我正在使用CGAL来计算两个凸多边形的交点区域。用于执行此操作的简短演示代码已发布在this问题的已接受答案中。但是，当我修改该代码以使用我感兴趣的多边形时，CGAL会在CGAL :: intersection（）例程中从深处抛出一个运行时异常。
这是一个简短的示例代码，它是从上面链接的SO问题中复制粘贴的，除了它使用我自己的多边形，它打印一些关于每个多边形的诊断，以显示它们是凸的并使用CCW绕组顺序。
#include <iostream>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/Polygon_with_holes_2.h>
#include <CGAL/Boolean_set_operations_2.h>
#include <CGAL/Polygon_2_algorithms.h>
typedef CGAL::Simple_cartesian<double> K;
typedef K::Point_2 Point;
typedef CGAL::Polygon_2<K> Polygon_2;
typedef CGAL::Polygon_with_holes_2<K> Polygon_with_holes_2;
using std::cout; using std::endl;
int main(){
bool IsSimple, IsConvex, IsClockwise;
double Area;
// Define the polygons. P is long and skinny, Q is 20 equally
// spaced points around a circle of radius 0.025. The top-right
// corner of P protudes into Q.
int np=7;
int nq=20;
Point points[]={
Point( 2.67905949256324049657e-02,-2.36307305336680428809e-02),
Point( 2.19804738309115066386e-02, 1.25954939609798088895e-02),
Point( 3.24142504626934169210e-03, 8.27109808759729503436e-03),
Point(-7.07297020897392769712e-02,-1.31780902623212625713e-01),
Point(-1.72945875771868884385e+00,-4.33625989924519217311e+00),
Point(-5.64696462817379796206e+00,-2.91346747524371210147e+01),
Point(-5.66016394049875870564e+00,-4.95259849820236013329e+01)};
Point points2[]={
Point( 2.50000000000000013878e-02, 0.00000000000000000000e+00),
Point( 2.37764129073788424429e-02, 7.72542485937368662852e-03),
Point( 2.02254248593736890571e-02, 1.46946313073118266929e-02),
Point( 1.46946313073118284276e-02, 2.02254248593736890571e-02),
Point( 7.72542485937368836324e-03, 2.37764129073788424429e-02),
Point( 1.53080849893419158600e-18, 2.49999999999999979183e-02),
Point(-7.72542485937368489379e-03, 2.37764129073788424429e-02),
Point(-1.46946313073118232234e-02, 2.02254248593736890571e-02),
Point(-2.02254248593736890571e-02, 1.46946313073118284276e-02),
Point(-2.37764129073788424429e-02, 7.72542485937368923060e-03),
Point(-2.50000000000000013878e-02, 3.06161699786838317201e-18),
Point(-2.37764129073788424429e-02,-7.72542485937368402643e-03),
Point(-2.02254248593736925266e-02,-1.46946313073118232234e-02),
Point(-1.46946313073118318970e-02,-2.02254248593736890571e-02),
Point(-7.72542485937369096533e-03,-2.37764129073788389734e-02),
Point(-4.59242549680257437283e-18,-2.50000000000000013878e-02),
Point( 7.72542485937368229171e-03,-2.37764129073788424429e-02),
Point( 1.46946313073118214887e-02,-2.02254248593736925266e-02),
Point( 2.02254248593736855877e-02,-1.46946313073118318970e-02),
Point( 2.37764129073788389734e-02,-7.72542485937369183269e-03)};
Polygon_2 polyP(points, points+np);
Polygon_2 polyQ(points2, points2+nq);
// Print some properties of polygon P. It is simple, convex, and CCW
// oriented
CGAL::set_pretty_mode(cout);
cout << "created the polygon P:" << endl;
cout << polyP << endl;
cout << endl;
IsSimple = polyP.is_simple();
IsConvex = polyP.is_convex();
IsClockwise = (polyP.orientation() == CGAL::CLOCKWISE);
Area = polyP.area();
cout << "polygon P is";
if (!IsSimple) cout << " not";
cout << " simple." << endl;
cout << "polygon P is";
if (!IsConvex) cout << " not";
cout << " convex." << endl;
cout << "polygon P is";
if (!IsClockwise) cout << " not";
cout << " clockwise oriented." << endl;
cout << "the area of polygon P is " << Area << endl;
cout << endl;
// Print some properties of polygon Q. It is simple, convex, and CCW
// oriented
cout << "created the polygon Q:" << endl;
cout << polyQ << endl;
cout << endl;
IsSimple = polyQ.is_simple();
IsConvex = polyQ.is_convex();
IsClockwise = (polyQ.orientation() == CGAL::CLOCKWISE);
Area = polyQ.area();
cout << "polygon Q is";
if (!IsSimple) cout << " not";
cout << " simple." << endl;
cout << "polygon Q is";
if (!IsConvex) cout << " not";
cout << " convex." << endl;
cout << "polygon Q is";
if (!IsClockwise) cout << " not";
cout << " clockwise oriented." << endl;
cout << "the area of polygon Q is " << Area << endl;
cout << endl;
// Compute the intersection
std::list<Polygon_with_holes_2> polyI;
CGAL::intersection(polyP, polyQ, std::back_inserter(polyI));
double totalArea = 0;
typedef std::list<Polygon_with_holes_2>::iterator LIT;
for(LIT lit = polyI.begin(); lit!=polyI.end(); lit++){
totalArea+=lit->outer_boundary().area();
}
cout << "TotalArea::" << totalArea;
return 0;
}
以下是测试程序的输出。
created the polygon P:
Polygon_2(
PointC2(0.0267906, -0.0236307)
PointC2(0.0219805, 0.0125955)
PointC2(0.00324143, 0.0082711)
PointC2(-0.0707297, -0.131781)
PointC2(-1.72946, -4.33626)
PointC2(-5.64696, -29.1347)
PointC2(-5.66016, -49.526)
)
polygon P is simple.
polygon P is convex.
polygon P is not clockwise oriented.
the area of polygon P is 71.1027
created the polygon Q:
Polygon_2(
PointC2(0.025, 0)
PointC2(0.0237764, 0.00772542)
PointC2(0.0202254, 0.0146946)
PointC2(0.0146946, 0.0202254)
PointC2(0.00772542, 0.0237764)
PointC2(1.53081e-18, 0.025)
PointC2(-0.00772542, 0.0237764)
PointC2(-0.0146946, 0.0202254)
PointC2(-0.0202254, 0.0146946)
PointC2(-0.0237764, 0.00772542)
PointC2(-0.025, 3.06162e-18)
PointC2(-0.0237764, -0.00772542)
PointC2(-0.0202254, -0.0146946)
PointC2(-0.0146946, -0.0202254)
PointC2(-0.00772542, -0.0237764)
PointC2(-4.59243e-18, -0.025)
PointC2(0.00772542, -0.0237764)
PointC2(0.0146946, -0.0202254)
PointC2(0.0202254, -0.0146946)
PointC2(0.0237764, -0.00772542)
)
polygon Q is simple.
polygon Q is convex.
polygon Q is not clockwise oriented.
the area of polygon Q is 0.00193136
terminate called after throwing an instance of 'CGAL::Precondition_exception'
what(): CGAL ERROR: precondition violation!
Expr: (m_traits.compare_y_at_x_2_object()(p, cv) == EQUAL) && compare_xy(cv.left(), p) == SMALLER && compare_xy(cv.right(), p) == LARGER
File: /usr/local/include/CGAL/Arr_segment_traits_2.h
Line: 706
Aborted (core dumped)
我不明白导致错误的原因。任何帮助将不胜感激。
答案 0 :(得分：1)
我可以重现这个错误（使用clang ++在MacOS上使用CGAL 4.9）。据我所知，这种类型的未被捕获的异常不应该发生，换句话说，你已经发现了CGAL中的一个错误。因此，请按照错误消息中的说明提交错误报告 - 您没有发布的部分（或者因为版本不同而可能没有发布？）：
说明：请参阅http://www.cgal.org/bug_report.html
上的错误报告说明libc ++ abi.dylib：以CGAL :: Precondition_exception类型的未捕获异常终止：CGAL错误：违反前提条件！
Expr :( m_traits.compare_y_at_x_2_object（）（p，cv）== EQUAL）＆amp;＆amp; compare_xy（cv.left（），p）== SMALLER＆amp;＆amp; compare_xy（cv.right（），p）== LARGER
文件：/usr/local/include/CGAL/Arr_segment_traits_2.h行：706
就我从该文件中看到的那样，函数throw将曲线分成两个子曲线给定一个分裂点。前提条件是分裂点位于曲线上而不是终点。显然，是否满足这一先决条件是调用者的问题，另一个CGAL例程。换句话说，您的输入没有任何问题。 CGAL实现有什么不对，或者更确切地说，是处理所用数字表示不精确的方法。
编辑以下sloriot的评论。
如果我更换
typedef CGAL::Simple_cartesian<double> K;
与
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
并使用Area和totalArea的相应类型（我只分别使用auto和decltype(Area)），代码编译（您必须将其与{{{ 1}}和libgmp）并且无崩溃地运行，报告
libmpfr