////////////////////////////////////////////////////////////////////// // LibFile: distributors.scad // Functions and modules to distribute children or copies of children. // Includes: // include // FileGroup: Basic Modeling // FileSummary: Shortcuts for translation, rotation, etc. Can act on geometry, paths, or can return a matrix. // 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) ... // // 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]]) { 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&Module: line_of() // // Usage: Spread `n` copies by a given spacing // line_of(spacing, [n], [p1=]) ... // Usage: Spread copies every given spacing along the line // line_of(spacing, [l=], [p1=]) ... // Usage: Spread `n` copies along the length of the line // line_of([n=], [l=], [p1=]) ... // Usage: Spread `n` copies along the line from `p1` to `p2` // line_of([n=], [p1=], [p2=]) ... // Usage: Spread copies every given spacing, centered along the line from `p1` to `p2` // line_of([spacing], [p1=], [p2=]) ... // Usage: As a function // pts = line_of([spacing], [n], [p1=]); // pts = line_of([spacing], [l=], [p1=]); // pts = line_of([n=], [l=], [p1=]); // pts = line_of([n=], [p1=], [p2=]); // pts = line_of([spacing], [p1=], [p2=]); // Description: // When called as a function, returns a list of points at evenly spread positions along a line. // When called as a module, copies `children()` at one or more evenly spread 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 spread is specified in one of several ways: // . // If You Know... | Then Use Something Like... // -------------------------------- | -------------------------------- // Spacing distance, Count | `line_of(spacing=10, n=5) ...` or `line_of(10, n=5) ...` // Spacing vector, Count | `line_of(spacing=[10,5], n=5) ...` or `line_of([10,5], n=5) ...` // Spacing distance, Line length | `line_of(spacing=10, l=50) ...` or `line_of(10, l=50) ...` // Spacing distance, Line vector | `line_of(spacing=10, l=[50,30]) ...` or `line_of(10, l=[50,30]) ...` // Spacing vector, Line length | `line_of(spacing=[10,5], l=50) ...` or `line_of([10,5], l=50) ...` // Line length, Count | `line_of(l=50, n=5) ...` // Line vector, Count | `line_of(l=[50,40], n=5) ...` // Line endpoints, Count | `line_of(p1=[10,10], p2=[60,-10], n=5) ...` // Line endpoints, Spacing distance | `line_of(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_of(10) sphere(d=1); // line_of(10, n=5) sphere(d=1); // line_of([10,5], n=5) sphere(d=1); // line_of(spacing=10, n=6) sphere(d=1); // line_of(spacing=[10,5], n=6) sphere(d=1); // line_of(spacing=10, l=50) sphere(d=1); // line_of(spacing=10, l=[50,30]) sphere(d=1); // line_of(spacing=[10,5], l=50) sphere(d=1); // line_of(l=50, n=4) sphere(d=1); // line_of(l=[50,-30], n=4) sphere(d=1); // Example(FlatSpin,VPD=133): // line_of(p1=[0,0,0], p2=[5,5,20], n=6) cube(size=[3,2,1],center=true); // Example(FlatSpin,VPD=133): // line_of(p1=[0,0,0], p2=[5,5,20], spacing=6) cube(size=[3,2,1],center=true); // Example: All Children are Copied at Each Spread Position // line_of(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_of() returns a list of points. // pts = line_of([10,5],n=5); // move_copies(pts) circle(d=2); module line_of(spacing, n, l, p1, p2) { pts = line_of(spacing=spacing, n=n, l=l, p1=p1, p2=p2); for (i=idx(pts)) { $idx = i; $pos = pts[i]; translate($pos) children(); } } function line_of(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_of()`.") let( spos = !is_undef(p1)? point3d(p1) : -(cnt-1)/2 * spc ) [for (i=[0:1:cnt-1]) i * spc + spos]; // Module: xcopies() // // Description: // Spreads out `n` copies of the children along a line on the X axis. // // Usage: // xcopies(spacing, [n], [sp]) ... // xcopies(l, [n], [sp]) ... // // Arguments: // spacing = spacing between copies. (Default: 1.0) // n = Number of copies to spread out. (Default: 2) // l = Length to spread copies over. // sp = If given as a point, copies will be spread on a line to the right of starting position `sp`. If given as a scalar, copies will be spread on a line to the right of starting position `[sp,0,0]`. If not given, copies will be spread 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); // } module xcopies(spacing, n, l, sp) { sp = is_finite(sp)? [sp,0,0] : sp; line_of( l=u_mul(l,RIGHT), spacing=u_mul(spacing,RIGHT), n=n, p1=sp ) children(); } // Module: ycopies() // // Description: // Spreads out `n` copies of the children along a line on the Y axis. // // Usage: // ycopies(spacing, [n], [sp]) ... // ycopies(l, [n], [sp]) ... // // Arguments: // spacing = spacing between copies. (Default: 1.0) // n = Number of copies to spread out. (Default: 2) // l = Length to spread copies over. // sp = If given as a point, copies will be spread on a line back from starting position `sp`. If given as a scalar, copies will be spread on a line back from starting position `[0,sp,0]`. If not given, copies will be spread 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); // } module ycopies(spacing, n, l, sp) { sp = is_finite(sp)? [0,sp,0] : sp; line_of( l=u_mul(l,BACK), spacing=u_mul(spacing,BACK), n=n, p1=sp ) children(); } // Module: zcopies() // // Description: // Spreads out `n` copies of the children along a line on the Z axis. // // Usage: // zcopies(spacing, [n], [sp]) ... // zcopies(l, [n], [sp]) ... // // Arguments: // spacing = spacing between copies. (Default: 1.0) // n = Number of copies to spread out. (Default: 2) // l = Length to spread copies over. // sp = If given as a point, copies will be spread on a line up from starting position `sp`. If given as a scalar, copies will be spread on a line up from starting position `[0,0,sp]`. If not given, copies will be spread 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: // 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); // } module zcopies(spacing, n, l, sp) { sp = is_finite(sp)? [0,0,sp] : sp; line_of( l=u_mul(l,UP), spacing=u_mul(spacing,UP), n=n, p1=sp ) children(); } // Module: grid2d() // // Description: // Makes a square or hexagonal grid of copies of children, with an optional masking polygon or region. // // Usage: // grid2d(spacing, size, [stagger], [scale], [inside]) ... // grid2d(n, size, [stagger], [scale], [inside]) ... // grid2d(spacing, n, [stagger], [scale], [inside]) ... // grid2d(spacing, inside, [stagger], [scale]) ... // grid2d(n, inside, [stagger], [scale]) ... // // Arguments: // size = The [X,Y] size to spread the copies over. // 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) // 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: // grid2d(size=50, spacing=10) cylinder(d=10, h=1); // grid2d(size=50, spacing=[10,15]) cylinder(d=10, h=1); // grid2d(spacing=10, n=[13,7], stagger=true) cylinder(d=6, h=5); // grid2d(spacing=10, n=[13,7], stagger="alt") cylinder(d=6, h=5); // grid2d(size=50, n=11, stagger=true) cylinder(d=5, h=1); // // Example: // poly = [[-25,-25], [25,25], [-25,25], [25,-25]]; // grid2d(spacing=5, stagger=true, inside=poly) // zrot(180/6) cylinder(d=5, h=1, $fn=6); // %polygon(poly); // // Example: Using `$row` and `$col` // grid2d(spacing=8, n=8) // color(($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); // grid2d(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); // } module grid2d(spacing, n, size, stagger=false, inside=undef, nonzero) { 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; $pos = pos; translate(pos) children(); } } } } } } // Module: grid3d() // // Description: // Makes a 3D grid of duplicate children. // // Usage: // grid3d(n, spacing) ... // grid3d(n=[Xn,Yn,Zn], spacing=[dX,dY,dZ]) ... // grid3d([xa], [ya], [za]) ... // // Arguments: // xa = array or range of X-axis values to offset by. (Default: [0]) // ya = array or range of Y-axis values to offset by. (Default: [0]) // za = array or range of Z-axis values to offset by. (Default: [0]) // n = Optional number of copies to have per axis. // spacing = spacing of copies per axis. Use with `n`. // // Side Effects: // `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually. // `$idx` is set to the [Xidx,Yidx,Zidx] index values of each child copy, when using `count` and `n`. // // Examples(FlatSpin,VPD=222): // grid3d(xa=[0:25:50],ya=[0,40],za=[-20:40:20]) sphere(r=5); // Examples(FlatSpin,VPD=800): // grid3d(n=[3, 4, 2], spacing=[60, 50, 40]) sphere(r=10); // Examples: // grid3d(ya=[-60:40:60],za=[0,70]) sphere(r=10); // grid3d(n=3, spacing=30) sphere(r=10); // grid3d(n=[3, 1, 2], spacing=30) sphere(r=10); // grid3d(n=[3, 4], spacing=[80, 60]) sphere(r=10); // Examples: // grid3d(n=[10, 10, 10], spacing=50) color($idx/9) cube(50, center=true); module grid3d(xa=[0], ya=[0], za=[0], n=undef, spacing=undef) { n = scalar_vec3(n, 1); spacing = scalar_vec3(spacing, undef); if (!is_undef(n) && !is_undef(spacing)) { for (xi = [0:1:n.x-1]) { for (yi = [0:1:n.y-1]) { for (zi = [0:1:n.z-1]) { $idx = [xi,yi,zi]; $pos = v_mul(spacing, $idx - (n-[1,1,1])/2); translate($pos) children(); } } } } else { for (xoff = xa, yoff = ya, zoff = za) { $pos = [xoff, yoff, zoff]; translate($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. // The first (unrotated) copy will be placed at the relative starting angle `sa`. // // Usage: // rot_copies(rots, [cp], [sa], [delta], [subrot]) ... // rot_copies(rots, v, [cp], [sa], [delta], [subrot]) ... // rot_copies(n, [v], [cp], [sa], [delta], [subrot]) ... // // 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. // `$axis` is set to the axis to rotate around, if `rots` was given as a list of angles instead of a list of [X,Y,Z] rotation angles. // // Example: // #cylinder(h=20, r1=5, r2=0); // rot_copies([[45,0,0],[0,45,90],[90,-45,270]]) cylinder(h=20, r1=5, r2=0); // // Example: // rot_copies([45, 90, 135], v=DOWN+BACK) // yrot(90) cylinder(h=20, r1=5, r2=0); // color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0); // // Example: // rot_copies(n=6, v=DOWN+BACK) // yrot(90) cylinder(h=20, r1=5, r2=0); // color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0); // // Example: // rot_copies(n=6, v=DOWN+BACK, delta=[10,0,0]) // yrot(90) cylinder(h=20, r1=5, r2=0); // color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0); // // Example: // rot_copies(n=6, v=UP+FWD, delta=[10,0,0], sa=45) // yrot(90) cylinder(h=20, r1=5, r2=0); // color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0); // // Example: // rot_copies(n=6, v=DOWN+BACK, delta=[20,0,0], subrot=false) // yrot(90) cylinder(h=20, r1=5, r2=0); // color("red",0.333) yrot(90) cylinder(h=20, r1=5, r2=0); module rot_copies(rots=[], v=undef, cp=[0,0,0], n=undef, sa=0, offset=0, delta=[0,0,0], subrot=true) { sang = sa + offset; angs = !is_undef(n)? (n<=0? [] : [for (i=[0:1:n-1]) i/n*360+sang]) : rots==[]? [] : assert(!is_string(rots), "Argument rots must be an angle, a list of angles, or a range of angles.") assert(!is_undef(rots[0]), "Argument rots must be an angle, a list of angles, or a range of angles.") [for (a=rots) a]; for ($idx = idx(angs)) { $ang = angs[$idx]; $axis = v; translate(cp) { rotate(a=$ang, v=v) { translate(delta) { rot(a=(subrot? sang : $ang), v=v, reverse=true) { translate(-cp) { children(); } } } } } } } // Module: xrot_copies() // // Usage: // xrot_copies(rots, [r], [cp], [sa], [subrot]) ... // xrot_copies(n, [r], [cp], [sa], [subrot]) ... // // Description: // Given an array of angles, rotates copies of the children to each of those angles around the X axis. // If given a count `n`, makes that many copies, rotated evenly around the X axis. // If given an offset radius `r`, distributes children around a ring of that radius. // If given a centerpoint `cp`, centers the ring around that centerpoint. // If `subrot` is true, each child will be rotated in place to keep the same size towards the center. // The first (unrotated) copy will be placed at the relative starting angle `sa`. // // Arguments: // rots = Optional array of rotation angles, in degrees, to make copies at. // cp = Centerpoint to rotate around. // n = Optional number of evenly distributed copies to be rotated around the ring. // sa = Starting angle, in degrees. For use with `n`. Angle is in degrees counter-clockwise from Y+, when facing the origin from X+. First unrotated copy is placed at that angle. // r = Radius to move children back (Y+), away from cp, before rotating. Makes rings of copies. // subrot = If false, don't sub-rotate children as they are copied around the ring. // // Side Effects: // `$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=undef, sa=0, r=0, subrot=true) { 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, [r], [cp], [sa], [subrot]) ... // yrot_copies(n, [r], [cp], [sa], [subrot]) ... // // 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 an offset radius `r`, distributes children around a ring of that radius. // 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. // 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 = Radius to move children left (X-), away from cp, before rotating. Makes rings of copies. // 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=undef, sa=0, r=0, subrot=true) { 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, [r], [cp], [sa], [subrot]) ... // zrot_copies(n, [r], [cp], [sa], [subrot]) ... // // 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 an offset radius `r`, distributes children around a ring of that radius. // 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. // 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 = Radius to move children right (X+), away from cp, before rotating. Makes rings of copies. Default: 0 // 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=undef, sa=0, r=0, subrot=true) { rot_copies(rots=rots, v=UP, cp=cp, n=n, sa=sa, delta=[r, 0, 0], subrot=subrot) children(); } // Module: arc_of() // // Description: // Evenly distributes n duplicate children around an ovoid arc on the XY plane. // // Usage: // arc_of(r|d, n, [sa], [ea], [rot] // arc_of(rx|dx, ry|dy, n, [sa], [ea], [rot] // // 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. // `$idx` is set to the index value of each child copy. // // Example: // #cube(size=[10,3,3],center=true); // arc_of(d=40, n=5) cube(size=[10,3,3],center=true); // // Example: // #cube(size=[10,3,3],center=true); // arc_of(d=40, n=5, sa=45, ea=225) cube(size=[10,3,3],center=true); // // Example: // #cube(size=[10,3,3],center=true); // arc_of(r=15, n=8, rot=false) cube(size=[10,3,3],center=true); // // Example: // #cube(size=[10,3,3],center=true); // arc_of(rx=20, ry=10, n=8) cube(size=[10,3,3],center=true); module arc_of( n=6, r=undef, rx=undef, ry=undef, d=undef, dx=undef, dy=undef, sa=0, ea=360, rot=true ) { rx = get_radius(r1=rx, r=r, d1=dx, d=d, dflt=1); ry = get_radius(r1=ry, r=r, d1=dy, d=d, dflt=1); sa = posmod(sa, 360); ea = posmod(ea, 360); n = (abs(ea-sa)<0.01)?(n+1):n; delt = (((ea<=sa)?360.0:0)+ea-sa)/(n-1); for ($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: ovoid_spread() // // Description: // Spreads children semi-evenly over the surface of a sphere. // // Usage: // ovoid_spread(r|d, n, [cone_ang], [scale], [perp]) ... // // Arguments: // r = Radius of the sphere to distribute over // d = Diameter of the sphere to distribute over // n = How many copies to evenly spread over the surface. // 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. // `$idx` is set to the index number of each child being copied. // // Example: // ovoid_spread(n=250, d=100, cone_ang=45, scale=[3,3,1]) // cylinder(d=10, h=10, center=false); // // Example: // ovoid_spread(n=500, d=100, cone_ang=180) // color(unit(point3d(v_abs($pos)))) // cylinder(d=8, h=10, center=false); module ovoid_spread(r=undef, d=undef, n=100, cone_ang=90, scale=[1,1,1], perp=true) { 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_spread() // // Description: // Uniformly spreads out copies of children along a path. Copies are located based on path length. If you specify `n` but not spacing then `n` copies will be placed // with one at path[0] of `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 at path[0] for `closed=true` or at the path center for open paths. // If you specify `sp` then the copies will start at `sp`. // // Usage: // path_spread(path), [n], [spacing], [sp], [rotate_children], [closed]) ... // // Arguments: // path = the path 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 // // 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_spread(spiral, n=100) circle(r=1); // Example(2D): // circle = regular_ngon(n=64, or=10); // stroke(circle,width=1,closed=true); // color("green") path_spread(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_spread(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_spread(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_spread(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_spread(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_spread(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_spread(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_spread(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_spread(sinwav, n=5, sp=18) rect([.2,1.5],anchor=FRONT); // Example(2D): // wedge = arc(angle=[0,100], r=10, $fn=64); // difference(){ // polygon(concat([[0,0]],wedge)); // path_spread(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_spread(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_spread(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, closed=false) { length = path_length(path,closed); distances = 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; if (true) for(i=[0:1:len(cutlist)-1]) { $pos = cutlist[i][0]; $idx = 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: mirror_copy() // // Description: // Makes a copy of the children, mirrored across the given plane. // // Usage: // mirror_copy(v, [cp], [offset]) ... // // 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) { 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; $idx = 1; children(); } } else { translate(off) children(); translate(cp) mirror(nv) translate(-cp) translate(off) children(); } } // Module: xflip_copy() // // Description: // Makes a copy of the children, mirrored across the X axis. // // Usage: // xflip_copy([x], [offset]) ... // // Arguments: // offset = Distance to offset children right, before copying. // x = The X coordinate of the mirroring plane. Default: 0 // // Side Effects: // `$orig` is true for the original instance of children. False for the copy. // `$idx` is set to the index value of each copy. // // Example: // xflip_copy() yrot(90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([0.01,15,15], center=true); // // Example: // xflip_copy(offset=5) yrot(90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([0.01,15,15], center=true); // // Example: // xflip_copy(x=-5) yrot(90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) left(5) cube([0.01,15,15], center=true); module xflip_copy(offset=0, x=0) { mirror_copy(v=[1,0,0], offset=offset, cp=[x,0,0]) children(); } // Module: yflip_copy() // // Description: // Makes a copy of the children, mirrored across the Y axis. // // Usage: // yflip_copy([y], [offset]) ... // // Arguments: // offset = Distance to offset children back, before copying. // y = The Y coordinate of the mirroring plane. Default: 0 // // Side Effects: // `$orig` is true for the original instance of children. False for the copy. // `$idx` is set to the index value of each copy. // // Example: // yflip_copy() xrot(-90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([15,0.01,15], center=true); // // Example: // yflip_copy(offset=5) xrot(-90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([15,0.01,15], center=true); // // Example: // yflip_copy(y=-5) xrot(-90) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) fwd(5) cube([15,0.01,15], center=true); module yflip_copy(offset=0, y=0) { mirror_copy(v=[0,1,0], offset=offset, cp=[0,y,0]) children(); } // Module: zflip_copy() // // Description: // Makes a copy of the children, mirrored across the Z axis. // // Usage: // zflip_copy([z], [offset]) ... // // Arguments: // offset = Distance to offset children up, before copying. // z = The Z coordinate of the mirroring plane. Default: 0 // // Side Effects: // `$orig` is true for the original instance of children. False for the copy. // `$idx` is set to the index value of each copy. // // Example: // zflip_copy() cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([15,15,0.01], center=true); // // Example: // zflip_copy(offset=5) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) cube([15,15,0.01], center=true); // // Example: // zflip_copy(z=-5) cylinder(h=20, r1=4, r2=0); // color("blue",0.25) down(5) cube([15,15,0.01], center=true); module zflip_copy(offset=0, z=0) { mirror_copy(v=[0,0,1], offset=offset, cp=[0,0,z]) children(); } //////////////////// // Section: Distributing children individually along a line /////////////////// // Module: distribute() // // Description: // Spreads out each individual child along the direction `dir`. // Every child is placed at a different position, in order. // This is useful for laying out groups of disparate objects // where you only really care about the spacing between them. // // Usage: // distribute(spacing, dir, [sizes]) ... // distribute(l, dir, [sizes]) ... // // Arguments: // spacing = Spacing to add between each child. (Default: 10.0) // sizes = Array containing how much space each child will need. // dir = Vector direction to distribute copies along. // l = Length to distribute copies along. // // Side Effects: // `$pos` is set to the relative centerpoint of each child copy, and can be used to modify each child individually. // `$idx` is set to the index number of each child being copied. // // Example: // distribute(sizes=[100, 30, 50], dir=UP) { // sphere(r=50); // cube([10,20,30], center=true); // cylinder(d=30, h=50, center=true); // } module distribute(spacing=undef, sizes=undef, dir=RIGHT, l=undef) { gaps = ($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: xdistribute() // // Description: // Spreads out each individual child 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]) ... // xdistribute(l, [sizes]) ... // // 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) { 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 each individual child 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]) // ydistribute(l, [sizes]) // // 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) { 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]) // zdistribute(l, [sizes]) // // 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) { 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); } } // vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap