Support for twisted cables.

Sweep now distbutes twists in proportion to segments lengths.
Added  spiral_paths(), segmented_path() and rounded_path_vertices() functions.
Added show_path(path) module.

readme.md

@@ -6569,6 +6569,8 @@ An additional twist around the path can be specified. If the path is closed this
 The vertices specify where the the path would be without any rounding.
 Each vertex, apart from the first and the last, has an associated radius and the path shortcuts the vertex with an arc specified by the radius.
 
+`spiral_paths()` makes a list of new paths that spiral around a given path. It can be used to make twisted wires that follow a rounded_path, for example.
+
 [utils/sweep.scad](utils/sweep.scad) Implementation.
 
 [tests/sweep.scad](tests/sweep.scad) Code for this example.
@@ -6585,12 +6587,16 @@ Each vertex, apart from the first and the last, has an associated radius and the
 | `path_length(path, i = 0, length = 0)` | Calculated the length along a path |
 | `rectangle_points(w, h)` | Generate the points of a rectangle |
 | `rounded_path(path)` | Convert a rounded_path, consisting of a start coordinate, vertex / radius pairs and then an end coordinate, to a path of points for sweep. |
+| `rounded_path_vertices(path)` | Show the unrounded version of a rounded_path for debug |
+| `segmented_path(path, min_segment)` | Add points to a path to enforce a minimum segment length |
 | `skin_faces(points, npoints, facets, loop, offset = 0)` | Create the mesh for the swept volume without end caps |
+| `spiral_paths(path, n, r, twists, start_angle)` | Create a new paths which sprial around the given path. Use for making twisted cables |
 | `sweep(path, profile, loop = false, twist = 0)` | Generate the point list and face list of the swept volume |
 
 ### Modules
 | Module | Description |
 |:--- |:--- |
+| `show_path(path)` | Show a path using a chain of hulls for debugging, duplicate points are highlighted. |
 | `sweep(path, profile, loop = false, twist = 0, convexity = 1)` | Draw a polyhedron that is the swept volume |
 
 ![sweep](tests/png/sweep.png)

tests/sweep.scad

@@ -53,4 +53,12 @@ path = bezier_path(p, n);
 
 color("blue") rotate(45) sweep(path, circle_points(5, $fn = 64));
 
-color("green") sweep(rounded_path([[-170, 0, 0], [-170, 170, 0], 10, [-170, 170, 30], 20, [-50, 170, 30], 10, [-130, 100, 40]]), circle_points(3, $fn = 64));
+vertices = [[-170, 0, 0], [-170, 170, 0], 10, [-170, 170, 30], 20, [-50, 170, 31], 10, [-130, 100, 40]];
+rounded_path = rounded_path(vertices);
+
+show_path(rounded_path_vertices(vertices));
+
+paths = spiral_paths(rounded_path, 2, 1.5, 15, 0);
+for(i = [0 : len(paths) - 1])
+    color(["red", "green"][i])
+        sweep(paths[i],  circle_points(1.5, $fn = 64));

utils/sweep.scad

@@ -29,6 +29,8 @@
 //! `rounded_path()` can be used to generate a path of lines connected by arcs, useful for wire runs, etc.
 //! The vertices specify where the the path would be without any rounding.
 //! Each vertex, apart from the first and the last, has an associated radius and the path shortcuts the vertex with an arc specified by the radius.
+//!
+//! `spiral_paths()` makes a list of new paths that spiral around a given path. It can be used to make twisted wires that follow a rounded_path, for example.
 //
 include <../utils/core/core.scad>
 
@@ -107,18 +109,19 @@ function helical_twist_per_segment(r, pitch, sides) = //! Calculate the twist ar
        ) step_angle * sin(slope);                   // angle tangent should rotate around z projected onto axis rotate_from_to() uses
 
 //
-// Generate all the surface points of the swept volume.
+// Generate all the transforms for the profile of the swept volume.
 //
-function skin_points(profile, path, loop, twist = 0) =
+function sweep_transforms(path, loop = false, twist = 0) =
     let(len = len(path),
         last = len - 1,
 
-        profile4 = [for(p = profile) [p.x, p.y, p.z, 1]],
-
         tangents = [tangent(path, loop ? last : 0, 0, 1),
                     for(i = [1 : last - 1]) tangent(path, i - 1, i, i + 1),
                     tangent(path, last - 1, last, loop ? 0 : last)],
 
+        lengths = [for(i = 0, t = 0; i < len; t = t + norm(path[min(i + 1, last)] - path[i]), i = i + 1) t],
+        length = lengths[last],
+
         rotations = [for(i = 0, rot = fs_frame(tangents);
                          i < len;
                          i = i + 1,
@@ -128,8 +131,20 @@ function skin_points(profile, path, loop, twist = 0) =
         rotation = missmatch + twist
     )
     [for(i = [0 : last])
-        let(za = rotation * i / last)
-            each profile4 * orientate(path[i], rotations[i] * rot3_z(za))
+        let(za = rotation * lengths[i] / length)
+            orientate(path[i], rotations[i] * rot3_z(za))
+    ];
+
+//
+// Generate all the surface points of the swept volume.
+//
+function skin_points(profile, path, loop, twist = 0) =
+    let(profile4 = [for(p = profile) [p.x, p.y, p.z, 1]],
+
+        transforms = sweep_transforms(path, loop, twist)
+    )
+    [for(t = transforms)
+        each profile4 * t
     ];
 
 function cap(facets, segment = 0, end) = //! Create the mesh for an end cap
@@ -211,3 +226,37 @@ function rounded_path(path) = //! Convert a rounded_path, consisting of a start
             cos(t) * x_axis + sin(t) * y_axis + centre, // Circular arc in the tiled xy plane.
         path[len - 1],                                  // Last point has no radius
     ];
+
+function segmented_path(path, min_segment) = [  //! Add points to a path to enforce a minimum segment length
+    for(i = [0 : len(path) - 2])
+            let(delta =
+                    assert(path[i] != path[i + 1], str("Coincident points at path[", i, "] = ", path[i]))
+                    path[i+1] - path[i],
+                segs = ceil(norm(delta) / min_segment)
+            )
+            for(j = [0 : segs - 1])
+                path[i] + delta * j / segs, // Linear interpolation
+            path[len(path) - 1]
+];
+
+function spiral_paths(path, n, r, twists, start_angle) = let( //! Create a new paths which sprial around the given path. Use for making twisted cables
+        segment = path_length(path) / twists / r2sides(2 * r),
+        transforms = sweep_transforms(segmented_path(path, segment), twist = 360 * twists),
+        initial = [r, 0, 0, 1] * rotate(start_angle)
+    ) [for(i = [0 : n - 1]) let(initial = [r, 0, 0, 1] * rotate(start_angle + i * 360 / n)) [for(t = transforms) initial * t]];
+
+function rounded_path_vertices(path) = [path[0], for(i = [1 : 2 : len(path) - 1]) path[i]]; //! Show the unrounded version of a rounded_path for debug
+
+module show_path(path) //! Show a path using a chain of hulls for debugging, duplicate points are highlighted.
+    for(i = [0 : len(path) - 2]) {
+        hull($fn = 16) {
+            translate(path[i])
+                sphere(0.1);
+
+            translate(path[i + 1])
+                sphere(0.1);
+        }
+        if(path[i] == path[i + 1])
+            translate(path[i])
+                color("red") sphere(1);
+    }