// Macros :
$macros={};
$macros["Angle2D_Points3D"]={
	name:"Angle2D_Points3D",
	parameters:["point","point","point"],
	exec:
	function (A,O,B){
Angle=Expression("Angle "+A+O+B,"","","","arg((B.coords2D()-O.coords2D())/(A.coords2D()-O.coords2D()))-PI","-10","-3");
STL(Angle,"c:#30614f;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
return [Angle];
}};

// Coordinates System :
SetCoords(800,29,119.8937449638333,true,802,652);


// Geometry :
P1=Point("P1",-2.99431801140497,-2.6773707010055583);
E6=Expression("E6","I est le milieu de [CG]. Pr\u00e9ciser la position de M sur [BC].","","","2","-6.589167768829879","-0.592191027325217");
E5=Expression("E5","Vous pouvez d\u00e9placer M, ouvrir la face BFGC et utiliser les informations de la figure","","","2","-6.589167768829879","-0.341969466483576");
Z=Point("Z","[0,0,1]","1");
Y=Point("Y","[0,1,0]","1");
tiers=Point("tiers","[1,1,1/3]","1");
E4=Expression("E4","On cherche le chemin minimal pour aller de A \u00e0 I en passant par l'ar\u00eate [BC]. ","","","1","-6.589167768829879","-0.09174790564193502");
X=Point("X","[1,0,0]","1");
H=Point("H","P1+[-1,-1,1]","0");
A=Point("A","P1+[1,-1,-1]","0");
F=Point("F","P1+[-1,1,-1]","0");
S21=Segment("S21",P1,Y);
G=Point("G","P1+[-1,1,1]","0");
B=Point("B","P1+[1,1,-1]","0");
D=Point("D","P1+[1,-1,1]","0");
S11=Segment("S11",P1,X);
S31=Segment("S31",P1,Z);
E2=Expression("E2","Ouvrir ","0","\u03C0/2","0","-6.386568480990069","-0.9438542453632855");
E=Point("E","P1+[-1,-1,-1]","0");
C=Point("C","P1+[1,1,1]","0");
angl22=Angle("angl22",E,H,D);
aDAB=Expression("aDAB","","","","arg((B.coords2D()-A.coords2D())/(D.coords2D()-A.coords2D()))-PI","-5.755095899357743","-4.09529287910819");
S107=Segment("S107",A,B);
S105=Segment("S105",H,G);
angl2=Angle("angl2",B,C,G);
aCBF=Expression("aCBF","","","","arg((F.coords2D()-B.coords2D())/(C.coords2D()-B.coords2D()))-PI","-3.2528802909413326","-3.9284785052137643");
S104=Segment("S104",D,C);
angl15=Angle("angl15",D,H,G);
angl111=Angle("angl111",F,E,A);
aGFE=Expression("aGFE","","","","arg((E.coords2D()-F.coords2D())/(G.coords2D()-F.coords2D()))-PI","-1.7515509258914868","-4.679143187738687");
angl26=Angle("angl26",F,E,A);
angl110=Angle("angl110",G,F,B);
angl25=Angle("angl25",G,H,E);
angl16=Angle("angl16",H,E,F);
angl12=Angle("angl12",G,H,E);
S108=Segment("S108",H,D);
S1010=Segment("S1010",F,B);
P2=Point("P2","[1-2*cos(E2),1+2*sin(E2),1]","1");
aDHE=Expression("aDHE","","","","arg((E.coords2D()-H.coords2D())/(D.coords2D()-H.coords2D()))-PI","-1.7515509258914868","-4.09529287910819");
angl28=Angle("angl28",D,H,G);
S109=Segment("S109",G,C);
angl19=Angle("angl19",H,G,C);
P3=Point("P3","[1-2*cos(E2),1+2*sin(E2),-1]","1");
Poly7=Polygon("Poly7","_G,_F,_E,_H");
angl211=Angle("angl211",A,E,H);
Poly1=Polygon("Poly1","_A,_B,_C,_D");
Poly2=Polygon("Poly2","_B,_F,_G,_C");
angl14=Angle("angl14",A,D,C);
S102=Segment("S102",H,E);
aHDC=Expression("aHDC","","","","arg((C.coords2D()-D.coords2D())/(H.coords2D()-D.coords2D()))-PI","-5.338059964621674","-4.7625503746859");
S1=Segment("S1",C,B);
angl21=Angle("angl21",F,G,H);
angl210=Angle("angl210",B,F,E);
angl11=Angle("angl11",C,G,F);
angl27=Angle("angl27",B,A,D);
S101=Segment("S101",G,F);
S103=Segment("S103",D,A);
aEAB=Expression("aEAB","","","","arg((B.coords2D()-A.coords2D())/(E.coords2D()-A.coords2D()))-PI","-4.003544973466255","-4.428921626897045");
angl1=Angle("angl1",D,C,B);
S106=Segment("S106",E,F);
angl13=Angle("angl13",H,D,A);
angl29=Angle("angl29",C,G,F);
angl17=Angle("angl17",E,A,B);
angl23=Angle("angl23",A,D,C);
angl18=Angle("angl18",E,H,D);
Poly6=Polygon("Poly6","_E,_A,_D,_H");
Poly5=Polygon("Poly5","_A,_E,_F,_B");
Poly4=Polygon("Poly4","_C,_G,_H,_D");
angl24=Angle("angl24",C,D,H);
S1011=Segment("S1011",E,A);
M=PointOn("M",S1,0.4800819640270156);
E36=Expression("E36","","","","S106.setDash((angl16>\u03C0)&&(angl26>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E35=Expression("E35","","","","S105.setDash((angl15>\u03C0)&&(angl25>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
S6=Segment("S6",P3,B);
E310=Expression("E310","","","","S1010.setDash((angl110>\u03C0)&&(angl210>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
S4=Segment("S4",C,P2);
I=MidPoint("I",C,P2);
E311=Expression("E311","","","","S1011.setDash((angl111>\u03C0)&&(angl211>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
S5=Segment("S5",P2,P3);
E32=Expression("E32","","","","S102.setDash((angl12>\u03C0)&&(angl22>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E33=Expression("E33","","","","S103.setDash((angl13>\u03C0)&&(angl23>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E34=Expression("E34","","","","S104.setDash((angl14>\u03C0)&&(angl24>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E7=Expression("E7","","","","Poly5.setOpacity(0.2*(aEAB<0));Poly1.setOpacity(0.2*(aDAB>0));Poly2.setOpacity(0.2*(aCBF>0));Poly6.setOpacity(0.2*(aDHE>0));Poly7.setOpacity(0.2*(aGFE>0));\"Visibilit\u00e9 des faces\"","-4.958296406526393","-2.8748892195791798");
Poly3=Polygon("Poly3","_B,_P3,_P2,_C");
E39=Expression("E39","","","","S109.setDash((angl19>\u03C0)&&(angl29>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E31=Expression("E31","","","","S101.setDash((angl11>\u03C0)&&(angl21>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E38=Expression("E38","","","","S108.setDash((angl18>\u03C0)&&(angl28>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
E37=Expression("E37","","","","S107.setDash((angl17>\u03C0)&&(angl27>\u03C0));\"Dash code\"","-5.280486719498422","-0.6236175098405722");
S3=Segment("S3",M,I);
S2=Segment("S2",A,M);
AI=Expression("AI","","","","d(A,I)","-6.505760581882665","-1.5930772706917808");
P4=Point("P4","M.coords3D()","1");
AM=Expression("AM","","","","d(A,P4)","-6.505760581882665","-1.9267060184806355");
MI=Expression("MI","","","","d(P4,I)","-6.505760581882665","-2.1769275793222764");
E1=Expression("E1","","","","d(P4,tiers)","-6.1321200911837686","-1.7920155447176207");
E3=Expression("E3","AI-AM-MI = ","","","AI-AM-MI","-6.505760581882665","-2.5105563271111313");


// Styles :
STL(P1,"c:#b40000;s:5;f:19;sp:1;fl:true");
STL(E6,"c:#62313d;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E5,"c:#385a19;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(Z,"c:#0000b2;h:1;o:1;s:1.5;sn:true;f:19");
STL(Y,"c:#0000b2;h:1;o:1;s:1.5;sn:true;f:19");
STL(tiers,"c:#0000b2;h:1;s:6;sn:true;f:13");
STL(E4,"c:#1d5579;s:7;f:17;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(X,"c:#0000b2;h:1;o:1;s:1.5;sn:true;f:19");
STL(H,"c:#0000b2;s:1.5;sn:true;f:19;np:1.7456654893864505");
STL(A,"c:#0000b2;s:1.5;sn:true;f:19;np:2.6881133813207416");
STL(F,"c:#0000b2;s:1.5;sn:true;f:19");
STL(S21,"c:#117dad;h:1;s:1;f:24");
STL(G,"c:#0000b2;s:1.5;sn:true;f:19");
STL(B,"c:#0000b2;s:1.5;sn:true;f:19;np:5.368243474204723");
STL(D,"c:#0000b2;s:1.5;sn:true;f:19;np:2.676529834996105");
STL(S11,"c:#117dad;h:1;s:1;f:24");
STL(S31,"c:#117dad;h:1;s:1;f:24");
STL(E2,"c:#6c7444;s:7;f:17;p:-1;cL:140;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E,"c:#0000b2;s:1.5;sn:true;f:19;np:5.645198745410107");
STL(C,"c:#0000b2;s:1.5;sn:true;f:19;np:3.6745886113013837");
STL(angl22,"c:#006633;h:2;s:4;f:24;p:1");
STL(aDAB,"c:#30614f;h:1;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(S107,"c:#006633;s:1;f:24");
STL(S105,"c:#006633;s:1;f:24");
STL(angl2,"c:#006633;h:2;s:4;f:24;p:1");
STL(aCBF,"c:#30614f;h:1;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(S104,"c:#006633;s:1;f:24");
STL(angl15,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl111,"c:#006633;h:2;s:4;f:24;p:1");
STL(aGFE,"c:#30614f;h:1;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(angl26,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl110,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl25,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl16,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl12,"c:#006633;h:2;s:4;f:24;p:1");
STL(S108,"c:#006633;s:1;f:24");
STL(S1010,"c:#006633;s:1;f:24");
STL(P2,"c:#0000b2;h:1;s:6;f:30");
STL(aDHE,"c:#30614f;h:1;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(angl28,"c:#006633;h:2;s:4;f:24;p:1");
STL(S109,"c:#006633;s:1;f:24");
STL(angl19,"c:#006633;h:2;s:4;f:24;p:1");
STL(P3,"c:#0000b2;h:1;s:6;f:30");
STL(Poly7,"c:#edaf35;s:1;f:30");
STL(angl211,"c:#006633;h:2;s:4;f:24;p:1");
STL(Poly1,"c:#966400;o:0.2;s:1;f:30");
STL(Poly2,"c:#0091ff;o:0.2;s:1;f:30");
STL(angl14,"c:#006633;h:2;s:4;f:24;p:1");
STL(S102,"c:#006633;s:1;f:24");
STL(aHDC,"c:#30614f;h:1;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(S1,"c:#006633;h:1;s:1;f:24");
STL(angl21,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl210,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl11,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl27,"c:#006633;h:2;s:4;f:24;p:1");
STL(S101,"c:#006633;s:1;f:24");
STL(S103,"c:#006633;s:1;f:24");
STL(aEAB,"c:#30614f;h:1;s:7;sn:true;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(angl1,"c:#006633;h:2;s:4;f:24;p:1");
STL(S106,"c:#006633;s:1;f:24");
STL(angl13,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl29,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl17,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl23,"c:#006633;h:2;s:4;f:24;p:1");
STL(angl18,"c:#006633;h:2;s:4;f:24;p:1");
STL(Poly6,"c:#ce6add;s:1;f:30");
STL(Poly5,"c:#3f2d07;s:1;f:30");
STL(Poly4,"c:#006633;h:1;o:0.2;s:1;f:30");
STL(angl24,"c:#006633;h:2;s:4;f:24;p:1");
STL(S1011,"c:#006633;s:1;f:24");
STL(M,"c:#b40000;o:1;s:6;sn:true;f:18;mg:[tiers,2]");
STL(E36,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E35,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(S6,"c:#006633;s:1;f:24");
STL(E310,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(S4,"c:#006633;s:1;f:24");
STL(I,"c:#0000b2;o:0.96;s:2;sn:true;f:17");
STL(E311,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(S5,"c:#006633;s:1;f:24");
STL(E32,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E33,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E34,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E7,"c:#3a691c;h:2;s:7;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MjtzOjEwO2Y6MzA=");
STL(Poly3,"c:#006633;o:0.2;s:1;f:30");
STL(E39,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E31,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E38,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(E37,"c:#780013;h:2;s:7;f:17;p:4;cL:200;cPT:YzojMDAwMGIyO2g6MjtzOjEuNTtmOjE5");
STL(S3,"c:#0000b2;o:0.05;s:2.5;f:24");
STL(S2,"c:#966400;s:2.5;f:24");
STL(AI,"c:#154561;s:7;sn:true;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(P4,"c:#0000b2;h:1;s:6;f:30");
STL(AM,"c:#154561;s:7;sn:true;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(MI,"c:#154561;s:7;sn:true;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E1,"c:#154561;h:1;s:7;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(E3,"c:#3a691c;s:7;f:17;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
SetCoordsStyle("3Dmode:true;isAxis:false;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:true;onlyPositive:false;color:#111111;fontSize:18;axisWidth:1;gridWidth:0.1");
SetGeneralStyle("background-color:#F8F8F8;degree:false;dragmoveable:true");