ep = 0.01;
t = 3; // thickness
w = 32; // width
dt = 36; // door thickness

hookDescent = 100;
backDescent = dt / 2;

module backSupport(descent, rakeAngle = 20, includeKicker = true) {
  topExt = sin(rakeAngle)*descent;

  difference() {
    union() {
      cube([t, descent, w]);

      if (includeKicker) {
        cube([topExt, t, w]);

        translate([topExt, -1, 0])
          rotate([0, 0, rakeAngle])
          translate([0, -t, 0])
          cube([t, descent + t, w]);
      }

    }

    union() {
      translate([-ep, -2*t, -ep])
        cube([topExt + 2*t, 2*t, w + 2*ep]);

      translate([topExt + 2*t/3, -ep, -ep])
        cube([t, descent, w + 2*ep]);
    }
  }
}

module hookAndSupport(descent, hookSize = 32, angle = 45, debug=false) {
  hw = hookSize / 2;
  hookDist = hookSize * 2.5;
  hookOffsetX = sin(angle) * hookDist;
  hookOffsetY = cos(angle) * hookDist;

  fpr = 2/5; // frame attachment point ratio
  aBAF = (90 - angle)/2;
  l = hookDist;
  lAC = hookDist * fpr;
  lCG = lAC * sin(angle);
  lCD = hookOffsetX;
  lCE = lCG/cos(angle);
  lAF = lAC*cos(angle) / cos(aBAF);
  lGE = lCE*sin(angle);
  lGF = lAF*sin(aBAF);
  lCF = lCG + lGF;
  lEF = sqrt(lGE*lGE + lGF*lGF);
  lCI = lCF*cos(angle);
  lFI = lCF*sin(angle);
  lDI = lCD - lCI;
  lDF = sqrt(lDI*lDI + lEF*lEF);
  aGEF = atan(lGF/lGE);
  aCAE = 90 - angle;
  aCEF = aCAE + aGEF;
  aEDF = atan(lFI/lDI) + 1;

  phi = (90 - angle)/2;
  g0 = l*fpr;
  g1 = g0*sin(angle);
  g2 = (g0 * cos(angle) * sin(phi))/cos(phi);
  o = (g0 * cos(angle))/cos(phi);
  p1 = (g0 * sin(angle))/cos(angle);

  translate([t/4, descent - t, 0])
  union() {
    color("Salmon")
      translate([-hookOffsetX, -hookOffsetY, 0])
      sphere(hookSize / 2);

    translate([0, 0, -hw/2])
    union() {
      color("LightBlue")
        rotate([0, 0, 270 - angle])
        translate([-t/2, -t/2, 0])
        cube([hookDist + t, t, hw]);

      color("LightGreen")
        translate([0, -lAC, 0])
        rotate([0, 0, 180 - angle])
        translate([-t/2, -t/2, 0])
        cube([lCF + t/2, t, hw]);

      color("Orange")
        rotate([0, 0, aBAF + 180])
        translate([-t/2, -t/2, 0])
        cube([lAF + t/2, t, hw]);

      color("Plum")
        translate([-lCD, -g0 -t/2, 0])
        cube([lCD + t/2, t, hw]);

      color("Turquoise")
        translate([-lCE, -lAC, 0])
        rotate([0, 0, aCEF])
        translate([-t/2, -t/2, 0])
        cube([lEF + t/2, t, hw]);

      color("SlateBlue")
        translate([-lCD + t/2, -lAC, 0])
        rotate([0, 0, aEDF])
        translate([-t/2, -t/2, 0])
        cube([lDF + t/2, t, hw]);

      color("Linen")
        translate([-lCD, -2*lAC, 0])
        cube([t, lAC, hw]);

       $fn=32;
       color("DodgerBlue")
        linear_extrude(height=hw)
        circle(r = t);

       translate([-lCI, -lAC + lFI, 0])
       color("DodgerBlue")
        linear_extrude(height=hw)
        circle(r = t);

       translate([-lCD + t/2, -lAC, 0])
       color("DodgerBlue")
        linear_extrude(height=hw)
        circle(r = t);

    }

    // Point Labels
    if (debug) {
      color("Red")
      translate([0, 0, w/2+1])
      union() {
        translate([-t/2, 0, 0])
        rotate([180, 0, 0])
        linear_extrude(height=1) text(text = "A",size = 4);

        translate([-hookOffsetX + t/2, -hookOffsetY + t/2, 0])
        rotate([0, 0, 180])
        linear_extrude(height=1) text(text = "B",size = 4);

        translate([t/2, -lAC + t/2, 0])
        rotate([0, 0, 180])
        linear_extrude(height=1) text(text = "C",size = 4);

        translate([-hookOffsetX + t/2, -lAC, 0]) union() {
          translate([0, -hookOffsetY + lAC, 0])
          cube([0.5, hookOffsetY - lAC, 1]);

          translate([0, t/2, 0])
          rotate([0, 0, 180])
          linear_extrude(height=1) text(text = "D",size = 4);
        }

        translate([-lCE + t/2, -lAC + t/2, 0])
        rotate([0, 0, 180])
        linear_extrude(height=1) text(text = "E",size = 4);

        translate([-t/2, 0, 0])
        rotate([0, 0, aBAF])
        translate([-lAF + t/2, 0, 0])
        rotate([0, 0, 180 - aBAF])
        linear_extrude(height=1) text(text = "F",size = 4);

        translate([0, -lAC + t/2, 0])
        rotate([0, 0, -angle])
        translate([-lCG + t/2, 0, 0])
        rotate([0, 0, 180 + angle])
        linear_extrude(height=1) text(text = "G",size = 4);

        translate([-lCE, 0, 0])
        union() {
          rotate([0, 0, 180])
          linear_extrude(height=1) text(text = "H",size = 4);

          translate([0, -lAC, 0])
          cube([0.5, lAC, 1]);

          cube([lCE, 0.5, 1]);
        }

        union() {
          translate([-lCI - t, -lAC + t/2, 0])
          rotate([0, 0, 180])
          linear_extrude(height=1) text(text = "I",size = 4);
          translate([-lCI, -lAC, 0])
          cube([0.5, lFI, 1]);
        }
      }
    }
  }
}

union() {
  translate([0, 0, -w/2]) union() {
    color("Moccasin")
      translate([t, 0, 0])
      cube([dt + 2*ep, t, w]);

    color("WhiteSmoke")
      cube([t, hookDescent, w]);

    color("WhiteSmoke")
      translate([dt + t, 0, 0])
      backSupport(descent = backDescent, rakeAngle = 36, includeKicker = false);
  }

  hookAndSupport(descent = hookDescent, hookSize = w, angle = 36, debug=false);
}