bool test(bool is_kernel_exact = true)
{
// types
typedef typename K::FT FT;
typedef typename K::Line_3 Line;
typedef typename K::Point_3 Point;
typedef typename K::Segment_3 Segment;
typedef typename K::Ray_3 Ray;
typedef typename K::Line_3 Line;
typedef typename K::Triangle_3 Triangle;
/* -------------------------------------
// Test data is something like that (in t supporting plane)
// Triangle is (p1,p2,p3)
//
// +E +1
// / \
// +C 6+ +8 +4 +B
// / 9++7 \
// 3+-------+5--+2
//
// +F +A
------------------------------------- */
Point p1(FT(1.), FT(0.), FT(0.));
Point p2(FT(0.), FT(1.), FT(0.));
Point p3(FT(0.), FT(0.), FT(1.));
Triangle t(p1,p2,p3);
// Edges of t
Segment s12(p1,p2);
Segment s21(p2,p1);
Segment s13(p1,p3);
Segment s23(p2,p3);
Segment s32(p3,p2);
Segment s31(p3,p1);
bool b = test_aux(is_kernel_exact,t,s12,"t-s12",s12);
b &= test_aux(is_kernel_exact,t,s21,"t-s21",s21);
b &= test_aux(is_kernel_exact,t,s13,"t-s13",s13);
b &= test_aux(is_kernel_exact,t,s23,"t-s23",s23);
// Inside points
Point p4(FT(0.5), FT(0.5), FT(0.));
Point p5(FT(0.), FT(0.75), FT(0.25));
Point p6(FT(0.5), FT(0.), FT(0.5));
Point p7(FT(0.25), FT(0.625), FT(0.125));
Point p8(FT(0.5), FT(0.25), FT(0.25));
Segment s14(p1,p4);
Segment s41(p4,p1);
Segment s24(p2,p4);
Segment s42(p4,p2);
Segment s15(p1,p5);
Segment s25(p2,p5);
Segment s34(p3,p4);
Segment s35(p3,p5);
Segment s36(p3,p6);
Segment s45(p4,p5);
Segment s16(p1,p6);
Segment s26(p2,p6);
Segment s62(p6,p2);
Segment s46(p4,p6);
Segment s48(p4,p8);
Segment s56(p5,p6);
Segment s65(p6,p5);
Segment s64(p6,p4);
Segment s17(p1,p7);
Segment s67(p6,p7);
Segment s68(p6,p8);
Segment s86(p8,p6);
Segment s78(p7,p8);
Segment s87(p8,p7);
b &= test_aux(is_kernel_exact,t,s14,"t-s14",s14);
b &= test_aux(is_kernel_exact,t,s41,"t-s41",s41);
b &= test_aux(is_kernel_exact,t,s24,"t-s24",s24);
b &= test_aux(is_kernel_exact,t,s42,"t-s42",s42);
b &= test_aux(is_kernel_exact,t,s15,"t-s15",s15);
b &= test_aux(is_kernel_exact,t,s25,"t-s25",s25);
b &= test_aux(is_kernel_exact,t,s34,"t-s34",s34);
b &= test_aux(is_kernel_exact,t,s35,"t-s35",s35);
b &= test_aux(is_kernel_exact,t,s36,"t-s36",s36);
b &= test_aux(is_kernel_exact,t,s45,"t-s45",s45);
b &= test_aux(is_kernel_exact,t,s16,"t-s16",s16);
b &= test_aux(is_kernel_exact,t,s26,"t-s26",s26);
b &= test_aux(is_kernel_exact,t,s62,"t-s62",s62);
b &= test_aux(is_kernel_exact,t,s46,"t-s46",s46);
b &= test_aux(is_kernel_exact,t,s65,"t-s65",s65);
b &= test_aux(is_kernel_exact,t,s64,"t-s64",s64);
b &= test_aux(is_kernel_exact,t,s48,"t-s48",s48);
b &= test_aux(is_kernel_exact,t,s56,"t-s56",s56);
b &= test_aux(is_kernel_exact,t,s17,"t-t17",s17);
b &= test_aux(is_kernel_exact,t,s67,"t-t67",s67);
b &= test_aux(is_kernel_exact,t,s68,"t-s68",s68);
b &= test_aux(is_kernel_exact,t,s86,"t-s86",s86);
b &= test_aux(is_kernel_exact,t,s78,"t-t78",s78);
b &= test_aux(is_kernel_exact,t,s87,"t-t87",s87);
// Outside points (in triangle plane)
Point pA(FT(-0.5), FT(1.), FT(0.5));
Point pB(FT(0.5), FT(1.), FT(-0.5));
Point pC(FT(0.5), FT(-0.5), FT(1.));
Point pE(FT(1.), FT(-1.), FT(1.));
Point pF(FT(-1.), FT(0.), FT(2.));
Segment sAB(pA,pB);
Segment sBC(pB,pC);
Segment s2E(p2,pE);
Segment sE2(pE,p2);
Segment s2A(p2,pA);
Segment s6E(p6,pE);
Segment sB8(pB,p8);
Segment sC8(pC,p8);
Segment s8C(p8,pC);
Segment s1F(p1,pF);
Segment sF6(pF,p6);
b &= test_aux(is_kernel_exact,t,sAB,"t-sAB",p2);
b &= test_aux(is_kernel_exact,t,sBC,"t-sBC",s46);
b &= test_aux(is_kernel_exact,t,s2E,"t-s2E",s26);
b &= test_aux(is_kernel_exact,t,sE2,"t-sE2",s62);
b &= test_aux(is_kernel_exact,t,s2A,"t-s2A",p2);
b &= test_aux(is_kernel_exact,t,s6E,"t-s6E",p6);
b &= test_aux(is_kernel_exact,t,sB8,"t-sB8",s48);
b &= test_aux(is_kernel_exact,t,sC8,"t-sC8",s68);
b &= test_aux(is_kernel_exact,t,s8C,"t-s8C",s86);
b &= test_aux(is_kernel_exact,t,s1F,"t-s1F",s13);
b &= test_aux(is_kernel_exact,t,sF6,"t-sF6",s36);
// Outside triangle plane
Point pa(FT(0.), FT(0.), FT(0.));
Point pb(FT(2.), FT(0.), FT(0.));
Point pc(FT(1.), FT(0.), FT(1.));
Point pe(FT(1.), FT(0.5), FT(0.5));
Segment sab(pa,pb);
Segment sac(pa,pc);
Segment sae(pa,pe);
Segment sa8(pa,p8);
Segment sb2(pb,p2);
b &= test_aux(is_kernel_exact,t,sab,"t-sab",p1);
b &= test_aux(is_kernel_exact,t,sac,"t-sac",p6);
b &= test_aux(is_kernel_exact,t,sae,"t-sae",p8);
b &= test_aux(is_kernel_exact,t,sa8,"t-sa8",p8);
b &= test_aux(is_kernel_exact,t,sb2,"t-sb2",p2);
// -----------------------------------
// ray queries
// -----------------------------------
// Edges of t
Ray r12(p1,p2);
Ray r21(p2,p1);
Ray r13(p1,p3);
Ray r23(p2,p3);
b &= test_aux(is_kernel_exact,t,r12,"t-r12",s12);
b &= test_aux(is_kernel_exact,t,r21,"t-r21",s21);
b &= test_aux(is_kernel_exact,t,r13,"t-r13",s13);
b &= test_aux(is_kernel_exact,t,r23,"t-r23",s23);
// In triangle
Point p9_(FT(0.), FT(0.5), FT(0.5));
Point p9(FT(0.25), FT(0.375), FT(0.375));
Ray r14(p1,p4);
Ray r41(p4,p1);
Ray r24(p2,p4);
Ray r42(p4,p2);
Ray r15(p1,p5);
Ray r25(p2,p5);
Ray r34(p3,p4);
Ray r35(p3,p5);
Ray r36(p3,p6);
Ray r45(p4,p5);
Ray r16(p1,p6);
Ray r26(p2,p6);
Ray r62(p6,p2);
Ray r46(p4,p6);
Ray r48(p4,p8);
Ray r56(p5,p6);
Ray r47(p4,p7);
Ray r89(p8,p9);
Ray r86(p8,p6);
Ray r68(p6,p8);
Segment r89_res(p8,p9_);
b &= test_aux(is_kernel_exact,t,r14,"t-r14",s12);
b &= test_aux(is_kernel_exact,t,r41,"t-r41",s41);
b &= test_aux(is_kernel_exact,t,r24,"t-r24",s21);
b &= test_aux(is_kernel_exact,t,r42,"t-r42",s42);
b &= test_aux(is_kernel_exact,t,r15,"t-r15",s15);
b &= test_aux(is_kernel_exact,t,r25,"t-r25",s23);
b &= test_aux(is_kernel_exact,t,r34,"t-r34",s34);
b &= test_aux(is_kernel_exact,t,r35,"t-r35",s32);
b &= test_aux(is_kernel_exact,t,r36,"t-r36",s31);
b &= test_aux(is_kernel_exact,t,r45,"t-r45",s45);
b &= test_aux(is_kernel_exact,t,r16,"t-r16",s13);
b &= test_aux(is_kernel_exact,t,r26,"t-r26",s26);
b &= test_aux(is_kernel_exact,t,r62,"t-r62",s62);
b &= test_aux(is_kernel_exact,t,r46,"t-r46",s46);
b &= test_aux(is_kernel_exact,t,r48,"t-r48",s46);
b &= test_aux(is_kernel_exact,t,r56,"t-r56",s56);
b &= test_aux(is_kernel_exact,t,r47,"t-r47",s45);
b &= test_aux(is_kernel_exact,t,r89,"t-t89",r89_res);
b &= test_aux(is_kernel_exact,t,r68,"t-r68",s64);
b &= test_aux(is_kernel_exact,t,r86,"t-r86",s86);
// Outside points (in triangre prane)
Ray rAB(pA,pB);
Ray rBC(pB,pC);
Ray r2E(p2,pE);
Ray rE2(pE,p2);
Ray r2A(p2,pA);
Ray r6E(p6,pE);
Ray rB8(pB,p8);
Ray rC8(pC,p8);
Ray r8C(p8,pC);
Ray r1F(p1,pF);
Ray rF6(pF,p6);
b &= test_aux(is_kernel_exact,t,rAB,"t-rAB",p2);
b &= test_aux(is_kernel_exact,t,rBC,"t-rBC",s46);
b &= test_aux(is_kernel_exact,t,r2E,"t-r2E",s26);
b &= test_aux(is_kernel_exact,t,rE2,"t-rE2",s62);
b &= test_aux(is_kernel_exact,t,r2A,"t-r2A",p2);
b &= test_aux(is_kernel_exact,t,r6E,"t-r6E",p6);
b &= test_aux(is_kernel_exact,t,rB8,"t-rB8",s46);
b &= test_aux(is_kernel_exact,t,rC8,"t-rC8",s64);
b &= test_aux(is_kernel_exact,t,r8C,"t-r8C",s86);
b &= test_aux(is_kernel_exact,t,r1F,"t-r1F",s13);
b &= test_aux(is_kernel_exact,t,rF6,"t-rF6",s31);
// Outside triangle plane
Ray rab(pa,pb);
Ray rac(pa,pc);
Ray rae(pa,pe);
Ray ra8(pa,p8);
Ray rb2(pb,p2);
b &= test_aux(is_kernel_exact,t,rab,"t-rab",p1);
b &= test_aux(is_kernel_exact,t,rac,"t-rac",p6);
b &= test_aux(is_kernel_exact,t,rae,"t-rae",p8);
b &= test_aux(is_kernel_exact,t,ra8,"t-ra8",p8);
b &= test_aux(is_kernel_exact,t,rb2,"t-rb2",p2);
// -----------------------------------
// Line queries
// -----------------------------------
// Edges of t
Line l12(p1,p2);
Line l21(p2,p1);
Line l13(p1,p3);
Line l23(p2,p3);
b &= test_aux(is_kernel_exact,t,l12,"t-l12",s12);
b &= test_aux(is_kernel_exact,t,l21,"t-l21",s21);
b &= test_aux(is_kernel_exact,t,l13,"t-l13",s13);
b &= test_aux(is_kernel_exact,t,l23,"t-l23",s23);
// In triangle
Line l14(p1,p4);
Line l41(p4,p1);
Line l24(p2,p4);
Line l42(p4,p2);
Line l15(p1,p5);
Line l25(p2,p5);
Line l34(p3,p4);
Line l35(p3,p5);
Line l36(p3,p6);
Line l45(p4,p5);
Line l16(p1,p6);
Line l26(p2,p6);
Line l62(p6,p2);
Line l46(p4,p6);
Line l48(p4,p8);
Line l56(p5,p6);
Line l47(p4,p7);
Line l89(p8,p9);
Line l86(p8,p6);
Line l68(p6,p8);
Segment l89_res(p1,p9_);
b &= test_aux(is_kernel_exact,t,l14,"t-l14",s12);
b &= test_aux(is_kernel_exact,t,l41,"t-l41",s21);
b &= test_aux(is_kernel_exact,t,l24,"t-l24",s21);
b &= test_aux(is_kernel_exact,t,l42,"t-l42",s12);
b &= test_aux(is_kernel_exact,t,l15,"t-l15",s15);
b &= test_aux(is_kernel_exact,t,l25,"t-l25",s23);
b &= test_aux(is_kernel_exact,t,l34,"t-l34",s34);
b &= test_aux(is_kernel_exact,t,l35,"t-l35",s32);
b &= test_aux(is_kernel_exact,t,l36,"t-l36",s31);
b &= test_aux(is_kernel_exact,t,l45,"t-l45",s45);
b &= test_aux(is_kernel_exact,t,l16,"t-l16",s13);
b &= test_aux(is_kernel_exact,t,l26,"t-l26",s26);
b &= test_aux(is_kernel_exact,t,l62,"t-l62",s62);
b &= test_aux(is_kernel_exact,t,l46,"t-l46",s46);
b &= test_aux(is_kernel_exact,t,l48,"t-l48",s46);
b &= test_aux(is_kernel_exact,t,l56,"t-l56",s56);
b &= test_aux(is_kernel_exact,t,l47,"t-l47",s45);
b &= test_aux(is_kernel_exact,t,l89,"t-t89",l89_res);
b &= test_aux(is_kernel_exact,t,l68,"t-l68",s64);
b &= test_aux(is_kernel_exact,t,l86,"t-l86",s46);
// Outside points (in triangle plane)
Line lAB(pA,pB);
Line lBC(pB,pC);
Line l2E(p2,pE);
Line lE2(pE,p2);
Line l2A(p2,pA);
Line l6E(p6,pE);
Line lB8(pB,p8);
Line lC8(pC,p8);
Line l8C(p8,pC);
Line l1F(p1,pF);
Line lF6(pF,p6);
b &= test_aux(is_kernel_exact,t,lAB,"t-lAB",p2);
b &= test_aux(is_kernel_exact,t,lBC,"t-lBC",s46);
b &= test_aux(is_kernel_exact,t,l2E,"t-l2E",s26);
b &= test_aux(is_kernel_exact,t,lE2,"t-lE2",s62);
b &= test_aux(is_kernel_exact,t,l2A,"t-l2A",p2);
b &= test_aux(is_kernel_exact,t,l6E,"t-l6E",s26);
b &= test_aux(is_kernel_exact,t,lB8,"t-lB8",s46);
b &= test_aux(is_kernel_exact,t,lC8,"t-lC8",s64);
b &= test_aux(is_kernel_exact,t,l8C,"t-l8C",s46);
b &= test_aux(is_kernel_exact,t,l1F,"t-l1F",s13);
b &= test_aux(is_kernel_exact,t,lF6,"t-lF6",s31);
// Outside triangle plane
Line lab(pa,pb);
Line lac(pa,pc);
Line lae(pa,pe);
Line la8(pa,p8);
Line lb2(pb,p2);
b &= test_aux(is_kernel_exact,t,lab,"t-lab",p1);
b &= test_aux(is_kernel_exact,t,lac,"t-lac",p6);
b &= test_aux(is_kernel_exact,t,lae,"t-lae",p8);
b &= test_aux(is_kernel_exact,t,la8,"t-la8",p8);
b &= test_aux(is_kernel_exact,t,lb2,"t-lb2",p2);
return b;
}
int main()
{
try
{
symbol k("k"),q("q"),p("p"),p1("p1"),p2("p2"),p3("p3"),ms("ms"),l("l"),s("s"),m1s("m1s"),m2s("m2s"),m3s("m3s");
symbol l1("l1"),l2("l2"),l3("l3"),l4("l4"),t("t"),p4("p4"),p5("p5"),p6("p6"),tp("tp"),v1("v1"),v2("v2"),l5("l5");
symbol k1("k1"),k2("k2"),k3("k3"),k4("k4"),k5("k5"),ms1("ms1"),ms2("ms2"),ms3("ms3"),ms4("ms4");
symbol s12("s12"),s23("s23"),s34("s34"),s45("s45"),s51("s51"),s13("s13"),s15("s15"),s56("s56"),s16("s16"),s123("s123"),s234("s234"),s345("s345");
lst inv_l;
inv_l.append(p1*p1 == 0);
inv_l.append( p2*p2 == 0);inv_l.append( p3*p3 == 0);inv_l.append( p4*p4 == 0);inv_l.append( p5*p5 == 0);inv_l.append( p6*p6 == 0);
inv_l.append(p1* p2 == s12/2);inv_l.append( p2* p3 == s23/2);inv_l.append( p3* p4 == s34/2);inv_l.append( p4* p5 == s45/2);
inv_l.append(p5* p6 == s56/2);inv_l.append( p1* p6 == s16/2);inv_l.append( p1* p3 == (-s12 + s123 - s23)/2);
inv_l.append(p2* p4 == (-s23 + s234 - s34)/2);
inv_l.append( p3* p5 == (-s34 + s345 - s45)/2);
inv_l.append(p1* p4 == (-s123 + s23 - s234 + s56)/2);
inv_l.append(p1* p5 == (-s16 + s234 - s56)/2);
inv_l.append( p2* p5 == (s16 - s234 + s34 - s345)/2);
inv_l.append( p2* p6 == (-s12 - s16 + s345)/2);
inv_l.append( p3* p6 == (s12 - s123 - s345 + s45)/2);
inv_l.append( p4* p6 == (s123 - s45 - s56)/2);
RoMB_loop_by_loop hexag(lst(k1),
lst(-pow(p1 + k1,2),-pow(p1 + p2 + k1,2),
-pow(p1 + p2 + p3 + k1,2),
-pow(p1 + p2 + p3 + p4 + k1,2),
-pow(p1+p2+p3+p4+p5+k1,2),-pow(k1,2)),
inv_l,
lst(1,1,1,1,1,1),true);
hexag.integrate_map(lst(s12 == -1, s23 == -2, s34 == -3, s45 == -4, s56 == -5, s16 == -6, s123 == -7, s234 == -8, s345 == -9));
/*
FRESULT for parameters: {s12==-1,s23==-2,s34==-3,s45==-4,s56==-5,s16==-6,s123==-7,s234==-8,s345==-9}
FRESULT anl : = -0.1955084880526298663-1/240*log(8)*log(6)+947/60480*log(2)^2-1/480*log(6)*log(4)+1/1080*log(3)*log(7)+131/7560*log(9)*log(2)+19/1260*log(9)^2-1/560*log(8)*log(4)+523/60480*log(3)^2-1/1080*log(7)*log(5)+41/4320*log(3)*log(5)-1/48*log(8)*log(5)-1/1080*log(7)*log(4)+22/945*log(6)*log(7)+19/3780*log(3)*log(4)+493/30240*Pi^2+43/1008*eps^(-2)+49/8640*log(5)^2-641/30240*log(2)*log(6)+1/1080*log(9)*log(5)-22/945*log(2)*log(7)+271/60480*log(4)^2-3/112*log(8)*log(3)-19/3780*log(9)*log(4)+1/1080*log(4)*log(5)-61/2520*log(9)*log(7)+61/5040*log(7)^2+1/168*log(3)*log(2)+1/168*log(8)*log(9)+13/3360*log(2)*log(4)-1/30240*(-1132.7960047725738361+576*log(8)-163*log(3)+264*log(9)+533*log(2)-479*log(6)-444*log(7)+271*log(4)-287*log(5))*eps^(-1)+47/1680*log(8)^2-17/1680*log(8)*log(2)+767/60480*log(6)^2-22/945*log(9)*log(6)-13/1890*log(3)*log(9)
FRESULT num: = 1.9907333428263254975E-4+(0.032177795803854872908)*eps^(-1)+(0.04265873015873015873)*eps^(-2)
eps^-2 term: 43/1008 +/- 0
eps^-1 term: 0.03746018534300839405-2/105*log(8)+163/30240*log(3)-11/1260*log(9)-533/30240*log(2)+479/30240*log(6)+37/2520*log(7)-271/30240*log(4)+41/4320*log(5) +/- 9.022403780167233619E-6
eps^0 term: -0.1955084880526298663-1/240*log(8)*log(6)+947/60480*log(2)^2-1/480*log(6)*log(4)+1/1080*log(3)*log(7)+131/7560*log(9)*log(2)+19/1260*log(9)^2-1/560*log(8)*log(4)+523/60480*log(3)^2-1/1080*log(7)*log(5)+41/4320*log(3)*log(5)-1/48*log(8)*log(5)-1/1080*log(7)*log(4)+22/945*log(6)*log(7)+19/3780*log(3)*log(4)+493/30240*Pi^2+49/8640*log(5)^2-641/30240*log(2)*log(6)+1/1080*log(9)*log(5)-22/945*log(2)*log(7)+271/60480*log(4)^2-3/112*log(8)*log(3)-19/3780*log(9)*log(4)+1/1080*log(4)*log(5)-61/2520*log(9)*log(7)+61/5040*log(7)^2+1/168*log(3)*log(2)+1/168*log(8)*log(9)+13/3360*log(2)*log(4)+47/1680*log(8)^2-17/1680*log(8)*log(2)+767/60480*log(6)^2-22/945*log(9)*log(6)-13/1890*log(3)*log(9) +/- 1.04620404922048185285E-4
*/
}
catch(std::exception &p)
{
std::cerr<<"******************************************************************"<<endl;
std::cerr<<" >>>ERROR: "<<p.what()<<endl;
std::cerr<<"******************************************************************"<<endl;
return 1;
}
return 0;
}