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updated documentation - NOTE TESTS FAIL
@yanglbme this algorithm does not give right answers
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Krishna Vedala
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@ -1,121 +1,195 @@
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/**
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* @file
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* @brief Get centre and radius of the
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* [smallest circle](https://en.wikipedia.org/wiki/Smallest-circle_problem)
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* that circumscribes given set of points.
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*
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* @see [other
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* implementation](https://www.nayuki.io/page/smallest-enclosing-circle)
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*/
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#include <cmath>
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#include <iostream>
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#include <vector>
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#include <math.h>
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using namespace std;
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/** Define a point */
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struct Point {
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double x, /**< abscissa */
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y; /**< ordinate */
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struct Point
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{
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double x, y;
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Point(double a = 0.0, double b = 0.0)
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{
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/** construct a point
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* \param [in] a absicca (default = 0.0)
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* \param [in] b ordinate (default = 0.0)
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*/
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Point(double a = 0.0, double b = 0.0) {
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x = a;
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y = b;
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}
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};
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double LenghtLine(Point A, Point B)
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{
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return sqrt(abs((B.x - A.x) * (B.x - A.x)) + abs((B.y - A.y) * (B.y - A.y)));
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/** Compute the Euclidian distance between two points \f$A\equiv(x_1,y_1)\f$ and
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* \f$B\equiv(x_2,y_2)\f$ using the formula:
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* \f[d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\f]
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*
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* \param [in] A point A
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* \param [in] B point B
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* \return ditance
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*/
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double LenghtLine(const Point &A, const Point &B) {
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double dx = B.x - A.x;
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double dy = B.y - A.y;
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return std::sqrt((dx * dx) + (dy * dy));
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}
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double TriangleArea(Point A, Point B, Point C)
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{
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/**
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* Compute the area of triangle formed by three points using [Heron's
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* formula](https://en.wikipedia.org/wiki/Heron%27s_formula).
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* If the lengths of the sides of the triangle are \f$a,\,b,\,c\f$ and
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* \f$s=\displaystyle\frac{a+b+c}{2}\f$ is the semi-perimeter then the area is
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* given by \f[A=\sqrt{s(s-a)(s-b)(s-c)}\f]
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* \param [in] A vertex A
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* \param [in] B vertex B
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* \param [in] C vertex C
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* \returns area of triangle
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*/
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double TriangleArea(const Point &A, const Point &B, const Point &C) {
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double a = LenghtLine(A, B);
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double b = LenghtLine(B, C);
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double c = LenghtLine(C, A);
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double p = (a + b + c) / 2;
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return sqrt(p * (p - a) * (p - b) * (p - c));
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return std::sqrt(p * (p - a) * (p - b) * (p - c));
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}
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bool PointInCircle(vector<Point> &P, Point Center, double R)
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{
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for (size_t i = 0; i < P.size(); i++)
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{
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/**
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* Check if a set of points lie within given circle. This is true if the
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* distance of all the points from the centre of the circle is less than the
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* radius of the circle
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* \param [in] P set of points to check
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* \param [in] Center coordinates to centre of the circle
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* \param [in] R radius of the circle
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* \returns True if P lies on or within the circle
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* \returns False if P lies outside the circle
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*/
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bool PointInCircle(const std::vector<Point> &P, const Point &Center, double R) {
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for (size_t i = 0; i < P.size(); i++) {
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if (LenghtLine(P[i], Center) > R)
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return false;
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}
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return true;
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}
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double circle(vector<Point> P)
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{
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/**
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* Find the centre and radius of a circle enclosing a set of points.\n
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* The function returns the radius of the circle and prints the coordinated of
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* the centre of the circle.
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* \param [in] P vector of points
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* \returns radius of the circle
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*/
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double circle(const std::vector<Point> &P) {
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double minR = INT8_MAX;
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double R;
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Point C;
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Point minC;
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for (size_t i = 0; i < P.size() - 2; i++)
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for (size_t j = i + 1; j < P.size(); j++)
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for (size_t k = j + 1; k < P.size(); k++)
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{
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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)));
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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)));
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R = (LenghtLine(P[i], P[j]) * LenghtLine(P[j], P[k]) * LenghtLine(P[k], P[i])) / (4 * TriangleArea(P[i], P[j], P[k]));
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if (!PointInCircle(P, C, R))
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{
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continue;
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/* This code is invalid and does not give correct result for TEST 3
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// for each point in the list
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for (size_t i = 0; i < P.size() - 2; i++)
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// for every subsequent point in the list
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for (size_t j = i + 1; j < P.size(); j++)
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// for every subsequent point in the list
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for (size_t k = j + 1; k < P.size(); k++) {
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// here, we now have picked three points from the given set
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of
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// points that we can use
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// viz., P[i], P[j] and P[k]
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C.x = -0.5 * ((P[i].y * (P[j].x * P[j].x + P[j].y * P[j].y -
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P[k].x * P[k].x - P[k].y * P[k].y)
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+ P[j].y * (P[k].x * P[k].x + P[k].y * P[k].y - P[i].x * P[i].x - P[i].y
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* P[i].y) + P[k].y * (P[i].x * P[i].x + P[i].y * P[i].y - P[j].x * P[j].x
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- P[j].y * P[j].y)) / (P[i].x * (P[j].y - P[k].y) + P[j].x * (P[k].y -
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P[i].y) + P[k].x * (P[i].y - P[j].y))); C.y = 0.5 * ((P[i].x * (P[j].x *
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P[j].x + P[j].y * P[j].y - P[k].x * P[k].x - P[k].y * P[k].y) + P[j].x *
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(P[k].x * P[k].x + P[k].y * P[k].y - P[i].x * P[i].x - P[i].y * P[i].y) +
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P[k].x * (P[i].x * P[i].x + P[i].y * P[i].y -
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P[j].x * P[j].x - P[j].y * P[j].y))
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/ (P[i].x * (P[j].y - P[k].y) + P[j].x * (P[k].y - P[i].y) + P[k].x *
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(P[i].y - P[j].y))); R = (LenghtLine(P[i], P[j]) * LenghtLine(P[j], P[k])
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* LenghtLine(P[k], P[i])) / (4 * TriangleArea(P[i], P[j], P[k])); if
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(!PointInCircle(P, C, R)) { continue;
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}
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if (R <= minR) {
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minR = R;
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minC = C;
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}
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}
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if (R <= minR)
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{
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minR = R;
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minC = C;
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}
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}
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*/
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// for each point in the list
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for (size_t i = 0; i < P.size() - 1; i++)
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for (size_t j = i + 1; j < P.size(); j++)
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{
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// for every subsequent point in the list
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for (size_t j = i + 1; j < P.size(); j++) {
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C.x = (P[i].x + P[j].x) / 2;
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C.y = (P[i].y + P[j].y) / 2;
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R = LenghtLine(C, P[i]);
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if (!PointInCircle(P, C, R))
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{
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if (!PointInCircle(P, C, R)) {
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continue;
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}
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if (R <= minR)
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{
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if (R <= minR) {
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minR = R;
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minC = C;
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}
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}
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cout << minC.x << " " << minC.y << endl;
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std::cout << minC.x << " " << minC.y << std::endl;
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return minR;
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}
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void test()
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{
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vector<Point> Pv(5);
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/** Test case: result should be:
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* \n Circle with
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* \n radius 3.318493136080724
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* \n centre at (3.0454545454545454 1.3181818181818181)
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*/
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void test() {
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std::vector<Point> Pv(5);
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Pv.push_back(Point(0, 0));
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Pv.push_back(Point(1, 3));
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Pv.push_back(Point(4, 1));
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Pv.push_back(Point(5, 4));
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Pv.push_back(Point(3, -2));
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cout << circle(Pv) << endl;
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std::cout << circle(Pv) << std::endl;
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}
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void test2()
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{
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vector<Point> Pv(4);
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/** Test case: result should be:
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* \n Circle with
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* \n radius 1.4142135623730951
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* \n centre at (1.0 1.0)
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*/
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void test2() {
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std::vector<Point> Pv(4);
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Pv.push_back(Point(0, 0));
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Pv.push_back(Point(0, 2));
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Pv.push_back(Point(2, 2));
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Pv.push_back(Point(2, 0));
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cout << circle(Pv) << endl;
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std::cout << circle(Pv) << std::endl;
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}
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void test3()
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{
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vector<Point> Pv(3);
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/** Test case: result should be:
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* \n Circle with
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* \n radius 1.821078397711709
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* \n centre at (2.142857142857143 1.7857142857142856)
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*/
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void test3() {
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std::vector<Point> Pv(3);
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Pv.push_back(Point(0.5, 1));
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Pv.push_back(Point(3.5, 3));
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Pv.push_back(Point(2.5, 0));
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cout << circle(Pv) << endl;
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std::cout << circle(Pv) << std::endl;
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}
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int main()
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{
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/** Main program */
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int main() {
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test();
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cout << endl;
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std::cout << std::endl;
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test2();
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cout << endl;
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std::cout << std::endl;
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test3();
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return 0;
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}
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