M1, Translation(2.F,3.F,4.F) | 1 0 0 2 | | 0 1 0 3 | | 0 0 1 4 | | 0 0 0 1 | M2, Inversion | 1 0 0 -2 | | 0 1 0 -3 | | 0 0 1 -4 | | 0 0 0 1 | Identity = M1*M2 | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | Identity = M2*M1 | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | M1, Rotation(1.25 rad, normal(-2.F,-1.F,3.F)), then Translation(2.F,3.F,4.F) | 0.511151 -0.663183 -0.54723 2 | | 0.858884 0.364375 0.36058 3 | | -0.0398737 -0.654132 0.755777 4 | | 0 0 0 1 | M2, Inversion | 0.51082 0.858452 -0.0397004 -3.43819 | | -0.662941 0.364187 -0.653764 2.84838 | | -0.546831 0.360498 0.755209 -3.00867 | | 0 0 0 1 | Identity = M1*M2 | 1 1.49012e-08 0 2.38419e-07 | | 0 1 0 4.76837e-07 | | -2.98023e-08 -2.98023e-08 1 4.76837e-07 | | 0 0 0 1 | Identity = M2*M1 | 1 9.31323e-09 -1.11759e-08 2.38419e-07 | | 1.86265e-08 1 -2.98023e-08 -2.38419e-07 | | -7.45058e-09 0 1 0 | | 0 0 0 1 |
Code:
Implementations of other functions and other operators are trivial.
/*Please refactor identifiers, as you like*/ #define eCG/*G++*/ /*#define eCV*//*VC++*/ /*Haters gonna hate ... */ typedef void v; #define ig else if #define ih else #define rK noexcept #define rU const noexcept #define rY (*this) #ifdef eCG #define okN(p)__attribute__((aligned(p))) #elif defined eCV #define okN(p)__declspec(align(p)) #endif #include<iostream> typedef float tR; struct okN(0x10) tR3x3{ tR m[0x10];/*Column-major, not row-major -- OpenGL FTW*/ #define o_(a,b)\ tR N##a##b()rU{return m[((b-1)*3)+(a-1)];}\ tR&N##a##b()rK{return m[((b-1)*3)+(a-1)];} o_(1,1)o_(1,2)o_(1,3) o_(2,1)o_(2,2)o_(2,3) o_(3,1)o_(3,2)o_(3,3) #undef o_ tR3x3()rK{} tR3x3( tR p11,tR p12,tR p13, tR p21,tR p22,tR p23, tR p31,tR p32,tR p33)rK{ #define o_(a,b)N##a##b()=p##a##b; o_(1,1)o_(1,2)o_(1,3) o_(2,1)o_(2,2)o_(2,3) o_(3,1)o_(3,2)o_(3,3) #undef o_ } tR3x3&operator*=(tR const&)rK;
/*Determinant*/
tR kDnt()rU{return
N11()*(N22()*N33()-N23()*N32())-
N12()*(N21()*N33()-N23()*N31())+
N13()*(N21()*N32()-N22()*N31());}
tR3x3 kIv()rU{tR3x3 l;
l.N11()=N22()*N33()-N23()*N32();
l.N12()=-N12()*N33()+N13()*N32();
l.N13()=N12()*N23()-N13()*N22();
l.N21()=-N21()*N33()+N23()*N31();
l.N22()=N11()*N33()-N13()*N31();
l.N23()=-N11()*N23()+N13()*N21();
l.N31()=N21()*N32()-N22()*N31();
l.N32()=-N11()*N32()+N12()*N31();
l.N33()=N11()*N22()-N12()*N21();
l*=1.F/(N11()*l.N11()+N21()*l.N12()+N31()*l.N13());return l;}
friend std::ostream&operator<<(std::ostream&,tR3x3 const&)rK;};
struct okN(0x10) tR4x4{
tR m[0x10];/*Column-major, not row-major -- OpenGL FTW*/
#define o_(a,b)\
tR N##a##b()rU{return m[((b-1)<<2)+(a-1)];}\
tR&N##a##b()rK{return m[((b-1)<<2)+(a-1)];}
o_(1,1)o_(1,2)o_(1,3)o_(1,4)
o_(2,1)o_(2,2)o_(2,3)o_(2,4)
o_(3,1)o_(3,2)o_(3,3)o_(3,4)
o_(4,1)o_(4,2)o_(4,3)o_(4,4)
#undef o_
tR4x4()rK{}
tR4x4(
tR p11,tR p12,tR p13,tR p14,
tR p21,tR p22,tR p23,tR p24,
tR p31,tR p32,tR p33,tR p34,
tR p41,tR p42,tR p43,tR p44)rK{
#define o_(a,b)N##a##b()=p##a##b;
o_(1,1)o_(1,2)o_(1,3)o_(1,4)
o_(2,1)o_(2,2)o_(2,3)o_(2,4)
o_(3,1)o_(3,2)o_(3,3)o_(3,4)
o_(4,1)o_(4,2)o_(4,3)o_(4,4)
#undef o_
}
tR4x4&operator*=(tR const&)rK;
/*Determinant*/
tR kDnt()rU{return
N11()*(N22()*(N33()*N44()-N43()*N34())-N23()*(N32()*N44()-N42()*N34())+N24()*(N32()*N43()-N42()*N33()))- N12()*(N21()*(N33()*N44()-N43()*N34())-N23()*(N31()*N44()-N41()*N34())+N24()*(N31()*N43()-N41()*N33()))+ N13()*(N21()*(N32()*N44()-N42()*N34())-N22()*(N31()*N44()-N41()*N34())+N24()*(N31()*N42()-N41()*N32()))- N14()*(N21()*(N32()*N43()-N42()*N33())-N22()*(N31()*N43()-N41()*N33())+N23()*(N31()*N42()-N41()*N32()));}
tR4x4 kIv()rU{tR4x4 l;
l.N11()=N22()*N33()*N44()-N22()*N43()*N34()-N23()*N32()*N44()+N23()*N42()*N34()+N24()*N32()*N43()-N24()*N42()*N33();
l.N12()=-N12()*N33()*N44()+N12()*N43()*N34()+N13()*N32()*N44()-N13()*N42()*N34()-N14()*N32()*N43()+N14()*N42()*N33();
l.N13()=N12()*N23()*N44()-N12()*N43()*N24()-N13()*N22()*N44()+N13()*N42()*N24()+N14()*N22()*N43()-N14()*N42()*N23();
l.N14()=-N12()*N23()*N34()+N12()*N33()*N24()+N13()*N22()*N34()-N13()*N32()*N24()-N14()*N22()*N33()+N14()*N32()*N23();
l.N21()=-N21()*N33()*N44()+N21()*N43()*N34()+N23()*N31()*N44()-N23()*N41()*N34()-N24()*N31()*N43()+N24()*N41()*N33();
l.N22()=N11()*N33()*N44()-N11()*N43()*N34()-N13()*N31()*N44()+N13()*N41()*N34()+N14()*N31()*N43()-N14()*N41()*N33();
l.N23()=-N11()*N23()*N44()+N11()*N43()*N24()+N13()*N21()*N44()-N13()*N41()*N24()-N14()*N21()*N43()+N14()*N41()*N23();
l.N24()=N11()*N23()*N34()-N11()*N33()*N24()-N13()*N21()*N34()+N13()*N31()*N24()+N14()*N21()*N33()-N14()*N31()*N23();
l.N31()=N21()*N32()*N44()-N21()*N42()*N34()-N22()*N31()*N44()+N22()*N41()*N34()+N24()*N31()*N42()-N24()*N41()*N32();
l.N32()=-N11()*N32()*N44()+N11()*N42()*N34()+N12()*N31()*N44()-N12()*N41()*N34()-N14()*N31()*N42()+N14()*N41()*N32();
l.N33()=N11()*N22()*N44()-N11()*N42()*N24()-N12()*N21()*N44()+N12()*N41()*N24()+N14()*N21()*N42()-N14()*N41()*N22();
l.N34()=-N11()*N22()*N34()+N11()*N32()*N24()+N12()*N21()*N34()-N12()*N31()*N24()-N14()*N21()*N32()+N14()*N31()*N22();
l.N41()=-N21()*N32()*N43()+N21()*N42()*N33()+N22()*N31()*N43()-N22()*N41()*N33()-N23()*N31()*N42()+N23()*N41()*N32();
l.N42()=N11()*N32()*N43()-N11()*N42()*N33()-N12()*N31()*N43()+N12()*N41()*N33()+N13()*N31()*N42()-N13()*N41()*N32();
l.N43()=-N11()*N22()*N43()+N11()*N42()*N23()+N12()*N21()*N43()-N12()*N41()*N23()-N13()*N21()*N42()+N13()*N41()*N22();
l.N44()=N11()*N22()*N33()-N11()*N32()*N23()-N12()*N21()*N33()+N12()*N31()*N23()+N13()*N21()*N32()-N13()*N31()*N22();
l*=1.F/(N11()*l.N11()+N21()*l.N12()+N31()*l.N13()+N41()*l.N14());return l;}
friend std::ostream&operator<<(std::ostream&,tR4x4 const&)rK;};
std::ostream&operator<<(std::ostream&q,tR3x3 const&p)rK{q
<<"| "<<p.N11()<<" "<<p.N12()<<" "<<p.N13()<<" |\n"
<<"| "<<p.N21()<<" "<<p.N22()<<" "<<p.N23()<<" |\n"
<<"| "<<p.N31()<<" "<<p.N32()<<" "<<p.N33()<<" |\n";return q;}
std::ostream&operator<<(std::ostream&q,tR4x4 const&p)rK{q
<<"| "<<p.N11()<<" "<<p.N12()<<" "<<p.N13()<<" "<<p.N14()<<" |\n"
<<"| "<<p.N21()<<" "<<p.N22()<<" "<<p.N23()<<" "<<p.N24()<<" |\n"
<<"| "<<p.N31()<<" "<<p.N32()<<" "<<p.N33()<<" "<<p.N34()<<" |\n"
<<"| "<<p.N41()<<" "<<p.N42()<<" "<<p.N43()<<" "<<p.N44()<<" |\n";return q;}
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