diff --git a/common.scad b/common.scad
index e9e4504..44f1513 100644
--- a/common.scad
+++ b/common.scad
@@ -244,7 +244,7 @@ function _list_pattern(list) =
 // Example:
 //   same_shape([3,[4,5]],[7,[3,4]]);   // Returns true
 //   same_shape([3,4,5], [7,[3,4]]);    // Returns false
-function same_shape(a,b) = _list_pattern(a) == b*0;
+function same_shape(a,b) = is_def(b) && _list_pattern(a) == b*0;
 
 
 // Function: is_bool_list()
diff --git a/paths.scad b/paths.scad
index c870b62..d3b18da 100644
--- a/paths.scad
+++ b/paths.scad
@@ -1225,11 +1225,17 @@ module path_spread(path, n, spacing, sp=undef, rotate_children=true, closed=fals
 //   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
+//   this point is path[5].  If the path is too short then path_cut fails with an error.  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]`.
+//   .
+//   If you give the very last point of the path as a cut point then the returned index will be
+//   one larger than the last index (so it will not be a valid index).  If you use the closed
+//   option then the returned index will be equal to the path length for cuts along the closing
+//   path segment, and if you give a point equal to the path length you will get an
+//   index of len(path)+1 for the index.  
 //
 // Arguments:
 //   path = path to cut
@@ -1246,8 +1252,10 @@ module path_spread(path, n, spacing, sp=undef, rotate_children=true, closed=fals
 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))
+    is_num(dists) ? path_cut(path, [dists],closed, direction)[0] :
+    assert(is_vector(dists))
+    assert(list_increasing(dists), "Cut distances must be an increasing list")
+    let(cuts = _path_cut(path,dists,closed))
     !direction
        ? cuts
        : let(
@@ -1260,20 +1268,23 @@ function path_cut(path, dists, closed=false, direction=false) =
 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)
-    ) is_undef(nextpoint)?
-        concat(result, repeat(undef,len(dists)-dind)) :
-        _path_cut(path, dists, closed, nextpoint[1], dists[dind],dind+1, concat(result, [nextpoint]));
+        lastpt = len(result)==0? [] : select(result,-1)[0],       // location of last cut point
+        dpartial = len(result)==0? 0 : norm(lastpt-select(path,pind)),  // remaining length in segment
+        nextpoint = dists[dind] <= dpartial+dtotal  // Do we have enough length left on the current segment?
+           ? [lerp(lastpt,select(path,pind),(dists[dind]-dtotal)/dpartial),pind] 
+           : _path_cut_single(path, dists[dind]-dtotal-dpartial, closed, pind)
+    ) 
+    _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<eps? [path[ind],ind+1] : undef) :
-    let(d = norm(path[ind]-select(path,ind+1))) d > dist ?
+    // If we get to the very end of the path (ind is last point or wraparound for closed case) then
+    // check if we are within epsilon of the final path point.  If not we're out of path, so we fail
+    ind==len(path)-(closed?0:1) ?
+       assert(dist<eps,"Path is too short for specified cut distance")
+       [select(path,ind),ind+1]
+    :let(d = norm(path[ind]-select(path,ind+1))) d > dist ?
         [lerp(path[ind],select(path,ind+1),dist/d), ind+1] :
         _path_cut_single(path, dist-d,closed, ind+1, eps);
 
@@ -1307,18 +1318,61 @@ function _path_cuts_dir(path, cuts, closed=false, eps=1e-2) =
             zeros = path[0]*0,
             nextind = cuts[ind][1],
             nextpath = unit(select(path, nextind+1)-select(path, nextind),zeros),
-            thispath = unit(select(path, nextind) - path[nextind-1],zeros),
-            lastpath = unit(path[nextind-1] - select(path, nextind-2),zeros),
+            thispath = unit(select(path, nextind) - select(path,nextind-1),zeros),
+            lastpath = unit(select(path,nextind-1) - select(path, nextind-2),zeros),
             nextdir =
                 nextind==len(path) && !closed? lastpath :
-                (nextind<=len(path)-2 || closed) && approx(cuts[ind][0], path[nextind],eps)?
-                    unit(nextpath+thispath) :
-                    (nextind>1 || closed) && approx(cuts[ind][0],path[nextind-1],eps)?
-                        unit(thispath+lastpath) :
-                        thispath
+                (nextind<=len(path)-2 || closed) && approx(cuts[ind][0], path[nextind],eps)
+                   ? unit(nextpath+thispath)
+              : (nextind>1 || closed) && approx(cuts[ind][0],select(path,nextind-1),eps)
+                   ? unit(thispath+lastpath)
+              :  thispath
         ) nextdir
     ];
 
+
+// Function: path_cut_segs()
+// Usage:
+//    path_list = path_cut_segs(path, cutdist, <closed>);
+// Description:
+//    Given a list of distances in `cutdist`, cut the path into
+//    subpaths at those lengths, returning a list of paths.
+//    If the input path is closed then the final path will include the
+//    original starting point.  The list of cut distances must be
+//    in ascending order.  If you repeat a distance you will get an
+//    empty list in that position in the output.
+// Arguments:
+//    path = path to cut
+//    cutdist = distance or list of distances where path is cut
+//    closed = set to true for a closed path.  Default: false
+function path_cut_segs(path,cutdist,closed) =
+  is_num(cutdist) ? path_cut_segs(path,[cutdist],closed) :
+  assert(is_vector(cutdist))
+  assert(select(cutdist,-1)<path_length(path,closed=closed),"Cut distances must be smaller than the path length")
+  assert(cutdist[0]>0, "Cut distances must be strictly positive")
+  let(
+      cutlist = path_cut(path,cutdist,closed=closed),
+      cuts = len(cutlist)
+  )
+  [
+      [ each slice(path,0,cutlist[0][1]),
+        if (!approx(cutlist[0][0], path[cutlist[0][1]-1])) cutlist[0][0]
+      ],
+      for(i=[0:1:cuts-2])
+          cutlist[i][0]==cutlist[i+1][0] ? []
+          :
+          [ if (!approx(cutlist[i][0], select(path,cutlist[i][1]))) cutlist[i][0],
+            each slice(path,cutlist[i][1], cutlist[i+1][1]),
+            if (!approx(cutlist[i+1][0], select(path,cutlist[i+1][1]-1))) cutlist[i+1][0],
+          ],
+      [
+        if (!approx(cutlist[cuts-1][0], select(path,cutlist[cuts-1][1]))) cutlist[cuts-1][0],
+        each select(path,cutlist[cuts-1][1],closed ? 0 : -1)
+      ]
+  ];
+
+
+
 // Input `data` is a list that sums to an integer. 
 // Returns rounded version of input data so that every 
 // entry is rounded to an integer and the sum is the same as
diff --git a/rounding.scad b/rounding.scad
index abfe0ba..a6c1d14 100644
--- a/rounding.scad
+++ b/rounding.scad
@@ -60,7 +60,8 @@ include <structs.scad>
 //   or you can specify a list that has length len(path)-2, omitting the two dummy values.
 //   .
 //   If your input path includes collinear points you must use a cut or radius value of zero for those "corners".  You can
-//   choose a nonzero joint parameter, which will cause extra points to be inserted.  
+//   choose a nonzero joint parameter when the collinear points form a 180 degree angle.  This will cause extra points to be inserted. 
+//   If the collinear points form a spike (0 degree angle) then round_corners will fail. 
 //   .
 //   Examples:
 //   * `method="circle", radius=2`:
@@ -75,7 +76,8 @@ include <structs.scad>
 //   ignored.  Note that $fn is interpreted as the number of points on the roundover curve, which is
 //   not equivalent to its meaning for rounding circles because roundovers are usually small fractions
 //   of a circular arc.  When doing continuous curvature rounding be sure to use lots of segments or the effect
-//   will be hidden by the discretization.
+//   will be hidden by the discretization.  Note that if you use $fn then $fn with "smooth" then $fn points are added at each corner, even
+//   if the "corner" is flat, with collinear points, so this guarantees a specific output length.  
 //
 // Figure(2D,Med):
 //   h = 18;
@@ -260,10 +262,16 @@ function round_corners(path, method="circle", radius, cut, joint, k, closed=true
         dk = [
               for(i=[0:1:len(path)-1])
                   let(
-                      angle = vector_angle(select(path,i-1,i+1))/2
+                      pathbit = select(path,i-1,i+1),
+                      angle = approx(pathbit[0],pathbit[1]) || approx(pathbit[1],pathbit[2]) ? undef
+                            : vector_angle(select(path,i-1,i+1))/2,
+                            f=echo(angle=angle)
                   )
                   (!closed && (i==0 || i==len(path)-1))  ? [0] :          // Force zeros at ends for non-closed
                   parm[i]==0 ? [0]    : // If no rounding requested then don't try to compute parameters
+                  assert(is_def(angle), str("Repeated point in path at index ",i," with nonzero rounding"))
+                  assert(!approx(angle,0), closed && i==0 ? "Closing the path causes it to turn back on itself at the end" :
+                                                            str("Path turns back on itself at index ",i," with nonzero rounding"))
                   (method=="chamfer" && measure=="joint")? [parm[i]] :
                   (method=="chamfer" && measure=="cut")  ? [parm[i]/cos(angle)] :
                   (method=="smooth" && measure=="joint") ? [parm[i],k[i]] :
@@ -277,10 +285,11 @@ function round_corners(path, method="circle", radius, cut, joint, k, closed=true
         lengths = [for(i=[0:1:len(path)]) norm(select(path,i)-select(path,i-1))],
         scalefactors = [
             for(i=[0:1:len(path)-1])
-                min(
+                if (closed || (i!=0 && i!=len(path)-1))
+                 min(
                     lengths[i]/(select(dk,i-1)[0]+dk[i][0]),
                     lengths[i+1]/(dk[i][0]+select(dk,i+1)[0])
-                )
+                 )
         ],
         dummy = verbose ? echo("Roundover scale factors:",scalefactors) : 0
     )
@@ -639,12 +648,12 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)
       d_next = is_vector(joint[i]) ? joint[i][1] : joint[i]
   )
   assert(d_first>=0 && d_next>=0, str("Joint value negative when adding path ",i+1))
+  assert(d_first<path_length(revresult),str("Path ",i," is too short for specified cut distance ",d_first))
+  assert(d_next<path_length(nextpath), str("Path ",i+1," is too short for specified cut distance ",d_next))
   let(
       firstcut = path_cut(revresult, d_first, direction=true),
       nextcut = path_cut(nextpath, d_next, direction=true)
   )
-  assert(is_def(firstcut),str("Path ",i," is too short for specified cut distance ",d_first))
-  assert(is_def(nextcut),str("Path ",i+1," is too short for specified cut distance ",d_next))
   assert(!loop || nextcut[1] < len(revresult)-1-firstcut[1], "Path is too short to close the loop")
   let(
      first_dir=firstcut[2],
diff --git a/tests/test_common.scad b/tests/test_common.scad
index 2397437..3568440 100644
--- a/tests/test_common.scad
+++ b/tests/test_common.scad
@@ -245,6 +245,12 @@ test_is_consistent();
 module test_same_shape() {
     assert(same_shape([3,[4,5]],[7,[3,4]]));
     assert(!same_shape([3,4,5], [7,[3,4]]));
+    assert(!same_shape([3,4,5],undef));
+    assert(!same_shape([5,3],3));
+    assert(!same_shape(undef,[3,4]));
+    assert(same_shape(4,5));
+    assert(!same_shape(5,undef));
+           
 }
 test_same_shape();