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	reduced epsilons in hyperpoint
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		| @@ -505,7 +505,7 @@ EX hyperpoint normalize(hyperpoint H) { | ||||
| /** like normalize but makes (ultra)ideal points material */ | ||||
| EX hyperpoint ultra_normalize(hyperpoint H) { | ||||
|   if(material(H) <= 0) { | ||||
|     H[LDIM] = hypot_d(LDIM, H) + 1e-6; | ||||
|     H[LDIM] = hypot_d(LDIM, H) + 1e-10; | ||||
|     } | ||||
|   return normalize(H); | ||||
|   } | ||||
| @@ -760,7 +760,7 @@ EX hyperpoint parabolic13(hyperpoint h) { | ||||
| EX transmatrix spintoc(const hyperpoint& H, int t, int f) { | ||||
|   transmatrix T = Id; | ||||
|   ld R = hypot(H[f], H[t]); | ||||
|   if(R >= 1e-12) { | ||||
|   if(R >= 1e-15) { | ||||
|     T[t][t] = +H[t]/R; T[t][f] = +H[f]/R; | ||||
|     T[f][t] = -H[f]/R; T[f][f] = +H[t]/R; | ||||
|     } | ||||
| @@ -774,7 +774,7 @@ EX transmatrix spintoc(const hyperpoint& H, int t, int f) { | ||||
| EX transmatrix rspintoc(const hyperpoint& H, int t, int f) { | ||||
|   transmatrix T = Id; | ||||
|   ld R = hypot(H[f], H[t]); | ||||
|   if(R >= 1e-12) { | ||||
|   if(R >= 1e-15) { | ||||
|     T[t][t] = +H[t]/R; T[t][f] = -H[f]/R; | ||||
|     T[f][t] = +H[f]/R; T[f][f] = +H[t]/R; | ||||
|     } | ||||
| @@ -853,7 +853,7 @@ EX transmatrix ggpushxto0(const hyperpoint& H, ld co) { | ||||
|     return mscale(PIU(ggpushxto0(d.second, co)), d.first * co); | ||||
|     } | ||||
|   transmatrix res = Id; | ||||
|   if(sqhypot_d(GDIM, H) < 1e-12) return res; | ||||
|   if(sqhypot_d(GDIM, H) < 1e-16) return res; | ||||
|   ld fac = -curvature()/(H[LDIM]+1); | ||||
|   for(int i=0; i<GDIM; i++) | ||||
|   for(int j=0; j<GDIM; j++) | ||||
|   | ||||
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