BOSL2/distributors.scad
2024-11-27 20:19:48 -05:00

2054 lines
89 KiB
OpenSCAD

//////////////////////////////////////////////////////////////////////
// LibFile: distributors.scad
// Functions and modules to distribute children or copies of children onto
// a line, a grid, or an arbitrary path. The $idx mechanism means that
// the "copies" of children can vary. Also includes shortcuts for mirroring.
// Includes:
// include <BOSL2/std.scad>
// FileGroup: Basic Modeling
// FileSummary: Copy or distribute objects onto a line, grid, or path. Mirror shortcuts.
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////
// Section: Adaptive Children Using `$` Variables
// The distributor methods create multiple copies of their children and place them in various ways. While many models
// require multiple identical copies of an object, this framework is more powerful than
// might be immediately obvious because of `$` variables. The distributors set `$` variables that the children can use to change their
// behavior from one child to the next within a single distributor invocation. This means the copies need not be identical.
// The {{xcopies()}} module sets `$idx` to the index number of the copy, and in the examples below we use `$idx`, but the various
// distributors offer a variety of `$` variables that you can use in your children. Check the "Side Effects" section for each module
// to learn what variables that module provides.
// .
// Two gotchas may lead to models that don't behave as expected. While `if` statements work to control modules, you cannot
// use them to make variable assignments in your child object. If you write a statement like
// ```
// if (condition) { c="red";}
// else {c="green";}
// ```
// then the `c` variable is set only in the scope of the `if` and `else` clauses and is not available later on when you actually
// try to use it. Instead you must use the ternary operator and write:
// ```
// c = condition ? "red" : "green";
// ```
// The second complication is
// that in OpenSCAD version 2021.01 and earlier, assignments in children were executed before their parent. This means
// that `$` variables like `$idx` are not available in assignments because the parent hasn't run to set them, so if you use them
// you will get a warning about an unknown variable.
// Two workarounds exist, neither of which are needed in newer versions of OpenSCAD. The workarounds solve the problem because
// **modules** execute after their parent, so the `$` variables **are** available in modules. You can put your assignments
// in a `let()` module, or you can wrap your child in a `union()`. Both methods appear below.
// Figure(2D,NoScales): This example shows how we can use `$idx` to produce **different** geometry at each index.
// xcopies(n=10, spacing=10)
// text(str($idx));
// Continues:
// ```
// xcopies(n=10, spacing=10)
// text(str($idx));
// ```
// Figure(2D,NoScales): Here the children are sometimes squares and sometimes circles as determined by the conditional `if` module. This use of `if` is OK because no variables are assigned.
// xcopies(n=4, spacing=10)
// if($idx%2==0) circle(r=3,$fn=16);
// else rect(6);
// Continues:
// ```
// xcopies(n=4, spacing=10)
// if($idx%2==0) circle(r=3,$fn=16);
// else rect(6);
// ```
// Figure(2D,NoScales): Suppose we would like to color odd and even index copies differently. In this example we compute the color for a given child from `$idx` using the ternary operator. The `let()` module is a module that sets variables and makes them available to its children. Note that multiple assignments in `let()` are separated by commas, not semicolons.
// xcopies(n=6, spacing=10){
// let(c = $idx % 2 == 0 ? "red" : "green")
// color(c) rect(6);
// }
// Continues:
// ```
// xcopies(n=6, spacing=10){
// let(c = $idx % 2 == 0 ? "red" : "green")
// color(c) rect(6);
// }
// ```
// Figure(2D,NoScales): This example shows how you can change the position of children adaptively. If you want to avoid repeating your code for each case, this requires storing a transformation matrix in a variable and then applying it using `multmatrix()`. We wrap our code in `union()` to ensure that it works in OpenSCAD 2021.01.
// xcopies(n=5,spacing=10)
// union()
// {
// shiftback = $idx%2==0 ? back(10) : IDENT;
// spin = zrot(180*$idx/4);
// multmatrix(shiftback*spin) stroke([[-4,0],[4,0]],endcap2="arrow2",width=3/4, color="red");
// }
// Continues:
// ```
// xcopies(n=5,spacing=10)
// union()
// {
// shiftback = $idx%2==0 ? back(10) : IDENT;
// spin = zrot(180*$idx/4);
// multmatrix(shiftback*spin) stroke([[-4,0],[4,0]],endcap2="arrow2",width=3/4,color="red");
// }
// ```
//////////////////////////////////////////////////////////////////////
// Section: Translating copies of all the children
//////////////////////////////////////////////////////////////////////
// Function&Module: move_copies()
// Synopsis: Translates copies of all children.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xcopies(), ycopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
// Usage:
// move_copies(a) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = move_copies(a, p=);
// Usage: Get Translation Matrices
// mats = move_copies(a);
// Description:
// When called as a module, translates copies of all children to each given translation offset.
// When called as a function, with no `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// Arguments:
// a = Array of XYZ offset vectors. Default `[[0,0,0]]`
// ---
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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();
}
}
function move_copies(a=[[0,0,0]],p=_NO_ARG) =
assert(is_list(a))
let(
mats = [
for (pos = a)
assert(is_vector(pos),"move_copies offsets should be a 2d or 3d vector.")
translate(pos)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: xcopies()
// Synopsis: Places copies of children along the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), ycopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
// Usage:
// xcopies(spacing, [n], [sp=]) CHILDREN;
// xcopies(l=, [n=], [sp=]) CHILDREN;
// xcopies(LIST) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = xcopies(spacing, [n], [sp=], p=);
// copies = xcopies(l=, [n=], [sp=], p=);
// copies = xcopies(LIST, p=);
// Usage: Get Translation Matrices
// mats = xcopies(spacing, [n], [sp=]);
// mats = xcopies(l=, [n=], [sp=]);
// mats = xcopies(LIST);
// Description:
// When called as a module, places `n` copies of the children along a line on the X axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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 = If given, the 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 segment to the right of starting position `[sp,0,0]`. If not given, copies will be placed along a line segment that is centered at [0,0,0].
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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)
{
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
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();
}
}
function xcopies(spacing, n, l, sp, p=_NO_ARG) =
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
let(
dir = RIGHT,
sp = is_finite(sp)? (sp*dir) : sp,
mats = is_vector(spacing)
? let(sp = default(sp,[0,0,0])) [for (n = spacing) translate(sp + n*dir)]
: line_copies(l=u_mul(l,dir), spacing=u_mul(spacing,dir), n=n, p1=sp)
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: ycopies()
// Synopsis: Places copies of children along the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
// Usage:
// ycopies(spacing, [n], [sp=]) CHILDREN;
// ycopies(l=, [n=], [sp=]) CHILDREN;
// ycopies(LIST) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = ycopies(spacing, [n], [sp=], p=);
// copies = ycopies(l=, [n=], [sp=], p=);
// copies = ycopies(LIST, p=);
// Usage: Get Translation Matrices
// mats = ycopies(spacing, [n], [sp=]);
// mats = ycopies(l=, [n=], [sp=]);
// mats = ycopies(LIST);
// Description:
// When called as a module, places `n` copies of the children along a line on the Y axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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 = If given, the 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].
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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)
{
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
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();
}
}
function ycopies(spacing, n, l, sp, p=_NO_ARG) =
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
let(
dir = BACK,
sp = is_finite(sp)? (sp*dir) : sp,
mats = is_vector(spacing)
? let(sp = default(sp,[0,0,0])) [for (n = spacing) translate(sp + n*dir)]
: line_copies(l=u_mul(l,dir), spacing=u_mul(spacing,dir), n=n, p1=sp)
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: zcopies()
// Synopsis: Places copies of children along the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
// Usage:
// zcopies(spacing, [n], [sp=]) CHILDREN;
// zcopies(l=, [n=], [sp=]) CHILDREN;
// zcopies(LIST) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = zcopies(spacing, [n], [sp=], p=);
// copies = zcopies(l=, [n=], [sp=], p=);
// copies = zcopies(LIST, p=);
// Usage: Get Translation Matrices
// mats = zcopies(spacing, [n], [sp=]);
// mats = zcopies(l=, [n=], [sp=]);
// mats = zcopies(LIST);
// Description:
// When called as a module, places `n` copies of the children along a line on the Z axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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 = If given, the 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].
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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)
// grid_copies([s2,s2],n=8,stagger=($idx%2)? true : "alt")
// sphere(d=s);
// Example: Hexagonal sphere packing
// s = 20;
// xyr = adj_ang_to_hyp(s/2,30);
// h = hyp_adj_to_opp(s,xyr);
// zcopies(h,n=8)
// back(($idx%2)*xyr*cos(60))
// grid_copies(s,n=[12,7],stagger=($idx%2)? "alt" : true)
// sphere(d=s);
// Example:
// zcopies([1,2,3,5,7]) sphere(d=1);
module zcopies(spacing, n, l, sp)
{
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
req_children($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 zcopies(spacing, n, l, sp, p=_NO_ARG) =
assert(is_undef(n) || num_defined([l,spacing])==1, "When n is given must give exactly one of spacing or l")
assert(is_def(n) || num_defined([l,spacing])>=1, "When n is not given must give at least one of spacing or l")
let(
dir = UP,
sp = is_finite(sp)? (sp*dir) : sp,
mats = is_vector(spacing)
? let(sp = default(sp,[0,0,0])) [for (n = spacing) translate(sp + n*dir)]
: line_copies(l=u_mul(l,dir), spacing=u_mul(spacing,dir), n=n, p1=sp)
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: line_copies()
// Synopsis: Places copies of children along an arbitrary line.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), zcopies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_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 to translate points, VNF, or Bezier patches
// copies = line_copies([spacing], [n], [p1=], p=);
// copies = line_copies([spacing], [l=], [p1=], p=);
// copies = line_copies([n=], [l=], [p1=], p=);
// copies = line_copies([n=], [p1=], [p2=], p=);
// copies = line_copies([spacing], [p1=], [p2=], p=);
// Usage: Get Translation Matrices
// mats = line_copies([spacing], [n], [p1=]);
// mats = line_copies([spacing], [l=], [p1=]);
// mats = line_copies([n=], [l=], [p1=]);
// mats = line_copies([n=], [p1=], [p2=]);
// mats = line_copies([spacing], [p1=], [p2=]);
// Description:
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
// 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.
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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=1.5);
// line_copies(10, n=5) sphere(d=3);
// line_copies([10,5], n=5) sphere(d=3);
// line_copies(spacing=10, n=6) sphere(d=3);
// line_copies(spacing=[10,5], n=6) sphere(d=3);
// line_copies(spacing=10, l=50) sphere(d=3);
// line_copies(spacing=10, l=[50,30]) sphere(d=3);
// line_copies(spacing=[10,5], l=50) sphere(d=3);
// line_copies(l=50, n=4) sphere(d=3);
// line_copies(l=[50,-30], n=4) sphere(d=3);
// Example(FlatSpin,VPD=133):
// line_copies(p1=[0,0,0], p2=[5,5,20], n=6) cuboid([3,2,1]);
// Example(FlatSpin,VPD=133):
// line_copies(p1=[0,0,0], p2=[5,5,20], spacing=6) cuboid([3,2,1]);
// 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 transform matrices.
// mats = line_copies([10,5],n=5);
// for (m = mats) multmatrix(m) circle(d=3);
// Example(2D): The functional form of line_copies() returns a list of points if given a point.
// pts = line_copies([10,5],n=5,p=[0,0,0]);
// move_copies(pts) circle(d=3);
module line_of(spacing, n, l, p1, p2) {
deprecate("line_copies");
line_copies(spacing, n, l, p1, p2) children();
}
module line_copies(spacing, n, l, p1, p2)
{
req_children($children);
pts = line_copies(spacing=spacing, n=n, l=l, p1=p1, p2=p2, p=[0,0,0]);
for (i=idx(pts)) {
$idx = i;
$pos = pts[i];
translate($pos) children();
}
}
function line_copies(spacing, n, l, p1, p2, p=_NO_ARG) =
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))
assert(is_undef(p2) || is_def(p1), "If p2 is given must also give p1")
assert(is_undef(p2) || is_undef(l), "Cannot give both p2 and l")
assert(is_undef(n) || num_defined([l,spacing,p2])==1,"If n is given then must give exactly one of 'l', 'spacing', or the 'p1'/'p2' pair")
assert(is_def(n) || num_defined([l,spacing,p2])>=1,"If n is given then must give at least one of 'l', 'spacing', or the 'p1'/'p2' pair")
let(
ll = is_def(l)? scalar_vec3(l, 0)
: is_def(spacing) && is_def(n)? (n-1) * scalar_vec3(spacing, 0)
: is_def(p1) && is_def(p2)? point3d(p2-p1)
: undef,
cnt = is_def(n)? n
: is_def(spacing) && is_def(ll) ? floor(norm(ll) / norm(scalar_vec3(spacing, 0)) + 1.000001)
: 2,
spc = cnt<=1? [0,0,0]
: is_undef(spacing) && is_def(ll)? ll/(cnt-1)
: is_num(spacing) && is_def(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]) translate(i * spc + spos, p=p)];
// Function&Module: grid_copies()
// Synopsis: Places copies of children in an [X,Y] grid.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
// 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;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = grid_copies(spacing, size=, [stagger=], [scale=], [inside=], p=);
// copies = grid_copies(n=, size=, [stagger=], [scale=], [inside=], p=);
// copies = grid_copies(spacing, [n], [stagger=], [scale=], [inside=], p=);
// copies = grid_copies(n=, inside=, [stagger], [scale], p=);
// Usage: Get Translation Matrices
// mats = grid_copies(spacing, size=, [stagger=], [scale=], [inside=]);
// mats = grid_copies(n=, size=, [stagger=], [scale=], [inside=]);
// mats = grid_copies(spacing, [n], [stagger=], [scale=], [inside=]);
// mats = grid_copies(n=, inside=, [stagger], [scale]);
// Description:
// When called as a module, makes a square or hexagonal grid of copies of children, with an optional masking polygon or region.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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.
// `$row` is set to the integer row number for each child.
// `$idx` is set to a unique index for each child, progressing across rows first, from the bottom
//
// 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() { // Needed for OpenSCAD 2021.01 as noted above
// 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, $fn=6);
// }
module grid2d(spacing, n, size, stagger=false, inside=undef, nonzero)
{
deprecate("grid_copies");
grid_copies(spacing, n, size, stagger, inside, nonzero) children();
}
module grid_copies(spacing, n, size, stagger=false, inside=undef, nonzero)
{
req_children($children);
dummy = 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];
dummy2 = assert(is_int(n[0]) && is_int(n[1]), "The number of rows/columns must be an integer");
offset = v_mul(spacing, n-[1,1])/2;
poslist =
stagger==false ?
[for (row = [0:1:n.y-1], col = [0:1:n.x-1])
let(
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)
)
[pos,row,col]
]
:
let( // 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])
let(
rowcols = ((row%2) == staggermod)? cols1 : cols2
)
if (rowcols > 0)
for (col = [0:1:rowcols-1])
let(
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)
)
[pos, row, col * 2 + ((row%2!=staggermod)? 1 : 0)]
];
for(i=idx(poslist)){
$idx=i;
$pos=poslist[i][0];
$row=poslist[i][1];
$col=poslist[i][2];
translate(poslist[i][0])children();
}
}
function grid_copies(spacing, n, size, stagger=false, inside=undef, nonzero, p=_NO_ARG) =
let(
dummy = 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,
mats = stagger == false
? [
for (row = [0:1:n.y-1], col = [0:1:n.x-1])
let( 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)
)
translate(pos)
]
: // stagger == true or stagger == "alt"
let(
staggermod = (stagger == "alt")? 1 : 0,
cols1 = ceil(n.x/2),
cols2 = n.x - cols1
)
[
for (row = [0:1:n.y-1])
let( rowcols = ((row%2) == staggermod)? cols1 : cols2 )
if (rowcols > 0)
for (col = [0:1:rowcols-1])
let(
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)
)
translate(pos)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
//////////////////////////////////////////////////////////////////////
// Section: Rotating copies of all children
//////////////////////////////////////////////////////////////////////
// Function&Module: rot_copies()
// Synopsis: Rotates copies of children.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// 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;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = rot_copies(rots, [cp=], [sa=], [delta=], [subrot=], p=);
// copies = rot_copies(rots, v, [cp=], [sa=], [delta=], [subrot=], p=);
// copies = rot_copies(n=, [v=], [cp=], [sa=], [delta=], [subrot=], p=);
// Usage: Get Translation Matrices
// mats = rot_copies(rots, [cp=], [sa=], [delta=], [subrot=]);
// mats = rot_copies(rots, v, [cp=], [sa=], [delta=], [subrot=]);
// mats = rot_copies(n=, [v=], [cp=], [sa=], [delta=], [subrot=]);
// Description:
// When called as a module:
// - 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`.
// .
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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. Instead maintain their native orientation. The false setting is only allowed when `delta` is given. Default: `true`
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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, cp=[0,0,0], n, sa=0, offset=0, delta=[0,0,0], subrot=true)
{
assert(subrot || norm(delta)>0, "subrot can only be false if delta is not zero");
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? 0 : $ang, v=v, reverse=true) {
translate(-cp) {
children();
}
}
}
}
}
}
}
function rot_copies(rots=[], v, cp=[0,0,0], n, sa=0, offset=0, delta=[0,0,0], subrot=true, p=_NO_ARG) =
assert(subrot || norm(delta)>0, "subrot can only be false if delta is not zero")
let(
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],
mats = [
for (ang = angs)
translate(cp) *
rot(a=ang, v=v) *
translate(delta) *
rot(a=subrot? 0 : ang, v=v, reverse=true) *
translate(-cp)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: xrot_copies()
// Synopsis: Rotates copies of children around the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// xrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// xrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = xrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=], p=);
// copies = xrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=], p=);
// Usage: Get Translation Matrices
// mats = xrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]);
// mats = xrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]);
// Description:
// When called as a module:
// - 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`.
// .
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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. Instead maintain their native orientation. The false setting is only allowed when `d` or `r` is given. Default: `true`
// subrot = If false, don't sub-rotate children as they are copied around the ring.
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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);
assert(all_nonnegative([r]), "d/r must be nonnegative");
assert(subrot || r>0, "subrot can only be false if d or r is given");
rot_copies(rots=rots, v=RIGHT, cp=cp, n=n, sa=sa, delta=[0, r, 0], subrot=subrot) children();
}
function xrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG) =
let( r = get_radius(r=r, d=d, dflt=0) )
assert(all_nonnegative([r]), "d/r must be nonnegative")
assert(subrot || r>0, "subrot can only be false if d or r is given")
rot_copies(rots=rots, v=RIGHT, cp=cp, n=n, sa=sa, delta=[0, r, 0], subrot=subrot, p=p);
// Function&Module: yrot_copies()
// Synopsis: Rotates copies of children around the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// yrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// yrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = yrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=], p=);
// copies = yrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=], p=);
// Usage: Get Translation Matrices
// mats = yrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]);
// mats = yrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]);
// Description:
// When called as a module:
// - 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`.
// .
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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. Instead maintain their native orientation. The false setting is only allowed when `d` or `r` is given. Default: `true`
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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);
assert(all_nonnegative([r]), "d/r must be nonnegative");
assert(subrot || r>0, "subrot can only be false if d or r is given");
rot_copies(rots=rots, v=BACK, cp=cp, n=n, sa=sa, delta=[-r, 0, 0], subrot=subrot) children();
}
function yrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG) =
let( r = get_radius(r=r, d=d, dflt=0) )
assert(all_nonnegative([r]), "d/r must be nonnegative")
assert(subrot || r>0, "subrot can only be false if d or r is given")
rot_copies(rots=rots, v=BACK, cp=cp, n=n, sa=sa, delta=[-r, 0, 0], subrot=subrot, p=p);
// Function&Module: zrot_copies()
// Synopsis: Rotates copies of children around the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// zrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]) CHILDREN;
// zrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = zrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=], p=);
// copies = zrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=], p=);
// Usage: Get Translation Matrices
// mats = zrot_copies(rots, [cp], [r=|d=], [sa=], [subrot=]);
// mats = zrot_copies(n=, [cp=], [r=|d=], [sa=], [subrot=]);
//
// Description:
// When called as a module:
// - 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`.
// .
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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. Instead maintain their native orientation. The false setting is only allowed when `d` or `r` is given. Default: `true`
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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)
{
req_children($children);
r = get_radius(r=r, d=d, dflt=0);
assert(all_nonnegative([r]), "d/r must be nonnegative");
assert(subrot || r>0, "subrot can only be false if d or r is given");
rot_copies(rots=rots, v=UP, cp=cp, n=n, sa=sa, delta=[r, 0, 0], subrot=subrot) children();
}
function zrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG) =
let( r = get_radius(r=r, d=d, dflt=0) )
assert(all_nonnegative([r]), "d/r must be nonnegative")
assert(subrot || r>0, "subrot can only be false if d or r is given")
rot_copies(rots=rots, v=UP, cp=cp, n=n, sa=sa, delta=[r, 0, 0], subrot=subrot, p=p);
// Function&Module: arc_copies()
// Synopsis: Distributes duplicates of children along an arc.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// arc_copies(n, r|d=, [sa=], [ea=], [rot=]) CHILDREN;
// arc_copies(n, rx=|dx=, ry=|dy=, [sa=], [ea=], [rot=]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = arc_copies(n, r|d=, [sa=], [ea=], [rot=], p=);
// copies = arc_copies(n, rx=|dx=, ry=|dy=, [sa=], [ea=], [rot=], p=);
// Usage: Get Translation Matrices
// mats = arc_copies(n, r|d=, [sa=], [ea=], [rot=]);
// mats = arc_copies(n, rx=|dx=, ry=|dy=, [sa=], [ea=], [rot=]);
//
//
// Description:
// When called as a module, evenly distributes n duplicate children around an ovoid arc on the XY plane.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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: true)
// sa = starting angle. (Default: 0.0)
// ea = ending angle. Will distribute copies CCW from sa to ea. (Default: 360.0)
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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);
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) children();
}
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();
}
}
}
}
function arc_copies(
n=6,
r=undef,
rx=undef, ry=undef,
d=undef, dx=undef, dy=undef,
sa=0, ea=360,
rot=true,
p=_NO_ARG
) =
let(
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),
mats = [
for (i = [0:1:n-1])
let(
ang = sa + (i * delt),
pos =[rx*cos(ang), ry*sin(ang), 0],
ang2 = rot? atan2(ry*sin(ang), rx*cos(ang)) : 0
)
translate(pos) * zrot(ang2)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Function&Module: sphere_copies()
// Synopsis: Distributes copies of children over the surface of a sphere.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// sphere_copies(n, r|d=, [cone_ang=], [scale=], [perp=]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = sphere_copies(n, r|d=, [cone_ang=], [scale=], [perp=], p=);
// Usage: Get Translation Matrices
// mats = sphere_copies(n, r|d=, [cone_ang=], [scale=], [perp=]);
//
// Description:
// When called as a module, spreads children semi-evenly over the surface of a sphere or ellipsoid.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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);
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) children();
}
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();
}
}
}
}
function sphere_copies(n=100, r=undef, d=undef, cone_ang=90, scale=[1,1,1], perp=true, p=_NO_ARG) =
let(
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)]],
mats = [
for (tp = theta_phis)
let(
xyz = spherical_to_xyz(r, tp[0], tp[1]),
pos = v_mul(xyz,point3d(scale,1))
)
translate(pos) *
(perp? rot(from=UP, to=xyz) : ident(4))
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
// Section: Placing copies of all children on a path
// Function&Module: path_copies()
// Synopsis: Uniformly distributes copies of children along a path.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Copiers
// See Also: line_copies(), move_copies(), xcopies(), ycopies(), zcopies(), grid_copies(), xflip_copy(), yflip_copy(), zflip_copy(), mirror_copy()
//
// 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;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = path_copies(path, [n], [spacing], [sp], [rotate_children], [closed=], p=);
// copies = path_copies(path, dist=, [rotate_children=], [closed=], p=);
// Usage: Get Translation Matrices
// mats = path_copies(path, [n], [spacing], [sp], [rotate_children], [closed=]);
// mats = path_copies(path, dist=, [rotate_children=], [closed=]);
//
// Description:
// When called as a module:
// - 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.
// .
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// 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
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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, $fn=64);
// difference(){
// polygon(concat([[0,0]],wedge));
// path_copies(wedge,n=5,spacing=3) fwd(.1) rect([1,4],anchor=FRONT);
// }
// Example(Spin,VPD=115): 3d example, with children rotated into the plane of the path
// tilted_circle = lift_plane([[0,0,0], [5,0,5], [0,2,3]],regular_ngon(n=64, or=12));
// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
// path_copies(tilted_circle, n=15,closed=true) {
// color("blue") cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
// color("red") xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
// }
// Example(Spin,VPD=115): 3d example, with rotate_children set to false
// tilted_circle = lift_plane([[0,0,0], [5,0,5], [0,2,3]], regular_ngon(n=64, or=12));
// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
// path_copies(tilted_circle, n=25,rotate_children=false,closed=true) {
// color("blue") cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
// color("red") xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
// }
module path_spread(path, n, spacing, sp=undef, rotate_children=true, dist, closed){
deprecate("path_copes");
path_copies(path,n,spacing,sp,dist,rotate_children,dist, closed) children();
}
module path_copies(path, n, spacing, sp=undef, dist, rotate_children=true, dist, closed)
{
req_children($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 = min(distances)>=0 && max(distances)<=length;
dummy = 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();
}
}
}
}
function path_copies(path, n, spacing, sp=undef, dist, rotate_children=true, dist, closed, p=_NO_ARG) =
let(
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 = min(distances)>=0 && max(distances)<=length,
dummy = assert(distOK,"Cannot fit all of the copies"),
cutlist = path_cut_points(path, distances, closed, direction=true),
planar = len(path[0])==2,
mats = [
for(i=[0:1:len(cutlist)-1])
translate(cutlist[i][0]) * (
!rotate_children? ident(4) :
planar? rot(from=[0,1],to=cutlist[i][3]) :
frame_map(x=cutlist[i][2], z=cutlist[i][3])
)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
//////////////////////////////////////////////////////////////////////
// Section: Making a copy of all children with reflection
//////////////////////////////////////////////////////////////////////
// Function&Module: xflip_copy()
// Synopsis: Makes a copy of children mirrored across the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: yflip_copy(), zflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// xflip_copy([offset], [x]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = xflip_copy([offset], [x], p=);
// Usage: Get Translation Matrices
// mats = xflip_copy([offset], [x]);
//
// Description:
// When called as a module, makes a copy of the children, mirrored across the X axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// Arguments:
// offset = Distance to offset children right, before copying.
// x = The X coordinate of the mirroring plane. Default: 0
// ---
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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($children);
mirror_copy(v=[1,0,0], offset=offset, cp=[x,0,0]) children();
}
function xflip_copy(offset=0, x=0, p=_NO_ARG) =
mirror_copy(v=[1,0,0], offset=offset, cp=[x,0,0], p=p);
// Function&Module: yflip_copy()
// Synopsis: Makes a copy of children mirrored across the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), zflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// yflip_copy([offset], [y]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = yflip_copy([offset], [y], p=);
// Usage: Get Translation Matrices
// mats = yflip_copy([offset], [y]);
//
// Description:
// When called as a module, makes a copy of the children, mirrored across the Y axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// Arguments:
// offset = Distance to offset children back, before copying.
// y = The Y coordinate of the mirroring plane. Default: 0
// ---
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// Side Effects:
// `$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();
}
function yflip_copy(offset=0, y=0, p=_NO_ARG) =
mirror_copy(v=[0,1,0], offset=offset, cp=[0,y,0], p=p);
// Function&Module: zflip_copy()
// Synopsis: Makes a copy of children mirrored across the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), yflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// zflip_copy([offset], [z]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = zflip_copy([offset], [z], p=);
// Usage: Get Translation Matrices
// mats = zflip_copy([offset], [z]);
//
// Description:
// When called as a module, makes a copy of the children, mirrored across the Z axis.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// Arguments:
// offset = Distance to offset children up, before copying.
// z = The Z coordinate of the mirroring plane. Default: 0
// ---
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// 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($children);
mirror_copy(v=[0,0,1], offset=offset, cp=[0,0,z]) children();
}
function zflip_copy(offset=0, z=0, p=_NO_ARG) =
mirror_copy(v=[0,0,1], offset=offset, cp=[0,0,z], p=p);
// Function&Module: mirror_copy()
// Synopsis: Makes a copy of children mirrored across a given plane.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), yflip_copy(), zflip_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
// Usage:
// mirror_copy(v, [cp], [offset]) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
// copies = mirror_copy(v, [cp], [offset], p=);
// Usage: Get Translation Matrices
// mats = mirror_copy(v, [cp], [offset]);
//
// Description:
// When called as a module, makes a copy of the children, mirrored across the given plane.
// When called as a function, *without* a `p=` argument, returns a list of transformation matrices, one for each copy.
// When called as a function, *with* a `p=` argument, returns a list of transformed copies of `p=`.
//
// Arguments:
// v = The normal vector of the plane to mirror across.
// offset = distance to offset away from the plane.
// cp = A point that lies on the mirroring plane.
// ---
// p = Either a point, pointlist, VNF or Bezier patch to be translated when used as a function.
//
// Side Effects:
// `$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;
$idx = 1;
children();
}
} else {
translate(off) children();
translate(cp) mirror(nv) translate(-cp) translate(off) children();
}
}
function mirror_copy(v=[0,0,1], offset=0, cp, p=_NO_ARG) =
let(
cp = is_vector(v,4)? plane_normal(v) * v[3] :
is_vector(cp)? cp :
is_num(cp)? cp*unit(v) :
[0,0,0],
nv = is_vector(v,4)? plane_normal(v) : unit(v),
off = nv*offset,
mats = [
translate(off),
translate(cp) *
mirror(nv) *
translate(-cp) *
translate(off)
]
)
p==_NO_ARG? mats : [for (m = mats) apply(m, p)];
////////////////////
// Section: Distributing children individually along a line
///////////////////
// Module: xdistribute()
// Synopsis: Distributes each child, individually, out along the X axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// xdistribute(spacing, [sizes]) CHILDREN;
// xdistribute(l=, [sizes=]) CHILDREN;
//
//
// Description:
// Spreads out the children individually along the X axis.
// Every child is placed at a different position, in order.
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
// l = Length to distribute copies along.
//
// Side Effects:
// `$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()
// Synopsis: Distributes each child, individually, out along the Y axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// ydistribute(spacing, [sizes]) CHILDREN;
// ydistribute(l=, [sizes=]) CHILDREN;
//
// 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.
//
// 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()
// Synopsis: Distributes each child, individually, out along the Z axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// zdistribute(spacing, [sizes]) CHILDREN;
// zdistribute(l=, [sizes=]) CHILDREN;
//
// 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.
//
// 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()
// Synopsis: Distributes each child, individually, out along an arbitrary line.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// distribute(spacing, sizes, dir) CHILDREN;
// distribute(l=, [sizes=], [dir=]) CHILDREN;
//
// 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.
//
// 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