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replace multiple std::sqrt by macros 

with more than 17 digits in case we have number types bigger than double
This commit is contained in:
Jane Tournois 2023-04-28 17:54:07 +02:00
parent ce738685e1
commit 2f88b29cda
2 changed files with 80 additions and 77 deletions
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152
Mesh_3/include/CGAL/Mesh_3/features_detection/features_detection.h
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@ -969,10 +969,10 @@ template<typename P>
std::vector<std::vector<P>> poly00012113(const int prec = 10)
{
return {
create_polyline((3.+ std::sqrt(5))/8, 2./3, P(0.30901699437494742,0.30901699437494742,(3. + std::sqrt(5))/8),
create_polyline((3.+ CGAL_SQRT5)/8, 2./3, P(0.30901699437494742,0.30901699437494742,(3. + CGAL_SQRT5)/8),
[](double z) { return P(-(-8*z*z + 7*z + (4*z*z - 3*z)*(-(z - 1.)*std::sqrt(16*z*z - 12*z + 1)/(2*z*(4*z - 3)) + (8*z*z - 7*z + 1)/(2*z*(4*z - 3))) - 1)/(z*(4*z - 3)), -(z - 1)*std::sqrt(16*z*z - 12*z + 1)/(2*z*(4*z - 3)) + (8*z*z - 7*z + 1)/(2*z*(4*z - 3)),z); },
prec),
create_polyline((3.+ std::sqrt(5))/8, 2./3, P(0.30901699437494742,0.30901699437494742,(3. + std::sqrt(5))/8),
create_polyline((3.+ CGAL_SQRT5)/8, 2./3, P(0.30901699437494742,0.30901699437494742,(3. + CGAL_SQRT5)/8),
[](double z) { return P( -(-8*z*z + 7*z + (4*z*z - 3*z)*((z - 1)*std::sqrt(16*z*z - 12*z + 1)/(2*z*(4*z - 3)) + (8*z*z - 7*z + 1)/(2*z*(4*z - 3))) - 1)/(z*(4*z - 3)),(z - 1)*std::sqrt(16*z*z - 12*z + 1)/(2*z*(4*z - 3)) + (8*z*z - 7*z + 1)/(2*z*(4*z - 3)),z); },
prec),
@ -1020,16 +1020,16 @@ template<typename P>
std::vector<std::vector<P>> poly00012131(const int prec = 10)
{
return {
create_polyline(0., (2. - std::sqrt(2))/2, P(0., 1./2,2./3),P((2. - std::sqrt(2))/2,1./2,1./std::sqrt(2)),
create_polyline(0., (2. - CGAL_SQRT2)/2, P(0., 1./2,2./3),P((2. - CGAL_SQRT2)/2,1./2,1./CGAL_SQRT2),
[](double x) { return P(x,1./2,(-2 + x)/(-3 + 2*x)); },
prec),
create_polyline((2. - std::sqrt(2))/2.,1./3,P((2. - std::sqrt(2))/2,1./2,1./std::sqrt(2)), P(1./3, 1./2,1.),
create_polyline((2. - CGAL_SQRT2)/2.,1./3,P((2. - CGAL_SQRT2)/2,1./2,1./CGAL_SQRT2), P(1./3, 1./2,1.),
[](double x) { return P(x,1./2,-x/(-1 + 2*x) ); },
prec),
create_polyline(1./2, 1./std::sqrt(2), P(1./3, 1.,1./2),P((2. - std::sqrt(2))/2,1./2,1./std::sqrt(2)),
create_polyline(1./2, 1./CGAL_SQRT2, P(1./3, 1.,1./2),P((2. - CGAL_SQRT2)/2,1./2,1./CGAL_SQRT2),
[](double z) { return P((z - 1)*(2*z*((z*z + z - 1)/(4*z*(z - 1)) - std::sqrt(9*z*z*z*z - 14*z*z*z + 7*z*z - 2*z + 1)/(4*z*(z - 1))) - 1)/(z*(2*z - 1)),(z*z + z - 1)/(4*z*(z - 1)) - std::sqrt(9*z*z*z*z - 14*z*z*z + 7*z*z - 2*z + 1)/(4*z*(z - 1)) ,z); },
prec),
create_polyline((2. - std::sqrt(2))/2,limit_value(1./2,-1.),P((2. - std::sqrt(2))/2,1./2,1./std::sqrt(2)), P(1./2,0. ,2./3),
create_polyline((2. - CGAL_SQRT2)/2,limit_value(1./2,-1.),P((2. - CGAL_SQRT2)/2,1./2,1./CGAL_SQRT2), P(1./2,0. ,2./3),
[](double x) { return P(x,(-1 - x + 3*x*x + std::sqrt(1 - 6*x + 19*x*x - 22*x*x*x + 9*x*x*x*x))/(4*(-1 + x)*x),(1. - 5*x + 3*x*x + std::sqrt(1 - 6*x + 19*x*x - 22*x*x*x + 9*x*x*x*x))/(2*(1 - 3*x + 2*x*x))); },
prec),
};
@ -1213,10 +1213,10 @@ return {
create_polyline(3./5,2./3, P(1./2,1./2,3./5),
[](double z) { return P(-(-7*z + 5 + (2*z - 2)*(3*z - 2)/(z - 1))/(2*(z - 1)),(3*z - 2)/(z - 1),z); },
prec),
create_polyline(1./2, 2.*std::sqrt(2)/17 + 5./17, P(1.,1./2.,1./2),
create_polyline(1./2, 2.*CGAL_SQRT2/17 + 5./17, P(1.,1./2.,1./2),
[](double z) { return P( -(2*z*((5*z - 1)/(4*z) - std::sqrt(17*z*z - 10*z + 1)/(4*z)) - 5*z + 1)/(2*z),(5*z - 1)/(4*z) - std::sqrt(17*z*z - 10*z + 1)/(4*z),z); },
prec),
create_polyline(1./2,2.* std::sqrt(2) /17 + 5./17, P(1./2,1.,1./2),
create_polyline(1./2,2.* CGAL_SQRT2 /17 + 5./17, P(1./2,1.,1./2),
[](double z) { return P( -(2*z*((5*z - 1)/(4*z) + std::sqrt(17*z*z - 10*z + 1)/(4*z)) - 5*z + 1)/(2*z),(5*z - 1)/(4*z) + std::sqrt(17*z*z - 10*z + 1)/(4*z),z); },
prec),
create_polyline(3./5,1., P(1./2.,1./2,3./5),P(1./2,1./2.,1.),
@ -2023,16 +2023,16 @@ return {
create_polyline(1./2,2./3,P(1./2,0.,2./3),P(2./3,1./2,2./3),
[](double x) { return P(x,(-1 + 2*x)/(x*(-1 + 3*x)),x/(1 - 2*x + 3*x*x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2,P(1./2,1.,1./2),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),
create_polyline(1./2,(CGAL_SQRT5-1)/2,P(1./2,1.,1./2),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,(1 - x)/x,x); },
prec),
create_polyline((std::sqrt(5)-1)/2,2./3,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),P(2./3,1./2,2./3),
create_polyline((CGAL_SQRT5-1)/2,2./3,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),P(2./3,1./2,2./3),
[](double x) { return P(x,(1 - x)/x,x); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2,P(1./2,2./3,2./3),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),
create_polyline(1./2,(CGAL_SQRT5-1)/2,P(1./2,2./3,2./3),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,1/(1+x),1/(1+x)); },
prec),
create_polyline((std::sqrt(5)-1)/2,1.,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1)/2,1.,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),P(1.,1./2,1./2),
[](double x) { return P(x,1/(1+x),1/(1+x)); },
prec),
};
@ -2070,10 +2070,10 @@ template<typename P>
std::vector<std::vector<P>> poly00012134(const int prec = 10)
{
return {
create_polyline(1-1./std::sqrt(3),1./2, P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1.),P(1./2,0.,2./3),
create_polyline(1-1./CGAL_SQRT3,1./2, P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1.),P(1./2,0.,2./3),
[](double x) { return P(x,(-1 + 2*x)/(x*(-2 + 3*x)),-x/(1 - 5*x + 3*x*x)); },
prec),
create_polyline(0.,1-1./std::sqrt(3), P(0.,1./2,2./3),P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1.),
create_polyline(0.,1-1./CGAL_SQRT3, P(0.,1./2,2./3),P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1.),
[](double x) { return P(x,1./2,(-2 + x)/(-3 + 2*x)); },
prec),
create_polyline(2./3,1., P(1./2,2./3,2./3),P(1./2,1.,1./2),
@ -2082,13 +2082,13 @@ return {
create_polyline(1./2,2./3, P(1./2,1.,1./2),P(1./2,2./3,2./3),
[](double z) { return P( -(z - 1)*(3*z - 1)/z,z/(3*z - 1),z); },
prec),
create_polyline(1-1./std::sqrt(3),1./2,P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1.),P(1./2,2./3,2./3),
create_polyline(1-1./CGAL_SQRT3,1./2,P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1.),P(1./2,2./3,2./3),
[](double x) { return P(x,(-1 - x*x + std::sqrt(1 - 6*x*x + 4*x*x*x + x*x*x*x))/(2*(-2 + x)*x),(-1 - 2*x + x*x - std::sqrt(1 - 6*x*x + 4*x*x*x + x*x*x*x))/(2*(-1 - 2*x + 2*x*x)) ); },
prec),
create_polyline(1./2,2./3, P(1./2,1./2,1.),P(1./2,2./3,2./3),
[](double y) { return P( 1./2,y,y/(-1 + 3*y)); },
prec),
create_polyline(1-1./std::sqrt(3),1./2, P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1.),P(1./2,1./2,1.),
create_polyline(1-1./CGAL_SQRT3,1./2, P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1.),P(1./2,1./2,1.),
[](double x) { return P(x ,1./2,x/(1-x)); },
prec),
};
@ -2171,25 +2171,25 @@ template<typename P>
std::vector<std::vector<P>> poly00012341(const int prec = 10)
{
return {
create_polyline(0.,1-1./std::sqrt(3), P(1./2,0.,2./3),P(1./2,1-1./std::sqrt(3),std::sqrt(3)-1),
create_polyline(0.,1-1./CGAL_SQRT3, P(1./2,0.,2./3),P(1./2,1-1./CGAL_SQRT3,CGAL_SQRT3-1),
[](double y) { return P(1./2,y,(-2 + y)/(-3 + 2*y)); },
prec),
create_polyline(0.,1-1./std::sqrt(3), P(0.,1./2,2./3),P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1),
create_polyline(0.,1-1./CGAL_SQRT3, P(0.,1./2,2./3),P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1),
[](double x) { return P(x,1./2,(-2 + x)/(-3 + 2*x)); },
prec),
create_polyline(1-1./std::sqrt(3),1./2,P(1./2,1-1./std::sqrt(3),std::sqrt(3)-1), P(1./2,1./2,1.),
create_polyline(1-1./CGAL_SQRT3,1./2,P(1./2,1-1./CGAL_SQRT3,CGAL_SQRT3-1), P(1./2,1./2,1.),
[](double y) { return P(1./2,y,-y/(-1 + y)); },
prec),
create_polyline(1-1./std::sqrt(3),1./2,P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1), P(1./2,1./2,1.),
create_polyline(1-1./CGAL_SQRT3,1./2,P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1), P(1./2,1./2,1.),
[](double x) { return P(x,1./2,-x/(-1 + x)); },
prec),
create_polyline(1-1./std::sqrt(3),1./2,P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1),P(1./2,1-1./std::sqrt(3),std::sqrt(3)-1),
create_polyline(1-1./CGAL_SQRT3,1./2,P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1),P(1./2,1-1./CGAL_SQRT3,CGAL_SQRT3-1),
[](double x) { return P(x,(-1 - 2*x + 2*x*x + std::sqrt(1 - 4*x + 12*x*x - 12*x*x*x + 4*x*x*x*x))/(2*(-2 + x)*x),(1 - 4*x + 2*x*x + std::sqrt(1 - 4*x + 12*x*x - 12*x*x*x + 4*x*x*x*x))/(2*(-1 + x)*(-1+x))); },
prec),
create_polyline(1./2,1., P(1./2,1-1./std::sqrt(3),std::sqrt(3)-1), P(1.,1./3,1./2) ,
create_polyline(1./2,1., P(1./2,1-1./CGAL_SQRT3,CGAL_SQRT3-1), P(1.,1./3,1./2) ,
[](double x) { return P(x,(1 + x - std::sqrt(1 - x + x*x))/(3*x),(x - std::sqrt(1 - x + x*x))/(-1 + x)); },
prec),
create_polyline(1./2,1.,P(1-1./std::sqrt(3),1./2,std::sqrt(3)-1),P(1./3,1.,1./2),
create_polyline(1./2,1.,P(1-1./CGAL_SQRT3,1./2,CGAL_SQRT3-1),P(1./3,1.,1./2),
[](double y) { return P((1 + y - std::sqrt(1 - y + y*y))/(3*y),y,(y - std::sqrt(1 - y + y*y))/(-1 + y)); },
prec),
};
@ -2368,16 +2368,16 @@ template<typename P>
std::vector<std::vector<P>> poly00121304(const int prec = 10)
{
return {
create_polyline(1./2,4.-2*std::sqrt(3), P(1./2,2./3,0.),P(4.-2*std::sqrt(3),(1.+1/std::sqrt(3))/2,(std::sqrt(3)-1)/2.),
create_polyline(1./2,4.-2*CGAL_SQRT3, P(1./2,2./3,0.),P(4.-2*CGAL_SQRT3,(1.+1/CGAL_SQRT3)/2,(CGAL_SQRT3-1)/2.),
[](double x) { return P(x,(2 + x - std::sqrt(4 - 8*x + x*x))/(6*x),(-2 + 5*x - x*x - std::sqrt(4 - 8*x + x*x) + x*std::sqrt(4 - 8*x + x*x))/(2*x)); },
prec),
create_polyline(1./2,4.-2*std::sqrt(3), P(1./2,1.,1./2),P(4.-2*std::sqrt(3),(1.+1/std::sqrt(3))/2,(std::sqrt(3)-1)/2.),
create_polyline(1./2,4.-2*CGAL_SQRT3, P(1./2,1.,1./2),P(4.-2*CGAL_SQRT3,(1.+1/CGAL_SQRT3)/2,(CGAL_SQRT3-1)/2.),
[](double x) { return P(x,(2 + x + std::sqrt(4 - 8*x + x*x))/(6*x),(-2 + 5*x - x*x + std::sqrt(4 - 8*x + x*x) - x*std::sqrt(4 - 8*x + x*x))/(2*x)); },
prec),
create_polyline(1./2,4.-2*std::sqrt(3), P(1./2,1./2,1.),P(4.-2*std::sqrt(3),(std::sqrt(3)-1)/2.,(1.+1/std::sqrt(3))/2),
create_polyline(1./2,4.-2*CGAL_SQRT3, P(1./2,1./2,1.),P(4.-2*CGAL_SQRT3,(CGAL_SQRT3-1)/2.,(1.+1/CGAL_SQRT3)/2),
[](double x) { return P(x,(-2 + 5*x - x*x + std::sqrt(4 - 8*x + x*x) - x*std::sqrt(4 - 8*x + x*x))/(2*x),(2 + x + std::sqrt(4 - 8*x + x*x))/(6*x)); },
prec),
create_polyline(1./2,4.-2*std::sqrt(3), P(1./2,0.,2./3),P(4.-2*std::sqrt(3),(std::sqrt(3)-1)/2.,(1.+1/std::sqrt(3))/2),
create_polyline(1./2,4.-2*CGAL_SQRT3, P(1./2,0.,2./3),P(4.-2*CGAL_SQRT3,(CGAL_SQRT3-1)/2.,(1.+1/CGAL_SQRT3)/2),
[](double x) { return P(x,(-2 + 5*x - x*x - std::sqrt(4 - 8*x + x*x) + x*std::sqrt(4 - 8*x + x*x))/(2*x),(2 + x - std::sqrt(4 - 8*x + x*x))/(6*x)); },
prec),
create_polyline(1./2,1., P(1./2,1.,1./2),P(1.,1./2,1./2),
@ -2474,16 +2474,16 @@ return {
create_polyline(1./3,1./2,P(1./3,1.,1./2),P(1./2,1./2,1.),
[](double x) { return P(x,x/(-1 + 4*x),-x/(-1 + x)); },
prec),
create_polyline(1./2,1/std::sqrt(3),P(1./2,0.,2./3),P(1/std::sqrt(3),(6-std::sqrt(3))/11,(3-std::sqrt(3))/2),
create_polyline(1./2,1/CGAL_SQRT3,P(1./2,0.,2./3),P(1/CGAL_SQRT3,(6-CGAL_SQRT3)/11,(3-CGAL_SQRT3)/2),
[](double x) { return P(x,(1 - 2*x)/(1 - 3*x + x*x),1/(1 + x)); },
prec),
create_polyline(1./std::sqrt(3),1.,P(1/std::sqrt(3),(6-std::sqrt(3))/11,(3-std::sqrt(3))/2),P(1.,1./3,1./2),
create_polyline(1./CGAL_SQRT3,1.,P(1/CGAL_SQRT3,(6-CGAL_SQRT3)/11,(3-CGAL_SQRT3)/2),P(1.,1./3,1./2),
[](double x) { return P(x,1/(2 + x),1/(1 + x)); },
prec),
create_polyline(1./2,1/std::sqrt(3),P(1./2,1./2,1.),P(1/std::sqrt(3),(6-std::sqrt(3))/11,(3-std::sqrt(3))/2),
create_polyline(1./2,1/CGAL_SQRT3,P(1./2,1./2,1.),P(1/CGAL_SQRT3,(6-CGAL_SQRT3)/11,(3-CGAL_SQRT3)/2),
[](double x) { return P(x,(-2 + 3*x)/(-3 + 4*x),(-2 + 3*x)/(-1 + x)); },
prec),
create_polyline(limit_value(0.,1),(3-std::sqrt(3))/2,P(1./2,2./3,0.),P(1/std::sqrt(3),(6-std::sqrt(3))/11,(3-std::sqrt(3))/2),
create_polyline(limit_value(0.,1),(3-CGAL_SQRT3)/2,P(1./2,2./3,0.),P(1/CGAL_SQRT3,(6-CGAL_SQRT3)/11,(3-CGAL_SQRT3)/2),
[](double z) { return P((-2*z*z + 5*z + ((3*z*z - 6*z + 2)/(2*(2*z*z - 6*z + 3)) + std::sqrt(z*z*z*z - 4*z*z*z + 12*z*z - 12*z + 4)/(2*(2*z*z - 6*z + 3)))*(2*z*z - 6*z + 3) - 2)/z,(3*z*z - 6*z + 2)/(2*(2*z*z - 6*z + 3)) + std::sqrt(z*z*z*z - 4*z*z*z + 12*z*z - 12*z + 4)/(2*(2*z*z - 6*z + 3)),z); },
prec),
};
@ -2605,10 +2605,10 @@ return {
create_polyline(1./2,1.,P(1./2,0.,2./3),P(1.,1./2,1./2),
[](double x) { return P(x,(-1 + 2*x)/(-1 + 2*x + x*x),1/(1 + x)); },
prec),
create_polyline(0.,4.-2*std::sqrt(3),P(0.,1./3,1./2),P(4.-2*std::sqrt(3),1/std::sqrt(3),(std::sqrt(3)-1)/2.),
create_polyline(0.,4.-2*CGAL_SQRT3,P(0.,1./3,1./2),P(4.-2*CGAL_SQRT3,1/CGAL_SQRT3,(CGAL_SQRT3-1)/2.),
[](double x) { return P(x,(4 - x - std::sqrt(4 - 8*x + x*x))/6,(-2 + 5*x - x*x + std::sqrt(4 - 8*x + x*x) - x*std::sqrt(4 - 8*x + x*x))/(2*x) ); },
prec),
create_polyline(1./2,4.-2*std::sqrt(3),P(1./2,2./3,0.),P(4.-2*std::sqrt(3),1/std::sqrt(3),(std::sqrt(3)-1)/2.),
create_polyline(1./2,4.-2*CGAL_SQRT3,P(1./2,2./3,0.),P(4.-2*CGAL_SQRT3,1/CGAL_SQRT3,(CGAL_SQRT3-1)/2.),
[](double x) { return P(x,(4 - x + std::sqrt(4 - 8*x + x*x))/6,(-2 + 5*x - x*x - std::sqrt(4 - 8*x + x*x) + x*std::sqrt(4 - 8*x + x*x))/(2*x) ); },
prec),
create_polyline(1./2,1.,P(1./2,1./2,1.),P(1.,1./2,1./2),
@ -2664,16 +2664,16 @@ return {
create_polyline(0.,1./3,P(0.,1./2,1./2),P(1./3,3./5,3./7),
[](double x) { return P(x,1/(2 - x),1/(2 + x)); },
prec),
create_polyline(1./3,(3.-std::sqrt(5))/2,P(1./3,3./5,3./7),P((3.-std::sqrt(5))/2,1./2,1./2),
create_polyline(1./3,(3.-CGAL_SQRT5)/2,P(1./3,3./5,3./7),P((3.-CGAL_SQRT5)/2,1./2,1./2),
[](double x) { return P(x,(-1 + 2*x)/(-1 + x + x*x),x/(1 - x + x*x)); },
prec),
create_polyline((3.-std::sqrt(5))/2,1./2,P((3.-std::sqrt(5))/2,1./2,1./2),P(1./2,0.,2./3),
create_polyline((3.-CGAL_SQRT5)/2,1./2,P((3.-CGAL_SQRT5)/2,1./2,1./2),P(1./2,0.,2./3),
[](double x) { return P(x,(-1 + 2*x)/(-1 + x + x*x),x/(1 - x + x*x)); },
prec),
create_polyline(0.,(3.-std::sqrt(5))/2,P(0.,1./2,1./2),P((3.-std::sqrt(5))/2,1./2,1./2),
create_polyline(0.,(3.-CGAL_SQRT5)/2,P(0.,1./2,1./2),P((3.-CGAL_SQRT5)/2,1./2,1./2),
[](double x) { return P(x,1./2,1./2); },
prec),
create_polyline((3.-std::sqrt(5))/2,1.,P((3.-std::sqrt(5))/2,1./2,1./2),P(1.,1./2,1./2),
create_polyline((3.-CGAL_SQRT5)/2,1.,P((3.-CGAL_SQRT5)/2,1./2,1./2),P(1.,1./2,1./2),
[](double x) { return P(x,1./2,1./2); },
prec),
};
@ -2692,22 +2692,22 @@ template<typename P>
std::vector<std::vector<P>> poly00122344(const int prec = 10)
{
return {
create_polyline(1./2,(std::sqrt(5)-1.)/2,P(1./2,1./3,1.),P((std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2,P(1./2,1./3,1.),P((CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2),
[](double x) { return P(x,x/(1 + x),(x*x)/(-1 + 2*x + x*x)); },
prec),
create_polyline((3.-std::sqrt(5))/2,1./2,P((3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2),P(1./2,1.,1./3),
create_polyline((3.-CGAL_SQRT5)/2,1./2,P((3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2),P(1./2,1.,1./3),
[](double x) { return P(x,(-1 + x)*(-1+x)/(2 - 4*x + x*x),(-1 + x)/(-2 + x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2,P(1./2,0.,2./3),P((std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2,P(1./2,0.,2./3),P((CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2),
[](double x) { return P(x,(-1 + 2*x)/(-1 + 2*x + x*x),1/(1 + x)); },
prec),
create_polyline((std::sqrt(5)-1.)/2,1.,P((std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2),P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1.)/2,1.,P((CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2),P(1.,1./2,1./2),
[](double x) { return P(x,x/(1 + x),1/(1 + x)); },
prec),
create_polyline(0.,(3.-std::sqrt(5))/2,P(0.,1./2,1./2),P((3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2),
create_polyline(0.,(3.-CGAL_SQRT5)/2,P(0.,1./2,1./2),P((3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2),
[](double x) { return P(x,1/(2 - x),(-1 + x)/(-2 + x)); },
prec),
create_polyline((3.-std::sqrt(5))/2,1./2,P((3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2),P(1./2,2./3,0.),
create_polyline((3.-CGAL_SQRT5)/2,1./2,P((3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2),P(1./2,2./3,0.),
[](double x) { return P(x,1/(2 - x),(1 - 2*x)/(2 - 4*x + x*x)); },
prec),
create_polyline(0.,1./2,P(0.,1./2,1./2),P(1./2,1./2,1./2),
@ -2716,10 +2716,10 @@ return {
create_polyline(1./2,1.,P(1./2,1./2,1./2),P(1.,1./2,1./2),
[](double x) { return P(x,1./2,1./2); },
prec),
create_polyline((3.-std::sqrt(5))/2,1./2,P((3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2),P(1./2,1./2,1./2),
create_polyline((3.-CGAL_SQRT5)/2,1./2,P((3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2),P(1./2,1./2,1./2),
[](double z) { return P(z,1-z,z); },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2,P(1./2,1./2,1./2),P((std::sqrt(5)-1.)/2,(3.-std::sqrt(5))/2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2,P(1./2,1./2,1./2),P((CGAL_SQRT5-1.)/2,(3.-CGAL_SQRT5)/2,(CGAL_SQRT5-1.)/2),
[](double z) { return P(z,1-z,z); },
prec),
};
@ -2773,25 +2773,25 @@ template<typename P>
std::vector<std::vector<P>> poly00123414(const int prec = 10)
{
return {
create_polyline((std::sqrt(5)-1)/2,2./3,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(3-std::sqrt(5))/2),P(2./3,1.,1./2),
create_polyline((CGAL_SQRT5-1)/2,2./3,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(3-CGAL_SQRT5)/2),P(2./3,1.,1./2),
[](double x) { return P(x,(1 - 2*x)/(-1 + x),(-1 + 2*x)/x); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2,P(1./2,2./3,0.),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(3-std::sqrt(5))/2),
create_polyline(1./2,(CGAL_SQRT5-1)/2,P(1./2,2./3,0.),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(3-CGAL_SQRT5)/2),
[](double x) { return P(x,1/(1 + x),(-1 + 2*x)/x); },
prec),
create_polyline((std::sqrt(5)-1)/2,1.,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(3-std::sqrt(5))/2),P(1.,1./2,1./3),
create_polyline((CGAL_SQRT5-1)/2,1.,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(3-CGAL_SQRT5)/2),P(1.,1./2,1./3),
[](double x) { return P(x,1/(1+x),1/(2+x)); },
prec),
create_polyline((3-std::sqrt(5))/2,1./2,P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(std::sqrt(5)-1)/2),P(1./2,0.,2./3),
create_polyline((3-CGAL_SQRT5)/2,1./2,P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(CGAL_SQRT5-1)/2),P(1./2,0.,2./3),
[](double x) { return P(x,(-1 + 2*x)/(-1 + x),1/(2 - x)); },
prec),
create_polyline(0.,(3-std::sqrt(5))/2,P(0.,1./3,1./2),P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(std::sqrt(5)-1)/2),
create_polyline(0.,(3-CGAL_SQRT5)/2,P(0.,1./3,1./2),P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,1/(3-x),1/(2 - x)); },
prec),
create_polyline((3-std::sqrt(5))/2,(std::sqrt(5)-1)/2,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(3-std::sqrt(5))/2),P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(std::sqrt(5)-1)/2),
create_polyline((3-CGAL_SQRT5)/2,(CGAL_SQRT5-1)/2,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(3-CGAL_SQRT5)/2),P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(CGAL_SQRT5-1)/2),
[](double z) { return P(1-z,1-z,z); },
prec),
create_polyline(1./3,(3-std::sqrt(5))/2,P(1./3,1./2,1.),P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(std::sqrt(5)-1)/2),
create_polyline(1./3,(3-CGAL_SQRT5)/2,P(1./3,1./2,1.),P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,(-1 + 2*x)/(-1 + x),(1 - 2*x)/x); },
prec),
};
@ -3134,28 +3134,28 @@ return {
create_polyline(1./2,1.,P(1./2,1./2.,1./2),P(1./2,1./2,1.),
[](double z) { return P(1./2,1./2,z); },
prec),
create_polyline((std::sqrt(5)-1)/2,1.,P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1)/2,1.,P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),P(1.,1./2,1./2),
[](double x) { return P(x,1/(1 + x),1/(1 + x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2,P(1./2.,1.,1./2),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),
create_polyline(1./2,(CGAL_SQRT5-1)/2,P(1./2.,1.,1./2),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,(1 - x)/x,x); },
prec),
create_polyline(0.,(3-std::sqrt(5))/2,P(0.,1./2,1./2),P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(3-std::sqrt(5))/2),
create_polyline(0.,(3-CGAL_SQRT5)/2,P(0.,1./2,1./2),P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2),
[](double x) { return P(x,(-1 + x)/(-2 + x),(-1 + x)/(-2 + x)); },
prec),
create_polyline((3-std::sqrt(5))/2,1./2,P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(3-std::sqrt(5))/2),P(1./2.,0.,1./2),
create_polyline((3-CGAL_SQRT5)/2,1./2,P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2),P(1./2.,0.,1./2),
[](double x) { return P(x,(-1 + 2*x)/(-1 + x),x); },
prec),
create_polyline((3-std::sqrt(5))/2,1./2,P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(3-std::sqrt(5))/2),P(1./2,1./2,1./2),
create_polyline((3-CGAL_SQRT5)/2,1./2,P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2),P(1./2,1./2,1./2),
[](double x) { return P(x,x,x); },
prec),
create_polyline<P> (1./2,(std::sqrt(5)-1)/2,P(1./2.,1./2,1./2),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),
create_polyline<P> (1./2,(CGAL_SQRT5-1)/2,P(1./2.,1./2,1./2),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,x,x); },
prec),
create_polyline((3-std::sqrt(5))/2,1./2,P((3-std::sqrt(5))/2,(3-std::sqrt(5))/2,(3-std::sqrt(5))/2),P(1./2,1./2,0.),
create_polyline((3-CGAL_SQRT5)/2,1./2,P((3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2,(3-CGAL_SQRT5)/2),P(1./2,1./2,0.),
[](double x) { return P(x,x,(-1 + 2*x)/(-1 + x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2,P(1./2.,1./2,1.),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2),
create_polyline(1./2,(CGAL_SQRT5-1)/2,P(1./2.,1./2,1.),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,x,(1 - x)/x); },
prec),
};
@ -3237,28 +3237,28 @@ return {
create_polyline(1./2,1., P(1./2,1./2,1.),P(1./2,1.,1./2),
[](double y) { return P(1./2,y,y/(-1 + 3*y) ); },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(1./2,1./2,1.),P((std::sqrt(5)-1.)/2,1./2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(1./2,1./2,1.),P((CGAL_SQRT5-1.)/2,1./2,(CGAL_SQRT5-1.)/2),
[](double x) { return P(x,1./2,(1 - x)/x) ; },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(1./2,0.,2./3),P((std::sqrt(5)-1)/2,1./2,(std::sqrt(5)-1)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(1./2,0.,2./3),P((CGAL_SQRT5-1)/2,1./2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,(1 - 2*x)/(1 - 3*x + x*x),1./(x+1)) ; },
prec),
create_polyline((std::sqrt(5)-1.)/2,1.,P((std::sqrt(5)-1.)/2,1./2,(std::sqrt(5)-1.)/2), P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1.)/2,1.,P((CGAL_SQRT5-1.)/2,1./2,(CGAL_SQRT5-1.)/2), P(1.,1./2,1./2),
[](double x) { return P(x,1./2,1./(x+1)) ; },
prec),
create_polyline((std::sqrt(5)-1.)/2,1.,P((std::sqrt(5)-1.)/2,(std::sqrt(5)-1.)/2,1./2), P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1.)/2,1.,P((CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1.)/2,1./2), P(1.,1./2,1./2),
[](double x) { return P(x,1./(x+1),1./2) ; },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(1./2,2./3,0.),P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,1./2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(1./2,2./3,0.),P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,1./2),
[](double x) { return P(x,1./(x+1),(1 - 2*x)/(1 - 3*x + x*x)) ; },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(1./2,1.,1./2),P((std::sqrt(5)-1.)/2,(std::sqrt(5)-1)/2,1./2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(1./2,1.,1./2),P((CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1)/2,1./2),
[](double x) { return P(x,(1 - x)/x,1./2) ; },
prec),
create_polyline((9-std::sqrt(17))/8.,limit_value((std::sqrt(5)-1.)/2,-1),P((9-std::sqrt(17))/8.,(std::sqrt(17)-3)/2.,(std::sqrt(17)-3)/2.), P((std::sqrt(5)-1)/2,(std::sqrt(5)-1)/2,1./2),
create_polyline((9-std::sqrt(17))/8.,limit_value((CGAL_SQRT5-1.)/2,-1),P((9-std::sqrt(17))/8.,(std::sqrt(17)-3)/2.,(std::sqrt(17)-3)/2.), P((CGAL_SQRT5-1)/2,(CGAL_SQRT5-1)/2,1./2),
[](double x) { return P(x,-std::sqrt(-x*(4*x*x - 9*x + 4))/(2*(x*x - x - 1)) + (x - 2)/(2*(x*x - x - 1)),-(-x + (-std::sqrt(-x*(4*x*x - 9*x + 4))/(2*(x*x - x - 1)) + (x - 2)/(2*(x*x - x - 1)))*(x*x - x - 1) + 2)/(x*x - x - 1)) ; },
prec),
create_polyline((9-std::sqrt(17))/8.,limit_value((std::sqrt(5)-1.)/2,-1),P((9-std::sqrt(17))/8.,(std::sqrt(17)-3)/2.,(std::sqrt(17)-3)/2.), P((std::sqrt(5)-1)/2,1./2,(std::sqrt(5)-1)/2),
create_polyline((9-std::sqrt(17))/8.,limit_value((CGAL_SQRT5-1.)/2,-1),P((9-std::sqrt(17))/8.,(std::sqrt(17)-3)/2.,(std::sqrt(17)-3)/2.), P((CGAL_SQRT5-1)/2,1./2,(CGAL_SQRT5-1)/2),
[](double x) { return P(x,std::sqrt(-x*(4*x*x - 9*x + 4))/(2*(x*x - x - 1)) + (x - 2)/(2*(x*x - x - 1)),-(-x + (std::sqrt(-x*(4*x*x - 9*x + 4))/(2*(x*x - x - 1)) + (x - 2)/(2*(x*x - x - 1)))*(x*x - x - 1) + 2)/(x*x - x - 1)) ; },
prec),
};
@ -3338,13 +3338,13 @@ return {
create_polyline(0.,1./2, P(0.,1./3,1./2),P(1./2,2./5,2./3),
[](double x) { return P(x,1./(3-x),1./(2-x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1)/2., P(1./2,2./5,2./3),P((std::sqrt(5)-1)/2.,1./2,(std::sqrt(5)-1)/2.),
create_polyline(1./2,(CGAL_SQRT5-1)/2., P(1./2,2./5,2./3),P((CGAL_SQRT5-1)/2.,1./2,(CGAL_SQRT5-1)/2.),
[](double x) { return P(x,-x/(-1 - x + x*x),1./(x+1)); },
prec),
create_polyline((std::sqrt(5)-1)/2.,1., P((std::sqrt(5)-1)/2.,1./2,(std::sqrt(5)-1)/2.),P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1)/2.,1., P((CGAL_SQRT5-1)/2.,1./2,(CGAL_SQRT5-1)/2.),P(1.,1./2,1./2),
[](double x) { return P(x,1./2,1./(x+1)); },
prec),
create_polyline((std::sqrt(5)-1)/2.,2./3, P((std::sqrt(5)-1)/2.,1./2,(std::sqrt(5)-1)/2.),P(2./3,3./5,1./2),
create_polyline((CGAL_SQRT5-1)/2.,2./3, P((CGAL_SQRT5-1)/2.,1./2,(CGAL_SQRT5-1)/2.),P(2./3,3./5,1./2),
[](double x) { return P(x,(1 - 2*x)/(1. - 3*x + x*x),(1. - x)/x); },
prec),
create_polyline(2./3,1., P(2./3,3./5,1./2),P(1.,1./2,1./2),
@ -3356,7 +3356,7 @@ return {
create_polyline(3./5,1., P(2./3,3./5,1./2),P(2./3,1.,1./2),
[](double y) { return P(2./3,y,1./2); },
prec),
create_polyline(1./2.,(std::sqrt(5)-1)/2., P(1./2,1./2,1.), P((std::sqrt(5)-1)/2.,1./2,(std::sqrt(5)-1)/2.),
create_polyline(1./2.,(CGAL_SQRT5-1)/2., P(1./2,1./2,1.), P((CGAL_SQRT5-1)/2.,1./2,(CGAL_SQRT5-1)/2.),
[](double x) { return P(x,1./2,(1. - x)/x); },
prec),
create_polyline(2./5,1./2, P(1./2,2./5,2./3),P(1./2,1./2,1.),
@ -3534,19 +3534,19 @@ return {
create_polyline(0.,1./2, P(0.,1./2,1./2),P(1./2,1./2,1.),
[](double x) { return P(x,1./2,(-1 + x)/(-2 + 3*x)); },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(1./2,1./2,1.),P(1./2,(std::sqrt(5)-1.)/2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(1./2,1./2,1.),P(1./2,(CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1.)/2),
[](double y) { return P(1./2,y,(1 - y)/y); },
prec),
create_polyline(1./2,(std::sqrt(5)-1.)/2, P(0.,1./2,1./2),P(1./2,(std::sqrt(5)-1.)/2,(std::sqrt(5)-1.)/2),
create_polyline(1./2,(CGAL_SQRT5-1.)/2, P(0.,1./2,1./2),P(1./2,(CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1.)/2),
[](double z) { return P((2*z*z - 3*z + 1)/(5*z*z - 5*z + 1),(-z*z + 2*z - 1)/(2*z*z - 1),z); },
prec),
create_polyline((std::sqrt(5)-1.)/2,1.,P(1./2,(std::sqrt(5)-1.)/2,(std::sqrt(5)-1.)/2), P(1.,1./2,1./2),
create_polyline((CGAL_SQRT5-1.)/2,1.,P(1./2,(CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1.)/2), P(1.,1./2,1./2),
[](double x) { return P(x,(-2 + 5*x - std::sqrt(4 - 8*x + 5*x*x))/(2*(-3 + 5*x)),(-2 + 4*x - x*x + x*std::sqrt(4 - 8*x + 5*x*x))/(2*(-1 + 2*x + x*x)) ); },
prec),
create_polyline(1./2,1., P(1./2,1.,1./2),P(1.,1./2,1./2),
[](double x) { return P(x,x/(-1 + 3*x),1./2); },
prec),
create_polyline((std::sqrt(5)-1.)/2,1., P(1./2,(std::sqrt(5)-1.)/2,(std::sqrt(5)-1.)/2),P(1./2,1.,1./2),
create_polyline((CGAL_SQRT5-1.)/2,1., P(1./2,(CGAL_SQRT5-1.)/2,(CGAL_SQRT5-1.)/2),P(1./2,1.,1./2),
[](double y) { return P(1./2,y,1./(y+1)); },
prec),
};

5
Number_types/include/CGAL/number_type_config.h
View File

@ -19,7 +19,10 @@
#include <CGAL/config.h>
#define CGAL_PI 3.14159265358979323846
#define CGAL_PI 3.141592653589793238462643383279502884
#define CGAL_SQRT2 1.414213562373095048801688724209698078
#define CGAL_SQRT3 1.732050807568877293527446341505872366
#define CGAL_SQRT5 2.236067977499789696409173668731276235
#ifdef CGAL_USE_NTS_NAMESPACE