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BOSL2/shapes2d.scad
Adrian Mariano 35f1dc4cb0 Change Extra Anchors to Named Anchors
2024-05-20 19:42:07 -04:00

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//////////////////////////////////////////////////////////////////////
// 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)
// 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): 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) {
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, _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) =
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)],
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-[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,qpos)],
qrpts = 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=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 ? [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),
D = 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);
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: 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, reates 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"
// ---
// 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="Helvetica");
// 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-$idx), size=10, anchor=str("baseline",CENTER), spin=-90);
module text(text, size=10, font="Helvetica", halign, valign, spacing=1.0, direction="ltr", language="en", script="latin", anchor="baseline", spin=0) {
no_children($children);
dummy1 =
assert(is_undef(anchor) || is_vector(anchor) || is_string(anchor), str("Got: ",anchor))
assert(is_undef(spin) || is_vector(spin,3) || is_num(spin), str("Got: ",spin));
anchor = default(anchor, CENTER);
spin = default(spin, 0);
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();
}
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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