle), and the Fernandez-Guasti squircle. They are visually almost indistinguishable, with the superellipse having slightly rounder "corners" than FG at the same corner radius. These two squircles have different, unintuitive methods for controlling how square or circular the shape is. A `squareness` parameter determines the shape, specifying the corner position linearly, with 0 being on the circle and 1 being the square. Vertices are positioned to be more dense near the corners to preserve smoothness at low values of `$fn`'.
//   .
//   For the "superellipse" style, the special case where the superellipse exponent is 4 results in a squircle at the geometric mean between radial points on the circle and square, corresponding to squareness=0.456786.
//   .
//   When called as a module, creates a 2D squircle with the desired squareness.    
//   When called as a function, returns a 2D path for a squircle.
// Arguments:
//   size = Same as the `size` parameter in `square()`, can be a single number or a vector `[xsize,ysize]`.
//   squareness = Value between 0 and 1. Controls the shape, setting the location of a squircle "corner" at the specified interpolated position between a circle and a square. When `squareness=0` the shape is a circle, and when `squareness=1` the shape is a square. Default: 0.5
//   ---
//   style = method for generating a squircle, "fg" for Fernández-Guasti and "superellipse" for superellipse. Default: "fg"
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   atype = anchor type, "box" for bounding box corners and sides, "perim" for the squircle corners. Default: "box"
//   $fn = Number of points. The special variables `$fs` and `$fa` are ignored. If set, `$fn` must be 12 or greater, and is rounded to the nearest multiple of 4. Points are generated so they are more dense around sharper curves. Default if not set: 48
// Examples(2D):
//   squircle(size=50, squareness=0.4);
//   squircle([80,60], 0.7, $fn=64);
// Example(2D,VPD=265,NoAxes): Ten increments of squareness parameter for a superellipse squircle
//   color("green") for(sq=[0:0.1:1])
//       stroke(squircle(100, sq, style="superellipse", $fn=96), closed=true, width=0.5);
// Example(2D): Standard vector anchors are based on the bounding box
//   squircle(50, 0.6) show_anchors();
// Example(2D): Perimeter anchors, anchoring at bottom left and spinning 20°
//   squircle([60,40], 0.5, anchor=(BOTTOM+LEFT), atype="perim", spin=20)
//       show_anchors();

module squircle(size, squareness=0.5, style="fg", anchor=CENTER, spin=0, atype="box" ) {
    check = assert(squareness >= 0 && squareness <= 1);
    anchorchk = assert(in_list(atype, ["box", "perim"]));
    size = is_num(size) ? [size,size] : point2d(size);
    assert(all_positive(size), "All components of size must be positive.");
    path = squircle(size, squareness, style, atype="box");
    if (atype == "box") {
        attachable(anchor, spin, two_d=true, size=size, extent=false) {
            polygon(path);
            children();
        }
    } else { // atype=="perim"
        attachable(anchor, spin, two_d=true, extent=true, path=path) {
            polygon(path);
            children();
        }
    }
}


function squircle(size, squareness=0.5, style="fg", anchor=CENTER, spin=0, atype="box") =
    assert(squareness >= 0 && squareness <= 1)
    assert(is_num(size) || is_vector(size,2))
    assert(in_list(atype, ["box", "perim"]))
    let(
        size = is_num(size) ? [size,size] : point2d(size),
        path = style == "fg" ? _squircle_fg(size, squareness)
            : style == "superellipse" ? _squircle_se(size, squareness)
            : assert(false, "Style must be \"fg\" or \"superellipse\"")
    ) reorient(anchor, spin, two_d=true, size=atype=="box"?size:undef, path=atype=="box"?undef:path, p=path, extent=true);


/* FG squircle functions */

function _squircle_fg(size, squareness) = [
    let(
        sq = _linearize_squareness(squareness),
        size = is_num(size) ? [size,size] : point2d(size),
        aspect = size[1] / size[0],
        r = 0.5 * size[0],
        astep = $fn>=12 ? 90/round($fn/4) : 360/48
    ) for(a=[360:-astep:0.01]) let(
        theta = a + sq * sin(4*a) * 30/PI, // tighter angle steps at corners
        p = squircle_radius_fg(sq, r, theta)
    ) p*[cos(theta), aspect*sin(theta)]
];

function squircle_radius_fg(squareness, r, angle) = let(
    s2a = abs(squareness*sin(2*angle))
    ) s2a>0 ? r*sqrt(2)/s2a * sqrt(1 - sqrt(1 - s2a*s2a)) : r;

function _linearize_squareness(s) =
    // from Chamberlain Fong (2016). "Squircular Calculations". arXiv.
    // https://arxiv.org/pdf/1604.02174v5
    let(c = 2 - 2*sqrt(2), d = 1 - 0.5*c*s)
    2 * sqrt((1+c)*s*s - c*s) / (d*d);


/* Superellipse squircle functions */

function _squircle_se(size, squareness) = [
    let(
        n = _squircle_se_exponent(squareness),
        size = is_num(size) ? [size,size] : point2d(size),
        ra = 0.5*size[0],
        rb = 0.5*size[1],
        astep = $fn>=12 ? 90/round($fn/4) : 360/48,
        fgsq = _linearize_squareness(min(0.998,squareness)) // works well for distributing theta
    ) for(a=[360:-astep:0.01]) let(
        theta = a + fgsq*sin(4*a)*30/PI, // tighter angle steps at corners
        x = cos(theta),
        y = sin(theta),
        r = (abs(x)^n + abs(y)^n)^(1/n) // superellipse
        //r = _superformula(theta=theta, m1=4,m2=4,n1=n,n2=n,n3=n,a=1,b=1)
    ) [ra*x, rb*y] / r
];

function squircle_radius_se(n, r, angle) = let(
    x = cos(angle),
    y = sin(angle)
) (abs(x)^n + abs(y)^n)^(1/n) / r;

function _squircle_se_exponent(squareness) = let(
    // limit squareness; error if >0.99889, limit is smaller for r>1
    s=min(0.998,squareness),
    rho = 1 + s*(sqrt(2)-1),
    x = rho / sqrt(2)
) log(0.5) / log(x);



// Function&Module: keyhole()
// Synopsis: Creates a 2D keyhole shape.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse(), egg(), glued_circles()
// Usage: As Module
//   keyhole(l/length=, r1/d1=, r2/d2=, [shoulder_r=], ...) [ATTACHMENTS];
// Usage: As Function
//   path = keyhole(l/length=, r1/d1=, r2/d2=, [shoulder_r=], ...);
// Description:
//   When called as a function, returns a 2D path forming a shape of two differently sized circles joined by a straight slot, making what looks like a keyhole.
//   When called as a module, creates a 2D shape of two differently sized circles joined by a straight slot, making what looks like a keyhole.  Uses "hull" style anchoring.  
// Arguments:
//   l = The distance between the centers of the two circles.  Default: `15`
//   r1= The radius of the back circle, centered on `[0,0]`.  Default: `2.5`
//   r2= The radius of the forward circle, centered on `[0,-length]`.  Default: `5`
//   ---
//   shoulder_r = The radius of the rounding of the shoulder between the larger circle, and the slot that leads to the smaller circle.  Default: `0`
//   d1= The diameter of the back circle, centered on `[0,0]`.
//   d2= The diameter of the forward circle, centered on `[0,-l]`.
//   length = An alternate name for the `l=` argument.
//   anchor = Translate so anchor point is at origin (0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Examples(2D):
//   keyhole(40, 10, 30);
//   keyhole(l=60, r1=20, r2=40);
// Example(2D): Making the forward circle larger than the back circle
//   keyhole(l=60, r1=40, r2=20);
// Example(2D): Centering on the larger hole:
//   keyhole(l=60, r1=40, r2=20, spin=180);
// Example(2D): Rounding the shoulders
//   keyhole(l=60, r1=20, r2=40, shoulder_r=20);
// Example(2D): Called as Function
//   stroke(closed=true, keyhole(l=60, r1=20, r2=40));

function keyhole(l, r1, r2, shoulder_r=0, d1, d2, length, anchor=CTR, spin=0) =
    let(
        l = first_defined([l,length,15]),
        r1 = get_radius(r=r1, d=d1, dflt=5),
        r2 = get_radius(r=r2, d=d2, dflt=10)
    )
    assert(is_num(l) && l>0)
    assert(l>=max(r1,r2))
    assert(is_undef(shoulder_r) || (is_num(shoulder_r) && shoulder_r>=0))
    let(
        cp1 = [0,0],
        cp2 = cp1 + [0,-l],
        shoulder_r = is_num(shoulder_r)? shoulder_r : min(r1,r2) / 2,
        minr = min(r1, r2) + shoulder_r,
        maxr = max(r1, r2) + shoulder_r,
        dy = opp_hyp_to_adj(minr, maxr),
        spt1 = r1>r2? cp1+[minr,-dy] : cp2+[minr,dy],
        spt2 = [-spt1.x, spt1.y],
        ds = spt1 - (r1>r2? cp1 : cp2),
        ang = atan2(abs(ds.y), abs(ds.x)),
        path = r1>r2? [
                if (shoulder_r<=0) spt1
                  else each arc(r=shoulder_r, cp=spt1, start=180-ang, angle=ang, endpoint=false),
                each arc(r=r2, cp=cp2, start=0, angle=-180, endpoint=false),
                if (shoulder_r<=0) spt2
                  else each arc(r=shoulder_r, cp=spt2, start=0, angle=ang, endpoint=false),
                each arc(r=r1, cp=cp1, start=180+ang, angle=-180-2*ang, endpoint=false),
            ] : [
                if (shoulder_r<=0) spt1
                  else each arc(r=shoulder_r, cp=spt1, start=180, angle=ang, endpoint=false),
                each arc(r=r2, cp=cp2, start=ang, angle=-180-2*ang, endpoint=false),
                if (shoulder_r<=0) spt2
                  else each arc(r=shoulder_r, cp=spt2, start=360-ang, angle=ang, endpoint=false),
                each arc(r=r1, cp=cp1, start=180, angle=-180, endpoint=false),
            ]
    ) reorient(anchor,spin, two_d=true, path=path, extent=true, p=path);


module keyhole(l, r1, r2, shoulder_r=0, d1, d2, length, anchor=CTR, spin=0) {
    path = keyhole(l=l, r1=r1, r2=r2, shoulder_r=shoulder_r, d1=d1, d2=d2, length=length);
    attachable(anchor,spin, two_d=true, path=path, extent=true) {
        polygon(path);
        children();
    }
}


// Function&Module: supershape()
// Synopsis: Creates a 2D [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: circle(), ellipse()
// Usage: As Module
//   supershape([step],[n=], [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]) [ATTACHMENTS];
// Usage: As Function
//   path = supershape([step], [n=], [m1=], [m2=], [n1=], [n2=], [n3=], [a=], [b=], [r=/d=]);
// Description:
//   When called as a function, returns a 2D path for the outline of the [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
//   When called as a module, creates a 2D [Superformula](https://en.wikipedia.org/wiki/Superformula) shape.
//   Note that the "hull" type anchoring (the default) is more intuitive for concave star-like shapes, but the anchor points do not
//   necesarily lie on the line of the anchor vector, which can be confusing, especially for simpler, ellipse-like shapes.
//   Note that the default step angle of 0.5 is very fine and can be slow, but due to the complex curves of the supershape,
//   many points are often required to give a good result.  
// Arguments:
//   step = The angle step size for sampling the superformula shape.  Smaller steps are slower but more accurate.  Default: 0.5
//   ---
//   n = Produce n points as output.  Alternative to step.  Not to be confused with shape parameters n1 and n2.  
//   m1 = The m1 argument for the superformula. Default: 4.
//   m2 = The m2 argument for the superformula. Default: m1.
//   n1 = The n1 argument for the superformula. Default: 1.
//   n2 = The n2 argument for the superformula. Default: n1.
//   n3 = The n3 argument for the superformula. Default: n2.
//   a = The a argument for the superformula.  Default: 1.
//   b = The b argument for the superformula.  Default: a.
//   r = Radius of the shape.  Scale shape to fit in a circle of radius r.
//   d = Diameter of the shape.  Scale shape to fit in a circle of diameter d.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
//   atype = Select "hull" or "intersect" style anchoring.  Default: "hull". 
// Example(2D):
//   supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,r=50);
// Example(2D): Called as Function
//   stroke(closed=true, supershape(step=0.5,m1=16,m2=16,n1=0.5,n2=0.5,n3=16,d=100));
// Examples(2D,Med):
//   for(n=[2:5]) right(2.5*(n-2)) supershape(m1=4,m2=4,n1=n,a=1,b=2);  // Superellipses
//   m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(.5,m1=m[i],n1=1);
//   m=[6,8,10,12]; for(i=[0:3]) right(2.7*i) supershape(.5,m1=m[i],n1=1,b=1.5);  // m should be even
//   m=[1,2,3,5]; for(i=[0:3]) fwd(1.5*i) supershape(m1=m[i],n1=0.4);
//   supershape(m1=5, n1=4, n2=1); right(2.5) supershape(m1=5, n1=40, n2=10);
//   m=[2,3,5,7]; for(i=[0:3]) right(2.5*i) supershape(m1=m[i], n1=60, n2=55, n3=30);
//   n=[0.5,0.2,0.1,0.02]; for(i=[0:3]) right(2.5*i) supershape(m1=5,n1=n[i], n2=1.7);
//   supershape(m1=2, n1=1, n2=4, n3=8);
//   supershape(m1=7, n1=2, n2=8, n3=4);
//   supershape(m1=7, n1=3, n2=4, n3=17);
//   supershape(m1=4, n1=1/2, n2=1/2, n3=4);
//   supershape(m1=4, n1=4.0,n2=16, n3=1.5, a=0.9, b=9);
//   for(i=[1:4]) right(3*i) supershape(m1=i, m2=3*i, n1=2);
//   m=[4,6,10]; for(i=[0:2]) right(i*5) supershape(m1=m[i], n1=12, n2=8, n3=5, a=2.7);
//   for(i=[-1.5:3:1.5]) right(i*1.5) supershape(m1=2,m2=10,n1=i,n2=1);
//   for(i=[1:3],j=[-1,1]) translate([3.5*i,1.5*j])supershape(m1=4,m2=6,n1=i*j,n2=1);
//   for(i=[1:3]) right(2.5*i)supershape(step=.5,m1=88, m2=64, n1=-i*i,n2=1,r=1);
// Examples:
//   linear_extrude(height=0.3, scale=0) supershape(step=1, m1=6, n1=0.4, n2=0, n3=6);
//   linear_extrude(height=5, scale=0) supershape(step=1, b=3, m1=6, n1=3.8, n2=16, n3=10);
function supershape(step=0.5, n, m1=4, m2, n1=1, n2, n3, a=1, b, r, d,anchor=CENTER, spin=0, atype="hull") =
    assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"")
    let(
        n = first_defined([n, ceil(360/step)]),
        angs = lerpn(360,0,n,endpoint=false),  
        r = get_radius(r=r, d=d, dflt=undef),
        m2 = is_def(m2) ? m2 : m1,
        n2 = is_def(n2) ? n2 : n1,
        n3 = is_def(n3) ? n3 : n2,
        b = is_def(b) ? b : a,
        // superformula returns r(theta), the point in polar coordinates
        rvals = [for (theta = angs) _superformula(theta=theta,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b)],
        scale = is_def(r) ? r/max(rvals) : 1,
        path = [for (i=idx(angs)) scale*rvals[i]*[cos(angs[i]), sin(angs[i])]]
    ) reorient(anchor,spin, two_d=true, path=path, p=path, extent=atype=="hull");

module supershape(step=0.5,n,m1=4,m2=undef,n1,n2=undef,n3=undef,a=1,b=undef, r=undef, d=undef, anchor=CENTER, spin=0, atype="hull") {
    check = assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"");
    path = supershape(step=step,n=n,m1=m1,m2=m2,n1=n1,n2=n2,n3=n3,a=a,b=b,r=r,d=d);
    attachable(anchor,spin,extent=atype=="hull", two_d=true, path=path) {
        polygon(path);
        children();
    }
}

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


// Function&Module: reuleaux_polygon()
// Synopsis: Creates a constant-width shape that is not circular.
// SynTags: Geom, Path
// Topics: Shapes (2D), Paths (2D), Path Generators, Attachable
// See Also: regular_ngon(), pentagon(), hexagon(), octagon()
// Usage: As Module
//   reuleaux_polygon(n, r|d=, ...) [ATTACHMENTS];
// Usage: As Function
//   path = reuleaux_polygon(n, r|d=, ...);
// Description:
//   When called as a module, creates a 2D Reuleaux Polygon; a constant width shape that is not circular.  Uses "intersect" type anchoring.  
//   When called as a function, returns a 2D path for a Reulaux Polygon.
// Arguments:
//   n = Number of "sides" to the Reuleaux Polygon.  Must be an odd positive number.  Default: 3
//   r = Radius of the shape.  Scale shape to fit in a circle of radius r.
//   ---
//   d = Diameter of the shape.  Scale shape to fit in a circle of diameter d.
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `CENTER`
//   spin = Rotate this many degrees around the Z axis after anchor.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "tip0", "tip1", etc. = Each tip has an anchor, pointing outwards.
// Examples(2D):
//   reuleaux_polygon(n=3, r=50);
//   reuleaux_polygon(n=5, d=100);
// Examples(2D): Standard vector anchors are based on extents
//   reuleaux_polygon(n=3, d=50) show_anchors(custom=false);
// Examples(2D): Named anchors exist for the tips
//   reuleaux_polygon(n=3, d=50) show_anchors(std=false);
module reuleaux_polygon(n=3, r, d, anchor=CENTER, spin=0) {
    check = assert(n>=3 && (n%2)==1);
    r = get_radius(r=r, d=d, dflt=1);
    path = reuleaux_polygon(n=n, r=r);
    anchors = [
        for (i = [0:1:n-1]) let(
            ca = 360 - i * 360/n,
            cp = polar_to_xy(r, ca)
        ) named_anchor(str("tip",i), cp, unit(cp,BACK), 0),
    ];
    attachable(anchor,spin, two_d=true, path=path, extent=false, anchors=anchors) {
        polygon(path);
        children();
    }
}


function reuleaux_polygon(n=3, r, d, anchor=CENTER, spin=0) =
    assert(n>=3 && (n%2)==1)
    let(
        r = get_radius(r=r, d=d, dflt=1),
        ssegs = max(3,ceil(segs(r)/n)),
        slen = norm(polar_to_xy(r,0)-polar_to_xy(r,180-180/n)),
        path = [
            for (i = [0:1:n-1]) let(
                ca = 180 - (i+0.5) * 360/n,
                sa = ca + 180 + (90/n),
                ea = ca + 180 - (90/n),
                cp = polar_to_xy(r, ca)
            ) each arc(n=ssegs-1, r=slen, cp=cp, angle=[sa,ea], endpoint=false)
        ],
        anchors = [
            for (i = [0:1:n-1]) let(
                ca = 360 - i * 360/n,
                cp = polar_to_xy(r, ca)
            ) named_anchor(str("tip",i), cp, unit(cp,BACK), 0),
        ]
    ) reorient(anchor,spin, two_d=true, path=path, extent=false, anchors=anchors, p=path);



// Section: Text

// Module: text()
// Synopsis: Creates an attachable block of text.
// SynTags: Geom
// Topics: Attachments, Text
// See Also: text3d(), attachable()
// Usage:
//   text(text, [size], [font], ...);
// Description:
//   Creates a 3D text block that can be attached to other attachable objects.
//   You cannot attach children to text.
//   .
//   Historically fonts were specified by their "body size", the height of the metal body
//   on which the glyphs were cast.  This means the size was an upper bound on the size
//   of the font glyphs, not a direct measurement of their size.  In digital typesetting,
//   the metal body is replaced by an invisible box, the em square, whose side length is
//   defined to be the font's size.  The glyphs can be contained in that square, or they
//   can extend beyond it, depending on the choices made by the font designer.  As a
//   result, the meaning of font size varies between fonts: two fonts at the "same" size
//   can differ significantly in the actual size of their characters.  Typographers
//   customarily specify the size in the units of "points".  A point is 1/72 inch.  In
//   OpenSCAD, you specify the size in OpenSCAD units (often treated as millimeters for 3d
//   printing), so if you want points you will need to perform a suitable unit conversion.
//   In addition, the OpenSCAD font system has a bug: if you specify size=s you will
//   instead get a font whose size is s/0.72.  For many fonts this means the size of
//   capital letters will be approximately equal to s, because it is common for fonts to
//   use about 70% of their height for the ascenders in the font.  To get the customary
//   font size, you should multiply your desired size by 0.72.
//   .
//   To find the fonts that you have available in your OpenSCAD installation,
//   go to the Help menu and select "Font List".  
// Arguments:
//   text = Text to create.
//   size = The font will be created at this size divided by 0.72.   Default: 10
//   font = Font to use.  Default: "Liberation Sans" (standard OpenSCAD default)
//   ---
//   halign = If given, specifies the horizontal alignment of the text.  `"left"`, `"center"`, or `"right"`.  Overrides `anchor=`.
//   valign = If given, specifies the vertical alignment of the text.  `"top"`, `"center"`, `"baseline"` or `"bottom"`.  Overrides `anchor=`.
//   spacing = The relative spacing multiplier between characters.  Default: `1.0`
//   direction = The text direction.  `"ltr"` for left to right.  `"rtl"` for right to left. `"ttb"` for top to bottom. `"btt"` for bottom to top.  Default: `"ltr"`
//   language = The language the text is in.  Default: `"en"`
//   script = The script the text is in.  Default: `"latin"`
//   anchor = Translate so anchor point is at origin (0,0,0).  See [anchor](attachments.scad#subsection-anchor).  Default: `"baseline"`
//   spin = Rotate this many degrees around the Z axis.  See [spin](attachments.scad#subsection-spin).  Default: `0`
// Named Anchors:
//   "baseline" = Anchors at the baseline of the text, at the start of the string.
//   str("baseline",VECTOR) = Anchors at the baseline of the text, modified by the X and Z components of the appended vector.
// Examples(2D):
//   text("Foobar", size=10);
//   text("Foobar", size=12, font="Liberation Mono");
//   text("Foobar", anchor=CENTER);
//   text("Foobar", anchor=str("baseline",CENTER));
// Example: Using line_copies() distributor
//   txt = "This is the string.";
//   line_copies(spacing=[10,-5],n=len(txt))
//       text(txt[$idx], size=10, anchor=CENTER);
// Example: Using arc_copies() distributor
//   txt = "This is the string";
//   arc_copies(r=50, n=len(txt), sa=0, ea=180)
//       text(select(txt,-1-$idx), size=10, anchor=str("baseline",CENTER), spin=-90);
module text(text, size=10, font, halign, valign, spacing=1.0, direction="ltr", language="en", script="latin", anchor="baseline", spin=0) {
    no_children($children);
    dummy1 =
        assert(is_undef(anchor) || is_vector(anchor) || is_string(anchor), str("Invalid anchor: ",anchor))
        assert(is_finite(spin), str("Invalid spin: ",spin));
    anchor = default(anchor, CENTER);
    geom = attach_geom(size=[size,size],two_d=true);
    anch = !any([for (c=anchor) c=="["])? anchor :
        let(
            parts = str_split(str_split(str_split(anchor,"]")[0],"[")[1],","),
            vec = [for (p=parts) parse_float(str_strip(p," ",start=true))]
        ) vec;
    ha = halign!=undef? halign :
        anchor=="baseline"? "left" :
        anchor==anch && is_string(anchor)? "center" :
        anch.x<0? "left" :
        anch.x>0? "right" :
        "center";
    va = valign != undef? valign :
        starts_with(anchor,"baseline")? "baseline" :
        anchor==anch && is_string(anchor)? "center" :
        anch.y<0? "bottom" :
        anch.y>0? "top" :
        "center";
    base = anchor=="baseline"? CENTER :
        anchor==anch && is_string(anchor)? CENTER :
        anch.z<0? BOTTOM :
        anch.z>0? TOP :
        CENTER;
    m = _attach_transform(base,spin,undef,geom);
    multmatrix(m) {
        $parent_anchor = anchor;
        $parent_spin   = spin;
        $parent_orient = undef;
        $parent_geom   = geom;
        $parent_size   = _attach_geom_size(geom);
        $attach_to   = undef;
        if (_is_shown()){
            _color($color) {
                _text(
                    text=text, size=size, font=font,
                    halign=ha, valign=va, spacing=spacing,
                    direction=direction, language=language,
                    script=script
                );
            }
        }
    }
}


// Section: Rounding 2D shapes

// Module: round2d()
// Synopsis: Rounds the corners of 2d objects.
// SynTags: Geom
// Topics: Rounding
// See Also: shell2d(), round3d(), minkowski_difference()
// Usage:
//   round2d(r) [ATTACHMENTS];
//   round2d(or=) [ATTACHMENTS];
//   round2d(ir=) [ATTACHMENTS];
//   round2d(or=, ir=) [ATTACHMENTS];
// Description:
//   Rounds arbitrary 2D objects.  Giving `r` rounds all concave and convex corners.  Giving just `ir`
//   rounds just concave corners.  Giving just `or` rounds convex corners.  Giving both `ir` and `or`
//   can let you round to different radii for concave and convex corners.  The 2D object must not have
//   any parts narrower than twice the `or` radius.  Such parts will disappear.
// Arguments:
//   r = Radius to round all concave and convex corners to.
//   ---
//   or = Radius to round only outside (convex) corners to.  Use instead of `r`.
//   ir = Radius to round only inside (concave) corners to.  Use instead of `r`.
// Examples(2D):
//   round2d(r=10) {square([40,100], center=true); square([100,40], center=true);}
//   round2d(or=10) {square([40,100], center=true); square([100,40], center=true);}
//   round2d(ir=10) {square([40,100], center=true); square([100,40], center=true);}
//   round2d(or=16,ir=8) {square([40,100], center=true); square([100,40], center=true);}
module round2d(r, or, ir)
{
    or = get_radius(r1=or, r=r, dflt=0);
    ir = get_radius(r1=ir, r=r, dflt=0);
    offset(or) offset(-ir-or) offset(delta=ir,chamfer=true) children();
}


// Module: shell2d()
// Synopsis: Creates a shell from 2D children.
// SynTags: Geom
// Topics: Shell
// See Also: round2d(), round3d(), minkowski_difference()
// Usage:
//   shell2d(thickness, [or], [ir])
// Description:
//   Creates a hollow shell from 2D children, with optional rounding.
// Arguments:
//   thickness = Thickness of the shell.  Positive to expand outward, negative to shrink inward, or a two-element list to do both.
//   or = Radius to round corners on the outside of the shell.  If given a list of 2 radii, [CONVEX,CONCAVE], specifies the radii for convex and concave corners separately.  Default: 0 (no outside rounding)
//   ir = Radius to round corners on the inside of the shell.  If given a list of 2 radii, [CONVEX,CONCAVE], specifies the radii for convex and concave corners separately.  Default: 0 (no inside rounding)
// Examples(2D):
//   shell2d(10) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(-10) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d([-10,10]) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,or=10) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,ir=10) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,or=[10,0]) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,or=[0,10]) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,ir=[10,0]) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(10,ir=[0,10]) {square([40,100], center=true); square([100,40], center=true);}
//   shell2d(8,or=[16,8],ir=[16,8]) {square([40,100], center=true); square([100,40], center=true);}
module shell2d(thickness, or=0, ir=0)
{
    thickness = is_num(thickness)? (
        thickness<0? [thickness,0] : [0,thickness]
    ) : (thickness[0]>thickness[1])? (
        [thickness[1],thickness[0]]
    ) : thickness;
    orad = is_finite(or)? [or,or] : or;
    irad = is_finite(ir)? [ir,ir] : ir;
    difference() {
        round2d(or=orad[0],ir=orad[1])
            offset(delta=thickness[1])
                children();
        round2d(or=irad[1],ir=irad[0])
            offset(delta=thickness[0])
                children();
    }
}


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