diff --git a/catear_headband.scad b/catear_headband.scad
index a54398d..2606ce1 100644
--- a/catear_headband.scad
+++ b/catear_headband.scad
@@ -1,9 +1,58 @@
 include <globals.scad>;
+include <primitives.scad>;
 
 use <headband.scad>;
 use <chamfer.scad>;
 
-module catear(height, thickness, fractal=0, side_len=30, bend_factor=0.5, stretch_factor=1.2, debug=false, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, details=true, end_caps=true) {
+/**
+ * unsupported parameters: chamfer, chamfer_shape, details, end_caps
+ */
+module catear_v3(height, thickness, fractal=0, side_len=30, bend_factor=0.15, stretch_factor=1.2, debug=false, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, details=true, end_caps=true, skew=2.0) {
+  S = side_len;
+  s = S/2;
+  sf = stretch_factor;
+  bf = bend_factor;
+  mn = 1.16; // magic number
+  f=skew*S*0.2;
+
+  a = skew*10;
+  R = [[cos(a), -sin(a), 0],
+       [sin(a),  cos(a), 0],
+       [     0,       0, 1]];
+
+  A = [ s   ,       0, 0];
+  B = [ S*bf, S*sf*mn, 0] * R;
+  C = [-S*bf, S*sf*mn, 0] * R;
+  D = [-s   ,       0, 0];
+
+  if (debug) translate([0, 0, height]) rotate(90) bezier_curve_debug([A, B, C, D]);
+}
+
+/**
+ * unsupported parameters: debug, chamfer, chamfer_shape, details, end_caps
+ */
+module catear_v2(height, thickness, fractal=0, side_len=30, bend_factor=0.15, stretch_factor=1.2, debug=false, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, details=true, end_caps=true, skew=2.0) {
+  r=side_len/2;
+  T=side_len+thickness;
+  S=side_len-thickness;
+  x_stretch = function (x) pow(x, abs(skew));
+  y_stretch = function (y) pow(y, 2.0);
+  E=1.6*stretch_factor;
+  a=y_stretch(r)+thickness/2;
+  b=y_stretch(r)-thickness/2;
+  e=(E*a-thickness)/b;
+  echo("E",E,"e",e, "a", a, "b", b, "c", thickness);
+  outer_remap = function (p) [scalc(x_stretch, p.x, T/2, -T/2)*sign(skew), scalc(y_stretch, p.y, 0, T/2)*E, p.z];
+  inner_remap = function (p) [scalc(x_stretch, p.x, S/2, -S/2)*sign(skew), scalc(y_stretch, p.y, 0, T/2)*e, p.z];
+  or = function (p) [p.x, 2*p.y, p.z];
+
+  arc(0.5, r, thickness, height, outer_remap=outer_remap, inner_remap=inner_remap);
+}
+
+/**
+ * unsupported parameters: skew
+ */
+module catear_v1(height, thickness, fractal=0, side_len=30, bend_factor=0.15, stretch_factor=1.2, debug=false, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, details=true, end_caps=true, skew=2.0) {
   $A=[0, side_len/2];
   $B=[0,-side_len/2];
   $C=[-(side_len/2/sin(120))*1.5*stretch_factor, 0];
@@ -76,7 +125,7 @@ module catear(height, thickness, fractal=0, side_len=30, bend_factor=0.5, stretc
   }
 }
 
-module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNESS, part=PART, stretch_len=STRETCH_LEN, tip_len=TIP_LEN, tip_bend=TIP_BEND, ear_scale=1.5, ear_bend_factor=0.15, ear_stretch_factor=1.2, ear_angle=42, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, with_rake=true, details=true) {
+module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNESS, part=PART, stretch_len=STRETCH_LEN, tip_len=TIP_LEN, tip_bend=TIP_BEND, ear_scale=1.5, ear_bend_factor=0.15, ear_stretch_factor=1.2, ear_angle=42, chamfer=CHAMFER, chamfer_shape=CHAMFER_SHAPE, with_rake=true, details=true, ear_skew=2.0) {
 
   $a=size/2*ear_scale;
   $delta=2*(acos($a/(size*2))-90);
@@ -84,7 +133,7 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
 
   union() {
     rotate( ear_angle, [0, 0, 1]) {
-      translate([-ear_offset, 0, 0]) catear(
+      translate([-ear_offset, 0, 0]) catear_v3(
         debug=debug,
         height=height,
         thickness=thickness,
@@ -93,11 +142,40 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
         stretch_factor=ear_stretch_factor,
         chamfer=chamfer,
         chamfer_shape=chamfer_shape,
-        details=details
+        details=details,
+        skew=ear_skew
+      );
+    }
+    rotate( ear_angle, [0, 0, 1]) {
+      translate([-ear_offset, 0, -2*height]) catear_v2(
+        debug=debug,
+        height=height,
+        thickness=thickness,
+        side_len=size/2*ear_scale,
+        bend_factor=ear_bend_factor,
+        stretch_factor=ear_stretch_factor,
+        chamfer=chamfer,
+        chamfer_shape=chamfer_shape,
+        details=details,
+        skew=ear_skew
+      );
+    }
+    rotate( ear_angle, [0, 0, 1]) {
+      translate([-ear_offset, 0, -height]) catear_v1(
+        debug=debug,
+        height=height,
+        thickness=thickness,
+        side_len=size/2*ear_scale,
+        bend_factor=ear_bend_factor,
+        stretch_factor=ear_stretch_factor,
+        chamfer=chamfer,
+        chamfer_shape=chamfer_shape,
+        details=details,
+        skew=ear_skew
       );
     }
     rotate(-ear_angle, [0, 0, 1]) {
-      translate([-ear_offset, 0, 0]) catear(
+      translate([-ear_offset, 0, 0]) catear_v3(
         debug=false,
         height=height,
         thickness=thickness,
@@ -106,7 +184,36 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
         stretch_factor=ear_stretch_factor,
         chamfer=chamfer,
         chamfer_shape=chamfer_shape,
-        details=details
+        details=details,
+        skew=-ear_skew
+      );
+    }
+    rotate(-ear_angle, [0, 0, 1]) {
+      translate([-ear_offset, 0, -2*height]) catear_v2(
+        debug=false,
+        height=height,
+        thickness=thickness,
+        side_len=size/2*ear_scale,
+        bend_factor=ear_bend_factor,
+        stretch_factor=ear_stretch_factor,
+        chamfer=chamfer,
+        chamfer_shape=chamfer_shape,
+        details=details,
+        skew=-ear_skew
+      );
+    }
+    rotate(-ear_angle, [0, 0, 1]) {
+      translate([-ear_offset, 0, -height]) catear_v1(
+        debug=false,
+        height=height,
+        thickness=thickness,
+        side_len=size/2*ear_scale,
+        bend_factor=ear_bend_factor,
+        stretch_factor=ear_stretch_factor,
+        chamfer=chamfer,
+        chamfer_shape=chamfer_shape,
+        details=details,
+        skew=-ear_skew
       );
     }
     headband(
@@ -123,4 +230,4 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
   };
 }
 
-catear_headband();
+rotate(-90) catear_headband(ear_bend_factor=0.15, ear_skew=2, debug=true);