[WIP] add polyhedron-based catears

catear_headband.scad

@@ -25,7 +25,12 @@ module catear_v3(height, thickness, fractal=0, side_len=30, bend_factor=0.15, st
   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]);
+  curve_vertices = bezier_curve_vertices([A, B, C, D], $fn);
+  if (debug) {
+    translate([0, 0, height]) rotate(90) bezier_curve_debug([A, B, C, D]);
+    echo("curve_vertices: ", curve_vertices);
+  }
+  rotate(90) render_curve(curve_vertices, width=thickness, height=height, chamfer=chamfer);
 }
 
 /**
@@ -125,13 +130,14 @@ module catear_v1(height, thickness, fractal=0, side_len=30, bend_factor=0.15, st
   }
 }
 
-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) {
+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, ear_version=3) {
 
   $a=size/2*ear_scale;
   $delta=2*(acos($a/(size*2))-90);
   ear_offset=size*sin(90-$delta/2);
 
   union() {
+    if (ear_version == 3 ) {
       rotate( ear_angle, [0, 0, 1]) {
         translate([-ear_offset, 0, 0]) catear_v3(
           debug=debug,
@@ -146,34 +152,6 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
           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_v3(
           debug=false,
@@ -188,8 +166,24 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
           skew=-ear_skew
         );
       }
+    }
+    if (ear_version == 2 ) {
+      rotate( ear_angle, [0, 0, 1]) {
+        translate([-ear_offset, 0, 0]) 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, -2*height]) catear_v2(
+        translate([-ear_offset, 0, 0]) catear_v2(
           debug=false,
           height=height,
           thickness=thickness,
@@ -202,8 +196,24 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
           skew=-ear_skew
         );
       }
+    }
+    if (ear_version == 1 ) {
+      rotate( ear_angle, [0, 0, 1]) {
+        translate([-ear_offset, 0, 0]) 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, -height]) catear_v1(
+        translate([-ear_offset, 0, 0]) catear_v1(
           debug=false,
           height=height,
           thickness=thickness,
@@ -216,6 +226,7 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
           skew=-ear_skew
         );
       }
+    }
     headband(
       size=size,
       height=height,
@@ -230,4 +241,4 @@ module catear_headband(debug=DEBUG, size=SIZE, height=HEIGHT, thickness=THICKNES
   };
 }
 
-rotate(-90) catear_headband(ear_bend_factor=0.15, ear_skew=2, debug=true);
+rotate(-90) catear_headband(ear_bend_factor=0.15, ear_skew=2, ear_version=3);

pressfit_catears.scad

@@ -50,9 +50,21 @@ g = function (p) [scalc(xremap, p.x, -S/2, S/2), scalc(yremap, p.y, 0, S/2)*e, p
 
 rotate([0, 90, 0]) color("yellow") arc(0.5, r, THICKNESS, HEIGHT, outer_remap=f, inner_remap=g);
 
-color("red") catear_v2(HEIGHT, THICKNESS, side_len=SIZE/2*EAR_SCALE, stretch_factor=EAR_STRETCH_FACTOR);
+color("red") catear_v2(
+  height=HEIGHT,
+  thickness=THICKNESS,
+  side_len=SIZE/2*EAR_SCALE,
+  stretch_factor=EAR_STRETCH_FACTOR
+);
 
 //     a =     b + c
 // x * a = y * b + c
-// y / x = a /(b + c)
+// y * b = x * a - c
-// y = x * a /(b + c) 
+// y     =(x * a - c)/ b
+
+//     100 =     95 + 5
+// x * 100 = y * 95 + 5
+// 5 * 100 = y * 95 + 5
+//     500 = y * 95 + 5
+//     495 = y * 95
+//       y = 495 / 95

primitives.scad

@@ -33,23 +33,91 @@ module bezier_curve_debug(control_points, $fn=$fn) {
   color("green") translate(bezier_spline(control_points, 0.5)) sphere(d=1, $fn=24);
 }
 
+// c^2=a^2+b^2 // a == b
+// c^2=2a^2 // /2
+// c^2/2=a^2 // sqrt
+// sqrt(c^2/2)=a
+chamfer_offset = function (c) sqrt((c*c)/2);
 
+rendered_curve_segment_vertices = function (p, v, n, width, height, chamfer)
+  let (d=normalize(n-p)) let (up=[0, 0, 1]) let (right=normalize(cross(d, up))) [
+  //p, v, n, width, height, chamfer_offset(chamfer), d, up, right,
+  v+up*(height/2)+right*(-width/2+chamfer_offset(chamfer)),
+  v+up*(height/2)+right*(width/2-chamfer_offset(chamfer)),
+  v+up*(height/2-chamfer_offset(chamfer))+right*(width/2),
+  v+up*(-height/2+chamfer_offset(chamfer))+right*(width/2),
+  v+up*(-height/2)+right*(width/2-chamfer_offset(chamfer)),
+  v+up*(-height/2)+right*(-width/2+chamfer_offset(chamfer)),
+  v+up*(-height/2+chamfer_offset(chamfer))+right*(-width/2),
+  v+up*(height/2-chamfer_offset(chamfer))+right*(-width/2)
+];
 
-rendered_curve_segment_vertices = function (p, v, n, width, height, chamfer) [];
+module render_curve(curve_vertices, width, height, chamfer, debug=false) {
+  /*
+   * vertex generation order:
+   * - we generate vertices segment by segment
+   * - one segement for every curve vertex provided
+   * - each segment has eight vertices that form the outer ring
+   * - the corners are chamfered so the vertices are pairs at the corners
+   * - we start with the top segment and move clockwise
+   * - top-down axis is determined globally by z-axis unless direction at start vertex is z
+   * - if direction at start vertes is z, top-down is y-adis instead
+   * - the left vertex of the top edge is 0, the other is 1
+   * - left-right axis is determined by normal between travel direction and up-down axis
+   * - the last vertex is part of the same corner as 0 but part of the left edge
+   * - segment edge n has vertices `n` and `(n+1)%8`
+   * - segment joining edge n has vertices local index `n` of both segments
+   * - global `i` index of local index `n` for segment `m` is `i=8*m+n`
+   * - so we have `count=length(curve_vertices)` segments and `count*8` vertices
+   * - we are not generating a thorus so the faces for our polyhedron are:
+   *   - two eight sided end cap faces
+   *   - `(count-1)*8` four sided mantle faces
+   * - direction at vertex is the vector from the previonus to the next vertex
+   *   - for the first an last vertex the only neighbor is mirrored around the vertex
+   * - the start end cap is face `0`
+   * - the face mantle face n has vertices `[n, +(n+1)%8, n+8, n+8+(n+1)%8]`
+   * - the stop end cap is face `count*8`
+   */
 
-module render_curve(curve_vertices, width, height, chamfer) {
+  start = let(v=curve_vertices[0], n=curve_vertices[1]) let(p=v+(v-n))
-  start = let(v=curve_vertices[0], n=curve_vertices[1]) let(p=v-n)
     rendered_curve_segment_vertices(p, v, n, width, height, chamfer);
+  echo("len(curve_vertices): ", len(curve_vertices));
   middle = [ for (i=[1:len(curve_vertices)-2]) let(
-    p = curve_vertives[i-1],
+    p = curve_vertices[i-1],
     v = curve_vertices[i],
-    n = curve_vertives[i+1]
+    n = curve_vertices[i+1]
-    ) rendered_curve_segment_vertices(p, v, n, width, height, chamfer)
+    ) each rendered_curve_segment_vertices(p, v, n, width, height, chamfer)
   ];
-  end = let(i=len(curve_vertices)) let(v=curve_vertices[i], p=curve_vertices[i-1]) let(n=v-p)
+  echo("len(middle): ", len(middle));
+  stop = let(i=len(curve_vertices))
+    let(v=curve_vertices[i-1], p=curve_vertices[i-2]) let(n=v+(v-p))
       rendered_curve_segment_vertices(p, v, n, width, height, chamfer);
 
-  // TODO
+  if (debug) {
+    echo(start);
+    color("#ff00ff") for (v = start) translate(v+[0, 0, height]) sphere(d=.25, $fn=16);
+    echo(middle);
+    color("white") for (v = middle) translate(v+[0, 0, height]) sphere(d=.25, $fn=16);
+    echo(stop);
+    color("cyan") for (v = stop) translate(v+[0, 0, height]) sphere(d=.25, $fn=16);
+  }
+
+  render_vertices = concat(start, middle, stop);
+  echo("len(render_vertices)", len(render_vertices));
+  echo(render_vertices);
+
+  start_cap = [ for (i=[0:1:7]) i];
+  echo(start_cap);
+  mantle = let (M=len(curve_vertices)-1) [ for (m=[0:M-1],n=[0:7]) let (i=m*8+n)
+    [i, i+8, n==7 ? i+1 : i+8+1, n==7 ? i-7 : i+1]
+  ];
+  echo(mantle);
+  end_cap = let (m=len(curve_vertices)-1) [ for (i=[m*8+7:-1:m*8]) i ];
+  echo(end_cap);
+
+  faces = concat([start_cap], mantle, [end_cap]);
+
+  translate([0, 0, debug ? height : 0]) polyhedron(points=render_vertices, faces=faces);
 }
 
 arc_vertex = function (a, r, t, translate=[0,0,0], remap=id) remap([