diff --git a/paths.scad b/paths.scad index b527d93..0399a09 100644 --- a/paths.scad +++ b/paths.scad @@ -38,17 +38,18 @@ function simplify3d_path(path, eps=1e-6) = simplify_path(path, eps=eps); // Function: path_length() // Usage: -// path3d_length(path) +// path_length(path,[closed]) // Description: // Returns the length of the path. // Arguments: // path = The list of points of the path to measure. +// closed = true if the path is closed. Default: false // Example: // path = [[0,0], [5,35], [60,-25], [80,0]]; // echo(path_length(path)); -function path_length(path) = +function path_length(path,closed=false) = len(path)<2? 0 : - sum([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])]); + sum([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])])+(closed?norm(path[len(path)-1]-path[0]):0); // Function: path3d_spiral() @@ -434,6 +435,220 @@ module debug_polygon(points, paths=undef, convexity=2, size=1) } } +// 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,close=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, close=true); +// color("purple") path_spread(heptagon, n=9, closed=true) square([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, close=true); +// color("purple") path_spread(heptagon, n=7, closed=true) square([0.5,3],anchor=FRONT); +// Example(2D): Don't rotate the children +// heptagon = regular_ngon(n=7, or=10); +// stroke(heptagon, width=1, close=true); +// color("red") path_spread(heptagon, n=9, closed=true, rotate_children=false) square([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) square([.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) square([.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,close=true); +// color("red")path_spread(circle, n=10, spacing=1, closed=true) square([.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) square([.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) square([.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)square([1,4],anchor=FRONT); +// } +// Example(Spin): 3d example, with children rotated into the plane of the path +// tilted_circle = lift_plane(regular_ngon(n=64, or=12), [0,0,0], [5,0,5], [0,2,3]); +// 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): 3d example, with rotate_children set to false +// tilted_circle = lift_plane(regular_ngon(n=64, or=12), [0,0,0], [5,0,5], [0,2,3]); +// 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) ? ( + is_def(n) && is_def(spacing) ? list_range(s=sp, step=spacing, n=n) : + is_def(n) ? list_range(s=sp, e=length, n=n) : + list_range(s=sp, step=spacing, e=length) + ) : + is_def(n) && is_undef(spacing) ? (closed ? let(range=list_range(s=0,e=length, n=n+1)) slice(range,0,-2) : + list_range(s=0, e=length, n=n) + ) : + let( n = is_def(n) ? n : floor(length/spacing)+(closed?0:1), + ptlist = list_range(s=0,step=spacing,n=n), + 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; + assert(distOK,"Cannot fit all of the copies"); + cutlist = path_cut(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 multmatrix(mat3_to_mat4(transpose([cutlist[i][2],cross(cutlist[i][3],cutlist[i][2]), cutlist[i][3]]))) children(); + } + else children(); + } + } +} + + +// Function: path_cut() +// +// Usage +// path_cut(path, dists, [closed], [direction]) +// +// Description: +// Cuts a path at a list of distances from the first point in the path. Returns a list of the cut points and indices of the next point in the path after that point. +// So for example, a return value entry of [[2,3], 5] means that the cut point was [2,3] and the next point on the path after this point is path[5]. +// If the path is too short then path_cut returns undef. If you set `direction` to true then `path_cut` will also return the tangent vector to the path +// and a normal vector to the path. It tries to find a normal vector that is coplanar to the path near the cut point. If this fails it will return a normal +// vector parallel to the xy plane. The output with direction vectors will be `[point, next_index, tangent, normal]`. +// +// Arguments: +// path = path to cut +// dists = distances where the path should be cut (a list) or a scalar single distance +// closed = set to true if the curve is closed. Default: false +// direction = set to true to return direction vectors. Default: false +// +// Example(NORENDER): +// square=[[0,0],[1,0],[1,1],[0,1]]; +// path_cut(square, [.5,1.5,2.5]); // Returns [[[0.5, 0], 1], [[1, 0.5], 2], [[0.5, 1], 3]] +// path_cut(square, [0,1,2,3]); // Returns [[[0, 0], 1], [[1, 0], 2], [[1, 1], 3], [[0, 1], 4]] +// path_cut(square, [0,0.8,1.6,2.4,3.2], closed=true); // Returns [[[0, 0], 1], [[0.8, 0], 1], [[1, 0.6], 2], [[0.6, 1], 3], [[0, 0.8], 4]] +// path_cut(square, [0,0.8,1.6,2.4,3.2]); // Returns [[[0, 0], 1], [[0.8, 0], 1], [[1, 0.6], 2], [[0.6, 1], 3], undef] +function path_cut(path, dists, closed=false, direction=false) = + let( long_enough = len(path) >= (closed ? 3 : 2)) + assert(long_enough,len(path)<2 ? "Two points needed to define a path" : "Closed path must include three points") + !is_list(dists) ? _path_cut(path, [dists],closed, direction)[0] : + let(cuts = _path_cut(path,dists,closed)) + !direction ? cuts : + let( dir = _path_cuts_dir(path, cuts, closed), + normals = _path_cuts_normals(path, cuts, dir, closed) + ) + zip(cuts, array_group(dir,1), array_group(normals,1)); + +// Main recursive path cut function +function _path_cut(path, dists, closed=false, pind=0, dtotal=0, dind=0, result=[]) = + dind == len(dists) ? result : + let( + lastpt = len(result)>0 ? select(result,-1)[0] : [], + dpartial = len(result)==0 ? 0 : norm(lastpt-path[pind]), + nextpoint = dpartial > dists[dind]-dtotal ? + [lerp(lastpt,path[pind], (dists[dind]-dtotal)/dpartial),pind] + : + _path_cut_single(path, dists[dind]-dtotal-dpartial, closed, pind) + ) + nextpoint == undef ? concat(result, replist(undef,len(dists)-dind)): + _path_cut(path, dists, closed, nextpoint[1], dists[dind],dind+1, concat(result, [nextpoint])); + +// Search for a single cut point in the path +function _path_cut_single(path, dist, closed=false, ind=0, eps=1e-7) = + ind>=len(path) ? undef : + ind==len(path)-1 && !closed ? (dist dist ? [lerp(path[ind],select(path,ind+1),dist/d), ind+1] : + _path_cut_single(path, dist-d,closed, ind+1, eps); + +// Find normal directions to the path, coplanar to local part of the path +// Or return a vector parallel to the x-y plane if the above fails +function _path_cuts_normals(path, cuts, dirs, closed=false) = + [for(i=[0:len(cuts)-1]) + len(path[0])==2? [-dirs[i].y,dirs[i].x] : + let( + plane = len(path)<3 ? undef : + let( start = max(min(cuts[i][1],len(path)-1),2)) + _path_plane(path, start, start-2) + ) + plane==undef ? normalize([-dirs[i].y, dirs[i].x,0]) : + normalize(cross(dirs[i],cross(plane[0],plane[1]))) + ]; + +// Scan from the specified point (ind) to find a noncoplanar triple to use +// to define the plane of the path. +function _path_plane(path, ind, i,closed) = + i<(closed?-1:0) ? undef : + !collinear(path[ind],path[ind-1], select(path,i)) ? [select(path,i)-path[ind-1],path[ind]-path[ind-1]] : _path_plane(path, ind, i-1); + +// Find the direction of the path at the cut points +function _path_cuts_dir(path, cuts, closed=false, eps=1e-2) = + [for(ind=[0:len(cuts)-1]) + let( + nextind = cuts[ind][1], + nextpath = normalize(select(path, nextind+1)-select(path, nextind)), + thispath = normalize(select(path, nextind) - path[nextind-1]), + lastpath = normalize(path[nextind-1] - select(path, nextind-2)), + nextdir = + nextind==len(path) && !closed ? lastpath : + (nextind<=len(path)-2 || closed) && approx(cuts[ind][0], path[nextind],eps) ? + normalize(nextpath+thispath) : + (nextind>1 || closed) && approx(cuts[ind][0],path[nextind-1],eps) ? + normalize(thispath+lastpath) : + thispath + ) + nextdir]; // vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap