diff --git a/hull.scad b/hull.scad
index da7d2c9..874e2c8 100644
--- a/hull.scad
+++ b/hull.scad
@@ -92,7 +92,7 @@ function hull2d_path(points) =
     assert(is_path(points,2),"Invalid input to hull2d_path")
     len(points) < 2 ? []
   : len(points) == 2 ? [0,1]
-  : let(tri=find_noncollinear_points(points, error=false))
+  : let(tri=noncollinear_triple(points, error=false))
     tri == [] ? _hull_collinear(points)
   : let(
         remaining = [ for (i = [0:1:len(points)-1]) if (i != tri[0] && i!=tri[1] && i!=tri[2]) i ],
@@ -170,7 +170,7 @@ function hull3d_faces(points) =
     assert(is_path(points,3),"Invalid input to hull3d_faces")
     len(points) < 3 ? list_range(len(points))
   : let ( // start with a single non-collinear triangle
-          tri = find_noncollinear_points(points, error=false)
+          tri = noncollinear_triple(points, error=false)
         )
     tri==[] ? _hull_collinear(points)
   : let(
@@ -250,7 +250,7 @@ function _find_conflicts(point, planes) = [
 
 
 function _find_first_noncoplanar(plane, points, i) = 
-    (i >= len(points) || !coplanar(plane, points[i]))? i :
+    (i >= len(points) || !points_on_plane([points[i]],plane))? i :
     _find_first_noncoplanar(plane, points, i+1);
 
 
diff --git a/rounding.scad b/rounding.scad
index 254d035..2dc2ea4 100644
--- a/rounding.scad
+++ b/rounding.scad
@@ -675,7 +675,7 @@ module offset_sweep(
                                 r = offset_type=="round"? this_offset : undef,
                                 do_chamfer = offset_type == "chamfer"
                         )
-                        assert(num_defined([r,delta])==1,"Must set `offset` to \"round\" or \"delta")
+                        assert(num_defined([r,delta])==1,str("Must set `offset` to ",round," or ",delta)
                         let(
                                 vertices_faces = offset(
                                         path, r=r, delta=delta, chamfer = do_chamfer, closed=true,
@@ -1532,7 +1532,7 @@ function rounded_prism(bottom, top, joint_bot, joint_top, joint_sides, k_bot, k_
      // Determine which points are concave by making bottom 2d if necessary
      bot_proj = len(bottom[0])==2 ? bottom :  project_plane(bottom, select(bottom,0,2)),
      bottom_sign = polygon_is_clockwise(bot_proj) ? 1 : -1,
-     concave = [for(i=[0:N-1]) bottom_sign*sign(point_left_of_segment2d(select(bot_proj,i+1), select(bot_proj, i-1,i)))>0],
+     concave = [for(i=[0:N-1]) bottom_sign*sign(point_left_of_line2d(select(bot_proj,i+1), select(bot_proj, i-1,i)))>0],
      top = is_undef(top) ? path3d(bottom,height/2) :
            len(top[0])==2 ? path3d(top,height/2) :
            top,
@@ -1547,11 +1547,11 @@ function rounded_prism(bottom, top, joint_bot, joint_top, joint_sides, k_bot, k_
    assert(jsvecok || jssingleok,
           str("Argument joint_sides is invalid.  All entries must be nonnegative, and it must be a number, 2-vector, or a length ",N," list those."))
    assert(is_num(k_sides) || is_vector(k_sides,N), str("Curvature parameter k_sides must be a number or length ",N," vector"))
-   assert(points_are_coplanar(bottom))
-   assert(points_are_coplanar(top))
+   assert(coplanar(bottom))
+   assert(coplanar(top))
    assert(!is_num(k_sides) || (k_sides>=0 && k_sides<=1), "Curvature parameter k_sides must be in interval [0,1]")
    let(
-     non_coplanar=[for(i=[0:N-1]) if (!points_are_coplanar(concat(select(top,i,i+1), select(bottom,i,i+1)))) [i,(i+1)%N]],
+     non_coplanar=[for(i=[0:N-1]) if (!coplanar(concat(select(top,i,i+1), select(bottom,i,i+1)))) [i,(i+1)%N]],
      k_sides_vec = is_num(k_sides) ? repeat(k_sides, N) : k_sides,
      kbad = [for(i=[0:N-1]) if (k_sides_vec[i]<0 || k_sides_vec[i]>1) i],
      joint_sides_vec = jssingleok ? repeat(joint_sides,N) : joint_sides,
diff --git a/vnf.scad b/vnf.scad
index b72902e..05fd82f 100644
--- a/vnf.scad
+++ b/vnf.scad
@@ -403,6 +403,16 @@ function _triangulate_planar_convex_polygons(polys) =
         outtris = concat(tris, newtris, newtris2)
     ) outtris;
 
+//**
+// this function may produce degenerate triangles:
+//    _triangulate_planar_convex_polygons([ [for(i=[0:1]) [i,i],
+//                                           [1,-1], [-1,-1],
+//                                           for(i=[-1:0]) [i,i] ] ] )
+//    == [[[-1, -1], [ 0,  0], [0,  0]]
+//        [[-1, -1], [-1, -1], [0,  0]]
+//        [[ 1, -1], [-1, -1], [0,  0]]
+//        [[ 0,  0], [ 1,  1], [1, -1]] ]
+//
 
 // Function: vnf_bend()
 // Usage:
@@ -647,7 +657,7 @@ function vnf_validate(vnf, show_warns=true, check_isects=false) =
         nonplanars = unique([
             for (face = faces) let(
                 faceverts = [for (k=face) varr[k]]
-            ) if (!points_are_coplanar(faceverts)) [
+            ) if (!coplanar(faceverts)) [
                 "ERROR",
                 "NONPLANAR",
                 "Face vertices are not coplanar",