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https://github.com/BelfrySCAD/BOSL2.git
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Added path_spread() and path_cut()
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Adrian Mariano
parent
0de637f020
commit
b8526998c7
1 changed files with 218 additions and 3 deletions
221
paths.scad
221
paths.scad
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@ -38,17 +38,18 @@ function simplify3d_path(path, eps=1e-6) = simplify_path(path, eps=eps);
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// Function: path_length()
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// Usage:
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// path3d_length(path)
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// path_length(path,[closed])
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// Description:
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// Returns the length of the path.
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// Arguments:
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// path = The list of points of the path to measure.
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// closed = true if the path is closed. Default: false
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// Example:
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// path = [[0,0], [5,35], [60,-25], [80,0]];
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// echo(path_length(path));
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function path_length(path) =
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function path_length(path,closed=false) =
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len(path)<2? 0 :
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sum([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])]);
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sum([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])])+(closed?norm(path[len(path)-1]-path[0]):0);
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// Function: path3d_spiral()
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@ -434,6 +435,220 @@ module debug_polygon(points, paths=undef, convexity=2, size=1)
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}
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}
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// Module: path_spread()
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//
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// Description:
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// 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
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// with one at path[0] of `closed` is true, or spanning the entire path from start to end if `closed` is false.
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// 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.
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// If you specify `sp` then the copies will start at `sp`.
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//
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// Usage:
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// path_spread(path), [n], [spacing], [sp], [rotate_children], [closed]) ...
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//
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// Arguments:
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// path = the path where children are placed
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// n = number of copies
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// spacing = space between copies
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// sp = if given, copies will start distance sp from the path start and spread beyond that point
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//
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// Side Effects:
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// `$pos` is set to the center of each copy
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// `$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`.
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// `$dir` is set to the direction vector of the path at the point where the copy is placed.
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// `$normal` is set to the direction of the normal vector to the path direction that is coplanar with the path at this point
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//
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// Example(2D):
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// spiral = [for(theta=[0:360*8]) theta * [cos(theta), sin(theta)]]/100;
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// stroke(spiral,width=.25);
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// color("red") path_spread(spiral, n=100) circle(r=1);
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// Example(2D):
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// circle = regular_ngon(n=64, or=10);
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// stroke(circle,width=1,close=true);
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// color("green")path_spread(circle, n=7, closed=true) circle(r=1+$idx/3);
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// Example(2D):
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// heptagon = regular_ngon(n=7, or=10);
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// stroke(heptagon, width=1, close=true);
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// color("purple") path_spread(heptagon, n=9, closed=true) square([0.5,3],anchor=FRONT);
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// Example(2D): Direction at the corners is the average of the two adjacent edges
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// heptagon = regular_ngon(n=7, or=10);
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// stroke(heptagon, width=1, close=true);
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// color("purple") path_spread(heptagon, n=7, closed=true) square([0.5,3],anchor=FRONT);
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// Example(2D): Don't rotate the children
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// heptagon = regular_ngon(n=7, or=10);
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// stroke(heptagon, width=1, close=true);
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// color("red") path_spread(heptagon, n=9, closed=true, rotate_children=false) square([0.5,3],anchor=FRONT);
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// Example(2D): Open path, specify `n`
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// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
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// stroke(sinwav,width=.1);
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// color("red")path_spread(sinwav, n=5) square([.2,1.5],anchor=FRONT);
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// Example(2D)): Open path, specify `n` and `spacing`
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// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
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// stroke(sinwav,width=.1);
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// color("red")path_spread(sinwav, n=5, spacing=1) square([.2,1.5],anchor=FRONT);
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// Example(2D)): Closed path, specify `n` and `spacing`, copies centered around circle[0]
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// circle = regular_ngon(n=64,or=10);
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// stroke(circle,width=.1,close=true);
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// color("red")path_spread(circle, n=10, spacing=1, closed=true) square([.2,1.5],anchor=FRONT);
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// Example(2D): Open path, specify `spacing`
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// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
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// stroke(sinwav,width=.1);
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// color("red")path_spread(sinwav, spacing=5) square([.2,1.5],anchor=FRONT);
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// Example(2D): Open path, specify `sp`
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// sinwav = [for(theta=[0:360]) 5*[theta/180, sin(theta)]];
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// stroke(sinwav,width=.1);
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// color("red")path_spread(sinwav, n=5, sp=18) square([.2,1.5],anchor=FRONT);
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// Example(2D):
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// wedge = arc(angle=[0,100], r=10, $fn=64);
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// difference(){
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// polygon(concat([[0,0]],wedge));
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// path_spread(wedge,n=5,spacing=3) fwd(.1)square([1,4],anchor=FRONT);
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// }
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// Example(Spin): 3d example, with children rotated into the plane of the path
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// tilted_circle = lift_plane(regular_ngon(n=64, or=12), [0,0,0], [5,0,5], [0,2,3]);
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// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
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// path_spread(tilted_circle, n=15,closed=true) {
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// color("blue")cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
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// color("red")xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
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// }
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// Example(Spin): 3d example, with rotate_children set to false
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// tilted_circle = lift_plane(regular_ngon(n=64, or=12), [0,0,0], [5,0,5], [0,2,3]);
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// path_sweep(regular_ngon(n=16,or=.1),tilted_circle);
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// path_spread(tilted_circle, n=25,rotate_children=false,closed=true) {
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// color("blue")cyl(h=3,r=.2, anchor=BOTTOM); // z-aligned cylinder
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// color("red")xcyl(h=10,r=.2, anchor=FRONT+LEFT); // x-aligned cylinder
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// }
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module path_spread(path, n, spacing, sp=undef, rotate_children=true, closed=false)
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{
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length = path_length(path,closed);
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distances = is_def(sp) ? (
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is_def(n) && is_def(spacing) ? list_range(s=sp, step=spacing, n=n) :
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is_def(n) ? list_range(s=sp, e=length, n=n) :
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list_range(s=sp, step=spacing, e=length)
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) :
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is_def(n) && is_undef(spacing) ? (closed ? let(range=list_range(s=0,e=length, n=n+1)) slice(range,0,-2) :
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list_range(s=0, e=length, n=n)
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) :
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let( n = is_def(n) ? n : floor(length/spacing)+(closed?0:1),
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ptlist = list_range(s=0,step=spacing,n=n),
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listcenter = mean(ptlist)
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)
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closed ? sort([for(entry=ptlist) posmod(entry-listcenter,length)]) :
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[for(entry=ptlist) entry + length/2-listcenter ];
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distOK = min(distances)>=0 && max(distances)<=length;
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assert(distOK,"Cannot fit all of the copies");
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cutlist = path_cut(path, distances, closed, direction=true);
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planar = len(path[0])==2;
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if (true) for(i=[0:1:len(cutlist)-1]) {
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$pos = cutlist[i][0];
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$idx = i;
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$dir = rotate_children ? (planar?[1,0]:[1,0,0]) : cutlist[i][2];
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$normal = rotate_children? (planar?[0,1]:[0,0,1]) : cutlist[i][3];
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translate($pos) {
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if (rotate_children) {
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if(planar) rot(from=[0,1],to=cutlist[i][3]) children();
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else multmatrix(mat3_to_mat4(transpose([cutlist[i][2],cross(cutlist[i][3],cutlist[i][2]), cutlist[i][3]]))) children();
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}
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else children();
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}
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}
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}
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// Function: path_cut()
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//
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// Usage
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// path_cut(path, dists, [closed], [direction])
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//
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// Description:
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// 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.
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// 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].
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// 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
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// 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
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// vector parallel to the xy plane. The output with direction vectors will be `[point, next_index, tangent, normal]`.
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//
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// Arguments:
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// path = path to cut
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// dists = distances where the path should be cut (a list) or a scalar single distance
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// closed = set to true if the curve is closed. Default: false
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// direction = set to true to return direction vectors. Default: false
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//
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// Example(NORENDER):
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// square=[[0,0],[1,0],[1,1],[0,1]];
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// path_cut(square, [.5,1.5,2.5]); // Returns [[[0.5, 0], 1], [[1, 0.5], 2], [[0.5, 1], 3]]
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// path_cut(square, [0,1,2,3]); // Returns [[[0, 0], 1], [[1, 0], 2], [[1, 1], 3], [[0, 1], 4]]
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// 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]]
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// 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]
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function path_cut(path, dists, closed=false, direction=false) =
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let( long_enough = len(path) >= (closed ? 3 : 2))
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assert(long_enough,len(path)<2 ? "Two points needed to define a path" : "Closed path must include three points")
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!is_list(dists) ? _path_cut(path, [dists],closed, direction)[0] :
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let(cuts = _path_cut(path,dists,closed))
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!direction ? cuts :
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let( dir = _path_cuts_dir(path, cuts, closed),
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normals = _path_cuts_normals(path, cuts, dir, closed)
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)
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zip(cuts, array_group(dir,1), array_group(normals,1));
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// Main recursive path cut function
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function _path_cut(path, dists, closed=false, pind=0, dtotal=0, dind=0, result=[]) =
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dind == len(dists) ? result :
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let(
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lastpt = len(result)>0 ? select(result,-1)[0] : [],
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dpartial = len(result)==0 ? 0 : norm(lastpt-path[pind]),
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nextpoint = dpartial > dists[dind]-dtotal ?
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[lerp(lastpt,path[pind], (dists[dind]-dtotal)/dpartial),pind]
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:
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_path_cut_single(path, dists[dind]-dtotal-dpartial, closed, pind)
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)
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nextpoint == undef ? concat(result, replist(undef,len(dists)-dind)):
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_path_cut(path, dists, closed, nextpoint[1], dists[dind],dind+1, concat(result, [nextpoint]));
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// Search for a single cut point in the path
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function _path_cut_single(path, dist, closed=false, ind=0, eps=1e-7) =
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ind>=len(path) ? undef :
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ind==len(path)-1 && !closed ? (dist<eps? [path[ind],ind+1] : undef) :
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let(d = norm(path[ind]-select(path,ind+1)))
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d > dist ? [lerp(path[ind],select(path,ind+1),dist/d), ind+1] :
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_path_cut_single(path, dist-d,closed, ind+1, eps);
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// Find normal directions to the path, coplanar to local part of the path
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// Or return a vector parallel to the x-y plane if the above fails
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function _path_cuts_normals(path, cuts, dirs, closed=false) =
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[for(i=[0:len(cuts)-1])
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len(path[0])==2? [-dirs[i].y,dirs[i].x] :
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let(
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plane = len(path)<3 ? undef :
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let( start = max(min(cuts[i][1],len(path)-1),2))
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_path_plane(path, start, start-2)
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)
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plane==undef ? normalize([-dirs[i].y, dirs[i].x,0]) :
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normalize(cross(dirs[i],cross(plane[0],plane[1])))
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];
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// Scan from the specified point (ind) to find a noncoplanar triple to use
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// to define the plane of the path.
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function _path_plane(path, ind, i,closed) =
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i<(closed?-1:0) ? undef :
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!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);
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// Find the direction of the path at the cut points
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function _path_cuts_dir(path, cuts, closed=false, eps=1e-2) =
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[for(ind=[0:len(cuts)-1])
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let(
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nextind = cuts[ind][1],
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nextpath = normalize(select(path, nextind+1)-select(path, nextind)),
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thispath = normalize(select(path, nextind) - path[nextind-1]),
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lastpath = normalize(path[nextind-1] - select(path, nextind-2)),
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nextdir =
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nextind==len(path) && !closed ? lastpath :
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(nextind<=len(path)-2 || closed) && approx(cuts[ind][0], path[nextind],eps) ?
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normalize(nextpath+thispath) :
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(nextind>1 || closed) && approx(cuts[ind][0],path[nextind-1],eps) ?
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normalize(thispath+lastpath) :
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thispath
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)
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nextdir];
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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