CGAL users discussion list

[Pedro Machado Manhães de Castro <>]

Hi Zengming,

Those are the "ugly" output of the root_of_2 function, you probably would prefer to output like that:

#include <CGAL/Exact_spherical_kernel_3.h>
#include <CGAL/Spherical_kernel_intersections.h>
#include <CGAL/Circular_arc_point_3.h>
 
typedef CGAL::Exact_spherical_kernel_3         Spherical_k;
typedef CGAL::Point_3<Spherical_k>             Point_3;
typedef CGAL::Sphere_3<Spherical_k>            Sphere_3;
typedef std::pair< CGAL::Circular_arc_point_3<Spherical_k>, unsigned> Point_pair;
 
int main() {
 
 Sphere_3 s1 = Sphere_3(Point_3(1.0,0.0,0.0), 1.0);
 Sphere_3 s2 = Sphere_3(Point_3(0.0,1.0,0.0), 1.0);
 Sphere_3 s3 = Sphere_3(Point_3(0.0,0.0,1.0), 1.0);
 
 std::vector< CGAL::Object > intersecs;
 CGAL::intersection(s1, s2, s3, std::back_inserter(intersecs));
 std::cout<<intersecs.size()<<std::endl;
 
 const Point_pair *p[2];
 for(int i=0; i<intersecs.size(); ++i)
 {
  if( p[i] = CGAL::object_cast<Point_pair>(&intersecs[i]) )
  {
   std::cout<<p[i]->second<<std::endl;
   //std::cout<<(p[i]->first).x()<<" "<<(p[i]->first).y()<<" "<<(p[i]->first).z()<<" "<<std::endl;
     double x = CGAL_NTS to_double((p[i]->first).x());
     double y = CGAL_NTS to_double((p[i]->first).y());
     double z = CGAL_NTS to_double((p[i]->first).z());
   std::cout << x << " " << y << " " << z << std::endl;
  }  
 }
 
  return 0;
}

However when you convert to double you lose the accuracy, be aware of that.

Best regards,
Pedro

On Fri, Mar 6, 2009 at 2:00 PM, zengming <> wrote:

Hi, Pedro

I rewrite the program, but can not get the right answer.

This is the program:

 

==============================================

 

#include <CGAL/Exact_spherical_kernel_3.h>

#include <CGAL/Spherical_kernel_intersections.h>
#include <CGAL/Circular_arc_point_3.h>

 

typedef CGAL::Exact_spherical_kernel_3         Spherical_k;
typedef CGAL::Point_3<Spherical_k>             Point_3;
typedef CGAL::Sphere_3<Spherical_k>            Sphere_3;

typedef std::pair< CGAL::Circular_arc_point_3<Spherical_k>, unsigned> Point_pair;

 

int main() {

 

 Sphere_3 s1 = Sphere_3(Point_3(1.0,0.0,0.0), 1.0);
 Sphere_3 s2 = Sphere_3(Point_3(0.0,1.0,0.0), 1.0);
 Sphere_3 s3 = Sphere_3(Point_3(0.0,0.0,1.0), 1.0);

 

 std::vector< CGAL::Object > intersecs;
 CGAL::intersection(s1, s2, s3, std::back_inserter(intersecs));
 std::cout<<intersecs.size()<<std::endl;
 

 const Point_pair *p[2];
 for(int i=0; i<intersecs.size(); ++i)
 {
  if( p[i] = CGAL::object_cast<Point_pair>(&intersecs[i]) )
  {
   std::cout<<p[i]->second<<std::endl;
   std::cout<<(p[i]->first).x()<<" "<<(p[i]->first).y()<<" "<<(p[i]->first).z()<<" "<<std::endl;
  }  
 }

 

  return 0;
}

===============================================

and follow is the output:

 

2
1
0256/768 -4/1 0.1875/27 01024/3072 -4/1 0.1875/27 01024/3072 -4/1 0.1875/27
1
0256/768 4/1 0.1875/27 01024/3072 4/1 0.1875/27 01024/3072 4/1 0.1875/27

Press any key to continue . . .

 

===============================================

In my case, 3 spheres are [center=(1.0, 0.0, 0.0), radius=1.0], [center=(0.0, 1.0, 0.0), radius=1.0],

[center=(0.0, 0.0, 1.0), radius=1.0], I figured out that they intersect in points (0, 0, 0) and (0.67, 0.67, 0.67).

In order to get the result, how should I write the program, and if I want to get the results in type double, how should i do?

 

2009-03-06

---

zengming

---

发件人： Pedro_Machado_Manh�es_de_Castro

发送时间： 2009-03-06  16:51:34

收件人：

抄送：

主题： Re: Re: [cgal-discuss] how to output a point's coordinate

Hi!

I think that what you probably want is a Circular_arc_point_3.
Since this line:
assign(pt3, intersecs[0]);
should not work as the type of pt3 is a Point_3 and the type of intersecs[0] is Circular_arc_point_3, your pt3 may keep to be uninitialized.

"Should not work" in this case means "assign(pt3, intersecs[0]);" will return 0, but wont assign anithing to pt3.

As your intersection (considering r = 1) is probably (0, 0, 0), that would "work" (because the value of an uninitialized pt3 would be (0,0,0) ).

The main difference between Point_3 and Circular_arc_point_3 is that Point_3 stores rationals as coordinates while Circular_arc_point_3 stores algebraic numbers of degree 2 (Root_of_2).
This happens because the intersection between 3 rational spheres (or 2 rational circles) may not be representable by rationals, however they are representable by Root_of_2.
By rational spheres (circles) I mean spheres with a rational center (placed on rational coordinates) and with rational squared radius.

So look at what Tom said and prefer using Circular_arc_point_3 instead of Point_3, because only the first one really works.

Pedro

PS: don't overlook the case where the intersection of three spheres can be a Circle_3 or even a Sphere_3.

On Fri, Mar 6, 2009 at 9:22 AM, zengming <> wrote:

 I saw the result by your method, thanks!

 

 

2009-03-06

---

zengming

---

发件人： Samuel Hornus

发送时间： 2009-03-06  16:13:53

收件人：

抄送：

主题： Re: [cgal-discuss] how to output a point's coordinate

"zengming"  < > wrote:

>  Point_3 pt3;

>  assign(pt3, intersecs[0]); 

> 

> //how can I output the coordinate of point pt3? 

 

The following should work:

 

std::cout  < < pt3;

 

-- 

sam

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