songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

Improving the Critical Points of a Circle Equation (returning a Root_for_spheres_2_3)

This commit is contained in:
Pedro Machado Manhaes de Castro 2006-08-09 08:54:33 +00:00
parent 320ad142ca
commit 4c2a391c50
1 changed files with 129 additions and 21 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

150
Algebraic_kernel_for_spheres/include/CGAL/Algebraic_kernel_for_spheres/internal_functions_on_roots_and_polynomials_2_3.h
View File

@ -149,9 +149,8 @@ namespace CGAL {
return res;
}
// ONLY the x is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
typename AK::Root_for_spheres_2_3
x_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
@ -168,15 +167,22 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.b()) && is_zero(p.c())));
const FT sqbc = CGAL::square(p.b()) + CGAL::square(p.c());
const FT sq_sum = sqbc + CGAL::square(p.a());
const FT delta = (sqbc * s.r_sq())/sq_sum;
return make_root_of_2(s.a(),i?-1:1,delta);
const FT cy = (p.a()*p.b())/sqbc;
const FT cz = (p.a()*p.c())/sqbc;
const Root_of_2 x = make_root_of_2(s.a(),i?-1:1,delta);
const Root_of_2 y = make_root_of_2(s.b(),i?(cy):(-cy),delta);
const Root_of_2 z = make_root_of_2(s.c(),i?(cz):(-cz),delta);
return Root_for_spheres_2_3(x,y,z);
}
// ONLY the x is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
x_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
@ -196,19 +202,29 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.b()) && is_zero(p.c())));
const FT sqbc = CGAL::square(p.b()) + CGAL::square(p.c());
const FT sq_sum = sqbc + CGAL::square(p.a());
const FT delta = (sqbc * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.a(),-1,delta);
*res++ = make_root_of_2(s.a(),1,delta);
const FT cy = (p.a()*p.b())/sqbc;
const FT cz = (p.a()*p.c())/sqbc;
const Root_of_2 x1 = make_root_of_2(s.a(),-1,delta);
const Root_of_2 y1 = make_root_of_2(s.b(),cy,delta);
const Root_of_2 z1 = make_root_of_2(s.c(),cz,delta);
const Root_of_2 x2 = make_root_of_2(s.a(),1,delta);
const Root_of_2 y2 = make_root_of_2(s.b(),-cy,delta);
const Root_of_2 z2 = make_root_of_2(s.c(),-cz,delta);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x2,y2,z2);
return res;
}
// ONLY the y is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
typename AK::Root_for_spheres_2_3
y_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
@ -225,15 +241,28 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.a()) && is_zero(p.c())));
const FT sqac = CGAL::square(p.a()) + CGAL::square(p.c());
const FT sq_sum = sqac + CGAL::square(p.b());
const FT delta = (sqac * s.r_sq())/sq_sum;
return make_root_of_2(s.b(),i?-1:1,delta);
const FT cx = (p.a()*p.b())/sqac;
const FT cz = (p.c()*p.b())/sqac;
if(!is_positive(cx)) {
const Root_of_2 x = make_root_of_2(s.a(),i?(cx):(-cx),delta);
const Root_of_2 y = make_root_of_2(s.b(),i?-1:1,delta);
const Root_of_2 z = make_root_of_2(s.c(),i?(cz):(-cz),delta);
return Root_for_spheres_2_3(x,y,z);
} else {
const Root_of_2 x = make_root_of_2(s.a(),i?(-cx):(cx),delta);
const Root_of_2 y = make_root_of_2(s.b(),i?1:-1,delta);
const Root_of_2 z = make_root_of_2(s.c(),i?(-cz):(cz),delta);
return Root_for_spheres_2_3(x,y,z);
}
}
// ONLY the y is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
y_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
@ -253,19 +282,34 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.a()) && is_zero(p.c())));
const FT sqac = CGAL::square(p.a()) + CGAL::square(p.c());
const FT sq_sum = sqac + CGAL::square(p.b());
const FT delta = (sqac * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.b(),-1,delta);
*res++ = make_root_of_2(s.b(),1,delta);
const FT cx = (p.a()*p.b())/sqac;
const FT cz = (p.c()*p.b())/sqac;
const Root_of_2 x1 = make_root_of_2(s.a(),cx,delta);
const Root_of_2 y1 = make_root_of_2(s.b(),-1,delta);
const Root_of_2 z1 = make_root_of_2(s.c(),cz,delta);
const Root_of_2 x2 = make_root_of_2(s.a(),-cx,delta);
const Root_of_2 y2 = make_root_of_2(s.b(),1,delta);
const Root_of_2 z2 = make_root_of_2(s.c(),-cz,delta);
if(!is_positive(cx)) {
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x2,y2,z2);
} else {
*res++ = Root_for_spheres_2_3(x2,y2,z2);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
}
return res;
}
// ONLY the z is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK>
typename AK::Root_of_2
typename AK::Root_for_spheres_2_3
z_critical_point( const std::pair<typename AK::Polynomial_for_spheres_2_3,
typename AK::Polynomial_1_3 > &c, bool i)
{
@ -282,15 +326,40 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.a()) && is_zero(p.b())));
const FT sqab = CGAL::square(p.a()) + CGAL::square(p.b());
const FT sq_sum = sqab + CGAL::square(p.c());
const FT delta = (sqab * s.r_sq())/sq_sum;
return make_root_of_2(s.c(),i?-1:1,delta);
const FT cx = (p.a()*p.c())/sqab;
const FT cy = (p.c()*p.b())/sqab;
if(is_negative(cx)) {
const Root_of_2 x = make_root_of_2(s.a(),i?(cx):(-cx),delta);
const Root_of_2 y = make_root_of_2(s.b(),i?(cy):(-cy),delta);
const Root_of_2 z = make_root_of_2(s.c(),i?-1:1,delta);
return Root_for_spheres_2_3(x,y,z);
} else if(is_zero(cx)) {
if(!is_positive(cy)) {
const Root_of_2 x = s.a();
const Root_of_2 y = make_root_of_2(s.b(),i?(cy):(-cy),delta);
const Root_of_2 z = make_root_of_2(s.c(),i?-1:1,delta);
return Root_for_spheres_2_3(x,y,z);
} else {
const Root_of_2 x = s.a();
const Root_of_2 y = make_root_of_2(s.b(),i?(-cy):(cy),delta);
const Root_of_2 z = make_root_of_2(s.c(),i?1:-1,delta);
return Root_for_spheres_2_3(x,y,z);
}
} else {
const Root_of_2 x = make_root_of_2(s.a(),i?(-cx):(cx),delta);
const Root_of_2 y = make_root_of_2(s.b(),i?(-cy):(cy),delta);
const Root_of_2 z = make_root_of_2(s.c(),i?1:-1,delta);
return Root_for_spheres_2_3(x,y,z);
}
}
// ONLY the z is given (Root_of_2), because the other coordinates may be Root_of_4
template <class AK, class OutputIterator>
OutputIterator
z_critical_points( const std::pair<typename AK::Polynomial_for_spheres_2_3,
@ -310,13 +379,52 @@ namespace CGAL {
CGAL_kernel_precondition((intersect<AK>(p,s)));
CGAL_kernel_precondition(sign(p.a() * s.a() + p.b() * s.b() +
p.c() * s.c() + p.d()) == ZERO);
CGAL_kernel_precondition(!(is_zero(p.a()) && is_zero(p.b())));
const FT sqab = CGAL::square(p.a()) + CGAL::square(p.b());
const FT sq_sum = sqab + CGAL::square(p.c());
const FT delta = (sqab * s.r_sq())/sq_sum;
*res++ = make_root_of_2(s.c(),-1,delta);
*res++ = make_root_of_2(s.c(),1,delta);
const FT cx = (p.a()*p.c())/sqab;
const FT cy = (p.c()*p.b())/sqab;
if(is_negative(cx)) {
const Root_of_2 x1 = make_root_of_2(s.a(),(cx),delta);
const Root_of_2 y1 = make_root_of_2(s.b(),(cy),delta);
const Root_of_2 z1 = make_root_of_2(s.c(),-1,delta);
const Root_of_2 x2 = make_root_of_2(s.a(),(-cx),delta);
const Root_of_2 y2 = make_root_of_2(s.b(),(-cy),delta);
const Root_of_2 z2 = make_root_of_2(s.c(),1,delta);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x2,y2,z2);
} else if(is_zero(cx)) {
if(!is_positive(cy)) {
const Root_of_2 x1 = s.a();
const Root_of_2 y1 = make_root_of_2(s.b(),(cy),delta);
const Root_of_2 z1 = make_root_of_2(s.c(),-1,delta);
const Root_of_2 y2 = make_root_of_2(s.b(),(-cy),delta);
const Root_of_2 z2 = make_root_of_2(s.c(),1,delta);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x1,y2,z2);
} else {
const Root_of_2 x1 = s.a();
const Root_of_2 y1 = make_root_of_2(s.b(),(-cy),delta);
const Root_of_2 z1 = make_root_of_2(s.c(),1,delta);
const Root_of_2 y2 = make_root_of_2(s.b(),(cy),delta);
const Root_of_2 z2 = make_root_of_2(s.c(),-1,delta);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x1,y2,z2);
}
} else {
const Root_of_2 x1 = make_root_of_2(s.a(),(-cx),delta);
const Root_of_2 y1 = make_root_of_2(s.b(),(-cy),delta);
const Root_of_2 z1 = make_root_of_2(s.c(),1,delta);
const Root_of_2 x2 = make_root_of_2(s.a(),(cx),delta);
const Root_of_2 y2 = make_root_of_2(s.b(),(cy),delta);
const Root_of_2 z2 = make_root_of_2(s.c(),-1,delta);
*res++ = Root_for_spheres_2_3(x1,y1,z1);
*res++ = Root_for_spheres_2_3(x2,y2,z2);
}
return res;
}