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+% geometricaverage.mp
+% L. Nobre G.
+% 2006
+
+input featpost3Dplus2D;
+
+verbatimtex \documentclass{article}\begin{document} etex
+
+%f := (5,3.5,1);
+%f := 0.4*(5,3.5,3);
+%f := 0.4*(5,1.5,1.5);
+f := 0.4*(2.5,5,1.5);
+beginfig(1);
+ cartaxes(1.5,2,1);
+ color va, vb, vc, vd, ve, vf;
+ va = black;
+ vb = (0,1.5,0);
+ vc = (1,1.5,0);
+ vd = red;
+ ve = (1,0.75,0);
+ vf = (0.5,1.5,0);
+ z3 = rp(va);
+ z4 = rp(vb);
+ z5 = rp(vc);
+ z6 = rp(vd);
+ z7 = rp(ve);
+ z9 = rp(vf);
+ draw z3--z4--z5--z6--cycle dashed evenly;
+ z1 = whatever[z3,z4];
+ z1 = whatever[z6,z5];
+ z2 = whatever[z6,z3];
+ z2 = whatever[z5,z4];
+ draw z1--z3 dashed evenly;
+ draw z1--z6 dashed evenly;
+ draw z2--z3 dashed evenly;
+ draw z2--z4 dashed evenly;
+ draw z2--z7 withcolor red;
+ draw z1--z9 withcolor red;
+ numeric laa, lba, lca;
+ laa = abs(z3-z1);
+ lba = abs(z4-z1);
+ lca = sqrt( laa )*sqrt( lba );
+ z8 = (lca/lba)[z1,z4];
+ draw z2--z8;
+
+ laa := 1/abs(z3-z2);
+ lba := 1/abs(z6-z2);
+ lca := 0.5*( laa + lba ); % What works is the arithmetic average of
+ % reciprocal distances!!
+ z10 = (lba/lca)[z2,z6];
+ draw z1--z10;
+ labels.top(1,2,3,4,5,6,7,8,9,10);
+endfig;
+
+verbatimtex \end{document} etex
+
+end;