mirror of
https://hub.njuu.cf/TheAlgorithms/C-Plus-Plus.git
synced 2023-10-11 13:05:55 +08:00
223 lines
6.8 KiB
C++
223 lines
6.8 KiB
C++
/**
|
|
* @file
|
|
* @brief Get centre and radius of the
|
|
* [smallest circle](https://en.wikipedia.org/wiki/Smallest-circle_problem)
|
|
* that circumscribes given set of points.
|
|
*
|
|
* @see [other
|
|
* implementation](https://www.nayuki.io/page/smallest-enclosing-circle)
|
|
*/
|
|
#include <cmath>
|
|
#include <iostream>
|
|
#include <vector>
|
|
|
|
/** Define a point */
|
|
struct Point
|
|
{
|
|
double x, /**< abscissa */
|
|
y; /**< ordinate */
|
|
|
|
/** construct a point
|
|
* \param [in] a absicca (default = 0.0)
|
|
* \param [in] b ordinate (default = 0.0)
|
|
*/
|
|
explicit Point(double a = 0.f, double b = 0.f)
|
|
{
|
|
x = a;
|
|
y = b;
|
|
}
|
|
};
|
|
|
|
/** Compute the Euclidian distance between two points \f$A\equiv(x_1,y_1)\f$ and
|
|
* \f$B\equiv(x_2,y_2)\f$ using the formula:
|
|
* \f[d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\f]
|
|
*
|
|
* \param [in] A point A
|
|
* \param [in] B point B
|
|
* \return ditance
|
|
*/
|
|
double LenghtLine(const Point &A, const Point &B)
|
|
{
|
|
double dx = B.x - A.x;
|
|
double dy = B.y - A.y;
|
|
return std::sqrt((dx * dx) + (dy * dy));
|
|
}
|
|
|
|
/**
|
|
* Compute the area of triangle formed by three points using [Heron's
|
|
* formula](https://en.wikipedia.org/wiki/Heron%27s_formula).
|
|
* If the lengths of the sides of the triangle are \f$a,\,b,\,c\f$ and
|
|
* \f$s=\displaystyle\frac{a+b+c}{2}\f$ is the semi-perimeter then the area is
|
|
* given by \f[A=\sqrt{s(s-a)(s-b)(s-c)}\f]
|
|
* \param [in] A vertex A
|
|
* \param [in] B vertex B
|
|
* \param [in] C vertex C
|
|
* \returns area of triangle
|
|
*/
|
|
double TriangleArea(const Point &A, const Point &B, const Point &C)
|
|
{
|
|
double a = LenghtLine(A, B);
|
|
double b = LenghtLine(B, C);
|
|
double c = LenghtLine(C, A);
|
|
double p = (a + b + c) / 2;
|
|
return std::sqrt(p * (p - a) * (p - b) * (p - c));
|
|
}
|
|
|
|
/**
|
|
* Check if a set of points lie within given circle. This is true if the
|
|
* distance of all the points from the centre of the circle is less than the
|
|
* radius of the circle
|
|
* \param [in] P set of points to check
|
|
* \param [in] Center coordinates to centre of the circle
|
|
* \param [in] R radius of the circle
|
|
* \returns True if P lies on or within the circle
|
|
* \returns False if P lies outside the circle
|
|
*/
|
|
bool PointInCircle(const std::vector<Point> &P, const Point &Center, double R)
|
|
{
|
|
for (size_t i = 0; i < P.size(); i++)
|
|
{
|
|
if (LenghtLine(P[i], Center) > R)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
* Find the centre and radius of a circle enclosing a set of points.\n
|
|
* The function returns the radius of the circle and prints the coordinated of
|
|
* the centre of the circle.
|
|
* \param [in] P vector of points
|
|
* \returns radius of the circle
|
|
*/
|
|
double circle(const std::vector<Point> &P)
|
|
{
|
|
double minR = INFINITY;
|
|
double R;
|
|
Point C;
|
|
Point minC;
|
|
|
|
/* This code is invalid and does not give correct result for TEST 3 */
|
|
// for each point in the list
|
|
for (size_t i = 0; i < P.size() - 2; i++)
|
|
// for every subsequent point in the list
|
|
for (size_t j = i + 1; j < P.size(); j++)
|
|
// for every subsequent point in the list
|
|
for (size_t k = j + 1; k < P.size(); k++)
|
|
{
|
|
// here, we now have picked three points from the given set of
|
|
// points that we can use
|
|
// viz., P[i], P[j] and P[k]
|
|
C.x = -0.5 * ((P[i].y * (P[j].x * P[j].x + P[j].y * P[j].y -
|
|
P[k].x * P[k].x - P[k].y * P[k].y) +
|
|
P[j].y * (P[k].x * P[k].x + P[k].y * P[k].y -
|
|
P[i].x * P[i].x - P[i].y * P[i].y) +
|
|
P[k].y * (P[i].x * P[i].x + P[i].y * P[i].y -
|
|
P[j].x * P[j].x - P[j].y * P[j].y)) /
|
|
(P[i].x * (P[j].y - P[k].y) +
|
|
P[j].x * (P[k].y - P[i].y) +
|
|
P[k].x * (P[i].y - P[j].y)));
|
|
C.y = 0.5 * ((P[i].x * (P[j].x * P[j].x + P[j].y * P[j].y -
|
|
P[k].x * P[k].x - P[k].y * P[k].y) +
|
|
P[j].x * (P[k].x * P[k].x + P[k].y * P[k].y -
|
|
P[i].x * P[i].x - P[i].y * P[i].y) +
|
|
P[k].x * (P[i].x * P[i].x + P[i].y * P[i].y -
|
|
P[j].x * P[j].x - P[j].y * P[j].y)) /
|
|
(P[i].x * (P[j].y - P[k].y) +
|
|
P[j].x * (P[k].y - P[i].y) +
|
|
P[k].x * (P[i].y - P[j].y)));
|
|
R = (LenghtLine(P[i], P[j]) * LenghtLine(P[j], P[k]) *
|
|
LenghtLine(P[k], P[i])) /
|
|
(4 * TriangleArea(P[i], P[j], P[k]));
|
|
if (!PointInCircle(P, C, R))
|
|
{
|
|
continue;
|
|
}
|
|
if (R <= minR)
|
|
{
|
|
minR = R;
|
|
minC = C;
|
|
}
|
|
}
|
|
|
|
// for each point in the list
|
|
for (size_t i = 0; i < P.size() - 1; i++)
|
|
// for every subsequent point in the list
|
|
for (size_t j = i + 1; j < P.size(); j++)
|
|
{
|
|
// check for diameterically opposite points
|
|
C.x = (P[i].x + P[j].x) / 2;
|
|
C.y = (P[i].y + P[j].y) / 2;
|
|
R = LenghtLine(C, P[i]);
|
|
if (!PointInCircle(P, C, R))
|
|
{
|
|
continue;
|
|
}
|
|
if (R <= minR)
|
|
{
|
|
minR = R;
|
|
minC = C;
|
|
}
|
|
}
|
|
std::cout << minC.x << " " << minC.y << std::endl;
|
|
return minR;
|
|
}
|
|
|
|
/** Test case: result should be:
|
|
* \n Circle with
|
|
* \n radius 3.318493136080724
|
|
* \n centre at (3.0454545454545454, 1.3181818181818181)
|
|
*/
|
|
void test()
|
|
{
|
|
std::vector<Point> Pv;
|
|
Pv.push_back(Point(0, 0));
|
|
Pv.push_back(Point(5, 4));
|
|
Pv.push_back(Point(1, 3));
|
|
Pv.push_back(Point(4, 1));
|
|
Pv.push_back(Point(3, -2));
|
|
std::cout << circle(Pv) << std::endl;
|
|
}
|
|
|
|
/** Test case: result should be:
|
|
* \n Circle with
|
|
* \n radius 1.4142135623730951
|
|
* \n centre at (1.0, 1.0)
|
|
*/
|
|
void test2()
|
|
{
|
|
std::vector<Point> Pv;
|
|
Pv.push_back(Point(0, 0));
|
|
Pv.push_back(Point(0, 2));
|
|
Pv.push_back(Point(2, 2));
|
|
Pv.push_back(Point(2, 0));
|
|
std::cout << circle(Pv) << std::endl;
|
|
}
|
|
|
|
/** Test case: result should be:
|
|
* \n Circle with
|
|
* \n radius 1.821078397711709
|
|
* \n centre at (2.142857142857143, 1.7857142857142856)
|
|
* @todo This test fails
|
|
*/
|
|
void test3()
|
|
{
|
|
std::vector<Point> Pv;
|
|
Pv.push_back(Point(0.5, 1));
|
|
Pv.push_back(Point(3.5, 3));
|
|
Pv.push_back(Point(2.5, 0));
|
|
Pv.push_back(Point(2, 1.5));
|
|
std::cout << circle(Pv) << std::endl;
|
|
}
|
|
|
|
/** Main program */
|
|
int main()
|
|
{
|
|
test();
|
|
std::cout << std::endl;
|
|
test2();
|
|
std::cout << std::endl;
|
|
test3();
|
|
return 0;
|
|
}
|