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BOSL2/mutators.scad
Adrian Mariano fe0586180e renamed is_region_simple to is_valid_region and fixed bugs and added examples 
fixed bugs in pair and triplet and added degenerate test cases
2021-11-03 22:30:01 -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], [closed]) {...}
// Description:
// Extrudes 2D children along the given 2D path, with optional rounded endcaps. This module works properly in general only if the given
// children are convex and symmetric across the Y axis. It works by constructing flat sections corresponding to each segment of the path and
// inserting rounded joints at each corner.
// 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. Default: false
// closed = If true, connect the starting point of the path to the ending point. Default: false
// 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]),caps=true)
// 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=false, closed=false) {
extra_ang = 0.1; // Extra angle for overlap of joints
assert(caps==false || closed==false, "Cannot have caps on a closed extrusion");
path = deduplicate(path);
for (p=pair(path,wrap=closed))
extrude_from_to(p[0],p[1]) xflip()rot(-90)children();
for (t=triplet(path,wrap=closed)) {
ang = -(180-vector_angle(t)) * sign(_point_left_of_line2d(t[2],[t[0],t[1]]));
delt = point3d(t[2] - t[1]);
if (ang!=0)
translate(t[1]) {
frame_map(y=delt, z=UP)
rotate(-sign(ang)*extra_ang/2)
rotate_extrude(angle=ang+sign(ang)*extra_ang)
if (ang<0)
right_half(planar=true) children();
else
left_half(planar=true) children();
}
}
if (caps) {
move_copies([path[0],last(path)])
rotate_extrude()
right_half(planar=true) children();
}
}
module new_path_extrude2d(path, caps=false, closed=false) {
extra_ang = 0.1; // Extra angle for overlap of joints
assert(caps==false || closed==false, "Cannot have caps on a closed extrusion");
path = deduplicate(path);
for (i=[0:1:len(path)-(closed?1:2)]){
// for (i=[0:1:1]){
difference(){
extrude_from_to(path[i],select(path,i+1)) xflip()rot(-90)children();
# for(t = [select(path,i-1,i+1)]){ //, select(path,i,i+2)]){
ang = -(180-vector_angle(t)) * sign(_point_left_of_line2d(t[2],[t[0],t[1]]));
echo(ang=ang);
delt = point3d(t[2] - t[1]);
if (ang!=0)
translate(t[1]) {
frame_map(y=delt, z=UP)
rotate(-sign(ang)*extra_ang/2)
rotate_extrude(angle=ang+sign(ang)*extra_ang)
if (ang<0)
left_half(planar=true) children();
else
right_half(planar=true) children();
}
}
}
}
for (t=triplet(path,wrap=closed)) {
ang = -(180-vector_angle(t)) * sign(_point_left_of_line2d(t[2],[t[0],t[1]]));
echo(oang=ang);
delt = point3d(t[2] - t[1]);
if (ang!=0)
translate(t[1]) {
frame_map(y=delt, z=UP)
rotate(-sign(ang)*extra_ang/2)
rotate_extrude(angle=ang+sign(ang)*extra_ang)
if (ang<0)
right_half(planar=true) children();
else
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)
// shuffle = if true then shuffle the hues in a random order. Default: false
// seed = seed to use for shuffle
// 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, shuffle=false, seed)
{
ll = len(list);
maxhues = first_defined([maxhues,ll]);
huestep = 360 / maxhues;
huelist = [for (i=[0:1:ll-1]) posmod(i*huestep+i*360/stride,360)];
hues = shuffle ? shuffle(huelist, seed=seed) : huelist;
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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