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BOSL2/distributors.scad
Adrian Mariano a7711edf0b distributors name normalization & bug fix
2022-10-22 23:15:35 -04:00

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//////////////////////////////////////////////////////////////////////
// LibFile: distributors.scad
// Functions and modules to distribute children or copies of children onto
// a line, a grid, or an arbitrary path. The $idx mechanism means that
// the "copies" of children can vary. Also includes shortcuts for mirroring.
// Includes:
// include <BOSL2/std.scad>
// FileGroup: Basic Modeling
// FileSummary: Copy or distribute objects onto a line, grid, or path. Mirror shortcuts.
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
// Section: Translating copies of all the children
//////////////////////////////////////////////////////////////////////
// Module: move_copies()
//
// Description:
// Translates copies of all children to each given translation offset.
//
// Usage:
// move_copies(a) CHILDREN;
//
// Arguments:
// a = Array of XYZ offset vectors. Default `[[0,0,0]]`
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// #sphere(r=10);
// move_copies([[-25,-25,0], [25,-25,0], [0,0,50], [0,25,0]]) sphere(r=10);
module move_copies(a=[[0,0,0]])
{
req_children($children);
assert(is_list(a));
for ($idx = idx(a)) {
$pos = a[$idx];
assert(is_vector($pos),"move_copies offsets should be a 2d or 3d vector.");
translate($pos) children();
}
}
// Module: xcopies()
//
// Description:
// Places out `n` copies of the children along a line on the X axis.
//
// Usage:
// xcopies(spacing, [n], [sp]) CHILDREN;
// xcopies(l, [n], [sp]) CHILDREN;
// xcopies(LIST) CHILDREN;
//
// Arguments:
// spacing = Given a scalar, specifies a uniform spacing between copies. Given a list of scalars, each one gives a specific position along the line. (Default: 1.0)
// n = Number of copies to place. (Default: 2)
// l = Length to place copies over.
// sp = If given as a point, copies will be placed on a line to the right of starting position `sp`. If given as a scalar, copies will be placed on a line to the right of starting position `[sp,0,0]`. If not given, copies will be placed along a line that is centered at [0,0,0].
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Examples:
// xcopies(20) sphere(3);
// xcopies(20, n=3) sphere(3);
// xcopies(spacing=15, l=50) sphere(3);
// xcopies(n=4, l=30, sp=[0,10,0]) sphere(3);
// Example:
// xcopies(10, n=3) {
// cube(size=[1,3,1],center=true);
// cube(size=[3,1,1],center=true);
// }
// Example:
// xcopies([1,2,3,5,7]) sphere(d=1);
module xcopies(spacing, n, l, sp)
{
req_children($children);
dir = RIGHT;
sp = is_finite(sp)? (sp*dir) : sp;
if (is_vector(spacing)) {
translate(default(sp,[0,0,0])) {
for (i = idx(spacing)) {
$idx = i;
$pos = spacing[i]*dir;
translate($pos) children();
}
}
} else {
line_copies(
l=u_mul(l,dir),
spacing=u_mul(spacing,dir),
n=n, p1=sp
) children();
}
}
// Module: ycopies()
//
// Description:
// Places `n` copies of the children along a line on the Y axis.
//
// Usage:
// ycopies(spacing, [n], [sp]) CHILDREN;
// ycopies(l, [n], [sp]) CHILDREN;
// ycopies(LIST) CHILDREN;
//
// Arguments:
// spacing = Given a scalar, specifies a uniform spacing between copies. Given a list of scalars, each one gives a specific position along the line. (Default: 1.0)
// n = Number of copies to place on the line. (Default: 2)
// l = Length to place copies over.
// sp = If given as a point, copies will be place on a line back from starting position `sp`. If given as a scalar, copies will be placed on a line back from starting position `[0,sp,0]`. If not given, copies will be placed along a line that is centered at [0,0,0].
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Examples:
// ycopies(20) sphere(3);
// ycopies(20, n=3) sphere(3);
// ycopies(spacing=15, l=50) sphere(3);
// ycopies(n=4, l=30, sp=[10,0,0]) sphere(3);
// Example:
// ycopies(10, n=3) {
// cube(size=[1,3,1],center=true);
// cube(size=[3,1,1],center=true);
// }
// Example:
// ycopies([1,2,3,5,7]) sphere(d=1);
module ycopies(spacing, n, l, sp)
{
req_children($children);
dir = BACK;
sp = is_finite(sp)? (sp*dir) : sp;
if (is_vector(spacing)) {
translate(default(sp,[0,0,0])) {
for (i = idx(spacing)) {
$idx = i;
$pos = spacing[i]*dir;
translate($pos) children();
}
}
} else {
line_copies(
l=u_mul(l,dir),
spacing=u_mul(spacing,dir),
n=n, p1=sp
) children();
}
}
// Module: zcopies()
//
// Description:
// Places `n` copies of the children along a line on the Z axis.
//
// Usage:
// zcopies(spacing, [n], [sp]) CHILDREN;
// zcopies(l, [n], [sp]) CHILDREN;
// zcopies(LIST) CHILDREN;
//
// Arguments:
// spacing = Given a scalar, specifies a uniform spacing between copies. Given a list of scalars, each one gives a specific position along the line. (Default: 1.0)
// n = Number of copies to place. (Default: 2)
// l = Length to place copies over.
// sp = If given as a point, copies will be placed on a line up from starting position `sp`. If given as a scalar, copies will be placed on a line up from starting position `[0,0,sp]`. If not given, copies will be placed on a line that is centered at [0,0,0].
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Examples:
// zcopies(20) sphere(3);
// zcopies(20, n=3) sphere(3);
// zcopies(spacing=15, l=50) sphere(3);
// zcopies(n=4, l=30, sp=[10,0,0]) sphere(3);
// Example:
// zcopies(10, n=3) {
// cube(size=[1,3,1],center=true);
// cube(size=[3,1,1],center=true);
// }
// Example: Cubic sphere packing
// s = 20;
// s2 = s * sin(45);
// zcopies(s2,n=8) union()
// grid_copies([s2,s2],n=8,stagger=($idx%2)? true : "alt")
// sphere(d=s);
// Example: Hexagonal sphere packing
// s = 20;
// xyr = adj_ang_to_hyp(s/2,30);
// h = hyp_adj_to_opp(s,xyr);
// zcopies(h,n=8) union()
// back(($idx%2)*xyr*cos(60))
// grid_copies(s,n=[12,7],stagger=($idx%2)? "alt" : true)
// sphere(d=s);
// Example:
// zcopies([1,2,3,5,7]) sphere(d=1);
module zcopies(spacing, n, l, sp)
{
req_children($children);
dir = UP;
sp = is_finite(sp)? (sp*dir) : sp;
if (is_vector(spacing)) {
translate(default(sp,[0,0,0])) {
for (i = idx(spacing)) {
$idx = i;
$pos = spacing[i]*dir;
translate($pos) children();
}
}
} else {
line_copies(
l=u_mul(l,dir),
spacing=u_mul(spacing,dir),
n=n, p1=sp
) children();
}
}
// Function&Module: line_copies()
//
// Usage: Place `n` copies at a given spacing along the line
// line_copies(spacing, [n], [p1=]) CHILDREN;
// Usage: Place as many copies as will fit at a given spacing
// line_copies(spacing, [l=], [p1=]) CHILDREN;
// Usage: Place `n` copies along the length of the line
// line_copies([n=], [l=], [p1=]) CHILDREN;
// Usage: Place `n` copies along the line from `p1` to `p2`
// line_copies([n=], [p1=], [p2=]) CHILDREN;
// Usage: Place copies at the given spacing, centered along the line from `p1` to `p2`
// line_copies([spacing], [p1=], [p2=]) CHILDREN;
// Usage: As a function
// pts = line_copies([spacing], [n], [p1=]);
// pts = line_copies([spacing], [l=], [p1=]);
// pts = line_copies([n=], [l=], [p1=]);
// pts = line_copies([n=], [p1=], [p2=]);
// pts = line_copies([spacing], [p1=], [p2=]);
// Description:
// When called as a function, returns a list of points at evenly spaced positions along a line.
// When called as a module, copies `children()` at one or more evenly spaced positions along a line.
// By default, the line will be centered at the origin, unless the starting point `p1` is given.
// The line will be pointed towards `RIGHT` (X+) unless otherwise given as a vector in `l`,
// `spacing`, or `p1`/`p2`. The psotion of the copies is specified in one of several ways:
// .
// If You Know... | Then Use Something Like...
// -------------------------------- | --------------------------------
// Spacing distance, Count | `line_copies(spacing=10, n=5) ...` or `line_copies(10, n=5) ...`
// Spacing vector, Count | `line_copies(spacing=[10,5], n=5) ...` or `line_copies([10,5], n=5) ...`
// Spacing distance, Line length | `line_copies(spacing=10, l=50) ...` or `line_copies(10, l=50) ...`
// Spacing distance, Line vector | `line_copies(spacing=10, l=[50,30]) ...` or `line_copies(10, l=[50,30]) ...`
// Spacing vector, Line length | `line_copies(spacing=[10,5], l=50) ...` or `line_copies([10,5], l=50) ...`
// Line length, Count | `line_copies(l=50, n=5) ...`
// Line vector, Count | `line_copies(l=[50,40], n=5) ...`
// Line endpoints, Count | `line_copies(p1=[10,10], p2=[60,-10], n=5) ...`
// Line endpoints, Spacing distance | `line_copies(p1=[10,10], p2=[60,-10], spacing=10) ...`
//
// Arguments:
// spacing = Either the scalar spacing distance along the X+ direction, or the vector giving both the direction and spacing distance between each set of copies.
// n = Number of copies to distribute along the line. (Default: 2)
// ---
// l = Either the scalar length of the line, or a vector giving both the direction and length of the line.
// p1 = If given, specifies the starting point of the line.
// p2 = If given with `p1`, specifies the ending point of line, and indirectly calculates the line length.
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Examples:
// line_copies(10) sphere(d=1);
// line_copies(10, n=5) sphere(d=1);
// line_copies([10,5], n=5) sphere(d=1);
// line_copies(spacing=10, n=6) sphere(d=1);
// line_copies(spacing=[10,5], n=6) sphere(d=1);
// line_copies(spacing=10, l=50) sphere(d=1);
// line_copies(spacing=10, l=[50,30]) sphere(d=1);
// line_copies(spacing=[10,5], l=50) sphere(d=1);
// line_copies(l=50, n=4) sphere(d=1);
// line_copies(l=[50,-30], n=4) sphere(d=1);
// Example(FlatSpin,VPD=133):
// line_copies(p1=[0,0,0], p2=[5,5,20], n=6) cube(size=[3,2,1],center=true);
// Example(FlatSpin,VPD=133):
// line_copies(p1=[0,0,0], p2=[5,5,20], spacing=6) cube(size=[3,2,1],center=true);
// Example: All children are copied to each position
// line_copies(l=20, n=3) {
// cube(size=[1,3,1],center=true);
// cube(size=[3,1,1],center=true);
// }
// Example(2D): The functional form of line_copies() returns a list of points.
// pts = line_copies([10,5],n=5);
// move_copies(pts) circle(d=2);
module line_of(spacing, n, l, p1, p2) {
deprecate("line_copies");
line_copies(spacing, n, l, p1, p2);
}
module line_copies(spacing, n, l, p1, p2)
{
req_children($children);
pts = line_copies(spacing=spacing, n=n, l=l, p1=p1, p2=p2);
for (i=idx(pts)) {
$idx = i;
$pos = pts[i];
translate($pos) children();
}
}
function line_copies(spacing, n, l, p1, p2) =
assert(is_undef(spacing) || is_finite(spacing) || is_vector(spacing))
assert(is_undef(n) || is_finite(n))
assert(is_undef(l) || is_finite(l) || is_vector(l))
assert(is_undef(p1) || is_vector(p1))
assert(is_undef(p2) || is_vector(p2))
let(
ll = !is_undef(l)? scalar_vec3(l, 0) :
(!is_undef(spacing) && !is_undef(n))? ((n-1) * scalar_vec3(spacing, 0)) :
(!is_undef(p1) && !is_undef(p2))? point3d(p2-p1) :
undef,
cnt = !is_undef(n)? n :
(!is_undef(spacing) && !is_undef(ll))? floor(norm(ll) / norm(scalar_vec3(spacing, 0)) + 1.000001) :
2,
spc = cnt<=1? [0,0,0] :
is_undef(spacing)? (ll/(cnt-1)) :
is_num(spacing) && !is_undef(ll)? (ll/(cnt-1)) :
scalar_vec3(spacing, 0)
)
assert(!is_undef(cnt), "Need two of `spacing`, 'l', 'n', or `p1`/`p2` arguments in `line_copies()`.")
let( spos = !is_undef(p1)? point3d(p1) : -(cnt-1)/2 * spc )
[for (i=[0:1:cnt-1]) i * spc + spos];
// Module: grid_copies()
//
// Description:
// Makes a square or hexagonal grid of copies of children, with an optional masking polygon or region.
//
// Usage:
// grid_copies(spacing, size=, [stagger=], [scale=], [inside=]) CHILDREN;
// grid_copies(n=, size=, [stagger=], [scale=], [inside=]) CHILDREN;
// grid_copies(spacing, [n], [stagger=], [scale=], [inside=]) CHILDREN;
// grid_copies(n=, inside=, [stagger], [scale]) CHILDREN;
//
// Arguments:
// spacing = Distance between copies in [X,Y] or scalar distance.
// n = How many columns and rows of copies to make. Can be given as `[COLS,ROWS]`, or just as a scalar that specifies both. If staggered, count both staggered and unstaggered columns and rows. Default: 2 (3 if staggered)
// size = The [X,Y] size to spread the copies over.
// ---
// stagger = If true, make a staggered (hexagonal) grid. If false, make square grid. If `"alt"`, makes alternate staggered pattern. Default: false
// inside = If given a list of polygon points, or a region, only creates copies whose center would be inside the polygon or region. Polygon can be concave and/or self crossing.
// nonzero = If inside is set to a polygon with self-crossings then use the nonzero method for deciding if points are in the polygon. Default: false
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$col` is set to the integer column number for each child.
// `$row` is set to the integer row number for each child.
//
// Examples:
// grid_copies(size=50, spacing=10) cylinder(d=10, h=1);
// grid_copies(size=50, spacing=[10,15]) cylinder(d=10, h=1);
// grid_copies(spacing=10, n=[13,7], stagger=true) cylinder(d=6, h=5);
// grid_copies(spacing=10, n=[13,7], stagger="alt") cylinder(d=6, h=5);
// grid_copies(size=50, n=11, stagger=true) cylinder(d=5, h=1);
//
// Example:
// poly = [[-25,-25], [25,25], [-25,25], [25,-25]];
// grid_copies(spacing=5, stagger=true, inside=poly)
// zrot(180/6) cylinder(d=5, h=1, $fn=6);
// %polygon(poly);
//
// Example: Using `$row` and `$col`
// grid_copies(spacing=8, n=8)
// color(($row+$col)%2?"black":"red")
// cube([8,8,0.01], center=false);
//
// Example:
// // Makes a grid of hexagon pillars whose tops are all
// // angled to reflect light at [0,0,50], if they were shiny.
// hexregion = circle(r=50.01,$fn=6);
// grid_copies(spacing=10, stagger=true, inside=hexregion) union() {
// // Note: The union() is needed or else $pos will be
// // inexplicably unreadable.
// ref_v = (unit([0,0,50]-point3d($pos)) + UP)/2;
// half_of(v=-ref_v, cp=[0,0,5])
// zrot(180/6)
// cylinder(h=20, d=10/cos(180/6)+0.01, $fn=6);
// }
function grid_copies(spacing, n, size, stagger=false, inside=undef, nonzero) = no_function("grid_copies");
module grid2d(spacing, n, size, stagger=false, inside=undef, nonzero)
{
deprecate("grid_copies");
grid_copies(spacing, n, size, stagger, inside, nonzero) children();
}
module grid_copies(spacing, n, size, stagger=false, inside=undef, nonzero)
{
req_children($children);
assert(in_list(stagger, [false, true, "alt"]));
bounds = is_undef(inside)? undef :
is_path(inside)? pointlist_bounds(inside) :
assert(is_region(inside))
pointlist_bounds(flatten(inside));
nonzero = is_path(inside) ? default(nonzero,false)
: assert(is_undef(nonzero), "nonzero only allowed if inside is a polygon")
false;
size = is_num(size)? [size, size] :
is_vector(size)? assert(len(size)==2) size :
bounds!=undef? [
for (i=[0:1]) 2*max(abs(bounds[0][i]),bounds[1][i])
] : undef;
spacing = is_num(spacing)? (
stagger!=false? polar_to_xy(spacing,60) :
[spacing,spacing]
) :
is_vector(spacing)? assert(len(spacing)==2) spacing :
size!=undef? (
is_num(n)? v_div(size,(n-1)*[1,1]) :
is_vector(n)? assert(len(n)==2) v_div(size,n-[1,1]) :
v_div(size,(stagger==false? [1,1] : [2,2]))
) :
undef;
n = is_num(n)? [n,n] :
is_vector(n)? assert(len(n)==2) n :
size!=undef && spacing!=undef? v_floor(v_div(size,spacing))+[1,1] :
[2,2];
offset = v_mul(spacing, n-[1,1])/2;
if (stagger == false) {
for (row = [0:1:n.y-1]) {
for (col = [0:1:n.x-1]) {
pos = v_mul([col,row],spacing) - offset;
if (
is_undef(inside) ||
(is_path(inside) && point_in_polygon(pos, inside, nonzero=nonzero)>=0) ||
(is_region(inside) && point_in_region(pos, inside)>=0)
) {
$col = col;
$row = row;
$pos = pos;
translate(pos) children();
}
}
}
} else {
// stagger == true or stagger == "alt"
staggermod = (stagger == "alt")? 1 : 0;
cols1 = ceil(n.x/2);
cols2 = n.x - cols1;
for (row = [0:1:n.y-1]) {
rowcols = ((row%2) == staggermod)? cols1 : cols2;
if (rowcols > 0) {
for (col = [0:1:rowcols-1]) {
rowdx = (row%2 != staggermod)? spacing.x : 0;
pos = v_mul([2*col,row],spacing) + [rowdx,0] - offset;
if (
is_undef(inside) ||
(is_path(inside) && point_in_polygon(pos, inside, nonzero=nonzero)>=0) ||
(is_region(inside) && point_in_region(pos, inside)>=0)
) {
$col = col * 2 + ((row%2!=staggermod)? 1 : 0);
$row = row;
$pos = pos;
translate(pos) children();
}
}
}
}
}
}
//////////////////////////////////////////////////////////////////////
// Section: Rotating copies of all children
//////////////////////////////////////////////////////////////////////
// Module: rot_copies()
//
// Description:
// Given a list of [X,Y,Z] rotation angles in `rots`, rotates copies of the children to each of those angles, regardless of axis of rotation.
// Given a list of scalar angles in `rots`, rotates copies of the children to each of those angles around the axis of rotation.
// If given a vector `v`, that becomes the axis of rotation. Default axis of rotation is UP.
// If given a count `n`, makes that many copies, rotated evenly around the axis.
// If given an offset `delta`, translates each child by that amount before rotating them into place. This makes rings.
// If given a centerpoint `cp`, centers the ring around that centerpoint.
// If `subrot` is true, each child will be rotated in place to keep the same size towards the center when making rings.
// The first (unrotated) copy will be placed at the relative starting angle `sa`.
//
// Usage:
// rot_copies(rots, [cp=], [sa=], [delta=], [subrot=]) CHILDREN;
// rot_copies(rots, v, [cp=], [sa=], [delta=], [subrot=]) CHILDREN;
// rot_copies(n=, [v=], [cp=], [sa=], [delta=], [subrot=]) CHILDREN;
//
// Arguments:
// rots = A list of [X,Y,Z] rotation angles in degrees. If `v` is given, this will be a list of scalar angles in degrees to rotate around `v`.
// v = If given, this is the vector of the axis to rotate around.
// cp = Centerpoint to rotate around. Default: `[0,0,0]`
// ---
// n = Optional number of evenly distributed copies, rotated around the axis.
// sa = Starting angle, in degrees. For use with `n`. Angle is in degrees counter-clockwise. Default: 0
// delta = [X,Y,Z] amount to move away from cp before rotating. Makes rings of copies. Default: `[0,0,0]`
// subrot = If false, don't sub-rotate children as they are copied around the ring. Only makes sense when used with `delta`. Default: `true`
//
// Side Effects:
// `$ang` is set to the rotation angle (or XYZ rotation triplet) of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index value of each child copy.
// `$axis` is set to the axis to rotate around, if `rots` was given as a list of angles instead of a list of [X,Y,Z] rotation angles.
//
// Example:
// #cylinder(h=20, r1=5, r2=0);
// rot_copies([[45,0,0],[0,45,90],[90,-45,270]]) cylinder(h=20, r1=5, r2=0);
//
// Example:
// rot_copies([45, 90, 135], v=DOWN+BACK)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// rot_copies(n=6, v=DOWN+BACK)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// rot_copies(n=6, v=DOWN+BACK, delta=[10,0,0])
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// rot_copies(n=6, v=UP+FWD, delta=[10,0,0], sa=45)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// rot_copies(n=6, v=DOWN+BACK, delta=[20,0,0], subrot=false)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
module rot_copies(rots=[], v=undef, cp=[0,0,0], n, sa=0, offset=0, delta=[0,0,0], subrot=true)
{
req_children($children);
sang = sa + offset;
angs = !is_undef(n)?
(n<=0? [] : [for (i=[0:1:n-1]) i/n*360+sang]) :
rots==[]? [] :
assert(!is_string(rots), "Argument rots must be an angle, a list of angles, or a range of angles.")
assert(!is_undef(rots[0]), "Argument rots must be an angle, a list of angles, or a range of angles.")
[for (a=rots) a];
for ($idx = idx(angs)) {
$ang = angs[$idx];
$axis = v;
translate(cp) {
rotate(a=$ang, v=v) {
translate(delta) {
rot(a=(subrot? sang : $ang), v=v, reverse=true) {
translate(-cp) {
children();
}
}
}
}
}
}
}
// Module: xrot_copies()
//
// Usage:
// xrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// xrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
//
// Description:
// Given an array of angles, rotates copies of the children to each of those angles around the X axis.
// If given a count `n`, makes that many copies, rotated evenly around the X axis.
// If given a radius `r` (or diameter `d`), distributes children around a ring of that size around the X axis.
// If given a centerpoint `cp`, centers the rotation around that centerpoint.
// If `subrot` is true, each child will be rotated in place to keep the same size towards the center when making rings.
// The first (unrotated) copy will be placed at the relative starting angle `sa`.
//
// Arguments:
// rots = Optional array of rotation angles, in degrees, to make copies at.
// cp = Centerpoint to rotate around.
// --
// n = Optional number of evenly distributed copies to be rotated around the ring.
// sa = Starting angle, in degrees. For use with `n`. Angle is in degrees counter-clockwise from Y+, when facing the origin from X+. First unrotated copy is placed at that angle.
// r = If given, makes a ring of child copies around the X axis, at the given radius. Default: 0
// d = If given, makes a ring of child copies around the X axis, at the given diameter.
// subrot = If false, don't sub-rotate children as they are copied around the ring.
//
// Side Effects:
// `$idx` is set to the index value of each child copy.
// `$ang` is set to the rotation angle of each child copy, and can be used to modify each child individually.
// `$axis` is set to the axis vector rotated around.
//
// Example:
// xrot_copies([180, 270, 315])
// cylinder(h=20, r1=5, r2=0);
// color("red",0.333) cylinder(h=20, r1=5, r2=0);
//
// Example:
// xrot_copies(n=6)
// cylinder(h=20, r1=5, r2=0);
// color("red",0.333) cylinder(h=20, r1=5, r2=0);
//
// Example:
// xrot_copies(n=6, r=10)
// xrot(-90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) xrot(-90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// xrot_copies(n=6, r=10, sa=45)
// xrot(-90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) xrot(-90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// xrot_copies(n=6, r=20, subrot=false)
// xrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
// color("red",0.333) xrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
module xrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true)
{
req_children($children);
r = get_radius(r=r, d=d, dflt=0);
rot_copies(rots=rots, v=RIGHT, cp=cp, n=n, sa=sa, delta=[0, r, 0], subrot=subrot) children();
}
// Module: yrot_copies()
//
// Usage:
// yrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// yrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
//
// Description:
// Given an array of angles, rotates copies of the children to each of those angles around the Y axis.
// If given a count `n`, makes that many copies, rotated evenly around the Y axis.
// If given a radius `r` (or diameter `d`), distributes children around a ring of that size around the Y axis.
// If given a centerpoint `cp`, centers the rotation around that centerpoint.
// If `subrot` is true, each child will be rotated in place to keep the same size towards the center when making rings.
// The first (unrotated) copy will be placed at the relative starting angle `sa`.
//
// Arguments:
// rots = Optional array of rotation angles, in degrees, to make copies at.
// cp = Centerpoint to rotate around.
// ---
// n = Optional number of evenly distributed copies to be rotated around the ring.
// sa = Starting angle, in degrees. For use with `n`. Angle is in degrees counter-clockwise from X-, when facing the origin from Y+.
// r = If given, makes a ring of child copies around the Y axis, at the given radius. Default: 0
// d = If given, makes a ring of child copies around the Y axis, at the given diameter.
// subrot = If false, don't sub-rotate children as they are copied around the ring.
//
// Side Effects:
// `$idx` is set to the index value of each child copy.
// `$ang` is set to the rotation angle of each child copy, and can be used to modify each child individually.
// `$axis` is set to the axis vector rotated around.
//
// Example:
// yrot_copies([180, 270, 315])
// cylinder(h=20, r1=5, r2=0);
// color("red",0.333) cylinder(h=20, r1=5, r2=0);
//
// Example:
// yrot_copies(n=6)
// cylinder(h=20, r1=5, r2=0);
// color("red",0.333) cylinder(h=20, r1=5, r2=0);
//
// Example:
// yrot_copies(n=6, r=10)
// yrot(-90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(-90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// yrot_copies(n=6, r=10, sa=45)
// yrot(-90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(-90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// yrot_copies(n=6, r=20, subrot=false)
// yrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
// color("red",0.333) yrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
module yrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true)
{
req_children($children);
r = get_radius(r=r, d=d, dflt=0);
rot_copies(rots=rots, v=BACK, cp=cp, n=n, sa=sa, delta=[-r, 0, 0], subrot=subrot) children();
}
// Module: zrot_copies()
//
// Usage:
// zrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// zrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
//
// Description:
// Given an array of angles, rotates copies of the children to each of those angles around the Z axis.
// If given a count `n`, makes that many copies, rotated evenly around the Z axis.
// If given a radius `r` (or diameter `d`), distributes children around a ring of that size around the Z axis.
// If given a centerpoint `cp`, centers the rotation around that centerpoint.
// If `subrot` is true, each child will be rotated in place to keep the same size towards the center when making rings.
// The first (unrotated) copy will be placed at the relative starting angle `sa`.
//
// Arguments:
// rots = Optional array of rotation angles, in degrees, to make copies at.
// cp = Centerpoint to rotate around. Default: [0,0,0]
// ---
// n = Optional number of evenly distributed copies to be rotated around the ring.
// sa = Starting angle, in degrees. For use with `n`. Angle is in degrees counter-clockwise from X+, when facing the origin from Z+. Default: 0
// r = If given, makes a ring of child copies around the Z axis, at the given radius. Default: 0
// d = If given, makes a ring of child copies around the Z axis, at the given diameter.
// subrot = If false, don't sub-rotate children as they are copied around the ring. Default: true
//
// Side Effects:
// `$idx` is set to the index value of each child copy.
// `$ang` is set to the rotation angle of each child copy, and can be used to modify each child individually.
// `$axis` is set to the axis vector rotated around.
//
// Example:
// zrot_copies([180, 270, 315])
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// zrot_copies(n=6)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// zrot_copies(n=6, r=10)
// yrot(90) cylinder(h=20, r1=5, r2=0);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0);
//
// Example:
// zrot_copies(n=6, r=20, sa=45)
// yrot(90) cylinder(h=20, r1=5, r2=0, center=true);
// color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0, center=true);
//
// Example:
// zrot_copies(n=6, r=20, subrot=false)
// yrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
// color("red",0.333) yrot(-90) cylinder(h=20, r1=5, r2=0, center=true);
module zrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true)
{
r = get_radius(r=r, d=d, dflt=0);
rot_copies(rots=rots, v=UP, cp=cp, n=n, sa=sa, delta=[r, 0, 0], subrot=subrot) children();
}
// Module: arc_copies()
//
// Description:
// Evenly distributes n duplicate children around an ovoid arc on the XY plane.
//
// Usage:
// arc_copies(n, r|d=, [sa=], [ea=], [rot=]) CHILDREN;
// arc_copies(n, rx=|dx=, ry=|dy=, [sa=], [ea=], [rot=]) CHILDREN;
//
// Arguments:
// n = number of copies to distribute around the circle. (Default: 6)
// r = radius of circle (Default: 1)
// ---
// rx = radius of ellipse on X axis. Used instead of r.
// ry = radius of ellipse on Y axis. Used instead of r.
// d = diameter of circle. (Default: 2)
// dx = diameter of ellipse on X axis. Used instead of d.
// dy = diameter of ellipse on Y axis. Used instead of d.
// rot = whether to rotate the copied children. (Default: false)
// sa = starting angle. (Default: 0.0)
// ea = ending angle. Will distribute copies CCW from sa to ea. (Default: 360.0)
//
// Side Effects:
// `$ang` is set to the rotation angle of each child copy, and can be used to modify each child individually.
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index value of each child copy.
//
// Example:
// #cube(size=[10,3,3],center=true);
// arc_copies(d=40, n=5) cube(size=[10,3,3],center=true);
//
// Example:
// #cube(size=[10,3,3],center=true);
// arc_copies(d=40, n=5, sa=45, ea=225) cube(size=[10,3,3],center=true);
//
// Example:
// #cube(size=[10,3,3],center=true);
// arc_copies(r=15, n=8, rot=false) cube(size=[10,3,3],center=true);
//
// Example:
// #cube(size=[10,3,3],center=true);
// arc_copies(rx=20, ry=10, n=8) cube(size=[10,3,3],center=true);
// Example(2D): Using `$idx` to alternate shapes
// arc_copies(r=50, n=19, sa=0, ea=180)
// if ($idx % 2 == 0) rect(6);
// else circle(d=6);
function arc_copies(n=6,r,rx,ry,d,dx,dy,sa=0,ea=360,rot=true) = no_function("arc_copies");
module arc_of(n=6,r,rx,ry,d,dx,dy,sa=0,ea=360,rot=true){
deprecate("arc_copies");
arc_copies(n,r,rx,ry,d,dx,dy,sa,ea,rot);
}
module arc_copies(
n=6,
r=undef,
rx=undef, ry=undef,
d=undef, dx=undef, dy=undef,
sa=0, ea=360,
rot=true
) {
req_children($children);
rx = get_radius(r1=rx, r=r, d1=dx, d=d, dflt=1);
ry = get_radius(r1=ry, r=r, d1=dy, d=d, dflt=1);
sa = posmod(sa, 360);
ea = posmod(ea, 360);
n = (abs(ea-sa)<0.01)?(n+1):n;
delt = (((ea<=sa)?360.0:0)+ea-sa)/(n-1);
for ($idx = [0:1:n-1]) {
$ang = sa + ($idx * delt);
$pos =[rx*cos($ang), ry*sin($ang), 0];
translate($pos) {
zrot(rot? atan2(ry*sin($ang), rx*cos($ang)) : 0) {
children();
}
}
}
}
// Module: sphere_copies()
//
// Description:
// Spreads children semi-evenly over the surface of a sphere or ellipsoid.
//
// Usage:
// sphere_copies(n, r|d=, [cone_ang=], [scale=], [perp=]) CHILDREN;
//
// Arguments:
// n = How many copies to evenly spread over the surface.
// r = Radius of the sphere to distribute over
// ---
// d = Diameter of the sphere to distribute over
// cone_ang = Angle of the cone, in degrees, to limit how much of the sphere gets covered. For full sphere coverage, use 180. Measured pre-scaling. Default: 180
// scale = The [X,Y,Z] scaling factors to reshape the sphere being covered.
// perp = If true, rotate children to be perpendicular to the sphere surface. Default: true
//
// Side Effects:
// `$pos` is set to the relative post-scaled centerpoint of each child copy, and can be used to modify each child individually.
// `$theta` is set to the theta angle of the child from the center of the sphere.
// `$phi` is set to the pre-scaled phi angle of the child from the center of the sphere.
// `$rad` is set to the pre-scaled radial distance of the child from the center of the sphere.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// sphere_copies(n=250, d=100, cone_ang=45, scale=[3,3,1])
// cylinder(d=10, h=10, center=false);
//
// Example:
// sphere_copies(n=500, d=100, cone_ang=180)
// color(unit(point3d(v_abs($pos))))
// cylinder(d=8, h=10, center=false);
function sphere_copies(n=100, r=undef, d=undef, cone_ang=90, scale=[1,1,1], perp=true) = no_function("sphere_copies");
module ovoid_spread(n=100, r=undef, d=undef, cone_ang=90, scale=[1,1,1], perp=true)
{
deprecate("sphere_copies");
sphere_copies(n,r,d,cone_ang,scale,perp);
}
module sphere_copies(n=100, r=undef, d=undef, cone_ang=90, scale=[1,1,1], perp=true)
{
req_children($children);
r = get_radius(r=r, d=d, dflt=50);
cnt = ceil(n / (cone_ang/180));
// Calculate an array of [theta,phi] angles for `n` number of
// points, almost evenly spaced across the surface of a sphere.
// This approximation is based on the golden spiral method.
theta_phis = [for (x=[0:1:n-1]) [180*(1+sqrt(5))*(x+0.5)%360, acos(1-2*(x+0.5)/cnt)]];
for ($idx = idx(theta_phis)) {
tp = theta_phis[$idx];
xyz = spherical_to_xyz(r, tp[0], tp[1]);
$pos = v_mul(xyz,point3d(scale,1));
$theta = tp[0];
$phi = tp[1];
$rad = r;
translate($pos) {
if (perp) {
rot(from=UP, to=xyz) children();
} else {
children();
}
}
}
}
// Section: Placing copies of all children on a path
// Module: path_copies()
//
// Description:
// Place copies all of the children at points along the path based on path length. You can specify `dist` as
// a scalar or distance list and the children will be placed at the specified distances from the start of the path. Otherwise the children are
// placed at uniformly spaced points along the path. If you specify `n` but not `spacing` then `n` copies will be placed
// with one at path[0] if `closed` is true, or spanning the entire path from start to end if `closed` is false.
// If you specify `spacing` but not `n` then copies will spread out starting from one set at path[0] for `closed=true` or at the path center for open paths.
// If you specify `sp` then the copies will start at distance `sp` from the start of the path.
//
// Usage: Uniformly distribute copies
// path_copies(path, [n], [spacing], [sp], [rotate_children], [closed=]) CHILDREN;
// Usage: Place copies at specified locations
// path_copies(path, dist=, [rotate_children=], [closed=]) CHILDREN;
//
// Arguments:
// path = path or 1-region where children are placed
// n = number of copies
// spacing = space between copies
// sp = if given, copies will start distance sp from the path start and spread beyond that point
// rotate_children = if true, rotate children to line up with curve normal. Default: true
// ---
// dist = Specify a list of distances to determine placement of children.
// closed = If true treat path as a closed curve. Default: false
//
// Side Effects:
// `$pos` is set to the center of each copy
// `$idx` is set to the index number of each copy. In the case of closed paths the first copy is at `path[0]` unless you give `sp`.
// `$dir` is set to the direction vector of the path at the point where the copy is placed.
// `$normal` is set to the direction of the normal vector to the path direction that is coplanar with the path at this point
//
// Example(2D):
// spiral = [for(theta=[0:360*8]) theta * [cos(theta), sin(theta)]]/100;
// stroke(spiral,width=.25);
// color("red") path_copies(spiral, n=100) circle(r=1);
// Example(2D):
// circle = regular_ngon(n=64, or=10);
// stroke(circle,width=1,closed=true);
// color("green") path_copies(circle, n=7, closed=true) circle(r=1+$idx/3);
// Example(2D):
// heptagon = regular_ngon(n=7, or=10);
// stroke(heptagon, width=1, closed=true);
// color("purple") path_copies(heptagon, n=9, closed=true) rect([0.5,3],anchor=FRONT);
// Example(2D): Direction at the corners is the average of the two adjacent edges
// heptagon = regular_ngon(n=7, or=10);
// stroke(heptagon, width=1, closed=true);
// color("purple") path_copies(heptagon, n=7, closed=true) rect([0.5,3],anchor=FRONT);
// Example(2D): Don't rotate the children
// heptagon = regular_ngon(n=7, or=10);
// stroke(heptagon, width=1, closed=true);
// color("red") path_copies(heptagon, n=9, closed=true, rotate_children=false) rect([0.5,3],anchor=FRONT);
// Example(2D): Open path, specify `n`
// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
// stroke(sinwav,width=.1);
// color("red") path_copies(sinwav, n=5) rect([.2,1.5],anchor=FRONT);
// Example(2D): Open path, specify `n` and `spacing`
// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
// stroke(sinwav,width=.1);
// color("red") path_copies(sinwav, n=5, spacing=1) rect([.2,1.5],anchor=FRONT);
// Example(2D): Closed path, specify `n` and `spacing`, copies centered around circle[0]
// circle = regular_ngon(n=64,or=10);
// stroke(circle,width=.1,closed=true);
// color("red") path_copies(circle, n=10, spacing=1, closed=true) rect([.2,1.5],anchor=FRONT);
// Example(2D): Open path, specify `spacing`
// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
// stroke(sinwav,width=.1);
// color("red") path_copies(sinwav, spacing=5) rect([.2,1.5],anchor=FRONT);
// Example(2D): Open path, specify `sp`
// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
// stroke(sinwav,width=.1);
// color("red") path_copies(sinwav, n=5, sp=18) rect([.2,1.5],anchor=FRONT);
// Example(2D): Open path, specify `dist`
// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
// stroke(sinwav,width=.1);
// color("red") path_copies(sinwav, dist=[1,4,9,16]) rect([.2,1.5],anchor=FRONT);
// Example(2D):
// wedge = arc(angle=[0,100], r=10, $fn=64);
// difference(){
// polygon(concat([[0,0]],wedge));
// path_copies(wedge,n=5,spacing=3) fwd(.1) rect([1,4],anchor=FRONT);
// }
// Example(Spin,VPD=115): 3d example, with children rotated into the plane of the path
// tilted_circle = lift_plane([[0,0,0], [5,0,5], [0,2,3]],regular_ngon(n=64, or=12));
// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
// path_copies(tilted_circle, n=15,closed=true) {
// color("blue") cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
// color("red") xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
// }
// Example(Spin,VPD=115): 3d example, with rotate_children set to false
// tilted_circle = lift_plane([[0,0,0], [5,0,5], [0,2,3]], regular_ngon(n=64, or=12));
// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
// path_copies(tilted_circle, n=25,rotate_children=false,closed=true) {
// color("blue") cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
// color("red") xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
// }
function path_copies(path, n, spacing, sp=undef, rotate_children=true, dist, closed) = no_function("path_copies");
module path_spread(path, n, spacing, sp=undef, rotate_children=true, dist, closed){
deprecate("path_copes");
path_copies(path,n,spacing,sp,dist,rotate_children,dist, closed) children();
}
module path_copies(path, n, spacing, sp=undef, dist, rotate_children=true, dist, closed)
{
req_children($children);
is_1reg = is_1region(path);
path = is_1reg ? path[0] : path;
closed = default(closed, is_1reg);
length = path_length(path,closed);
distind = is_def(dist) ? sortidx(dist) : undef;
distances =
is_def(dist) ? assert(is_undef(n) && is_undef(spacing) && is_undef(sp), "Can't use n, spacing or undef with dist")
select(dist,distind)
: is_def(sp)? ( // Start point given
is_def(n) && is_def(spacing)? count(n,sp,spacing) :
is_def(n)? lerpn(sp, length, n) :
list([sp:spacing:length])
)
: is_def(n) && is_undef(spacing)? lerpn(0,length,n,!closed) // N alone given
: ( // No start point and spacing is given, N maybe given
let(
n = is_def(n)? n : floor(length/spacing)+(closed?0:1),
ptlist = count(n,0,spacing),
listcenter = mean(ptlist)
) closed?
sort([for(entry=ptlist) posmod(entry-listcenter,length)]) :
[for(entry=ptlist) entry + length/2-listcenter ]
);
distOK = is_def(n) || (min(distances)>=0 && max(distances)<=length);
assert(distOK,"Cannot fit all of the copies");
cutlist = path_cut_points(path, distances, closed, direction=true);
planar = len(path[0])==2;
for(i=[0:1:len(cutlist)-1]) {
$pos = cutlist[i][0];
$idx = is_def(dist) ? distind[i] : i;
$dir = rotate_children ? (planar?[1,0]:[1,0,0]) : cutlist[i][2];
$normal = rotate_children? (planar?[0,1]:[0,0,1]) : cutlist[i][3];
translate($pos) {
if (rotate_children) {
if(planar) {
rot(from=[0,1],to=cutlist[i][3]) children();
} else {
frame_map(x=cutlist[i][2], z=cutlist[i][3])
children();
}
} else {
children();
}
}
}
}
//////////////////////////////////////////////////////////////////////
// Section: Making a copy of all children with reflection
//////////////////////////////////////////////////////////////////////
// Module: xflip_copy()
//
// Description:
// Makes a copy of the children, mirrored across the X axis.
//
// Usage:
// xflip_copy([offset], [x]) CHILDREN;
//
// Arguments:
// offset = Distance to offset children right, before copying.
// x = The X coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
// `$idx` is set to the index value of each copy.
//
// Example:
// xflip_copy() yrot(90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([0.01,15,15], center=true);
//
// Example:
// xflip_copy(offset=5) yrot(90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([0.01,15,15], center=true);
//
// Example:
// xflip_copy(x=-5) yrot(90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) left(5) cube([0.01,15,15], center=true);
module xflip_copy(offset=0, x=0)
{
req_children($children);
mirror_copy(v=[1,0,0], offset=offset, cp=[x,0,0]) children();
}
// Module: yflip_copy()
//
// Description:
// Makes a copy of the children, mirrored across the Y axis.
//
// Usage:
// yflip_copy([offset], [y]) CHILDREN;
//
// Arguments:
// offset = Distance to offset children back, before copying.
// y = The Y coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
// `$idx` is set to the index value of each copy.
//
// Example:
// yflip_copy() xrot(-90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([15,0.01,15], center=true);
//
// Example:
// yflip_copy(offset=5) xrot(-90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([15,0.01,15], center=true);
//
// Example:
// yflip_copy(y=-5) xrot(-90) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) fwd(5) cube([15,0.01,15], center=true);
module yflip_copy(offset=0, y=0)
{
req_children($children);
mirror_copy(v=[0,1,0], offset=offset, cp=[0,y,0]) children();
}
// Module: zflip_copy()
//
// Description:
// Makes a copy of the children, mirrored across the Z axis.
//
// Usage:
// zflip_copy([offset], [z]) CHILDREN;
//
// Arguments:
// offset = Distance to offset children up, before copying.
// z = The Z coordinate of the mirroring plane. Default: 0
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
// `$idx` is set to the index value of each copy.
//
// Example:
// zflip_copy() cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([15,15,0.01], center=true);
//
// Example:
// zflip_copy(offset=5) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) cube([15,15,0.01], center=true);
//
// Example:
// zflip_copy(z=-5) cylinder(h=20, r1=4, r2=0);
// color("blue",0.25) down(5) cube([15,15,0.01], center=true);
module zflip_copy(offset=0, z=0)
{
req_children($children);
mirror_copy(v=[0,0,1], offset=offset, cp=[0,0,z]) children();
}
// Module: mirror_copy()
//
// Description:
// Makes a copy of the children, mirrored across the given plane.
//
// Usage:
// mirror_copy(v, [cp], [offset]) CHILDREN;
//
// Arguments:
// v = The normal vector of the plane to mirror across.
// offset = distance to offset away from the plane.
// cp = A point that lies on the mirroring plane.
//
// Side Effects:
// `$orig` is true for the original instance of children. False for the copy.
// `$idx` is set to the index value of each copy.
//
// Example:
// mirror_copy([1,-1,0]) zrot(-45) yrot(90) cylinder(d1=10, d2=0, h=20);
// color("blue",0.25) zrot(-45) cube([0.01,15,15], center=true);
//
// Example:
// mirror_copy([1,1,0], offset=5) rot(a=90,v=[-1,1,0]) cylinder(d1=10, d2=0, h=20);
// color("blue",0.25) zrot(45) cube([0.01,15,15], center=true);
//
// Example:
// mirror_copy(UP+BACK, cp=[0,-5,-5]) rot(from=UP, to=BACK+UP) cylinder(d1=10, d2=0, h=20);
// color("blue",0.25) translate([0,-5,-5]) rot(from=UP, to=BACK+UP) cube([15,15,0.01], center=true);
module mirror_copy(v=[0,0,1], offset=0, cp)
{
req_children($children);
cp = is_vector(v,4)? plane_normal(v) * v[3] :
is_vector(cp)? cp :
is_num(cp)? cp*unit(v) :
[0,0,0];
nv = is_vector(v,4)? plane_normal(v) : unit(v);
off = nv*offset;
if (cp == [0,0,0]) {
translate(off) {
$orig = true;
$idx = 0;
children();
}
mirror(nv) translate(off) {
$orig = false;
$idx = 1;
children();
}
} else {
translate(off) children();
translate(cp) mirror(nv) translate(-cp) translate(off) children();
}
}
////////////////////
// Section: Distributing children individually along a line
///////////////////
// Module: xdistribute()
//
// Description:
// Spreads out the children individually along the X axis.
// Every child is placed at a different position, in order.
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// xdistribute(spacing, [sizes]) CHILDREN;
// xdistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
// l = Length to distribute copies along.
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// xdistribute(sizes=[100, 10, 30], spacing=40) {
// sphere(r=50);
// cube([10,20,30], center=true);
// cylinder(d=30, h=50, center=true);
// }
module xdistribute(spacing=10, sizes=undef, l=undef)
{
req_children($children);
dir = RIGHT;
gaps = ($children < 2)? [0] :
!is_undef(sizes)? [for (i=[0:1:$children-2]) sizes[i]/2 + sizes[i+1]/2] :
[for (i=[0:1:$children-2]) 0];
spc = !is_undef(l)? ((l - sum(gaps)) / ($children-1)) : default(spacing, 10);
gaps2 = [for (gap = gaps) gap+spc];
spos = dir * -sum(gaps2)/2;
spacings = cumsum([0, each gaps2]);
for (i=[0:1:$children-1]) {
$pos = spos + spacings[i] * dir;
$idx = i;
translate($pos) children(i);
}
}
// Module: ydistribute()
//
// Description:
// Spreads out the children individually along the Y axis.
// Every child is placed at a different position, in order.
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// ydistribute(spacing, [sizes]) CHILDREN;
// ydistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
// l = Length to distribute copies along.
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// ydistribute(sizes=[30, 20, 100], spacing=40) {
// cylinder(d=30, h=50, center=true);
// cube([10,20,30], center=true);
// sphere(r=50);
// }
module ydistribute(spacing=10, sizes=undef, l=undef)
{
req_children($children);
dir = BACK;
gaps = ($children < 2)? [0] :
!is_undef(sizes)? [for (i=[0:1:$children-2]) sizes[i]/2 + sizes[i+1]/2] :
[for (i=[0:1:$children-2]) 0];
spc = !is_undef(l)? ((l - sum(gaps)) / ($children-1)) : default(spacing, 10);
gaps2 = [for (gap = gaps) gap+spc];
spos = dir * -sum(gaps2)/2;
spacings = cumsum([0, each gaps2]);
for (i=[0:1:$children-1]) {
$pos = spos + spacings[i] * dir;
$idx = i;
translate($pos) children(i);
}
}
// Module: zdistribute()
//
// Description:
// Spreads out each individual child along the Z axis.
// Every child is placed at a different position, in order.
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// zdistribute(spacing, [sizes]) CHILDREN;
// zdistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
// l = Length to distribute copies along.
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// zdistribute(sizes=[30, 20, 100], spacing=40) {
// cylinder(d=30, h=50, center=true);
// cube([10,20,30], center=true);
// sphere(r=50);
// }
module zdistribute(spacing=10, sizes=undef, l=undef)
{
req_children($children);
dir = UP;
gaps = ($children < 2)? [0] :
!is_undef(sizes)? [for (i=[0:1:$children-2]) sizes[i]/2 + sizes[i+1]/2] :
[for (i=[0:1:$children-2]) 0];
spc = !is_undef(l)? ((l - sum(gaps)) / ($children-1)) : default(spacing, 10);
gaps2 = [for (gap = gaps) gap+spc];
spos = dir * -sum(gaps2)/2;
spacings = cumsum([0, each gaps2]);
for (i=[0:1:$children-1]) {
$pos = spos + spacings[i] * dir;
$idx = i;
translate($pos) children(i);
}
}
// Module: distribute()
//
// Description:
// Spreads out the children individually along the direction `dir`.
// Every child is placed at a different position, in order.
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// distribute(spacing, sizes, dir) CHILDREN;
// distribute(l=, [sizes=], [dir=]) CHILDREN;
//
// Arguments:
// spacing = Spacing to add between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
// dir = Vector direction to distribute copies along. Default: RIGHT
// l = Length to distribute copies along.
//
// Side Effects:
// `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually.
// `$idx` is set to the index number of each child being copied.
//
// Example:
// distribute(sizes=[100, 30, 50], dir=UP) {
// sphere(r=50);
// cube([10,20,30], center=true);
// cylinder(d=30, h=50, center=true);
// }
module distribute(spacing=undef, sizes=undef, dir=RIGHT, l=undef)
{
req_children($children);
gaps = ($children < 2)? [0] :
!is_undef(sizes)? [for (i=[0:1:$children-2]) sizes[i]/2 + sizes[i+1]/2] :
[for (i=[0:1:$children-2]) 0];
spc = !is_undef(l)? ((l - sum(gaps)) / ($children-1)) : default(spacing, 10);
gaps2 = [for (gap = gaps) gap+spc];
spos = dir * -sum(gaps2)/2;
spacings = cumsum([0, each gaps2]);
for (i=[0:1:$children-1]) {
$pos = spos + spacings[i] * dir;
$idx = i;
translate($pos) children(i);
}
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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