boost::polygon 布尔减法导致额外的行
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【中文标题】boost::polygon 布尔减法导致额外的行【英文标题】：boost::polygon boolean subtract results in additional lines 【发布时间】：2020-06-30 06:58:06 【问题描述】：我有一个矩形，里面有一个圆圈。现在我进行布尔减法运算，使用 boost::polygon 和以下（伪）代码从较大的矩形中减去圆：
boost::polygon::polygon_with_holes_data<int> rect;
boost::polygon::polygon_with_holes_data<int> circle;
// fill both with data here
boost::polygon::polygon_set_data<int> result=rect-circle;
在“结果”之后包含一堆坐标对，其中每个坐标对都标有附加值 -1 或 1。然后我通过以下方式获取结果数据：
std::vector<boost::polygon::polygon_data<int>> outputData;
result.get<std::vector<boost::polygon::polygon_data<int>>>(outputData);
现在“outputData”包含一个坐标列表，形成以下结果：
因此，孔被合并到一个完整的、封闭的多边形坐标数组中，我预计会在其中出现类似 boost::polygon::polygon_with_holes_data 的东西，其中轮廓和孔会被分开。
所以我的问题是：我在这里做错了吗？如何将轮廓和孔分开，以便摆脱连接它们的额外线？是否有一个函数可以从返回的 boost::polygon::polygon_set_data 中获取 boost::polygon::polygon_with_holes_data 或者这里还有什么神奇之处？
谢谢:-)
【问题讨论】：
能否包含源数据？它可能是无效的。例如。未关闭、方向错误等。如果您的输入不满足前提条件，算法的行为将是未定义的（GIGO） @sehe：假设我从一个矩形中减去一个三角形 -78020,-72350,110650,-7660,7090,69510,-78020,-72350 -147530,127670,163140,127670,163140,-143280,-147530,-143280,-147530,127670 - 希望我的坐标没有错字。两者都是封闭的，并且都产生一个由 11 个输出坐标元素组成的单个数组，该数组再次包含从轮廓到孔的这条附加线。 【参考方案1】：我不厌其烦地自己生成了一些数据。我不知道你使用什么数据，也不知道你如何渲染它。我怀疑这些过程有问题：
让我们创建一个 polygon_data 工厂：
template <typename T>
auto make_rect(T x1, T y1, T x2, T y2)
auto r = bp::rectangle_data(x1, y1, x2, y2);
bp::polygon_data<T> p;
bp::assign(p, r);
return p;
到目前为止一切顺利。对于圈子我用了你的新发现from your other question：
template <typename T>
auto make_circle(T x, T y, T radius)
std::vector<bp::polygon_data<T> > ps;
bp::assign(ps, bp::rectangle_data(x-1, y-1, x+1, y+1));
bp::resize(ps, radius, true, 512);
assert(ps.size() == 1);
return ps.front();
现在让我们从简单的开始：
int main()
auto rect = make_rect(0, 0, 1000, 1000);
auto circle = make_circle(500, 500, 400);
auto difference = rect - circle;
std::cout << std::fixed;
std::cout << "rect area: " << area(rect) << "\n";
std::cout << "circle area: " << area(circle) << "\n";
std::cout << "difference area: " << area(difference) << "\n";
打印
rect area: 1000000.000000
circle area: 505481.000000
difference area: 494519.000000
转换和检查
现在看看这些几何图形是否能正确渲染，我知道除了通过 Boost Geometry 之外没有其他技术¹
所以，让我们转换为polygon_with_holes_data 并进行一些检查：
bp::polygon_with_holes_data<int> result(rect.begin(), rect.end(),
&circle, &circle+1);
std::cout << "result area: " << area(result) << "\n";
assert(area(rect) - area(circle) == area(difference));
assert(bp::equivalence(result, rect - circle));
断言通过，这会打印出预期的结果：
result area: 494519.000000
正确匹配差异区域。
渲染 SVG
现在我们适应 Boost Geometry 并编写一个 SVG：
namespace bg = boost::geometry;
std::cout << bg::wkt(rect);
std::cout << bg::wkt(result);
using C = bg::coordinate_type<decltype(result)>::type;
using PT = bg::model::d2::point_xy<C>;
std::ofstream svg("output.svg");
boost::geometry::svg_mapper<PT> mapper(svg, 400, 400);
mapper.add(result);
mapper.map(result, "fill-opacity:0.3;fill:rgb(153,204,0);stroke:rgb(153,204,0);stroke-width:2");
这写了 WKT 和 output.svg:
这里看起来不错。
可能出了什么问题？如何调试？
就像我在 cmets 中提到的那样，许多库/工具对它们的输入都有限制/不变量。诸如外环和内环的方向、自相交以及多边形环上闭合点的存在。
现在，如果您不知道哪些数据是可接受的，您可以点击文档，或者您可以使用库 API 进行诊断。例如在 Boost Geometry 中，我喜欢做一个快速而简单的诊断功能：
template<typename G>
void auto_correct(G& geo)
std::string reason;
while (!bg::is_valid(geo, reason))
std::cout << "Trying to auto-correct broken input data: " << reason << "\n";
bg::correct(geo);
您可以添加wkt打印来调试实际应用了哪些更改。
参见例如boost read_wkt produced invalid polygon 获取诊断和修复示例。
（注意：不要在生产中使用它，更正可能无法达到您的预期，并且对于某些输入，循环甚至可能是无限的）
现场演示
一如既往：Live On Coliru
#include <boost/polygon/polygon.hpp>
#include <boost/polygon/gtl.hpp>
#include <boost/polygon/rectangle_data.hpp>
#include <boost/polygon/polygon_set_data.hpp>
#include <boost/polygon/polygon_data.hpp>
#include <iostream>
namespace bp = boost::polygon;
#ifndef NO_GEO
#include <fstream>
#include <boost/geometry.hpp>
#include <boost/geometry/io/io.hpp>
#include <boost/geometry/geometries/adapted/boost_polygon.hpp>
namespace bg = boost::geometry;
/*
* template<typename G>
* void auto_correct(G& geo)
* std::string reason;
* while (!bg::is_valid(geo, reason))
* std::cout << "Trying to auto-correct broken input data: " << reason << "\n";
* bg::correct(geo);
*
*
*/
#endif
template <typename T>
auto make_rect(T x1, T y1, T x2, T y2)
auto r = bp::rectangle_data(x1, y1, x2, y2);
bp::polygon_data<T> p;
bp::assign(p, r);
return p;
template <typename T>
auto make_circle(T x, T y, T radius)
std::vector<bp::polygon_data<T> > ps;
bp::assign(ps, bp::rectangle_data(x-1, y-1, x+1, y+1));
bp::resize(ps, radius, true, 512);
assert(ps.size() == 1);
return ps.front();
int main()
auto rect = make_rect(0, 0, 1000, 1000);
auto circle = make_circle(500, 500, 400);
auto difference = rect - circle;
std::cout << std::fixed;
std::cout << "rect area: " << area(rect) << "\n";
std::cout << "circle area: " << area(circle) << "\n";
std::cout << "difference area: " << area(difference) << "\n";
bp::polygon_with_holes_data<int> result(rect.begin(), rect.end(),
&circle, &circle+1);
std::cout << "result area: " << area(result) << "\n";
assert(area(rect) - area(circle) == area(difference));
assert(bp::equivalence(result, rect - circle));
#ifndef NO_GEO
std::cout << bg::wkt(rect) << "\n";
std::cout << bg::wkt(result) << "\n";
using C = bg::coordinate_type<decltype(result)>::type;
using PT = bg::model::d2::point_xy<C>;
std::ofstream svg("output.svg");
boost::geometry::svg_mapper<PT> mapper(svg, 400, 400);
mapper.add(result);
mapper.map(result, "fill-opacity:0.3;fill:rgb(153,204,0);stroke:rgb(153,204,0);stroke-width:2");
#endif
打印
rect area: 1000000.000000
circle area: 505481.000000
difference area: 494519.000000
result area: 494519.000000
POLYGON((0 0,1000 0,1000 1000,0 1000))
POLYGON((0 0,1000 0,1000 1000,0 1000,0 0),(900 527,899 527,899 530,899 532,899 535,899 537,898 537,898 540,898 542,898 545,898 547,897 547,897 550,897 552,897 555,897 557,896 557,896 560,896 562,895 562,895 564,895 566,894 566,894 569,894 571,893 571,893 574,893 576,892 576,892 579,892 581,891 581,891 584,891 586,890 586,890 589,890 591,889 591,889 593,889 595,888 595,888 598,888 600,887 600,887 603,887 605,886 605,885 608,885 610,884 610,884 612,884 614,883 614,883 617,883 619,882 619,881 622,881 624,880 624,880 626,880 628,879 628,878 631,878 633,877 633,876 636,876 638,875 638,875 640,875 642,874 642,873 645,873 647,872 647,871 649,871 651,870 651,869 654,869 656,868 656,867 658,867 660,866 660,865 663,865 665,864 665,863 667,863 669,862 669,861 672,861 674,860 674,859 676,859 678,858 678,857 681,857 683,854 685,854 687,853 687,852 689,852 691,851 691,850 694,850 696,847 698,847 700,846 700,845 702,845 704,842 706,842 708,841 708,840 710,840 712,837 715,837 717,834 719,834 721,833 721,832 723,832 725,829 727,829 729,826 731,826 733,823 735,823 737,820 739,820 741,817 743,817 745,814 747,814 749,811 752,808 754,808 756,805 758,805 760,802 762,802 764,799 767,795 771,792 773,792 775,789 778,785 782,782 785,778 789,775 792,773 792,771 795,767 799,764 802,762 802,760 805,758 805,756 808,754 808,752 811,749 814,747 814,745 817,743 817,741 820,739 820,737 823,735 823,733 826,731 826,729 829,727 829,725 832,723 832,721 833,721 834,719 834,717 837,715 837,712 840,710 840,708 841,708 842,706 842,704 845,702 845,700 846,700 847,698 847,696 850,694 850,691 851,691 852,689 852,687 853,687 854,685 854,683 857,681 857,678 858,678 859,676 859,674 860,674 861,672 861,669 862,669 863,667 863,665 864,665 865,663 865,660 866,660 867,658 867,656 868,656 869,654 869,651 870,651 871,649 871,647 872,647 873,645 873,642 874,642 875,640 875,638 875,638 876,636 876,633 877,633 878,631 878,628 879,628 880,626 880,624 880,624 881,622 881,619 882,619 883,617 883,614 883,614 884,612 884,610 884,610 885,608 885,605 886,605 887,603 887,600 887,600 888,598 888,595 888,595 889,593 889,591 889,591 890,589 890,586 890,586 891,584 891,581 891,581 892,579 892,576 892,576 893,574 893,571 893,571 894,569 894,566 894,566 895,564 895,562 895,562 896,560 896,557 896,557 897,555 897,552 897,550 897,547 897,547 898,545 898,542 898,540 898,537 898,537 899,535 899,532 899,530 899,527 899,527 900,525 900,523 900,521 900,518 900,516 900,513 900,511 900,508 900,506 900,503 900,501 900,498 900,496 900,493 900,491 900,488 900,486 900,483 900,481 900,478 900,476 900,474 900,472 900,469 899,467 899,464 899,462 899,459 898,457 898,454 898,452 898,449 897,447 897,444 897,442 897,439 896,437 896,435 895,433 895,430 894,428 894,425 893,423 893,420 892,418 892,415 891,413 891,410 890,408 890,406 889,404 889,401 888,399 888,396 887,394 887,391 885,389 885,387 884,385 884,382 883,380 883,377 881,375 881,373 880,371 880,368 878,366 878,363 876,361 876,359 875,357 875,354 873,352 873,348 871,345 869,343 869,339 867,336 865,334 865,330 863,327 861,325 861,321 859,318 857,316 857,312 854,308 852,305 850,303 850,299 847,295 845,291 842,287 840,282 837,278 834,274 832,270 829,266 826,262 823,258 820,254 817,250 814,247 811,243 808,239 805,235 802,232 799,228 795,224 792,221 789,217 785,214 782,210 778,207 775,204 771,200 767,197 764,194 760,191 756,188 752,185 749,182 745,179 741,176 737,173 733,170 729,167 725,165 721,162 717,159 712,157 708,154 704,152 700,149 696,147 691,145 687,142 683,140 678,138 674,136 669,134 665,132 660,130 656,128 651,126 647,124 642,123 638,121 633,119 628,118 624,116 619,115 614,114 610,112 605,111 600,110 595,109 591,108 586,107 581,106 576,105 571,104 566,103 562,102 557,102 555,102 552,101 547,101 545,101 542,100 537,100 535,100 532,99 527,99 525,99 523,99 521,99 518,99 516,99 513,99 511,99 508,99 506,99 503,99 501,99 498,99 496,99 493,99 491,99 488,99 486,99 483,99 481,99 478,99 476,99 474,99 472,100 467,100 464,100 462,101 457,101 454,101 452,102 447,102 444,102 442,103 437,104 433,105 428,106 423,107 418,108 413,109 408,110 404,111 399,112 394,114 389,115 385,116 380,118 375,119 371,121 366,123 361,124 357,126 352,128 348,130 343,132 339,134 334,136 330,138 325,140 321,142 316,145 312,147 308,149 303,152 299,154 295,157 291,159 287,162 282,165 278,167 274,170 270,173 266,176 262,179 258,182 254,185 250,188 247,191 243,194 239,197 235,200 232,204 228,207 224,210 221,214 217,217 214,221 210,224 207,228 204,232 200,235 197,239 194,243 191,247 188,250 185,254 182,258 179,262 176,266 173,270 170,274 167,278 165,282 162,287 159,291 157,295 154,299 152,303 149,308 147,312 145,316 142,321 140,325 138,330 136,334 134,339 132,343 130,348 128,352 126,357 124,361 123,366 121,371 119,375 118,380 116,385 115,389 114,394 112,399 111,404 110,408 109,413 108,418 107,423 106,428 105,433 104,437 103,442 102,444 102,447 102,452 101,454 101,457 101,462 100,464 100,467 100,472 99,474 99,476 99,478 99,481 99,483 99,486 99,488 99,491 99,493 99,496 99,498 99,501 99,503 99,506 99,508 99,511 99,513 99,516 99,518 99,521 99,523 99,525 99,527 99,532 100,535 100,537 100,542 101,545 101,547 101,552 102,555 102,557 102,562 103,566 104,571 105,576 106,581 107,586 108,591 109,595 110,600 111,605 112,610 114,614 115,619 116,624 118,628 119,633 121,638 123,642 124,647 126,651 128,656 130,660 132,665 134,669 136,674 138,678 140,683 142,687 145,691 147,696 149,700 152,704 154,708 157,712 159,717 162,721 165,725 167,729 170,733 173,737 176,741 179,745 182,749 185,752 188,756 191,760 194,764 197,767 200,771 204,775 207,778 210,782 214,785 217,789 221,792 224,795 228,799 232,802 235,805 239,808 243,811 247,814 250,817 254,820 258,823 262,826 266,829 270,832 274,834 278,837 282,840 287,842 291,845 295,847 299,850 303,850 305,852 308,854 312,857 316,857 318,859 321,861 325,861 327,863 330,865 334,865 336,867 339,869 343,869 345,871 348,873 352,873 354,875 357,875 359,876 361,876 363,878 366,878 368,880 371,880 373,881 375,881 377,883 380,883 382,884 385,884 387,885 389,885 391,887 394,887 396,888 399,888 401,889 404,889 406,890 408,890 410,891 413,891 415,892 418,892 420,893 423,893 425,894 428,894 430,895 433,895 435,896 437,896 439,897 442,897 444,897 447,897 449,898 452,898 454,898 457,898 459,899 462,899 464,899 467,899 469,900 472,900 474,900 476,900 478,900 481,900 483,900 486,900 488,900 491,900 493,900 496,900 498,900 501,900 503,900 506,900 508,900 511,900 513,900 516,900 518,900 521,900 523,900 525,900 527))
¹（我不知道如何使用 Boost Polygon 输出/输入任何几何数据，而且我没有任何支持 WKT/DSV 的渲染工具）。
【讨论】：
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