Changed the semantics of the minEnclosingTriangle function such that:

1. The function receives a set of points as input instead of a convex polygon with more than three vertices
2. The convex hull P is computed inside the function
3.1. If the number of vertices of P is greater than three then the algorithm which was implemented before executes
3.2. Otherwise the vertices of the triangle are picked from the vertices of the given polygon and the area computed

modules/imgproc/include/opencv2/imgproc.hpp

@@ -1451,8 +1451,8 @@ CV_EXPORTS_W void boxPoints(RotatedRect box, OutputArray points);
 CV_EXPORTS_W void minEnclosingCircle( InputArray points,
                                       CV_OUT Point2f& center, CV_OUT float& radius );
 
-//! computes the minimal enclosing triangle for a convex polygon defined by at least three points
-CV_EXPORTS_W void minEnclosingTriangle( InputArray convexPolygon,
+//! computes the minimal enclosing triangle for a set of points
+CV_EXPORTS_W void minEnclosingTriangle( InputArray points,
                                         CV_OUT OutputArray triangle, CV_OUT double& area );
 
 //! matches two contours using one of the available algorithms

modules/imgproc/src/min_enclosing_triangle.cpp

@@ -156,10 +156,10 @@ static bool areOnTheSameSideOfLine(const cv::Point2f &p1, const cv::Point2f &p2,
 
 static double areaOfTriangle(const cv::Point2f &a, const cv::Point2f &b, const cv::Point2f &c);
 
-static void copyConvexPolygon(cv::InputArray convexPolygon);
-
 static void copyResultingTriangle(const std::vector<cv::Point2f> &resultingTriangle, cv::OutputArray triangle);
 
+static void createConvexHull(cv::InputArray points);
+
 static double distanceBtwPoints(const cv::Point2f &a, const cv::Point2f &b);
 
 static double distanceFromPointToLine(const cv::Point2f &a, const cv::Point2f &linePointB,
@@ -184,7 +184,7 @@ static double height(const cv::Point2f &polygonPoint);
 
 static double height(unsigned int polygonPointIndex);
 
-static void initialise();
+static void initialise(std::vector<cv::Point2f> &triangle, double &area);
 
 static unsigned int intersects(double angleGammaAndPoint, unsigned int polygonPointIndex);
 
@@ -240,6 +240,8 @@ static double oppositeAngle(double angle);
 
 static unsigned int predecessor(unsigned int index);
 
+static void returnMinimumAreaEnclosingTriangle(std::vector<cv::Point2f> &triangle, double &area);
+
 static void searchForBTangency();
 
 static int sign(double number);
@@ -258,20 +260,20 @@ static void updateSidesCA();
 ///////////////////////////////////// Main functions /////////////////////////////////////
 
 
-//! Find the minimum enclosing triangle and its area for the given polygon
+//! Find the minimum enclosing triangle and its area for the given set of points
 /*!
 * The overall complexity of the algorithm is theta(n) where "n" represents the number
-* of vertices in the convex polygon
+* of vertices in the convex hull of the points
 *
-* @param convexPolygon  Convex polygon defined by at least three points
+* @param points         Set of points
 * @param triangle       Minimum area triangle enclosing the given polygon
 * @param area           Area of the minimum area enclosing triangle
 */
-void cv::minEnclosingTriangle(cv::InputArray convexPolygon,
+void cv::minEnclosingTriangle(cv::InputArray points,
                               CV_OUT cv::OutputArray triangle, CV_OUT double& area) {
     std::vector<cv::Point2f> resultingTriangle;
 
-    copyConvexPolygon(convexPolygon);
+    createConvexHull(points);
     findMinEnclosingTriangle(resultingTriangle, area);
     copyResultingTriangle(resultingTriangle, triangle);
 }
@@ -280,37 +282,35 @@ void cv::minEnclosingTriangle(cv::InputArray convexPolygon,
 /////////////////////////////// Helper functions definition //////////////////////////////
 
 
-//! Copy the provided convex polygon to the global variable "polygon"
+//! Create the convex hull of the given set of points
 /*!
-* @param convexPolygon The provided convex polygon
+* @param points The provided set of points
 */
-static void copyConvexPolygon(cv::InputArray convexPolygon) {
-    cv::Mat convexPolygonMat = convexPolygon.getMat();
+static void createConvexHull(cv::InputArray points) {
+    cv::Mat pointsMat = points.getMat();
 
-    convexPolygonMat.copyTo(polygon);
+    CV_Assert((pointsMat.checkVector(2) > 0) &&
+              ((pointsMat.depth() == CV_32F) || (pointsMat.depth() == CV_32S)));
+
+    convexHull(points, polygon, true, true);
 }
 
-//! Find the minimum enclosing triangle and its area for the given polygon
+//! Find the minimum enclosing triangle and its area
 /*!
 * The overall complexity of the algorithm is theta(n) where "n" represents the number
 * of vertices in the convex polygon
 *
-* @param convexPolygon  Convex polygon defined by at least three points
 * @param triangle       Minimum area triangle enclosing the given polygon
 * @param area           Area of the minimum area enclosing triangle
 */
 static void findMinEnclosingTriangle( std::vector<cv::Point2f> &triangle, double& area) {
-    // Check if the polygon is convex and is a k-gon with k > 3
-    CV_Assert(isContourConvex(polygon) && (polygon.size() > 3));
-
-    area = std::numeric_limits<double>::max();
+    initialise(triangle, area);
 
-    // Clear all points previously stored in the vector
-    triangle.clear();
-
-    initialise();
-
-    findMinimumAreaEnclosingTriangle(triangle, area);
+    if (polygon.size() > 3) {
+        findMinimumAreaEnclosingTriangle(triangle, area);
+    } else {
+        returnMinimumAreaEnclosingTriangle(triangle, area);
+    }
 }
 
 //! Copy resultingTriangle to the OutputArray triangle
@@ -320,9 +320,14 @@ static void copyResultingTriangle(const std::vector<cv::Point2f> &resultingTrian
 }
 
 //! Initialisation function
-static void initialise() {
+static void initialise(std::vector<cv::Point2f> &triangle, double &area) {
     nrOfPoints = static_cast<unsigned int>(polygon.size());
+    area = std::numeric_limits<double>::max();
+
+    // Clear all points previously stored in the vector
+    triangle.clear();
 
+    // Initialise the values of the indices for the algorithm
     a = 1;
     b = 2;
     c = 0;
@@ -353,6 +358,19 @@ static void findMinimumAreaEnclosingTriangle(std::vector<cv::Point2f> &triangle,
     }
 }
 
+//! Return the minimum area enclosing (pseudo-)triangle in case the convex polygon has at most three points
+/*!
+* @param triangle   Minimum area triangle enclosing the given polygon
+* @param area       Area of the minimum area enclosing triangle
+*/
+static void returnMinimumAreaEnclosingTriangle(std::vector<cv::Point2f> &triangle, double &area) {
+    for (int i = 0; i < 3; i++) {
+        triangle.push_back(polygon[i % nrOfPoints]);
+    }
+
+    area = areaOfTriangle(triangle[0], triangle[1], triangle[2]);
+}
+
 //! Advance b to the right chain
 /*!
 * See paper [2] for more details