问题
请使用C++11标准实现二维坐标转换公式：
有两套笛卡尔坐标系：XOY和X'O'Y'，X'O'Y'相对于XOY坐标系进行了平移(x_shift, y_shift)和旋转（angle，弧度）变换，一个点在XOY坐标系中的坐标为：(x, y)，计算该点在X'O'Y'坐标系中的坐标：(x_prime, y_prime)。
要求
1.使用C++标准库（STL库）算法；
2.使用C++11标准的Lambda表达式；
3.使用C++11标准库中的随机数生成器生成1000个[-100, 100]内的均匀随机数坐标进行测试；
4.使用C++11标准库中的计时方法计算坐标转换函数所花费的时间。
公式
公式推导就不说了（见这篇博客），如下所示：
x = x_prime * cos(angle) - y_prime * sin(angle) + x_shift
y = y_prime * cos(angle) + x_prime * sin(angle) + y_shift
x_prime = (x - x_shift) * cos(angle) + (y - y_shift) * sin(angle)
y_prime = (y - y_shift) * cos(angle) - (x - x_shift) * sin(angle)代码
// Author: David Hopper
// E-mail: [email protected]
#include <algorithm>
#include <chrono>
#include <cmath>
#include <fstream>
#include <iostream>
#include <random>
struct Point {
explicit Point() : x(0.0), y(0.0) {}
explicit Point(double x_i, double y_i) : x(x_i), y(y_i) {}
double x;
double y;
};
// 2D coordinate transform
void CoordinateTransform2D(std::vector<Point>& points, double x_shift,
double y_shift, double angle);
int main(int argc, char** argv) {
double x_shift, y_shift, angle;
bool initialized = true;
// Parse parameters.
if (argc > 3) {
try {
x_shift = std::stod(argv[1]);
y_shift = std::stod(argv[2]);
angle = std::stod(argv[3]);
} catch (...) {
initialized = false;
}
} else {
initialized = false;
}
if (!initialized) {
std::cout << "Usage: \n"
<< "\t" << argv[0]
<< " x_shift y_shit angle(rad) result_file_name\n"
<< "Example: \n"
<< "\t" << argv[0] << " 1 1 0.785 test.txt" << std::endl;
std::cout
<< "The default transform parameters: (1.0, 1.0, PI/4.0) are used. "
<< std::endl;
x_shift = 1.0;
y_shift = 1.0;
angle = M_PI / 4.0;
}
std::string file_name;
if (argc > 4) {
file_name = argv[4];
}
if (file_name.empty()) {
file_name = "test.txt";
}
std::ofstream fout(file_name);
if (!fout.is_open()) {
std::cerr << "Cannot open the file: " << file_name << " to write results. "
<< std::endl;
return 1;
}
constexpr int kSize = 1000;
std::vector<Point> points(kSize);
std::random_device rd;
std::mt19937 gen(rd());
constexpr double kBound = 100.0;
std::uniform_real_distribution<double> dis(-kBound, kBound);
auto rand_num([&]() mutable {
Point point(dis(gen), dis(gen));
return point;
});
std::generate(std::begin(points), std::end(points), rand_num);
// Add a special point (0, 0) to check the correctness of the result.
points.emplace_back(0.0, 0.0);
fout << "Points before transformation: " << std::endl;
for (const auto& point : points) {
fout << "(" << point.x << ", " << point.y << "), ";
}
fout << std::endl;
auto start_time = std::chrono::steady_clock::now();
CoordinateTransform2D(points, x_shift, y_shift, angle);
auto end_time = std::chrono::steady_clock::now();
fout << "Elapsed time in milliseconds: "
<< std::chrono::duration_cast<std::chrono::microseconds>(end_time -
start_time)
.count()
<< " µs" << std::endl;
fout << "Points after transformation: " << std::endl;
for (const auto& point : points) {
fout << "(" << point.x << ", " << point.y << "), ";
}
fout << std::endl;
fout.close();
// Use the following line to avoid the disappearance of the command line
// window when debugging in VSCode.
// std::cin.get();
return 0;
}
// 2D coordinate transform
// Original: XOY
// Transformed: X'O'Y':
// Translation: (x_shift, y_shift)
// Rotation: angle (rad)
// A coordinate represented in XOY: (x, y)
// A coordinate represented in X'O'Y': (x_prime, y_prime)
// Transformation formula:
// x = x_prime * cos(angle) - y_prime * sin(angle) + x_shift
// y = y_prime * cos(angle) + x_prime * sin(angle) + y_shift
// x_prime = (x - x_shift) * cos(angle) + (y - y_shift) * sin(angle)
// y_prime = (y - y_shift) * cos(angle) - (x - x_shift) * sin(angle)
void CoordinateTransform2D(std::vector<Point>& points, double x_shift,
double y_shift, double angle) {
std::transform(
std::begin(points), std::end(points), std::begin(points),
[=](const Point& point) {
double sin_val = std::sin(angle);
double cos_val = std::cos(angle);
Point trans_point(
(point.x - x_shift) * cos_val + (point.y - y_shift) * sin_val,
(point.y - y_shift) * cos_val - (point.x - x_shift) * sin_val);
return trans_point;
});
}编译指令
g++ -g -Wall -std=c++11 *.cpp -o test结果
执行如下指令：
./test 2.5 3.5 0.3476 result.txt在我机器上运行的结果如下：
Points before transformation
: (-77.5781, -87.3832),
(-83.8756, 61.0616),
(-84.294, -66.2067),
(79.6666, -50.0785),
(51.431, -28.4307),
(28.015, -71.6604),
(-5.37682, -39.0528),
(41.22, -8.97904),
(23.5979, -0.766472),
(35.9552, 3.61348),
(-17.6709, -63.0485),
(-68.5905, 4.51262),
(-92.8113, -83.9421),
(12.4378, 64.148),
(96.0308, -8.80373),
(39.6931, -28.4047),
(68.6329, 3.90714),
(-51.5738, -59.8949),
(63.0394, 24.2507),
(73.0724, -16.5424),
(-71.7909, 34.4098),
(-68.4305, 83.0725),
(-29.6809, 20.3638),
(-42.6257, -11.7805),
(-37.8868, 87.9958),
(-39.1441, 22.0786),
(-66.9905, -99.1343),
(11.394, 11.3881),
(-87.4088, 63.9272),
(93.9925, 70.4119),
(31.8355, 69.0841),
(-31.8731, -14.2943),
(57.5755, -47.0277),
(23.22, -99.6089),
(5.62697, -56.566),
(-56.8397, 13.7043),
(86.8864, 15.4661),
(5.47267, -5.41087),
(89.8262, -3.27915),
(-67.9456, 83.7751),
(97.0269, -72.6176),
(-62.165, 33.209),
(-23.4851, 47.6277),
(-22.5981, 38.6406),
(33.6895, 47.2239),
(-45.787, -20.7522),
(-45.8599, 85.4983),
(-87.3818, -89.8228),
(-82.1598, 87.1015),
(61.2795, -79.3586),
(-81.7094, -68.8969),
(94.1826, 35.8195),
(85.9987, -64.7438),
(5.94861, 47.0071),
(8.991, -48.4177),
(71.3585, 54.5151),
(-53.2155, 24.6063),
(-24.9944, 25.2277),
(-64.247, -4.00024),
(-38.7513, 27.5486),
(79.6492, -38.3925),
(-47.9822, -58.4295),
(-6.54801, 8.18575),
(92.4573, -55.9509),
(-44.6852, -71.8078),
(-86.8836, -99.3402),
(-60.4751, -18.7272),
(72.8438, -69.4679),
(24.2197, 27.2442),
(45.3163, 24.8003),
(-65.9832, -7.75722),
(69.8527, 80.8503),
(64.5131, 68.5267),
(-25.6696, -82.3117),
(8.82541, -94.0497),
(32.8733, 8.85101),
(32.6841, 34.6735),
(76.7519, -10.8524),
(31.7331, -14.6872),
(-83.6959, 58.1023),
(-67.4745, 18.6664),
(82.4146, -65.6839),
(88.5779, -53.3474),
(-31.9977, 73.2969),
(98.2983, 58.8218),
(83.7289, -17.6113),
(20.0972, -76.0503),
(97.4192, 11.9273),
(-92.438, 19.1106),
(-0.700133, 35.6394),
(68.8822, -29.9761),
(-62.683, 22.4781),
(-99.5006, 16.6045),
(19.446, 81.8101),
(17.9358, -92.64),
(45.1965, 43.3707),
(-93.2082, 59.4847),
(-58.4242, -37.5873),
(43.0549, -28.3448),
(-93.3692, -51.5951),
(-53.614, 24.4164),
(24.2341, 92.84),
(37.499, 19.2326),
(-22.4033, 45.0909),
(20.307, -0.29493),
(-52.0971, -53.3076),
(58.8245, -53.8125),
(95.2489, -78.3257),
(-41.0256, 55.2024),
(-14.4644, 34.508),
(25.7844, 75.6408),
(-71.3978, -59.1554),
(-5.71356, 20.0457),
(-65.6621, 31.3185),
(-55.3855, -37.0243),
(-87.4738, 55.0381),
(0.772477, -81.4926),
(3.82026, 54.003),
(-88.6321, -26.3469),
(-60.9882, -57.8289),
(15.0225, -42.4481),
(42.462, -71.8801),
(71.5321, -11.6107),
(-64.0469, -76.19),
(72.8118, 76.4698),
(-87.7303, -10.6825),
(18.4812, 24.6976),
(-97.5296, 31.9099),
(31.0148, 0.0796089),
(17.1559, -42.7295),
(85.094, 89.6993),
(44.8592, 6.24716),
(50.6028, 6.19735),
(-35.8976, -64.4989),
(-21.2344, 20.1233),
(44.4093, 47.0952),
(84.7519, 23.0534),
(15.5612, -54.4332),
(68.6918, -11.5925),
(-97.7517, 27.0815),
(-36.6702, 35.7727),
(-84.8862, -47.2677),
(-65.0126, 23.5853),
(74.5878, 22.2154),
(79.354, -70.8478),
(-92.041, 96.7357),
(95.6583, 22.42),
(-35.8284, 33.2501),
(72.094, -34.6758),
(-97.2803, -98.0475),
(59.3516, 76.9435),
(0.302791, -8.42592),
(-84.6728, 0.9551),
(41.1433, -26.5596),
(50.0171, -3.31827),
(-68.303, 75.0512),
(-84.965, 68.7322),
(60.3342, 45.2335),
(-16.1795, 78.2285),
(64.5663, 66.7366),
(34.7501, 79.5964),
(-83.2571, -40.5917),
(-63.1333, 38.276),
(66.616, 45.7663),
(-0.507822, -61.6959),
(84.5285, 89.2285),
(53.3768, 42.9477),
(91.6024, 13.4678),
(-7.22239, 33.2572),
(-97.6589, 47.0923),
(-31.862, -31.0655),
(42.4726, -66.4831),
(86.4271, 16.0946),
(37.4338, 84.248),
(93.157, -94.7163),
(76.8847, -25.0756),
(-64.39, -67.7898),
(-61.8416, -96.5264),
(-58.7373, 15.5093),
(39.9738, 9.13985),
(-73.5342, -13.9573),
(-61.9008, -25.341),
(-67.1476, -65.992),
(45.4513, -79.1555),
(-53.2211, -15.1549),
(13.9876, 89.1),
(-40.1955, 68.3748),
(-95.1469, 69.9005),
(-53.3964, -10.3213),
(80.7919, -4.49677),
(-21.9766, 68.0915),
(25.3349, 58.8641),
(90.1438, -15.9264),
(97.825, 47.8761),
(-15.067, -1.23593),
(-92.7184, -93.9363),
(85.3088, 98.0805),
(55.9273, 14.5769),
(98.9196, -41.9317),
(23.8729, -59.3623),
(69.8144, 57.5852),
(-75.1776, -73.7797),
(74.2376, 43.4575),
(46.1616, 0.461441),
(-26.5788, -56.9401),
(61.3088, -29.169),
(-61.0427, 62.2345),
(-28.7369, -5.51974),
(99.1903, -12.967),
(9.39403, -31.3599),
(-20.3627, -49.4254),
(51.4046, -96.2963),
(-17.9145, 96.2364),
(-15.2607, -50.0682),
(47.3527, -41.5359),
(29.6257, -56.4046),
(-86.487, 24.1516),
(-51.0425, 89.5741),
(56.1279, 18.8455),
(-27.8427, 88.4714),
(-96.1119, -25.8452),
(98.3718, -90.1805),
(-97.4358, -65.0356),
(-85.4703, 89.9322),
(-20.2096, 94.5287),
(27.5646, -51.9427),
(-16.388, 98.0704),
(-82.1905, 71.9339),
(34.5105, 50.6436),
(-82.3188, 28.137),
(65.9578, -88.7528),
(73.7016, -76.3054),
(-96.7707, -18.3056),
(-12.8469, 99.1525),
(-10.9591, 34.8166),
(-60.0732, 76.5184),
(85.5555, 69.7545),
(-12.7069, 73.6799),
(93.1526, -40.1999),
(88.6107, -41.8136),
(-63.1025, -77.3641),
(-58.3198, 84.0293),
(23.9521, 61.4485),
(45.9851, 47.008),
(-72.0084, -17.7366),
(44.7278, 62.8821),
(-89.2908, -50.3842),
(98.8171, -23.5265),
(-19.4029, -65.0703),
(93.8293, 36.2134),
(-22.8926, 98.0867),
(-44.4062, 9.10804),
(-20.6237, 23.2924),
(-51.1454, 27.6162),
(19.1023, -50.6689),
(-33.012, -83.5364),
(37.976, 9.18598),
(19.3601, 33.3324),
(-37.5405, 52.9104),
(53.7549, -48.6245),
(35.3439, -79.8122),
(-4.64331, 4.17503),
(64.4792, 95.5033),
(-29.5845, 57.368),
(-53.0951, 42.1904),
(-53.596, -68.8121),
(26.1298, 41.2376),
(-29.9801, -78.0155),
(28.1525, 70.441),
(65.4107, 80.1551),
(-75.2687, -86.5318),
(74.2148, -10.101),
(-2.4074, 62.971),
(96.7457, -91.3725),
(68.6882, -77.6094),
(90.7202, -74.0459),
(37.7684, 37.4356),
(-7.69563, 28.4682),
(-16.7575, 35.1254),
(71.4322, 88.2727),
(-62.2872, -91.1342),
(-99.508, 52.8819),
(49.137, -34.5048),
(-12.0107, 21.772),
(-93.2157, -96.8514),
(67.4561, 59.3426),
(35.7987, 74.5853),
(34.0507, -68.6856),
(-1.53645, -73.379),
(-30.9802, 3.43155),
(1.99845, 79.6953),
(-34.3016, 17.3936),
(95.6872, -56.594),
(-72.4482, 24.2116),
(70.3997, 77.3241),
(40.3846, 30.563),
(77.5438, 60.36),
(83.4394, -11.3853),
(-46.7177, 19.0094),
(-24.5617, 78.2526),
(-67.5029, 12.3404),
(-55.4943, -6.30098),
(-18.296, -51.0827),
(73.5155, 53.5889),
(85.5373, -63.091),
(31.9837, 21.4853),
(-11.1668, -64.973),
(66.8852, 24.496),
(-72.5159, 62.1248),
(-92.7247, -84.4592),
(-22.3886, -76.7409),
(4.02519, -54.9095),
(-14.9718, -38.2115),
(-36.6671, -77.6903),
(-21.891, -42.8908),
(54.5952, 51.2786),
(46.5729, 89.1238),
(5.05963, -81.8841),
(-40.8332, -76.8383),
(21.6376, -80.3501),
(-11.5402, 18.5105),
(-33.8785, -87.5541),
(-93.2362, -72.9517),
(96.814, 45.9883),
(46.6838, 16.2302),
(94.592, 52.1871),
(97.0211, -11.559),
(50.3171, 46.9901),
(-22.9708, -0.200422),
(-35.6795, -40.0975),
(-5.27098, 83.9628),
(35.004, 88.5378),
(82.5937, 34.371),
(-6.64858, -89.9371),
(25.5821, -14.3431),
(-74.7579, -39.5065),
(-2.20952, -19.8945),
(-21.7713, -0.96182),
(-6.34966, 16.2697),
(21.0971, -62.3715),
(-41.0622, 10.2926),
(-3.79913, -65.7104),
(93.4164, 50.9937),
(30.361, 75.5258),
(86.711, 49.3824),
(91.9482, 9.46496),
(-61.1404, 9.26342),
(41.8247, -62.5428),
(44.1086, 31.8891),
(50.3996, 27.1204),
(-55.689, -73.9055),
(-0.996773, -74.3519),
(3.39302, -44.0298),
(-15.295, -77.3373),
(-2.16862, -10.7588),
(95.5738, -94.4982),
(26.802, 70.2067),
(18.5987, 60.3176),
(7.63016, -79.4473),
(72.4133, 26.9154),
(33.8524, -83.2854),
(12.0486, -29.3414),
(-45.2474, -86.0333),
(49.2163, 61.8432),
(95.2645, -19.5205),
(89.0934, 87.4703),
(26.3268, -77.3398),
(-97.6786, -64.9349),
(80.1859, -32.4256),
(98.3036, 35.9289),
(28.1649, 45.681),
(44.4568, -13.6348),
(-65.0365, -21.8937),
(-22.0346, 11.292),
(-75.5983, 39.0269),
(-62.8504, 3.83846),
(98.2661, -4.20043),
(-75.5713, -42.5437),
(34.5144, -50.5297),
(-8.54322, 74.9361),
(63.5331, 19.2862),
(-60.1199, 86.0846),
(-85.1278, 56.1231),
(27.7078, -78.8735),
(-10.5933, -86.9551),
(13.8288, -45.3784),
(58.8993, -44.4447),
(-1.46549, 88.2752),
(78.0623, -59.9916),
(13.9677, -54.4379),
(-30.2445, -44.7888),
(-5.69231, -77.6514),
(84.8596, 92.0101),
(42.3381, 80.1895),
(54.6714, -63.17),
(-10.4496, 46.631),
(-10.2001, -86.2838),
(-82.1127, -77.6268),
(-7.67664, 30.4565),
(-57.9896, -82.3092),
(-20.236, 0.00991379),
(-41.6764, -17.2745),
(-53.425, 84.484),
(10.4193, 28.2007),
(-33.2082, 87.3548),
(-85.6149, 75.7367),
(-97.568, 50.0437),
(-82.1624, -71.7992),
(-51.8178, 76.5797),
(77.3224, 4.98283),
(32.5513, -97.1004),
(16.71, 19.1812),
(-76.238, -44.5224),
(-69.7624, -53.3314),
(78.7816, -52.2001),
(-59.875, -6.15161),
(-70.1723, -65.5477),
(99.3456, -14.3295),
(46.0398, -91.2418),
(-55.7919, 36.067),
(-65.4935, -74.3411),
(-17.6, -64.389),
(2.59777, 56.9736),
(-93.5099, -90.7236),
(-21.3914, 52.0802),
(-99.7032, 1.73801),
(-38.0834, -49.838),
(-45.8733, 34.6685),
(67.2158, 2.91041),
(57.5324, -83.7844),
(33.4653, -45.9943),
(33.3014, -72.3164),
(-90.7327, -41.8963),
(-99.1823, 70.0442),
(-52.2419, 58.607),
(-76.4839, 12.5528),
(12.9478, 71.9872),
(-73.7241, -98.9287),
(88.1415, -87.8598),
(-10.5511, 17.1935),
(65.3053, -74.294),
(-20.3433, -21.776),
(-34.5016, 11.3149),
(16.5264, 40.2724),
(26.5099, 51.6167),
(-1.90181, 7.74322),
(-7.57388, 43.3591),
(-59.6054, 43.0039),
(-82.996, -87.2616),
(-59.1889, 40.9657),
(52.5785, -94.1886),
(-32.2872, 12.7364),
(41.5173, 97.3748),
(-82.5658, -55.1713),
(42.3808, -34.9895),
(69.2724, 36.0649),
(-45.2348, -36.6868),
(92.5277, 15.2292),
(-21.5321, -66.4662),
(62.7319, 24.2659),
(-98.7305, 33.3339),
(72.7639, 61.31),
(-32.8932, -30.8003),
(58.4874, 38.1179),
(-40.9007, 5.89031),
(17.6545, 29.5727),
(-79.5371, 82.8612),
(-92.729, 11.6084),
(93.8482, -35.0316),
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