在使用CGAL::Exact_predicates_inexact_constructions_kernel内核尝试在3D空间内相交两个三角形时，我遇到了一个非常奇怪的错误。本质上，我有两个不应相交的三角形。测试时，函数CGAL::do_intersect始终返回false，但是函数CGAL::intersection会根据三角形的顶点顺序建立一个交集。
当我使用CGAL::Exact_predicates_exact_constructions_kernel内核时，该错误消失了，但是我不能在实际情况下使用它。
以下是包含该错误的最少代码。三角形B和C相等(最大为顶点的排列)，并且应返回与三角形A相同的交点。
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Intersections.h>
#include <iostream>
#include <vector>
typedef CGAL::Exact_predicates_inexact_constructions_kernel Kernel;
typedef Kernel::Point_3 Point_3;
typedef Kernel::Triangle_3 Triangle_3;
int main(int argc, char *argv[])
{
std::vector<Point_3> APoints(3);
std::vector<Point_3> BPoints(3);
APoints[0] = Point_3(2, 2, 0.9423616295572568);
APoints[1] = Point_3(0.9685134704003172, 2, 0.9678422992674797);
APoints[2] = Point_3(2, 1.124710354419025, 1.068692504586136);
BPoints[0] = Point_3(2.5, 2.5, 1.442361629557257);
BPoints[1] = Point_3(1.588259113885977, 2.5, 0.5);
BPoints[2] = Point_3(2.5, 1.624710354419025, 1.568692504586136);
Triangle_3 TriangleA(APoints[0],APoints[1],APoints[2]);
Triangle_3 TriangleB(BPoints[0],BPoints[1],BPoints[2]);
Triangle_3 TriangleC(BPoints[2],BPoints[1],BPoints[0]);
std::cout.precision(16);
std::cout << " - Tried to intersect: " << std::endl;
std::cout << " - Triangle (A) " << " : "
<< "(" << TriangleA.vertex(0) << ") "
<< "(" << TriangleA.vertex(1) << ") "
<< "(" << TriangleA.vertex(2) << ") " << std::endl;
std::cout << " - Triangle (B) " << " : "
<< "(" << TriangleB.vertex(0) << ") "
<< "(" << TriangleB.vertex(1) << ") "
<< "(" << TriangleB.vertex(2) << ") " << std::endl;
std::cout << " - Triangle (C) " << " : "
<< "(" << TriangleC.vertex(0) << ") "
<< "(" << TriangleC.vertex(1) << ") "
<< "(" << TriangleC.vertex(2) << ") " << std::endl;
if( TriangleB.vertex(0)==TriangleC.vertex(2) &&
TriangleB.vertex(1)==TriangleC.vertex(1) &&
TriangleB.vertex(2)==TriangleC.vertex(0))
{
std::cout << " - Triangles (B) and (C) have the same vertices " << std::endl;
}
bool bIntersectAB = CGAL::do_intersect(TriangleA,TriangleB);
bool bIntersectAC = CGAL::do_intersect(TriangleA,TriangleC);
bool bIntersectInexactAB = CGAL::intersection(TriangleA,TriangleB);
bool bIntersectInexactAC = CGAL::intersection(TriangleA,TriangleC);
if(bIntersectAB)
{
std::cout << " --> A and B are intersecting (exact) ..." << std::endl;
}
if(bIntersectAC)
{
std::cout << " --> A and C are intersecting (exact) ..." << std::endl;
}
if(bIntersectInexactAB)
{
std::cout << " --> A and B are intersecting (inexact) ..." << std::endl;
}
if(bIntersectInexactAC)
{
std::cout << " --> A and C are intersecting (inexact) ..." << std::endl;
}
return 0;
}
这是输出...
- Tried to intersect:
- Triangle (A) : (2 2 0.9423616295572568) (0.9685134704003172 2 0.9678422992674797) (2 1.124710354419025 1.068692504586136)
- Triangle (B) : (2.5 2.5 1.442361629557257) (1.588259113885977 2.5 0.5) (2.5 1.624710354419025 1.568692504586136)
- Triangle (C) : (2.5 1.624710354419025 1.568692504586136) (1.588259113885977 2.5 0.5) (2.5 2.5 1.442361629557257)
- Triangles (B) and (C) have the same vertices
--> A and C are intersecting (inexact) ...
...以及带有两个三角形的图形(A:顶点1、2、3； B:顶点11、12、13)和“相交”(段21-22)，使用该程序的类似版本找到。
有什么事吗我在OS X 10.10.5(Yosemite)上使用CGAL 4.6.1。提前致谢!
最佳答案
我也将此问题发送到了CGAL的邮件列表中，并且开发人员回答说，尽管这种行为不是错误，但是
这是不幸的。 intersection是一种通用函数，对所有CGAL内核都以相同的方式实现，并且它使用的一步并不总是由不精确的内核正确处理，因此会出现交集错误。根据CGAL的GitHub页面上的this线程，
关于c++ - 错误的3D三角形之间的不精确交点(CGAL)，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/32951886/