C++ 助推点_圆以奇怪的形状出现
我正试图使用Boost的几何库在地球上创建一个半径为10米的多边形 这是我的建议 为了编译这个示例，我使用了最新的Clang和Boost 1.73.0 我首先在我的生产环境中发现了这个问题，即Clang12和Boost1.71.0 使用半径为1000m的圆和32个点可产生预期结果： 但是，将其缩小到10米会产生意想不到的结果： 我使用了一个工具来显示结果，并确认了其他可视化工具中的结果是相同的 这似乎是一个浮点舍入错误，但这里的所有内容都应该使用双精度浮点，而双精度浮点是有效的。计算似乎出了问题 使用半径为0.0001时也会发生同样的情况 发生了什么，我应该手动计算圆吗 编辑1 如果使用C++ 助推点_圆以奇怪的形状出现,c++,boost,gis,boost-geometry,C++,Boost,Gis,Boost Geometry,我正试图使用Boost的几何库在地球上创建一个半径为10米的多边形 这是我的建议 为了编译这个示例，我使用了最新的Clang和Boost 1.73.0 我首先在我的生产环境中发现了这个问题，即Clang12和Boost1.71.0 使用半径为1000m的圆和32个点可产生预期结果： 但是，将其缩小到10米会产生意想不到的结果： 我使用了一个工具来显示结果，并确认了其他可视化工具中的结果是相同的 这似乎是一个浮点舍入错误，但这里的所有内容都应该使用双精度浮点，而双精度浮点是有效的。计算似乎出了
bg:：area点（4.9 52.1）点（4.9 52.1000001）std:：fixedstd::cout << std::fixed << bg::wkt(result) << std::endl;
std:：cout似乎确实存在准确性问题。我试着解决问题，但没有达到我想要的程度
BGL使用一些硬限定的std:：abs
和std:：acos
调用，这使得使用多精度类型变得很困难。我试着修补其中的一些，但拉比特洞太深了，一个下午都打不开
这是一个可能有助于进一步精确定位/调试/跟踪事物的测试平台。注意
- 对于
float
而言，精度应确保库有效
将报告由于尖峰而无效
long-double
似乎做得很合理
然而，总体问题（缺乏控制/可预测性）仍然存在
imk_
#include <boost/geometry.hpp>
#include <iostream>
#ifdef TRY_BOOST_MULTIPRECISION
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
namespace bmp = boost::multiprecision;
using OctFloat = bmp::cpp_bin_float_oct;
using Decimal = bmp::number<bmp::cpp_dec_float<50>, bmp::et_off>;
using LongDecimal = bmp::number<bmp::cpp_dec_float<100>, bmp::et_off>;
namespace boost::multiprecision {
inline auto mod(OctFloat const& a, OctFloat const& b) { return fmod(a, b); }
inline auto mod(Decimal const& a, Decimal const& b) { return fmod(a, b); }
inline auto mod(LongDecimal const& a, LongDecimal const& b) { return fmod(a, b); }
inline auto abs(OctFloat const& a) { return fabs(a); }
inline auto abs(Decimal const& a) { return fabs(a); }
inline auto abs(LongDecimal const& a) { return fabs(a); }
}
namespace std { // sadly BG overqualifies std::abs in places
inline auto abs(OctFloat const& a) { return fabs(a); }
}
#endif
template <typename F, typename DegreeOrRadian>
void do_test(int n, F offset = {}) {
namespace bg = boost::geometry;
std::cout << "----- " << __PRETTY_FUNCTION__ << " n:" << n << " offset: " << offset << " ----\n";
bg::model::point<F, 2, bg::cs::geographic<bg::degree> > Amsterdam { 4.9, 52.1 + offset };
typedef bg::model::point<F, 2, bg::cs::geographic<DegreeOrRadian> > point;
// Declare the geographic_point_circle strategy (with n points)
// Default template arguments (taking Andoyer strategy)
bg::strategy::buffer::geographic_point_circle<> point_strategy(n);
// Declare the distance strategy (one kilometer, around the point, on Earth)
bg::strategy::buffer::distance_symmetric<F> distance_strategy(10.0);
// Declare other necessary strategies, unused for point
bg::strategy::buffer::join_round join_strategy;
bg::strategy::buffer::end_round end_strategy;
bg::strategy::buffer::side_straight side_strategy;
// Declare/fill a point on Earth, near Amsterdam
point p;
bg::convert(Amsterdam, p);
// Create the buffer of a point on the Earth
bg::model::multi_polygon<bg::model::polygon<point> > result;
bg::buffer(p, result,
distance_strategy, side_strategy,
join_strategy, end_strategy, point_strategy);
std::string reason;
is_valid(result, reason);
//std::cout << "result: " << wkt(result) << "\n";
std::cout << reason << "\n";
std::cout << "result: " << (bg::is_simple(result)?"simple":"compound") << "\n";
auto area = bg::area(result);
std::cout << "reference: " << bg::dsv(Amsterdam) << std::endl;
std::cout << "point: " << bg::dsv(p) << std::endl;
std::cout << "area: " << area << " m²" << std::endl;
}
int main() {
for (long double offset : { 0.l/*, 1e-7l*/ }) {
for (int n : { 36 }) {
do_test<float, boost::geometry::degree>(n, offset);
do_test<double, boost::geometry::degree>(n, offset);
do_test<long double, boost::geometry::degree>(n, offset);
do_test<float, boost::geometry::radian>(n, offset);
do_test<double, boost::geometry::radian>(n, offset);
do_test<long double, boost::geometry::radian>(n, offset);
// not working yet
//do_test<OctFloat, boost::geometry::radian>(n, offset);
//do_test<Decimal, boost::geometry::degree>();
//do_test<LongDecimal, boost::geometry::degree>();
}
}
}
在我的机器上
CharStyle超过处理时间据我所知，有两个不准确的来源，面积算法和点上的地理缓冲区算法
对于前者提出了一个解决方案。使用此修复程序，上述错误函数（godbolt.org/z/sTGqKK）返回的相对错误小于1%。下面的代码通过使用策略扩展了这一点
#include <boost/geometry.hpp>
#include <cmath>
#include <iostream>
template <typename CT>
void error_function(CT area, CT theoreticalArea)
{
std::cout << "area: " << area << " m², ";
std::cout << "error: " << area - theoreticalArea << " m²,\t";
std::cout << "normalised error: " << fabs(100 * (area - theoreticalArea)
/ theoreticalArea) << "%" << std::endl;
}
template <typename F, typename DegreeOrRadian>
void do_test(int n, F radius, F offset = {}) {
namespace bg = boost::geometry;
std::cout
<< "----- " << __PRETTY_FUNCTION__
<< " n:" << n << " radius:" << radius << " offset:" << offset
<< " ----\n";
bg::model::point<F, 2, bg::cs::geographic<bg::degree> > Amsterdam { 4.9, 52.1 + offset };
typedef bg::model::point<F, 2, bg::cs::geographic<DegreeOrRadian> > point;
// Declare the geographic_point_circle strategy (with n points)
// Default template arguments (taking Andoyer strategy)
bg::strategy::buffer::geographic_point_circle<> point_strategy(n);
// Declare the distance strategy (ten metres, around the point, on Earth)
bg::strategy::buffer::distance_symmetric<F> distance_strategy(radius);
// Declare other necessary strategies, unused for point
bg::strategy::buffer::join_round join_strategy;
bg::strategy::buffer::end_round end_strategy;
bg::strategy::buffer::side_straight side_strategy;
// Declare/fill a point on Earth, near Amsterdam
point p;
bg::convert(Amsterdam, p);
// Create the buffer of a point on the Earth
bg::model::multi_polygon<bg::model::polygon<point> > result;
bg::buffer(p, result,
distance_strategy, side_strategy,
join_strategy, end_strategy, point_strategy);
auto area = bg::area(result);
auto areat = bg::area(result,bg::strategy::area::geographic<bg::strategy::thomas>());
auto areav = bg::area(result,bg::strategy::area::geographic<bg::strategy::vincenty>());
auto areak = bg::area(result,bg::strategy::area::geographic<bg::strategy::karney>());
// Assumes that the Earth is flat, which it clearly is.
// A = n/2 * R^2 * sin(2*pi/n) where R is the circumradius
auto theoreticalArea = n * radius * radius * std::sin(2.0 * 3.142 / n) / 2.0;
std::cout << "reference: " << bg::dsv(Amsterdam) << std::endl;
std::cout << "point: " << bg::dsv(p) << std::endl;
std::cout << "radius: " << radius << " m" << std::endl;
error_function(area, theoreticalArea);
error_function(areat, theoreticalArea);
error_function(areav, theoreticalArea);
error_function(areak, theoreticalArea);
}
int main() {
double offset = 1e-7;
int n = 8;
do_test<double, boost::geometry::degree>(n, 10.);
do_test<long double, boost::geometry::degree>(n, 10.);
do_test<double, boost::geometry::radian>(n, 10.);
do_test<long double, boost::geometry::radian>(n, 10.);
do_test<double, boost::geometry::degree>(n, 10., offset);
do_test<long double, boost::geometry::degree>(n, 10., offset);
do_test<double, boost::geometry::degree>(n, 1000.);
do_test<double, boost::geometry::degree>(n, 1000., offset);
do_test<double, boost::geometry::degree>(n, 1.);
do_test<long double, boost::geometry::degree>(n, 1.);
}
一些评论：
- 使用不同的策略（即在boost geometry中执行地理计算的算法）控制算法的精度和性能
- 地理缓冲区中仍然存在一个问题，请随时在github上提交一个问题以保持跟踪
- “理论面积”仅适用于小面积，随着面积的增长，预计助推几何算法将比该面积更精确
- 地球不是平的；）
有关boost:：geometry:：buffer工作原理的更多详细信息：如果我阅读，我认为我看不到双精度的实际数字，但单精度精度精度列出了最差情况1.64-2.37m精度。如果你将半径为10m的圆除以这种精度，就像在整数网格（10m/~2m=5）上画一个r=5的圆。这可以解释你展示的形状。“分辨率对于GPS来说已经足够了”这一点几乎不相关，因为你也不能用GPS精确地勾勒出一个半径为10米的圆。@sehe是的，我们看到的几乎就像它显示一个浮动一样。double的机器epsilon是2.22e-16，根据我们的研究，它的刻度精度应该远小于1mm（精确到2.471304e-11米）。到目前为止，这是一个勇敢的努力，感谢您的研究。正如您所说，它在编译器资源管理器上超时，所以我需要进一步研究您的测试结果以进行验证。然而，我已经尝试在我的生产环境中使用了longdouble
，尽管如此，我仍然得到了各种各样的领域。然而，我注意到的一件事——一条线索——是圆多边形的内存表示似乎是正确的，但WKT输出却不是。我手工绘制了多边形结果的外环（num points=8），它确实是一个八角形。但没有解释区域问题。您可能也想在邮件列表中发布@adamwulkiewicz@barendgehrels@mloskot和其他人在那里通常反应很快，拥有GIS技能。我不了解这些投影/坐标系统是如何实现的。我验证了你的发现，并编写了一个错误函数来显示这些区域有多远。现在只是等待邮件列表的回复。我们已经为此提交了一份错误报告，因为我认为这是一个可以避免的暗流：问题是，如果你在AARC64（比如智能手机，甚至是新的M1苹果Mac）上编译，就不可能得到好的结果：long double
似乎不受支持。感谢更新。我同意这似乎不太理想。该票将有助于未来的访客/参考！Vissarion干得好@请注意，bg:：convert
不会在单位之间进行转换，因此使用弧度的示例无法正常工作。您可以使用bg:：transform
。看见
#include <boost/geometry.hpp>
#include <cmath>
#include <iostream>
template <typename CT>
void error_function(CT area, CT theoreticalArea)
{
std::cout << "area: " << area << " m², ";
std::cout << "error: " << area - theoreticalArea << " m²,\t";
std::cout << "normalised error: " << fabs(100 * (area - theoreticalArea)
/ theoreticalArea) << "%" << std::endl;
}
template <typename F, typename DegreeOrRadian>
void do_test(int n, F radius, F offset = {}) {
namespace bg = boost::geometry;
std::cout
<< "----- " << __PRETTY_FUNCTION__
<< " n:" << n << " radius:" << radius << " offset:" << offset
<< " ----\n";
bg::model::point<F, 2, bg::cs::geographic<bg::degree> > Amsterdam { 4.9, 52.1 + offset };
typedef bg::model::point<F, 2, bg::cs::geographic<DegreeOrRadian> > point;
// Declare the geographic_point_circle strategy (with n points)
// Default template arguments (taking Andoyer strategy)
bg::strategy::buffer::geographic_point_circle<> point_strategy(n);
// Declare the distance strategy (ten metres, around the point, on Earth)
bg::strategy::buffer::distance_symmetric<F> distance_strategy(radius);
// Declare other necessary strategies, unused for point
bg::strategy::buffer::join_round join_strategy;
bg::strategy::buffer::end_round end_strategy;
bg::strategy::buffer::side_straight side_strategy;
// Declare/fill a point on Earth, near Amsterdam
point p;
bg::convert(Amsterdam, p);
// Create the buffer of a point on the Earth
bg::model::multi_polygon<bg::model::polygon<point> > result;
bg::buffer(p, result,
distance_strategy, side_strategy,
join_strategy, end_strategy, point_strategy);
auto area = bg::area(result);
auto areat = bg::area(result,bg::strategy::area::geographic<bg::strategy::thomas>());
auto areav = bg::area(result,bg::strategy::area::geographic<bg::strategy::vincenty>());
auto areak = bg::area(result,bg::strategy::area::geographic<bg::strategy::karney>());
// Assumes that the Earth is flat, which it clearly is.
// A = n/2 * R^2 * sin(2*pi/n) where R is the circumradius
auto theoreticalArea = n * radius * radius * std::sin(2.0 * 3.142 / n) / 2.0;
std::cout << "reference: " << bg::dsv(Amsterdam) << std::endl;
std::cout << "point: " << bg::dsv(p) << std::endl;
std::cout << "radius: " << radius << " m" << std::endl;
error_function(area, theoreticalArea);
error_function(areat, theoreticalArea);
error_function(areav, theoreticalArea);
error_function(areak, theoreticalArea);
}
int main() {
double offset = 1e-7;
int n = 8;
do_test<double, boost::geometry::degree>(n, 10.);
do_test<long double, boost::geometry::degree>(n, 10.);
do_test<double, boost::geometry::radian>(n, 10.);
do_test<long double, boost::geometry::radian>(n, 10.);
do_test<double, boost::geometry::degree>(n, 10., offset);
do_test<long double, boost::geometry::degree>(n, 10., offset);
do_test<double, boost::geometry::degree>(n, 1000.);
do_test<double, boost::geometry::degree>(n, 1000., offset);
do_test<double, boost::geometry::degree>(n, 1.);
do_test<long double, boost::geometry::degree>(n, 1.);
}
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::degree] n:8 radius:10 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 281.272 m², error: -1.59991 m², normalised error: 0.565596%
area: 282.843 m², error: -0.0284134 m², normalised error: 0.0100446%
area: 281.749 m², error: -1.12206 m², normalised error: 0.396666%
area: 282.843 m², error: -0.028415 m², normalised error: 0.0100452%
----- void do_test(int, F, F) [with F = long double; DegreeOrRadian = boost::geometry::degree] n:8 radius:10 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 283.57 m², error: 0.698736 m², normalised error: 0.247015%
area: 282.843 m², error: -0.0284201 m², normalised error: 0.010047%
area: 283.568 m², error: 0.696594 m², normalised error: 0.246258%
area: 282.843 m², error: -0.0284255 m², normalised error: 0.0100489%
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::radian] n:8 radius:10 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 282.715 m², error: -0.156633 m², normalised error: 0.0553726%
area: 282.843 m², error: -0.0286857 m², normalised error: 0.0101409%
area: 280.578 m², error: -2.29311 m², normalised error: 0.810656%
area: 282.843 m², error: -0.0286896 m², normalised error: 0.0101423%
----- void do_test(int, F, F) [with F = long double; DegreeOrRadian = boost::geometry::radian] n:8 radius:10 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 283.135 m², error: 0.263058 m², normalised error: 0.0929955%
area: 282.843 m², error: -0.0287086 m², normalised error: 0.010149%
area: 283.164 m², error: 0.292786 m², normalised error: 0.103505%
area: 282.843 m², error: -0.0287018 m², normalised error: 0.0101466%
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::degree] n:8 radius:10 offset:1e-07 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 281.749 m², error: -1.12206 m², normalised error: 0.396666%
area: 282.843 m², error: -0.0283973 m², normalised error: 0.010039%
area: 281.749 m², error: -1.12206 m², normalised error: 0.396666%
area: 282.843 m², error: -0.0284534 m², normalised error: 0.0100588%
----- void do_test(int, F, F) [with F = long double; DegreeOrRadian = boost::geometry::degree] n:8 radius:10 offset:1e-07 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 10 m
area: 283.569 m², error: 0.697826 m², normalised error: 0.246694%
area: 282.843 m², error: -0.0284078 m², normalised error: 0.0100427%
area: 283.568 m², error: 0.696529 m², normalised error: 0.246235%
area: 282.843 m², error: -0.0283946 m², normalised error: 0.010038%
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::degree] n:8 radius:1000 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 1000 m
area: 2.82843e+06 m², error: -284.28 m², normalised error: 0.0100498%
area: 2.82843e+06 m², error: -284.27 m², normalised error: 0.0100494%
area: 2.82843e+06 m², error: -284.259 m², normalised error: 0.0100491%
area: 2.82843e+06 m², error: -284.27 m², normalised error: 0.0100494%
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::degree] n:8 radius:1000 offset:1e-07 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 1000 m
area: 2.82843e+06 m², error: -284.372 m², normalised error: 0.010053%
area: 2.82843e+06 m², error: -284.27 m², normalised error: 0.0100494%
area: 2.82843e+06 m², error: -284.282 m², normalised error: 0.0100499%
area: 2.82843e+06 m², error: -284.27 m², normalised error: 0.0100494%
----- void do_test(int, F, F) [with F = double; DegreeOrRadian = boost::geometry::degree] n:8 radius:1 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 1 m
area: 2.81749 m², error: -0.0112205 m², normalised error: 0.396663%
area: 2.8285 m², error: -0.000219998 m², normalised error: 0.0077773%
area: 2.83391 m², error: 0.0051987 m², normalised error: 0.183783%
area: 2.82848 m², error: -0.000234082 m², normalised error: 0.00827521%
----- void do_test(int, F, F) [with F = long double; DegreeOrRadian = boost::geometry::degree] n:8 radius:1 offset:0 ----
reference: (4.9, 52.1)
point: (4.9, 52.1)
radius: 1 m
area: 2.83535 m², error: 0.00663946 m², normalised error: 0.234717%
area: 2.82844 m², error: -0.000278463 m², normalised error: 0.00984417%
area: 2.83392 m², error: 0.005205 m², normalised error: 0.184006%
area: 2.82842 m², error: -0.000294424 m², normalised error: 0.0104084%