CGAL Precondition_exception with Polygon intersection and inexact constructions kernel - c++

Question

I'm using CGAL and got into some weird bug, which I can't reproduce in a small test program. Here is the test code that works as given, but when I have the exact same code in my larger program (a ROS node) it spits an error:
#include <vector>
#include <boost/shared_ptr.hpp>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Polygon_with_holes_2.h>
#include <CGAL/Boolean_set_operations_2.h>
#include "print.h"
typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::FT Ft;
typedef Kernel::Point_2 Point;
typedef Kernel::Segment_2 Segment;
typedef Kernel::Direction_2 Direction;
typedef Kernel::Line_2 Line;
typedef Kernel::Vector_2 Vector;
typedef CGAL::Polygon_2<Kernel> Polygon;
typedef CGAL::Polygon_with_holes_2<Kernel> PolygonWithHoles;
main() {
Polygon poly;
float scale = 4.0/100;
float max_y = 500*scale;
poly.push_back(Point(76*scale, max_y-496*scale));
poly.push_back(Point(660*scale, max_y-496*scale));
poly.push_back(Point(660*scale, max_y-48*scale));
poly.push_back(Point(71*scale, max_y-54*scale));
// Holes must be clock wise!!
Polygon holes[10];
holes[0].push_back(Point(131*scale, max_y-86*scale));
holes[0].push_back(Point(179*scale, max_y-85*scale));
holes[0].push_back(Point(180*scale, max_y-238*scale));
holes[0].push_back(Point(133*scale, max_y-239*scale));
holes[1].push_back(Point(237*scale, max_y-84*scale));
holes[1].push_back(Point(286*scale, max_y-84*scale));
holes[1].push_back(Point(288*scale, max_y-237*scale));
holes[1].push_back(Point(240*scale, max_y-238*scale));
// Why does this hole make intersection() error?
holes[2].push_back(Point(345*scale, max_y-84*scale));
holes[2].push_back(Point(393*scale, max_y-83*scale));
holes[2].push_back(Point(396*scale, max_y-236*scale));
holes[2].push_back(Point(348*scale, max_y-236*scale));
PolygonWithHoles polyHoles(poly);
polyHoles.outer_boundary() = poly;
for (int i=0; i<3; ++i)
polyHoles.add_hole(holes[i]);
std::cout << "\nPolygon:" << std::endl;
print_polygon_with_holes(polyHoles);
Polygon selection;
float minx = -5.7669;
float miny = -2.13124;
float maxx = 0.396996;
float maxy = 4.88933;
selection.push_back(Point(minx, miny));
selection.push_back(Point(maxx, miny));
selection.push_back(Point(maxx, maxy));
selection.push_back(Point(minx, maxy));
std::cout << "\nSelection:" << std::endl;
print_polygon(selection);
std::vector<PolygonWithHoles> result;
CGAL::intersection(polyHoles, selection, std::back_inserter(result));
std::cout << "Intersection:" << std::endl;
if (!result.empty())
print_polygon_with_holes(result.front());
}
The error:
terminate called after throwing an instance of 'CGAL::Precondition_exception'
what(): CGAL ERROR: precondition violation!
Expr: comp_f(object, parentP->object) != SMALLER
File: /usr/include/CGAL/Multiset.h
Line: 2128
I found 2 ways to fix this:
Shift one point a little bit: replace 83 with 84.
Use Exact_predicates_exact_constructions_kernel
My question is: what could cause the problem to exist only in the larger program?
I'd like to keep using the unexact_constructions, I don't see why I'd have to use the exact_constructions in this case (points aren't close to each other or anything), but since I don't know what the intersection() algorithm does I might be wrong about that.

Answer 1

The intersect function constructs new points - new points of intersections. If you are not using exact constructions, then these new points are not promised to be correct. If you then use these inexact points for further computations you'll run into problems. Unless you have significant constraints on the running time, I believe you're better of with exact constructions.
Example: Consider the unit circle x^2+y^2=1 and the line y=x and let p be a constructed point of intersection. Then circle.has_on_boundary (p) will return TRUE only if you use the exact constructions.