Wall holder for a paper roll

// A wall holder for one paper roll (brown paper / kraft paper). Two identical brackets,
// each with one arm carrying an open-top slot. A rod through the roll core drops into
// the slots from above. Built from straight rectangles; corners and edges are polished
// afterwards as a final step, never as part of the construction.

/* [Parts] */
// Render the assembly, or one part laid down for printing.
part = "assembly"; // [assembly, bracket, cap]

/* [Sizes] */
// Largest diameter of a full roll.
roll_diameter = 100; // [40:5:250]
// Width of the paper. Only sizes the preview and the rod length.
paper_width = 1000; // [200:10:1600]
// Diameter of the rod through the roll core.
rod_diameter = 20; // [8:1:35]
// Width of the bracket along the wall. This is the print height.
bracket_width = 22; // [14:1:40]
// Hole diameter for the wall screws. The countersink follows it.
screw_diameter = 4.5; // [3:0.5:6]

/* [Colour] */
// Colour the printed parts are shown in. Display only, the STL carries no colour.
color_print = "SteelBlue"; // [SteelBlue, White, Gainsboro, Silver, DimGray, Black, SlateGray, FireBrick, ForestGreen, Goldenrod]

/* [Hidden] */
rod_fit = 0.6;      // spare room for the rod in the slot
back_t = 8;         // back plate thickness
under = 12;         // material under the rod
lip = 10;           // lip in front of the slot
rise = 6;           // arm height above the top of the rod
funnel = 5;         // funnel at the slot entry
wall_gap = 10;      // room between a full roll and the wall
tab = 24;           // back plate above and below the arm, for the screws
round_r = 3;        // profile corner polish
chamfer = 1.2;      // face edge polish
smoothness = 48;

cap_wall = 5;
cap_depth = 12;
cap_fit = 0.3;
cap_screw_d = 3.5;
cap_end = 4;

head_d = 2 * screw_diameter;
slot_w = rod_diameter + rod_fit;
arm_h = under + rod_diameter + rise;
// The slot never cuts into the back plate, however small the roll.
seat_x = max(wall_gap + roll_diameter / 2, back_t + slot_w / 2 + 6);
reach = seat_x + slot_w / 2 + lip;
height = arm_h + 2 * tab;
seat_z = tab + under + rod_diameter / 2;

side_gap = 5;
play = 2;
bracket_y = paper_width / 2 + side_gap + bracket_width / 2;
rod_len = 2 * (bracket_y + bracket_width / 2 + play + cap_depth);
core_id = max(rod_diameter + 2, min(rod_diameter + 20, roll_diameter * 0.5));

echo(str("Rod length: ", rod_len, " mm"));
echo(str("Bracket: ", reach, " x ", height, " x ", bracket_width, " mm"));

// The polish: a closing pass rounds the concave corners, an opening pass the convex
// ones. Applied over the finished straight shape, never during it.
module polish2d(r) {
  if (r > 0)
    offset(r = r, $fn = smoothness)
      offset(r = -2 * r, $fn = smoothness)
        offset(r = r, $fn = smoothness)
          children();
  else
    children();
}

// Extrude with a 45 degree chamfer on both faces, built from thin slices so it stays
// fast. One slice per 0.2 mm, the same as a print layer.
module polish_extrude(h, c) {
  if (c > 0) {
    n = ceil(c / 0.2);
    s = c / n;
    translate([0, 0, c]) linear_extrude(height = h - 2 * c) children();
    for (i = [0 : n - 1]) {
      inset = c - (i + 0.5) * s;
      translate([0, 0, i * s])
        linear_extrude(height = s + 0.001) offset(delta = -inset) children();
      translate([0, 0, h - (i + 1) * s - 0.001])
        linear_extrude(height = s + 0.001) offset(delta = -inset) children();
    }
  } else {
    linear_extrude(height = h) children();
  }
}

// ---- Bracket ----
// One 2D profile of axis-aligned squares, in the XZ plane.
// Origin: the wall at x = 0, the underside of the back plate at z = 0.

module profile_raw() {
  // Back plate against the wall.
  square([back_t, height]);
  difference() {
    // The arm, in the middle of the plate.
    translate([0, tab]) square([reach, arm_h]);
    // The slot, open at the top, with a round seat for the rod.
    translate([seat_x, tab + under + slot_w / 2]) {
      circle(d = slot_w, $fn = smoothness);
      translate([-slot_w / 2, 0]) square([slot_w, arm_h]);
    }
    // The funnel, so the rod finds the slot when it drops in from above.
    translate([seat_x, tab + arm_h])
      polygon([[-slot_w / 2 - funnel, 1], [slot_w / 2 + funnel, 1],
               [slot_w / 2 + funnel, 0], [slot_w / 2, -funnel],
               [-slot_w / 2, -funnel], [-slot_w / 2 - funnel, 0]]);
  }
}

module profile() {
  polish2d(round_r) profile_raw();
}

module wall_screw(z) {
  cs = (head_d - screw_diameter) / 2;
  translate([-1, 0, z]) rotate([0, 90, 0])
    cylinder(d = screw_diameter, h = back_t + 2, $fn = 32);
  translate([back_t - cs, 0, z]) rotate([0, 90, 0])
    cylinder(d1 = screw_diameter, d2 = head_d, h = cs + 0.01, $fn = 32);
  translate([back_t, 0, z]) rotate([0, 90, 0])
    cylinder(d = head_d, h = 2, $fn = 32);
}

module bracket() {
  difference() {
    translate([0, bracket_width / 2, 0])
      rotate([90, 0, 0])
        polish_extrude(bracket_width, chamfer) profile();
    // One screw below the arm, one above it.
    wall_screw(tab / 2);
    wall_screw(height - tab / 2);
  }
}

// ---- Rod end cap ----
// A cup over the rod end, wider than the slot, so the rod cannot wander sideways.

module cap() {
  R = rod_diameter / 2 + cap_wall;
  rb = (rod_diameter + cap_fit) / 2;
  H = cap_end + cap_depth;
  c = chamfer;
  sr = cap_screw_d / 2;
  difference() {
    rotate_extrude($fn = smoothness)
      polygon([[sr, 0], [R - c, 0], [R, c], [R, H - c], [R - c, H],
               [rb, H], [rb, cap_end], [sr, cap_end]]);
    translate([0, 0, -0.01])
      cylinder(d1 = 2 * cap_screw_d, d2 = cap_screw_d, h = cap_screw_d / 2, $fn = 32);
  }
}

// ---- Preview only: rod and roll ----

module rod() {
  translate([seat_x, rod_len / 2, seat_z]) rotate([90, 0, 0])
    cylinder(d = rod_diameter, h = rod_len, $fn = smoothness);
}

module roll() {
  // The roll hangs on the rod by its core, so it sits a little lower than the rod.
  translate([seat_x, paper_width / 2, seat_z - (core_id - rod_diameter) / 2])
    rotate([90, 0, 0])
      difference() {
        cylinder(d = roll_diameter, h = paper_width, $fn = smoothness);
        translate([0, 0, -1])
          cylinder(d = core_id, h = paper_width + 2, $fn = smoothness);
      }
}

// ---- Layout ----

if (part == "bracket") {
  // On its side, ready to print. Print it twice, left and right are the same.
  color(color_print) translate([0, 0, bracket_width / 2]) rotate([90, 0, 0]) bracket();
} else if (part == "cap") {
  color(color_print) cap();
} else {
  for (s = [-1, 1])
    color(color_print) translate([0, s * bracket_y, 0]) bracket();
  color("SaddleBrown") rod();
  color(color_print) translate([seat_x, rod_len / 2 + cap_end, seat_z])
    rotate([90, 0, 0]) cap();
  color(color_print) translate([seat_x, -(rod_len / 2 + cap_end), seat_z])
    rotate([-90, 0, 0]) cap();
  color("Tan") roll();
}