+function prop_x(gamma) = hp_k / (2 * sin(gamma/2)) - hppT[0];
+
+module PropProfileAssignments(gamma){
+ // https://en.wikipedia.org/wiki/Solution_of_triangles#Two_sides_and_the_included_angle_given_(SAS)
+ x = prop_x(gamma);
+ p = phone_height + prlp10[0] - hppB[0];
+ b = p + x;
+
+ q = phone_height - hppT[0] - prcp1[0]; // $prpp7[0] is 0 by definition
+ a = q + x;
+ c = sqrt(a*a + b*b - 2*a*b*cos(gamma));
+ $prp_alpha = acos( (b*b + c*c - a*a) / (2*b*c) );
+
+ $prp_theta = 90 - $prp_alpha;
+ beta = 180 - $prp_alpha - gamma;
+ psi = 90 - beta;
+
+ //echo("abc", a,b,c);
+
+ v1 = [ [ cos(psi), -sin(psi) ], // x
+ [ sin(psi), cos(psi) ] ]; // y
+
+ $prpp7 = [0, c + (lpp13[1] - $prpp10[1] - hp_k) ];
+
+ $prp_r1 = prc_r1;
+ $prp_r11 = prop_main_th/2;
+
+ $prpp1 = $prpp7 + [1,0] *
+ // this is approximate, but will do
+ (prop_main_th/2 + prop_prop_gap + prcp1[0] - cppA[0]);
+ $prpp3 = $prpp1 +
+ v1[0] * -$prp_r1 +
+ v1[1] * ((prcp2[1] - prcp1[1]) - prop_prop_gap);
+ $prpp12 = $prpp3 + v1[0] *
+ (prop_end_dia + prop_caserecess_taper * ($prpp1[1] - $prpp3[1]));
+ $prp_r8 = prop_main_th;
+ $prpp4 = [ prop_main_th/2, $prpp3[1] ];
+ $prp_r5 = $prp_r8;
+ $prpp5 = [ $prpp12[0] - $prp_r5,
+ $prpp3[1] - prop_prong_h + $prp_r5 ];
+ $prpp6 = $prpp4 + [0,-1] * (prop_prong_h +
+ prop_prong_heel_slope * ($prpp5[0] - $prpp4[0]));
+ $prpp8 = $prpp4 + [0,-1] * $prp_r8;
+ $prpp9 = $prpp8 + [-1,0] * $prp_r8;
+
+ children();
+}
+
+module PropProfile(gamma, cut=0, rot=0){ ////toplevel
+ PropProfileAssignments(gamma){
+
+ //#circleat($prpp3,1);
+ //#circleat($prpp12,1);
+
+ if (!cut) {
+ hull(){
+ translate($prpp8)
+ intersection(){
+ circle($prp_r8);
+ polygon([[-20,-0], [20,20], [0,0]]);
+ }
+ rectfromto($prpp6, $prpp9);
+ translate($prpp5) intersection(){
+ circle($prp_r5);
+ polygon([[-10,-10], [0,0], [10,0]]);
+ }
+ rectfromto($prpp12 + [0,-0.1], $prpp3);
+ }
+ hull(){
+ circleat($prpp1, $prp_r1);
+ rectfromto($prpp12 + [0,-0.1], $prpp3);
+ }
+ }
+ // main shaft
+ rotate([0,0, rot*-$prp_theta]){
+ hull(){
+ extra = cut ? prop_recess_slop : 0;
+ rectfromto($prpp6, $prpp9);
+ circleat($prpp11, $prp_r11 + extra);
+ circleat($prpp10, $prp_r10 + extra);
+ }
+ }
+ }
+}
+
+module PropAggregateProfile(){
+ for (angle = prop_angles)
+ PropProfile(angle, 0,0);
+}
+
+module Prop(){ ////toplevel
+ hw = prop_main_width/2;
+ linextr(-hw, +hw)
+ PropAggregateProfile();
+}
+