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BOSL2/mutators.scad
Adrian Mariano 3c6e9804a8 phillips_drive bugfix: 
wing angle corrected from ~70 deg to 92 deg
   adjusted cutouts so length "b" in the spec is correct
      (this causes the cutout to not align with the end so it
       doesn't look as pretty, but the spec wins, right?)
   Changed construction method to avoid z-fighting which gave
       rise to failed render

doc fixes and shifting in paths.scad
decompose_path -> polygon_parts
2021-09-21 19:19:02 -04:00

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//////////////////////////////////////////////////////////////////////
// LibFile: mutators.scad
// Functions and modules to mutate children in various ways.
// Includes:
// include <BOSL2/std.scad>
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Section: Volume Division Mutators
//////////////////////////////////////////////////////////////////////
// Module: bounding_box()
// Usage:
// bounding_box() ...
// Description:
// Returns the smallest axis-aligned square (or cube) shape that contains all the 2D (or 3D)
// children given. The module children() is supposed to be a 3d shape when planar=false and
// a 2d shape when planar=true otherwise the system will issue a warning of mixing dimension
// or scaling by 0.
// Arguments:
// excess = The amount that the bounding box should be larger than needed to bound the children, in each axis.
// planar = If true, creates a 2D bounding rectangle. Is false, creates a 3D bounding cube. Default: false
// Example(3D):
// module shapes() {
// translate([10,8,4]) cube(5);
// translate([3,0,12]) cube(2);
// }
// #bounding_box() shapes();
// shapes();
// Example(2D):
// module shapes() {
// translate([10,8]) square(5);
// translate([3,0]) square(2);
// }
// #bounding_box(planar=true) shapes();
// shapes();
module bounding_box(excess=0, planar=false) {
// a 3d (or 2d when planar=true) approx. of the children projection on X axis
module _xProjection() {
if (planar) {
projection()
rotate([90,0,0])
linear_extrude(1, center=true)
hull()
children();
} else {
xs = excess<.1? 1: excess;
linear_extrude(xs, center=true)
projection()
rotate([90,0,0])
linear_extrude(xs, center=true)
projection()
hull()
children();
}
}
// a bounding box with an offset of 1 in all axis
module _oversize_bbox() {
if (planar) {
minkowski() {
_xProjection() children(); // x axis
rotate(-90) _xProjection() rotate(90) children(); // y axis
}
} else {
minkowski() {
_xProjection() children(); // x axis
rotate(-90) _xProjection() rotate(90) children(); // y axis
rotate([0,-90,0]) _xProjection() rotate([0,90,0]) children(); // z axis
}
}
}
// offsets a cube by `excess`
module _shrink_cube() {
intersection() {
translate((1-excess)*[ 1, 1, 1]) children();
translate((1-excess)*[-1,-1,-1]) children();
}
}
if(planar) {
offset(excess-1/2) _oversize_bbox() children();
} else {
render(convexity=2)
if (excess>.1) {
_oversize_bbox() children();
} else {
_shrink_cube() _oversize_bbox() children();
}
}
}
// Function&Module: half_of()
//
// Usage: as module
// half_of(v, [cp], [s], [planar]) ...
// Usage: as function
// result = half_of(p,v,[cp]);
//
// Description:
// Slices an object at a cut plane, and masks away everything that is on one side. The v parameter is either a plane specification or
// a normal vector. The s parameter is needed for the module
// version to control the size of the masking cube, which affects preview display.
// When called as a function, you must supply a vnf, path or region in p. If planar is set to true for the module version the operation
// is performed in and UP and DOWN are treated as equivalent to BACK and FWD respectively.
//
// Arguments:
// p = path, region or VNF to slice. (Function version)
// v = Normal of plane to slice at. Keeps everything on the side the normal points to. Default: [0,0,1] (UP)
// cp = If given as a scalar, moves the cut plane along the normal by the given amount. If given as a point, specifies a point on the cut plane. Default: [0,0,0]
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, it messes with centering your view. Ignored for function version. Default: 1000
// planar = If true, perform a 2D operation. When planar, a `v` of `UP` or `DOWN` becomes equivalent of `BACK` and `FWD` respectively.
//
// Examples:
// half_of(DOWN+BACK, cp=[0,-10,0]) cylinder(h=40, r1=10, r2=0, center=false);
// half_of(DOWN+LEFT, s=200) sphere(d=150);
// Example(2D):
// half_of([1,1], planar=true) circle(d=50);
module half_of(v=UP, cp, s=1000, planar=false)
{
cp = is_vector(v,4)? assert(cp==undef, "Don't use cp with plane definition.") plane_normal(v) * v[3] :
is_vector(cp)? cp :
is_num(cp)? cp*unit(v) :
[0,0,0];
v = is_vector(v,4)? plane_normal(v) : v;
if (cp != [0,0,0]) {
translate(cp) half_of(v=v, s=s, planar=planar) translate(-cp) children();
} else if (planar) {
v = (v==UP)? BACK : (v==DOWN)? FWD : v;
ang = atan2(v.y, v.x);
difference() {
children();
rotate(ang+90) {
back(s/2) square(s, center=true);
}
}
} else {
difference() {
children();
rot(from=UP, to=-v) {
up(s/2) cube(s, center=true);
}
}
}
}
function half_of(p, v=UP, cp) =
is_vnf(p) ?
assert(is_vector(v) && (len(v)==3 || len(v)==4),str("Must give 3-vector or plane specification",v))
assert(select(v,0,2)!=[0,0,0], "vector v must be nonzero")
let(
plane = is_vector(v,4) ? assert(cp==undef, "Don't use cp with plane definition.") v
: is_undef(cp) ? [each v, 0]
: is_num(cp) ? [each v, cp*(v*v)/norm(v)]
: assert(is_vector(cp,3),"Centerpoint must be a 3-vector")
[each v, cp*v]
)
vnf_halfspace(plane, p)
: is_path(p) || is_region(p) ?
let(
v = (v==UP)? BACK : (v==DOWN)? FWD : v,
cp = is_undef(cp) ? [0,0]
: is_num(cp) ? v*cp
: assert(is_vector(cp,2) || (is_vector(cp,3) && cp.z==0),"Centerpoint must be 2-vector")
cp
)
assert(is_vector(v,2) || (is_vector(v,3) && v.z==0),"Must give 2-vector")
assert(!all_zero(v), "Vector v must be nonzero")
let(
bounds = pointlist_bounds(move(-cp,p)),
L = 2*max(flatten(bounds)),
n = unit(v),
u = [-n.y,n.x],
box = [cp+u*L, cp+(v+u)*L, cp+(v-u)*L, cp-u*L]
)
intersection(box,p)
: assert(false, "Input must be a region, path or VNF");
/* This code cut 3d paths but leaves behind connecting line segments
is_path(p) ?
//assert(len(p[0]) == d, str("path must have dimension ", d))
let(z = [for(x=p) (x-cp)*v])
[ for(i=[0:len(p)-1]) each concat(z[i] >= 0 ? [p[i]] : [],
// we assume a closed path here;
// to make this correct for an open path,
// just replace this by [] when i==len(p)-1:
let(j=(i+1)%len(p))
// the remaining path may have flattened sections, but this cannot
// create self-intersection or whiskers:
z[i]*z[j] >= 0 ? [] : [(z[j]*p[i]-z[i]*p[j])/(z[j]-z[i])]) ]
:
*/
// Function&Module: left_half()
//
// Usage: as module
// left_half([s], [x]) ...
// left_half(planar=true, [s], [x]) ...
// Usage: as function
// result = left_half(p, [x]);
//
// Description:
// Slices an object at a vertical Y-Z cut plane, and masks away everything that is right of it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// x = The X coordinate of the cut-plane. Default: 0
// planar = If true, perform a 2D operation.
//
// Examples:
// left_half() sphere(r=20);
// left_half(x=-8) sphere(r=20);
// Example(2D):
// left_half(planar=true) circle(r=20);
module left_half(s=1000, x=0, planar=false)
{
dir = LEFT;
difference() {
children();
translate([x,0,0]-dir*s/2) {
if (planar) {
square(s, center=true);
} else {
cube(s, center=true);
}
}
}
}
function left_half(p,x=0) = half_of(p, LEFT, [x,0,0]);
// Function&Module: right_half()
//
// Usage: as module
// right_half([s], [x]) ...
// right_half(planar=true, [s], [x]) ...
// Usage: as function
// result = right_half(p, [x]);
//
// Description:
// Slices an object at a vertical Y-Z cut plane, and masks away everything that is left of it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// x = The X coordinate of the cut-plane. Default: 0
// planar = If true perform a 2D operation.
//
// Examples(FlatSpin,VPD=175):
// right_half() sphere(r=20);
// right_half(x=-5) sphere(r=20);
// Example(2D):
// right_half(planar=true) circle(r=20);
module right_half(s=1000, x=0, planar=false)
{
dir = RIGHT;
difference() {
children();
translate([x,0,0]-dir*s/2) {
if (planar) {
square(s, center=true);
} else {
cube(s, center=true);
}
}
}
}
function right_half(p,x=0) = half_of(p, RIGHT, [x,0,0]);
// Function&Module: front_half()
//
// Usage:
// front_half([s], [y]) ...
// front_half(planar=true, [s], [y]) ...
// Usage: as function
// result = front_half(p, [y]);
//
// Description:
// Slices an object at a vertical X-Z cut plane, and masks away everything that is behind it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// y = The Y coordinate of the cut-plane. Default: 0
// planar = If true perform a 2D operation.
//
// Examples(FlatSpin,VPD=175):
// front_half() sphere(r=20);
// front_half(y=5) sphere(r=20);
// Example(2D):
// front_half(planar=true) circle(r=20);
module front_half(s=1000, y=0, planar=false)
{
dir = FWD;
difference() {
children();
translate([0,y,0]-dir*s/2) {
if (planar) {
square(s, center=true);
} else {
cube(s, center=true);
}
}
}
}
function front_half(p,y=0) = half_of(p, FRONT, [0,y,0]);
// Function&Module: back_half()
//
// Usage:
// back_half([s], [y]) ...
// back_half(planar=true, [s], [y]) ...
// Usage: as function
// result = back_half(p, [y]);
//
// Description:
// Slices an object at a vertical X-Z cut plane, and masks away everything that is in front of it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// y = The Y coordinate of the cut-plane. Default: 0
// planar = If true perform a 2D operation.
//
// Examples:
// back_half() sphere(r=20);
// back_half(y=8) sphere(r=20);
// Example(2D):
// back_half(planar=true) circle(r=20);
module back_half(s=1000, y=0, planar=false)
{
dir = BACK;
difference() {
children();
translate([0,y,0]-dir*s/2) {
if (planar) {
square(s, center=true);
} else {
cube(s, center=true);
}
}
}
}
function back_half(p,y=0) = half_of(p, BACK, [0,y,0]);
// Function&Module: bottom_half()
//
// Usage:
// bottom_half([s], [z]) ...
// Usage: as function
// result = bottom_half(p, [z]);
//
// Description:
// Slices an object at a horizontal X-Y cut plane, and masks away everything that is above it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// z = The Z coordinate of the cut-plane. Default: 0
//
// Examples:
// bottom_half() sphere(r=20);
// bottom_half(z=-10) sphere(r=20);
module bottom_half(s=1000, z=0)
{
dir = DOWN;
difference() {
children();
translate([0,0,z]-dir*s/2) {
cube(s, center=true);
}
}
}
function bottom_half(p,z=0) = half_of(p,BOTTOM,[0,0,z]);
// Function&Module: top_half()
//
// Usage:
// top_half([s], [z]) ...
// result = top_half(p, [z]);
//
// Description:
// Slices an object at a horizontal X-Y cut plane, and masks away everything that is below it.
//
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may be incorrect. Default: 10000
// z = The Z coordinate of the cut-plane. Default: 0
//
// Examples(Spin,VPD=175):
// top_half() sphere(r=20);
// top_half(z=5) sphere(r=20);
module top_half(s=1000, z=0)
{
dir = UP;
difference() {
children();
translate([0,0,z]-dir*s/2) {
cube(s, center=true);
}
}
}
function top_half(p,z=0) = half_of(p,UP,[0,0,z]);
//////////////////////////////////////////////////////////////////////
// Section: Warp Mutators
//////////////////////////////////////////////////////////////////////
// Module: chain_hull()
//
// Usage:
// chain_hull() ...
//
// Description:
// Performs hull operations between consecutive pairs of children,
// then unions all of the hull results. This can be a very slow
// operation, but it can provide results that are hard to get
// otherwise.
//
// Side Effects:
// `$idx` is set to the index value of the first child of each hulling pair, and can be used to modify each child pair individually.
// `$primary` is set to true when the child is the first in a chain pair.
//
// Example:
// chain_hull() {
// cube(5, center=true);
// translate([30, 0, 0]) sphere(d=15);
// translate([60, 30, 0]) cylinder(d=10, h=20);
// translate([60, 60, 0]) cube([10,1,20], center=false);
// }
// Example: Using `$idx` and `$primary`
// chain_hull() {
// zrot( 0) right(100) if ($primary) cube(5+3*$idx,center=true); else sphere(r=10+3*$idx);
// zrot( 45) right(100) if ($primary) cube(5+3*$idx,center=true); else sphere(r=10+3*$idx);
// zrot( 90) right(100) if ($primary) cube(5+3*$idx,center=true); else sphere(r=10+3*$idx);
// zrot(135) right(100) if ($primary) cube(5+3*$idx,center=true); else sphere(r=10+3*$idx);
// zrot(180) right(100) if ($primary) cube(5+3*$idx,center=true); else sphere(r=10+3*$idx);
// }
module chain_hull()
{
union() {
if ($children == 1) {
children();
} else if ($children > 1) {
for (i =[1:1:$children-1]) {
$idx = i;
hull() {
let($primary=true) children(i-1);
let($primary=false) children(i);
}
}
}
}
}
// Module: path_extrude2d()
// Usage:
// path_extrude2d(path, [caps]) {...}
// Description:
// Extrudes 2D children along the given 2D path, with optional rounded endcaps.
// Arguments:
// path = The 2D path to extrude the geometry along.
// caps = If true, caps each end of the path with a `rotate_extrude()`d copy of the children. This may interact oddly when given asymmetric profile children.
// Example:
// path = [
// each right(50, p=arc(d=100,angle=[90,180])),
// each left(50, p=arc(d=100,angle=[0,-90])),
// ];
// path_extrude2d(path,caps=false) {
// fwd(2.5) square([5,6],center=true);
// fwd(6) square([10,5],center=true);
// }
// Example:
// path_extrude2d(arc(d=100,angle=[180,270]))
// trapezoid(w1=10, w2=5, h=10, anchor=BACK);
// Example:
// include <BOSL2/beziers.scad>
// path = bezier_path([
// [-50,0], [-25,50], [0,0], [50,0]
// ]);
// path_extrude2d(path, caps=false)
// trapezoid(w1=10, w2=1, h=5, anchor=BACK);
module path_extrude2d(path, caps=true) {
thin = 0.01;
path = deduplicate(path);
for (p=pair(path)) {
delt = p[1]-p[0];
translate(p[0]) {
rot(from=BACK,to=delt) {
minkowski() {
cube([thin,norm(delt),thin], anchor=FRONT);
rotate([90,0,0]) linear_extrude(height=thin,center=true) children();
}
}
}
}
for (t=triplet(path)) {
ang = v_theta(t[2]-t[1]) - v_theta(t[1]-t[0]);
delt = t[2] - t[1];
translate(t[1]) {
minkowski() {
cube(thin,center=true);
if (ang >= 0) {
rotate(90-ang)
rot(from=LEFT,to=delt)
rotate_extrude(angle=ang+0.01)
right_half(planar=true) children();
} else {
rotate(-90)
rot(from=RIGHT,to=delt)
rotate_extrude(angle=-ang+0.01)
left_half(planar=true) children();
}
}
}
}
if (caps) {
move_copies([path[0],last(path)])
rotate_extrude()
right_half(planar=true) children();
}
}
// Module: cylindrical_extrude()
// Usage:
// cylindrical_extrude(size, ir|id, or|od, [convexity]) ...
// Description:
// Extrudes all 2D children outwards, curved around a cylindrical shape.
// Arguments:
// or = The outer radius to extrude to.
// od = The outer diameter to extrude to.
// ir = The inner radius to extrude from.
// id = The inner diameter to extrude from.
// size = The [X,Y] size of the 2D children to extrude. Default: [1000,1000]
// convexity = The max number of times a line could pass though a wall. Default: 10
// spin = Amount in degrees to spin around cylindrical axis. Default: 0
// orient = The orientation of the cylinder to wrap around, given as a vector. Default: UP
// Example:
// cylindrical_extrude(or=50, ir=45)
// text(text="Hello World!", size=10, halign="center", valign="center");
// Example: Spin Around the Cylindrical Axis
// cylindrical_extrude(or=50, ir=45, spin=90)
// text(text="Hello World!", size=10, halign="center", valign="center");
// Example: Orient to the Y Axis.
// cylindrical_extrude(or=40, ir=35, orient=BACK)
// text(text="Hello World!", size=10, halign="center", valign="center");
module cylindrical_extrude(or, ir, od, id, size=1000, convexity=10, spin=0, orient=UP) {
assert(is_num(size) || is_vector(size,2));
size = is_num(size)? [size,size] : size;
ir = get_radius(r=ir,d=id);
or = get_radius(r=or,d=od);
index_r = or;
circumf = 2 * PI * index_r;
width = min(size.x, circumf);
assert(width <= circumf, "Shape would more than completely wrap around.");
sides = segs(or);
step = circumf / sides;
steps = ceil(width / step);
rot(from=UP, to=orient) rot(spin) {
for (i=[0:1:steps-2]) {
x = (i+0.5-steps/2) * step;
zrot(360 * x / circumf) {
fwd(or*cos(180/sides)) {
xrot(-90) {
linear_extrude(height=or-ir, scale=[ir/or,1], center=false, convexity=convexity) {
yflip()
intersection() {
left(x) children();
rect([quantup(step,pow(2,-15)),size.y],center=true);
}
}
}
}
}
}
}
}
// Module: extrude_from_to()
// Description:
// Extrudes a 2D shape between the 3d points pt1 and pt2. Takes as children a set of 2D shapes to extrude.
// Arguments:
// pt1 = starting point of extrusion.
// pt2 = ending point of extrusion.
// convexity = max number of times a line could intersect a wall of the 2D shape being extruded.
// twist = number of degrees to twist the 2D shape over the entire extrusion length.
// scale = scale multiplier for end of extrusion compared the start.
// slices = Number of slices along the extrusion to break the extrusion into. Useful for refining `twist` extrusions.
// Example(FlatSpin,VPD=200,VPT=[0,0,15]):
// extrude_from_to([0,0,0], [10,20,30], convexity=4, twist=360, scale=3.0, slices=40) {
// xcopies(3) circle(3, $fn=32);
// }
module extrude_from_to(pt1, pt2, convexity, twist, scale, slices) {
assert(is_vector(pt1));
assert(is_vector(pt2));
pt1 = point3d(pt1);
pt2 = point3d(pt2);
rtp = xyz_to_spherical(pt2-pt1);
translate(pt1) {
rotate([0, rtp[2], rtp[1]]) {
if (rtp[0] > 0) {
linear_extrude(height=rtp[0], convexity=convexity, center=false, slices=slices, twist=twist, scale=scale) {
children();
}
}
}
}
}
// Module: spiral_sweep()
// Description:
// Takes a closed 2D polygon path, centered on the XY plane, and sweeps/extrudes it along a 3D spiral path
// of a given radius, height and twist. The origin in the profile traces out the helix of the specified radius.
// If twist is positive the path will be right-handed; if twist is negative the path will be left-handed.
// .
// Higbee specifies tapering applied to the ends of the extrusion and is given as the linear distance
// over which to taper.
// Arguments:
// poly = Array of points of a polygon path, to be extruded.
// h = height of the spiral to extrude along.
// r = Radius of the spiral to extrude along. Default: 50
// twist = number of degrees of rotation to spiral up along height.
// ---
// d = Diameter of the spiral to extrude along.
// higbee = Length to taper thread ends over.
// higbee1 = Taper length at start
// higbee2 = Taper length at end
// internal = direction to taper the threads with higbee. If true threads taper outward; if false they taper inward. Default: false
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
// center = If given, overrides `anchor`. A true value sets `anchor=CENTER`, false sets `anchor=BOTTOM`.
// Example:
// poly = [[-10,0], [-3,-5], [3,-5], [10,0], [0,-30]];
// spiral_sweep(poly, h=200, r=50, twist=1080, $fn=36);
module spiral_sweep(poly, h, r, twist=360, higbee, center, r1, r2, d, d1, d2, higbee1, higbee2, internal=false, anchor, spin=0, orient=UP) {
higsample = 10; // Oversample factor for higbee tapering
dummy1=assert(is_num(twist) && twist != 0);
bounds = pointlist_bounds(poly);
yctr = (bounds[0].y+bounds[1].y)/2;
xmin = bounds[0].x;
xmax = bounds[1].x;
poly = path3d(clockwise_polygon(poly));
anchor = get_anchor(anchor,center,BOT,BOT);
r1 = get_radius(r1=r1, r=r, d1=d1, d=d, dflt=50);
r2 = get_radius(r1=r2, r=r, d1=d2, d=d, dflt=50);
sides = segs(max(r1,r2));
dir = sign(twist);
ang_step = 360/sides*dir;
anglist = [for(ang = [0:ang_step:twist-EPSILON]) ang,
twist];
higbee1 = first_defined([higbee1, higbee, 0]);
higbee2 = first_defined([higbee2, higbee, 0]);
higang1 = 360 * higbee1 / (2 * r1 * PI);
higang2 = 360 * higbee2 / (2 * r2 * PI);
dummy2=assert(higbee1>=0 && higbee2>=0)
assert(higang1 < dir*twist/2,"Higbee1 is more than half the threads")
assert(higang2 < dir*twist/2,"Higbee2 is more than half the threads");
function polygon_r(N,theta) =
let( alpha = 360/N )
cos(alpha/2)/(cos(posmod(theta,alpha)-alpha/2));
higofs = pow(0.05,2); // Smallest hig scale is the square root of this value
function taperfunc(x) = sqrt((1-higofs)*x+higofs);
interp_ang = [
for(i=idx(anglist,e=-2))
each lerpn(anglist[i],anglist[i+1],
(higang1>0 && higang1>dir*anglist[i+1]
|| (higang2>0 && higang2>dir*(twist-anglist[i]))) ? ceil((anglist[i+1]-anglist[i])/ang_step*higsample)
: 1,
endpoint=false),
last(anglist)
];
skewmat = affine3d_skew_xz(xa=atan2(r2-r1,h));
points = [
for (a = interp_ang) let (
hsc = dir*a<higang1 ? taperfunc(dir*a/higang1)
: dir*(twist-a)<higang2 ? taperfunc(dir*(twist-a)/higang2)
: 1,
u = a/twist,
r = lerp(r1,r2,u),
mat = affine3d_zrot(a)
* affine3d_translate([polygon_r(sides,a)*r, 0, h * (u-0.5)])
* affine3d_xrot(90)
* skewmat
* scale([hsc,lerp(hsc,1,0.25),1], cp=[internal ? xmax : xmin, yctr, 0]),
pts = apply(mat, poly)
) pts
];
vnf = vnf_vertex_array(
points, col_wrap=true, caps=true, reverse=dir>0?true:false,
style=higbee1>0 || higbee2>0 ? "quincunx" : "alt"
);
attachable(anchor,spin,orient, r1=r1, r2=r2, l=h) {
vnf_polyhedron(vnf, convexity=ceil(2*dir*twist/360));
children();
}
}
// Module: path_extrude()
// Description:
// Extrudes 2D children along a 3D path. This may be slow.
// Arguments:
// path = array of points for the bezier path to extrude along.
// convexity = maximum number of walls a ran can pass through.
// clipsize = increase if artifacts are left. Default: 1000
// Example(FlatSpin,VPD=600,VPT=[75,16,20]):
// path = [ [0, 0, 0], [33, 33, 33], [66, 33, 40], [100, 0, 0], [150,0,0] ];
// path_extrude(path) circle(r=10, $fn=6);
module path_extrude(path, convexity=10, clipsize=100) {
function polyquats(path, q=q_ident(), v=[0,0,1], i=0) = let(
v2 = path[i+1] - path[i],
ang = vector_angle(v,v2),
axis = ang>0.001? unit(cross(v,v2)) : [0,0,1],
newq = q_mul(quat(axis, ang), q),
dist = norm(v2)
) i < (len(path)-2)?
concat([[dist, newq, ang]], polyquats(path, newq, v2, i+1)) :
[[dist, newq, ang]];
epsilon = 0.0001; // Make segments ever so slightly too long so they overlap.
ptcount = len(path);
pquats = polyquats(path);
for (i = [0:1:ptcount-2]) {
pt1 = path[i];
pt2 = path[i+1];
dist = pquats[i][0];
q = pquats[i][1];
difference() {
translate(pt1) {
q_rot(q) {
down(clipsize/2/2) {
if ((dist+clipsize/2) > 0) {
linear_extrude(height=dist+clipsize/2, convexity=convexity) {
children();
}
}
}
}
}
translate(pt1) {
hq = (i > 0)? q_slerp(q, pquats[i-1][1], 0.5) : q;
q_rot(hq) down(clipsize/2+epsilon) cube(clipsize, center=true);
}
translate(pt2) {
hq = (i < ptcount-2)? q_slerp(q, pquats[i+1][1], 0.5) : q;
q_rot(hq) up(clipsize/2+epsilon) cube(clipsize, center=true);
}
}
}
}
//////////////////////////////////////////////////////////////////////
// Section: Offset Mutators
//////////////////////////////////////////////////////////////////////
// Module: minkowski_difference()
// Usage:
// minkowski_difference() { base_shape(); diff_shape(); ... }
// Description:
// Takes a 3D base shape and one or more 3D diff shapes, carves out the diff shapes from the
// surface of the base shape, in a way complementary to how `minkowski()` unions shapes to the
// surface of its base shape.
// Arguments:
// planar = If true, performs minkowski difference in 2D. Default: false (3D)
// Example:
// minkowski_difference() {
// union() {
// cube([120,70,70], center=true);
// cube([70,120,70], center=true);
// cube([70,70,120], center=true);
// }
// sphere(r=10);
// }
module minkowski_difference(planar=false) {
difference() {
bounding_box(excess=0, planar=planar) children(0);
render(convexity=20) {
minkowski() {
difference() {
bounding_box(excess=1, planar=planar) children(0);
children(0);
}
for (i=[1:1:$children-1]) children(i);
}
}
}
}
// Module: round2d()
// Usage:
// round2d(r) ...
// round2d(or) ...
// round2d(ir) ...
// round2d(or, ir) ...
// 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()
// Usage:
// shell2d(thickness, [or], [ir], [fill], [round])
// 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();
}
}
// Module: offset3d()
// Usage:
// offset3d(r, [size], [convexity]);
// Description:
// Expands or contracts the surface of a 3D object by a given amount. This is very, very slow.
// No really, this is unbearably slow. It uses `minkowski()`. Use this as a last resort.
// This is so slow that no example images will be rendered.
// Arguments:
// r = Radius to expand object by. Negative numbers contract the object.
// size = Maximum size of object to be contracted, given as a scalar. Default: 100
// convexity = Max number of times a line could intersect the walls of the object. Default: 10
module offset3d(r=1, size=100, convexity=10) {
n = quant(max(8,segs(abs(r))),4);
if (r==0) {
children();
} else if (r>0) {
render(convexity=convexity)
minkowski() {
children();
sphere(r, $fn=n);
}
} else {
size2 = size * [1,1,1];
size1 = size2 * 1.02;
render(convexity=convexity)
difference() {
cube(size2, center=true);
minkowski() {
difference() {
cube(size1, center=true);
children();
}
sphere(-r, $fn=n);
}
}
}
}
// Module: round3d()
// Usage:
// round3d(r) ...
// round3d(or) ...
// round3d(ir) ...
// round3d(or, ir) ...
// Description:
// Rounds arbitrary 3D 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 3D object must not have
// any parts narrower than twice the `or` radius. Such parts will disappear. This is an *extremely*
// slow operation. I cannot emphasize enough just how slow it is. It uses `minkowski()` multiple times.
// Use this as a last resort. This is so slow that no example images will be rendered.
// 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`.
module round3d(r, or, ir, size=100)
{
or = get_radius(r1=or, r=r, dflt=0);
ir = get_radius(r1=ir, r=r, dflt=0);
offset3d(or, size=size)
offset3d(-ir-or, size=size)
offset3d(ir, size=size)
children();
}
//////////////////////////////////////////////////////////////////////
// Section: Colors
//////////////////////////////////////////////////////////////////////
// Function&Module: HSL()
// Usage:
// HSL(h,[s],[l],[a]) ...
// rgb = HSL(h,[s],[l]);
// Description:
// When called as a function, returns the [R,G,B] color for the given hue `h`, saturation `s`, and lightness `l` from the HSL colorspace.
// When called as a module, sets the color to the given hue `h`, saturation `s`, and lightness `l` from the HSL colorspace.
// Arguments:
// h = The hue, given as a value between 0 and 360. 0=red, 60=yellow, 120=green, 180=cyan, 240=blue, 300=magenta.
// s = The saturation, given as a value between 0 and 1. 0 = grayscale, 1 = vivid colors. Default: 1
// l = The lightness, between 0 and 1. 0 = black, 0.5 = bright colors, 1 = white. Default: 0.5
// a = When called as a module, specifies the alpha channel as a value between 0 and 1. 0 = fully transparent, 1=opaque. Default: 1
// Example:
// HSL(h=120,s=1,l=0.5) sphere(d=60);
// Example:
// rgb = HSL(h=270,s=0.75,l=0.6);
// color(rgb) cube(60, center=true);
function HSL(h,s=1,l=0.5) =
let(
h=posmod(h,360)
) [
for (n=[0,8,4]) let(
k=(n+h/30)%12
) l - s*min(l,1-l)*max(min(k-3,9-k,1),-1)
];
module HSL(h,s=1,l=0.5,a=1) color(HSL(h,s,l),a) children();
// Function&Module: HSV()
// Usage:
// HSV(h,[s],[v],[a]) ...
// rgb = HSV(h,[s],[v]);
// Description:
// When called as a function, returns the [R,G,B] color for the given hue `h`, saturation `s`, and value `v` from the HSV colorspace.
// When called as a module, sets the color to the given hue `h`, saturation `s`, and value `v` from the HSV colorspace.
// Arguments:
// h = The hue, given as a value between 0 and 360. 0=red, 60=yellow, 120=green, 180=cyan, 240=blue, 300=magenta.
// s = The saturation, given as a value between 0 and 1. 0 = grayscale, 1 = vivid colors. Default: 1
// v = The value, between 0 and 1. 0 = darkest black, 1 = bright. Default: 1
// a = When called as a module, specifies the alpha channel as a value between 0 and 1. 0 = fully transparent, 1=opaque. Default: 1
// Example:
// HSV(h=120,s=1,v=1) sphere(d=60);
// Example:
// rgb = HSV(h=270,s=0.75,v=0.9);
// color(rgb) cube(60, center=true);
function HSV(h,s=1,v=1) =
assert(s>=0 && s<=1)
assert(v>=0 && v<=1)
let(
h = posmod(h,360),
c = v * s,
hprime = h/60,
x = c * (1- abs(hprime % 2 - 1)),
rgbprime = hprime <=1 ? [c,x,0]
: hprime <=2 ? [x,c,0]
: hprime <=3 ? [0,c,x]
: hprime <=4 ? [0,x,c]
: hprime <=5 ? [x,0,c]
: hprime <=6 ? [c,0,x]
: [0,0,0],
m=v-c
)
rgbprime+[m,m,m];
module HSV(h,s=1,v=1,a=1) color(HSV(h,s,v),a) children();
// Module: rainbow()
// Usage:
// rainbow(list) ...
// Description:
// Iterates the list, displaying children in different colors for each list item.
// This is useful for debugging lists of paths and such.
// Arguments:
// list = The list of items to iterate through.
// stride = Consecutive colors stride around the color wheel divided into this many parts.
// maxhues = max number of hues to use (to prevent lots of indistinguishable hues)
// Side Effects:
// Sets the color to progressive values along the ROYGBIV spectrum for each item.
// Sets `$idx` to the index of the current item in `list` that we want to show.
// Sets `$item` to the current item in `list` that we want to show.
// Example(2D):
// rainbow(["Foo","Bar","Baz"]) fwd($idx*10) text(text=$item,size=8,halign="center",valign="center");
// Example(2D):
// rgn = [circle(d=45,$fn=3), circle(d=75,$fn=4), circle(d=50)];
// rainbow(rgn) stroke($item, closed=true);
module rainbow(list, stride=1, maxhues)
{
ll = len(list);
maxhues = first_defined([maxhues,ll]);
huestep = 360 / maxhues;
hues = [for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)];
echo(hues=hues);
s = [for (i=[0:1:ll-1]) [.5,.7,1][posmod(i,3)]];
for($idx=idx(list)) {
$item = list[$idx];
HSV(h=hues[$idx]) children();
}
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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