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1564 lines
66 KiB
C++
1564 lines
66 KiB
C++
/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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// INFORMATION REGARDING THE CONTRIBUTION:
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//
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// Author: Ovidiu Parvu
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// Affiliation: Brunel University
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// Created: 11.09.2013
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// E-mail: <ovidiu.parvu[AT]gmail.com>
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// Web: http://people.brunel.ac.uk/~cspgoop
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//
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// These functions were implemented during Ovidiu Parvu's first year as a PhD student at
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// Brunel University, London, UK. The PhD project is supervised by prof. David Gilbert (principal)
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// and prof. Nigel Saunders (second).
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//
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// THE IMPLEMENTATION OF THE MODULES IS BASED ON THE FOLLOWING PAPERS:
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//
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// [1] V. Klee and M. C. Laskowski, "Finding the smallest triangles containing a given convex
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// polygon", Journal of Algorithms, vol. 6, no. 3, pp. 359-375, Sep. 1985.
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// [2] J. O'Rourke, A. Aggarwal, S. Maddila, and M. Baldwin, "An optimal algorithm for finding
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// minimal enclosing triangles", Journal of Algorithms, vol. 7, no. 2, pp. 258-269, Jun. 1986.
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//
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// The overall complexity of the algorithm is theta(n) where "n" represents the number
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// of vertices in the convex polygon.
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//
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2000, Intel Corporation, all rights reserved.
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// Copyright (C) 2013, OpenCV Foundation, all rights reserved.
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// Copyright (C) 2013, Ovidiu Parvu, all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of the copyright holders may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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#include "precomp.hpp"
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#include <algorithm>
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#include <cmath>
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#include <limits>
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#include <vector>
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///////////////////////////////// Constants definitions //////////////////////////////////
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// Intersection of line and polygon
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#define INTERSECTS_BELOW 1
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#define INTERSECTS_ABOVE 2
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#define INTERSECTS_CRITICAL 3
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// Error messages
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#define ERR_SIDE_B_GAMMA "The position of side B could not be determined, because gamma(b) could not be computed."
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#define ERR_VERTEX_C_ON_SIDE_B "The position of the vertex C on side B could not be determined, because the considered lines do not intersect."
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// Possible values for validation flag
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#define VALIDATION_SIDE_A_TANGENT 0
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#define VALIDATION_SIDE_B_TANGENT 1
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#define VALIDATION_SIDES_FLUSH 2
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// Threshold value for comparisons
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#define EPSILON 1E-5
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////////////////////////////// Helper functions declarations /////////////////////////////
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namespace minEnclosingTriangle {
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static void advance(unsigned int &index, unsigned int nrOfPoints);
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static void advanceBToRightChain(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int &b,
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unsigned int c);
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static bool almostEqual(double number1, double number2);
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static double angleOfLineWrtOxAxis(const cv::Point2f &a, const cv::Point2f &b);
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static bool areEqualPoints(const cv::Point2f &point1, const cv::Point2f &point2);
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static bool areIdenticalLines(const std::vector<double> &side1Params,
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const std::vector<double> &side2Params, double sideCExtraParam);
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static bool areIdenticalLines(double a1, double b1, double c1, double a2, double b2, double c2);
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static bool areIntersectingLines(const std::vector<double> &side1Params,
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const std::vector<double> &side2Params,
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double sideCExtraParam, cv::Point2f &intersectionPoint1,
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cv::Point2f &intersectionPoint2);
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static bool areOnTheSameSideOfLine(const cv::Point2f &p1, const cv::Point2f &p2,
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const cv::Point2f &a, const cv::Point2f &b);
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static double areaOfTriangle(const cv::Point2f &a, const cv::Point2f &b, const cv::Point2f &c);
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static void copyResultingTriangle(const std::vector<cv::Point2f> &resultingTriangle, cv::OutputArray triangle);
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static void createConvexHull(cv::InputArray points, std::vector<cv::Point2f> &polygon);
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static double distanceBtwPoints(const cv::Point2f &a, const cv::Point2f &b);
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static double distanceFromPointToLine(const cv::Point2f &a, const cv::Point2f &linePointB,
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const cv::Point2f &linePointC);
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static bool findGammaIntersectionPoints(const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int c, unsigned int polygonPointIndex,
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const cv::Point2f &side1StartVertex, const cv::Point2f &side1EndVertex,
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const cv::Point2f &side2StartVertex, const cv::Point2f &side2EndVertex,
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cv::Point2f &intersectionPoint1, cv::Point2f &intersectionPoint2);
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static void findMinEnclosingTriangle(cv::InputArray points,
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CV_OUT cv::OutputArray triangle, CV_OUT double &area);
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static void findMinEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
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std::vector<cv::Point2f> &triangle, double &area);
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static void findMinimumAreaEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
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std::vector<cv::Point2f> &triangle, double &area);
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static cv::Point2f findVertexCOnSideB(const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int a, unsigned int c,
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const cv::Point2f &sideBStartVertex,
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const cv::Point2f &sideBEndVertex,
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const cv::Point2f &sideCStartVertex,
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const cv::Point2f &sideCEndVertex);
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static bool gamma(unsigned int polygonPointIndex, cv::Point2f &gammaPoint,
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const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int a, unsigned int c);
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static bool greaterOrEqual(double number1, double number2);
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static double height(const cv::Point2f &polygonPoint, const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int c);
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static double height(unsigned int polygonPointIndex, const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int c);
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static void initialise(std::vector<cv::Point2f> &triangle, double &area);
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static unsigned int intersects(double angleGammaAndPoint, unsigned int polygonPointIndex,
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const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int c);
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static bool intersectsAbove(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex,
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const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int c);
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static unsigned int intersectsAboveOrBelow(unsigned int succPredIndex, unsigned int pointIndex,
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const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int c);
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static bool intersectsBelow(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex,
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const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
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unsigned int c);
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static bool isAngleBetween(double angle1, double angle2, double angle3);
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static bool isAngleBetweenNonReflex(double angle1, double angle2, double angle3);
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static bool isFlushAngleBtwPredAndSucc(double &angleFlushEdge, double anglePred, double angleSucc);
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static bool isGammaAngleBtw(double &gammaAngle, double angle1, double angle2);
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static bool isGammaAngleEqualTo(double &gammaAngle, double angle);
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static bool isLocalMinimalTriangle(cv::Point2f &vertexA, cv::Point2f &vertexB,
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cv::Point2f &vertexC, const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int b,
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unsigned int validationFlag, const cv::Point2f &sideAStartVertex,
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const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
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const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
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const cv::Point2f &sideCEndVertex);
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static bool isNotBTangency(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int b,
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unsigned int c);
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static bool isOppositeAngleBetweenNonReflex(double angle1, double angle2, double angle3);
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static bool isPointOnLineSegment(const cv::Point2f &point, const cv::Point2f &lineSegmentStart,
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const cv::Point2f &lineSegmentEnd);
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static bool isValidMinimalTriangle(const cv::Point2f &vertexA, const cv::Point2f &vertexB,
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const cv::Point2f &vertexC, const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int b,
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unsigned int validationFlag, const cv::Point2f &sideAStartVertex,
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const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
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const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
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const cv::Point2f &sideCEndVertex);
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static bool lessOrEqual(double number1, double number2);
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static void lineEquationDeterminedByPoints(const cv::Point2f &p, const cv::Point2f &q,
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double &a, double &b, double &c);
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static std::vector<double> lineEquationParameters(const cv::Point2f& p, const cv::Point2f &q);
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static bool lineIntersection(const cv::Point2f &a1, const cv::Point2f &b1, const cv::Point2f &a2,
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const cv::Point2f &b2, cv::Point2f &intersection);
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static bool lineIntersection(double a1, double b1, double c1, double a2, double b2, double c2,
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cv::Point2f &intersection);
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static double maximum(double number1, double number2, double number3);
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static cv::Point2f middlePoint(const cv::Point2f &a, const cv::Point2f &b);
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static bool middlePointOfSideB(cv::Point2f &middlePointOfSideB, const cv::Point2f &sideAStartVertex,
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const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
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const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
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const cv::Point2f &sideCEndVertex);
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static void moveAIfLowAndBIfHigh(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int &a, unsigned int &b,
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unsigned int c);
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static double oppositeAngle(double angle);
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static unsigned int predecessor(unsigned int index, unsigned int nrOfPoints);
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static void returnMinimumAreaEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
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std::vector<cv::Point2f> &triangle, double &area);
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static void searchForBTangency(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int &b,
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unsigned int c);
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static int sign(double number);
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static unsigned int successor(unsigned int index, unsigned int nrOfPoints);
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static void updateMinimumAreaEnclosingTriangle(std::vector<cv::Point2f> &triangle, double &area,
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const cv::Point2f &vertexA, const cv::Point2f &vertexB,
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const cv::Point2f &vertexC);
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static void updateSideB(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int b,
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unsigned int c, unsigned int &validationFlag,
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cv::Point2f &sideBStartVertex, cv::Point2f &sideBEndVertex);
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static void updateSidesBA(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int b,
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unsigned int c, unsigned int &validationFlag,
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cv::Point2f &sideAStartVertex, cv::Point2f &sideAEndVertex,
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cv::Point2f &sideBStartVertex, cv::Point2f &sideBEndVertex,
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const cv::Point2f &sideCStartVertex, const cv::Point2f &sideCEndVertex);
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static void updateSidesCA(const std::vector<cv::Point2f> &polygon,
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unsigned int nrOfPoints, unsigned int a, unsigned int c,
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cv::Point2f &sideAStartVertex, cv::Point2f &sideAEndVertex,
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cv::Point2f &sideCStartVertex, cv::Point2f &sideCEndVertex);
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}
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///////////////////////////////////// Main functions /////////////////////////////////////
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//! Find the minimum enclosing triangle for the given set of points and return its area
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/*!
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* @param points Set of points
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* @param triangle Minimum area triangle enclosing the given set of points
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*/
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double cv::minEnclosingTriangle(cv::InputArray points, CV_OUT cv::OutputArray triangle) {
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double area;
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minEnclosingTriangle::findMinEnclosingTriangle(points, triangle, area);
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return area;
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}
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/////////////////////////////// Helper functions definition //////////////////////////////
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namespace minEnclosingTriangle {
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//! Find the minimum enclosing triangle and its area
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/*!
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* @param points Set of points
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* @param triangle Minimum area triangle enclosing the given set of points
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* @param area Area of the minimum area enclosing triangle
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*/
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static void findMinEnclosingTriangle(cv::InputArray points,
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CV_OUT cv::OutputArray triangle, CV_OUT double &area) {
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std::vector<cv::Point2f> resultingTriangle, polygon;
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createConvexHull(points, polygon);
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findMinEnclosingTriangle(polygon, resultingTriangle, area);
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copyResultingTriangle(resultingTriangle, triangle);
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}
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//! Create the convex hull of the given set of points
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/*!
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* @param points The provided set of points
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* @param polygon The polygon representing the convex hull of the points
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*/
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static void createConvexHull(cv::InputArray points, std::vector<cv::Point2f> &polygon) {
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cv::Mat pointsMat = points.getMat();
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std::vector<cv::Point2f> pointsVector;
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CV_Assert((pointsMat.checkVector(2) > 0) &&
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((pointsMat.depth() == CV_32F) || (pointsMat.depth() == CV_32S)));
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pointsMat.convertTo(pointsVector, CV_32F);
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convexHull(pointsVector, polygon, true, true);
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}
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//! Find the minimum enclosing triangle and its area
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/*!
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* The overall complexity of the algorithm is theta(n) where "n" represents the number
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* of vertices in the convex polygon
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*
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* @param polygon The polygon representing the convex hull of the points
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* @param triangle Minimum area triangle enclosing the given polygon
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* @param area Area of the minimum area enclosing triangle
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*/
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static void findMinEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
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std::vector<cv::Point2f> &triangle, double &area) {
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initialise(triangle, area);
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if (polygon.size() > 3) {
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findMinimumAreaEnclosingTriangle(polygon, triangle, area);
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} else {
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returnMinimumAreaEnclosingTriangle(polygon, triangle, area);
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}
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}
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//! Copy resultingTriangle to the OutputArray triangle
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/*!
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* @param resultingTriangle Minimum area triangle enclosing the given polygon found by the algorithm
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* @param triangle Minimum area triangle enclosing the given polygon returned to the user
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*/
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static void copyResultingTriangle(const std::vector<cv::Point2f> &resultingTriangle,
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cv::OutputArray triangle) {
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cv::Mat(resultingTriangle).copyTo(triangle);
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}
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//! Initialisation function
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/*!
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* @param triangle Minimum area triangle enclosing the given polygon
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* @param area Area of the minimum area enclosing triangle
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*/
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static void initialise(std::vector<cv::Point2f> &triangle, double &area) {
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area = std::numeric_limits<double>::max();
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// Clear all points previously stored in the vector
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triangle.clear();
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}
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//! Find the minimum area enclosing triangle for the given polygon
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/*!
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* @param polygon The polygon representing the convex hull of the points
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* @param triangle Minimum area triangle enclosing the given polygon
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* @param area Area of the minimum area enclosing triangle
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*/
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static void findMinimumAreaEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
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std::vector<cv::Point2f> &triangle, double &area) {
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// Algorithm specific variables
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unsigned int validationFlag;
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cv::Point2f vertexA, vertexB, vertexC;
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cv::Point2f sideAStartVertex, sideAEndVertex;
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cv::Point2f sideBStartVertex, sideBEndVertex;
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cv::Point2f sideCStartVertex, sideCEndVertex;
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unsigned int a, b, c;
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unsigned int nrOfPoints;
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// Variables initialisation
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nrOfPoints = static_cast<unsigned int>(polygon.size());
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a = 1;
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b = 2;
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c = 0;
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// Main algorithm steps
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for (c = 0; c < nrOfPoints; c++) {
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advanceBToRightChain(polygon, nrOfPoints, b, c);
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moveAIfLowAndBIfHigh(polygon, nrOfPoints, a, b, c);
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searchForBTangency(polygon, nrOfPoints, a ,b, c);
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updateSidesCA(polygon, nrOfPoints, a, c, sideAStartVertex, sideAEndVertex,
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sideCStartVertex, sideCEndVertex);
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if (isNotBTangency(polygon, nrOfPoints, a, b, c)) {
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updateSidesBA(polygon, nrOfPoints, a, b, c, validationFlag, sideAStartVertex,
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sideAEndVertex, sideBStartVertex, sideBEndVertex,
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sideCStartVertex, sideCEndVertex);
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} else {
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updateSideB(polygon, nrOfPoints, a, b, c, validationFlag,
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sideBStartVertex, sideBEndVertex);
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}
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if (isLocalMinimalTriangle(vertexA, vertexB, vertexC, polygon, nrOfPoints, a, b,
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validationFlag, sideAStartVertex, sideAEndVertex,
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sideBStartVertex, sideBEndVertex, sideCStartVertex,
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sideCEndVertex)) {
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updateMinimumAreaEnclosingTriangle(triangle, area, vertexA, vertexB, vertexC);
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}
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}
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}
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//! Return the minimum area enclosing (pseudo-)triangle in case the convex polygon has at most three points
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/*!
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* @param polygon The polygon representing the convex hull of the points
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* @param triangle Minimum area triangle enclosing the given polygon
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* @param area Area of the minimum area enclosing triangle
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*/
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static void returnMinimumAreaEnclosingTriangle(const std::vector<cv::Point2f> &polygon,
|
|
std::vector<cv::Point2f> &triangle, double &area) {
|
|
unsigned int nrOfPoints = static_cast<unsigned int>(polygon.size());
|
|
|
|
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
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param b Index b
|
|
* @param c Index c
|
|
*/
|
|
static void advanceBToRightChain(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int &b,
|
|
unsigned int c) {
|
|
while (greaterOrEqual(height(successor(b, nrOfPoints), polygon, nrOfPoints, c),
|
|
height(b, polygon, nrOfPoints, c))) {
|
|
advance(b, nrOfPoints);
|
|
}
|
|
}
|
|
|
|
//! Move "a" if it is low and "b" if it is high
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param c Index c
|
|
*/
|
|
static void moveAIfLowAndBIfHigh(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int &a, unsigned int &b,
|
|
unsigned int c) {
|
|
cv::Point2f gammaOfA;
|
|
|
|
while(height(b, polygon, nrOfPoints, c) > height(a, polygon, nrOfPoints, c)) {
|
|
if ((gamma(a, gammaOfA, polygon, nrOfPoints, a, c)) && (intersectsBelow(gammaOfA, b, polygon, nrOfPoints, c))) {
|
|
advance(b, nrOfPoints);
|
|
} else {
|
|
advance(a, nrOfPoints);
|
|
}
|
|
}
|
|
}
|
|
|
|
//! Search for the tangency of side B
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param c Index c
|
|
*/
|
|
static void searchForBTangency(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int &b,
|
|
unsigned int c) {
|
|
cv::Point2f gammaOfB;
|
|
|
|
while (((gamma(b, gammaOfB, polygon, nrOfPoints, a, c)) &&
|
|
(intersectsBelow(gammaOfB, b, polygon, nrOfPoints, c))) &&
|
|
(greaterOrEqual(height(b, polygon, nrOfPoints, c),
|
|
height(predecessor(a, nrOfPoints), polygon, nrOfPoints, c)))
|
|
) {
|
|
advance(b, nrOfPoints);
|
|
}
|
|
}
|
|
|
|
//! Check if tangency for side B was not obtained
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param c Index c
|
|
*/
|
|
static bool isNotBTangency(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int b,
|
|
unsigned int c) {
|
|
cv::Point2f gammaOfB;
|
|
|
|
if (((gamma(b, gammaOfB, polygon, nrOfPoints, a, c)) &&
|
|
(intersectsAbove(gammaOfB, b, polygon, nrOfPoints, c))) ||
|
|
(height(b, polygon, nrOfPoints, c) < height(predecessor(a, nrOfPoints), polygon, nrOfPoints, c))) {
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
//! Update sides A and C
|
|
/*!
|
|
* Side C will have as start and end vertices the polygon points "c" and "c-1"
|
|
* Side A will have as start and end vertices the polygon points "a" and "a-1"
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param c Index c
|
|
* @param sideAStartVertex Start vertex for defining side A
|
|
* @param sideAEndVertex End vertex for defining side A
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static void updateSidesCA(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int c,
|
|
cv::Point2f &sideAStartVertex, cv::Point2f &sideAEndVertex,
|
|
cv::Point2f &sideCStartVertex, cv::Point2f &sideCEndVertex) {
|
|
sideCStartVertex = polygon[predecessor(c, nrOfPoints)];
|
|
sideCEndVertex = polygon[c];
|
|
|
|
sideAStartVertex = polygon[predecessor(a, nrOfPoints)];
|
|
sideAEndVertex = polygon[a];
|
|
}
|
|
|
|
//! Update sides B and possibly A if tangency for side B was not obtained
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param c Index c
|
|
* @param validationFlag Flag used for validation
|
|
* @param sideAStartVertex Start vertex for defining side A
|
|
* @param sideAEndVertex End vertex for defining side A
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static void updateSidesBA(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int b,
|
|
unsigned int c, unsigned int &validationFlag,
|
|
cv::Point2f &sideAStartVertex, cv::Point2f &sideAEndVertex,
|
|
cv::Point2f &sideBStartVertex, cv::Point2f &sideBEndVertex,
|
|
const cv::Point2f &sideCStartVertex, const cv::Point2f &sideCEndVertex) {
|
|
// Side B is flush with edge [b, b-1]
|
|
sideBStartVertex = polygon[predecessor(b, nrOfPoints)];
|
|
sideBEndVertex = polygon[b];
|
|
|
|
// Find middle point of side B
|
|
cv::Point2f sideBMiddlePoint;
|
|
|
|
if ((middlePointOfSideB(sideBMiddlePoint, sideAStartVertex, sideAEndVertex, sideBStartVertex,
|
|
sideBEndVertex, sideCStartVertex, sideCEndVertex)) &&
|
|
(height(sideBMiddlePoint, polygon, nrOfPoints, c) <
|
|
height(predecessor(a, nrOfPoints), polygon, nrOfPoints, c))) {
|
|
sideAStartVertex = polygon[predecessor(a, nrOfPoints)];
|
|
sideAEndVertex = findVertexCOnSideB(polygon, nrOfPoints, a, c,
|
|
sideBStartVertex, sideBEndVertex,
|
|
sideCStartVertex, sideCEndVertex);
|
|
|
|
validationFlag = VALIDATION_SIDE_A_TANGENT;
|
|
} else {
|
|
validationFlag = VALIDATION_SIDES_FLUSH;
|
|
}
|
|
}
|
|
|
|
//! Set side B if tangency for side B was obtained
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param c Index c
|
|
* @param validationFlag Flag used for validation
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
*/
|
|
static void updateSideB(const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int b,
|
|
unsigned int c, unsigned int &validationFlag,
|
|
cv::Point2f &sideBStartVertex, cv::Point2f &sideBEndVertex) {
|
|
if (!gamma(b, sideBStartVertex, polygon, nrOfPoints, a, c)) {
|
|
CV_Error(cv::Error::StsInternal, ERR_SIDE_B_GAMMA);
|
|
}
|
|
|
|
sideBEndVertex = polygon[b];
|
|
|
|
validationFlag = VALIDATION_SIDE_B_TANGENT;
|
|
}
|
|
|
|
//! Update the triangle vertices after all sides were set and check if a local minimal triangle was found or not
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param vertexA Vertex A of the enclosing triangle
|
|
* @param vertexB Vertex B of the enclosing triangle
|
|
* @param vertexC Vertex C of the enclosing triangle
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param validationFlag Flag used for validation
|
|
* @param sideAStartVertex Start vertex for defining side A
|
|
* @param sideAEndVertex End vertex for defining side A
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static bool isLocalMinimalTriangle(cv::Point2f &vertexA, cv::Point2f &vertexB,
|
|
cv::Point2f &vertexC, const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int b,
|
|
unsigned int validationFlag, const cv::Point2f &sideAStartVertex,
|
|
const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
|
|
const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
|
|
const cv::Point2f &sideCEndVertex) {
|
|
if ((!lineIntersection(sideAStartVertex, sideAEndVertex,
|
|
sideBStartVertex, sideBEndVertex, vertexC)) ||
|
|
(!lineIntersection(sideAStartVertex, sideAEndVertex,
|
|
sideCStartVertex, sideCEndVertex, vertexB)) ||
|
|
(!lineIntersection(sideBStartVertex, sideBEndVertex,
|
|
sideCStartVertex, sideCEndVertex, vertexA))) {
|
|
return false;
|
|
}
|
|
|
|
return isValidMinimalTriangle(vertexA, vertexB, vertexC, polygon, nrOfPoints, a, b,
|
|
validationFlag, sideAStartVertex, sideAEndVertex,
|
|
sideBStartVertex, sideBEndVertex, sideCStartVertex,
|
|
sideCEndVertex);
|
|
}
|
|
|
|
//! Check if the found minimal triangle is valid
|
|
/*!
|
|
* This means that all midpoints of the triangle should touch the polygon
|
|
*
|
|
* See paper [2] for more details
|
|
*
|
|
* @param vertexA Vertex A of the enclosing triangle
|
|
* @param vertexB Vertex B of the enclosing triangle
|
|
* @param vertexC Vertex C of the enclosing triangle
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param b Index b
|
|
* @param validationFlag Flag used for validation
|
|
* @param sideAStartVertex Start vertex for defining side A
|
|
* @param sideAEndVertex End vertex for defining side A
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static bool isValidMinimalTriangle(const cv::Point2f &vertexA, const cv::Point2f &vertexB,
|
|
const cv::Point2f &vertexC, const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int a, unsigned int b,
|
|
unsigned int validationFlag, const cv::Point2f &sideAStartVertex,
|
|
const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
|
|
const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
|
|
const cv::Point2f &sideCEndVertex) {
|
|
cv::Point2f midpointSideA = middlePoint(vertexB, vertexC);
|
|
cv::Point2f midpointSideB = middlePoint(vertexA, vertexC);
|
|
cv::Point2f midpointSideC = middlePoint(vertexA, vertexB);
|
|
|
|
bool sideAValid = (validationFlag == VALIDATION_SIDE_A_TANGENT)
|
|
? (areEqualPoints(midpointSideA, polygon[predecessor(a, nrOfPoints)]))
|
|
: (isPointOnLineSegment(midpointSideA, sideAStartVertex, sideAEndVertex));
|
|
|
|
bool sideBValid = (validationFlag == VALIDATION_SIDE_B_TANGENT)
|
|
? (areEqualPoints(midpointSideB, polygon[b]))
|
|
: (isPointOnLineSegment(midpointSideB, sideBStartVertex, sideBEndVertex));
|
|
|
|
bool sideCValid = isPointOnLineSegment(midpointSideC, sideCStartVertex, sideCEndVertex);
|
|
|
|
return (sideAValid && sideBValid && sideCValid);
|
|
}
|
|
|
|
//! Update the current minimum area enclosing triangle if the newly obtained one has a smaller area
|
|
/*!
|
|
* @param triangle Minimum area triangle enclosing the given polygon
|
|
* @param area Area of the minimum area triangle enclosing the given polygon
|
|
* @param vertexA Vertex A of the enclosing triangle
|
|
* @param vertexB Vertex B of the enclosing triangle
|
|
* @param vertexC Vertex C of the enclosing triangle
|
|
*/
|
|
static void updateMinimumAreaEnclosingTriangle(std::vector<cv::Point2f> &triangle, double &area,
|
|
const cv::Point2f &vertexA, const cv::Point2f &vertexB,
|
|
const cv::Point2f &vertexC) {
|
|
double triangleArea = areaOfTriangle(vertexA, vertexB, vertexC);
|
|
|
|
if (triangleArea < area) {
|
|
triangle.clear();
|
|
|
|
triangle.push_back(vertexA);
|
|
triangle.push_back(vertexB);
|
|
triangle.push_back(vertexC);
|
|
|
|
area = triangleArea;
|
|
}
|
|
}
|
|
|
|
//! Return the middle point of side B
|
|
/*!
|
|
* @param middlePointOfSideB Middle point of side B
|
|
* @param sideAStartVertex Start vertex for defining side A
|
|
* @param sideAEndVertex End vertex for defining side A
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static bool middlePointOfSideB(cv::Point2f &middlePointOfSideB, const cv::Point2f &sideAStartVertex,
|
|
const cv::Point2f &sideAEndVertex, const cv::Point2f &sideBStartVertex,
|
|
const cv::Point2f &sideBEndVertex, const cv::Point2f &sideCStartVertex,
|
|
const cv::Point2f &sideCEndVertex) {
|
|
cv::Point2f vertexA, vertexC;
|
|
|
|
if ((!lineIntersection(sideBStartVertex, sideBEndVertex, sideCStartVertex, sideCEndVertex, vertexA)) ||
|
|
(!lineIntersection(sideBStartVertex, sideBEndVertex, sideAStartVertex, sideAEndVertex, vertexC))) {
|
|
return false;
|
|
}
|
|
|
|
middlePointOfSideB = middlePoint(vertexA, vertexC);
|
|
|
|
return true;
|
|
}
|
|
|
|
//! Check if the line intersects below
|
|
/*!
|
|
* Check if the line determined by gammaPoint and polygon[polygonPointIndex] intersects
|
|
* the polygon below the point polygon[polygonPointIndex]
|
|
*
|
|
* @param gammaPoint Gamma(p)
|
|
* @param polygonPointIndex Index of the polygon point which is considered when determining the line
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static bool intersectsBelow(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex,
|
|
const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int c) {
|
|
double angleOfGammaAndPoint = angleOfLineWrtOxAxis(polygon[polygonPointIndex], gammaPoint);
|
|
|
|
return (intersects(angleOfGammaAndPoint, polygonPointIndex, polygon, nrOfPoints, c) == INTERSECTS_BELOW);
|
|
}
|
|
|
|
//! Check if the line intersects above
|
|
/*!
|
|
* Check if the line determined by gammaPoint and polygon[polygonPointIndex] intersects
|
|
* the polygon above the point polygon[polygonPointIndex]
|
|
*
|
|
* @param gammaPoint Gamma(p)
|
|
* @param polygonPointIndex Index of the polygon point which is considered when determining the line
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static bool intersectsAbove(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex,
|
|
const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int c) {
|
|
double angleOfGammaAndPoint = angleOfLineWrtOxAxis(gammaPoint, polygon[polygonPointIndex]);
|
|
|
|
return (intersects(angleOfGammaAndPoint, polygonPointIndex, polygon, nrOfPoints, c) == INTERSECTS_ABOVE);
|
|
}
|
|
|
|
//! Check if/where the line determined by gammaPoint and polygon[polygonPointIndex] intersects the polygon
|
|
/*!
|
|
* @param angleGammaAndPoint Angle determined by gammaPoint and polygon[polygonPointIndex] wrt Ox axis
|
|
* @param polygonPointIndex Index of the polygon point which is considered when determining the line
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static unsigned int intersects(double angleGammaAndPoint, unsigned int polygonPointIndex,
|
|
const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int c) {
|
|
double anglePointPredecessor = angleOfLineWrtOxAxis(polygon[predecessor(polygonPointIndex, nrOfPoints)],
|
|
polygon[polygonPointIndex]);
|
|
double anglePointSuccessor = angleOfLineWrtOxAxis(polygon[successor(polygonPointIndex, nrOfPoints)],
|
|
polygon[polygonPointIndex]);
|
|
double angleFlushEdge = angleOfLineWrtOxAxis(polygon[predecessor(c, nrOfPoints)],
|
|
polygon[c]);
|
|
|
|
if (isFlushAngleBtwPredAndSucc(angleFlushEdge, anglePointPredecessor, anglePointSuccessor)) {
|
|
if ((isGammaAngleBtw(angleGammaAndPoint, anglePointPredecessor, angleFlushEdge)) ||
|
|
(almostEqual(angleGammaAndPoint, anglePointPredecessor))) {
|
|
return intersectsAboveOrBelow(predecessor(polygonPointIndex, nrOfPoints),
|
|
polygonPointIndex, polygon, nrOfPoints, c);
|
|
} else if ((isGammaAngleBtw(angleGammaAndPoint, anglePointSuccessor, angleFlushEdge)) ||
|
|
(almostEqual(angleGammaAndPoint, anglePointSuccessor))) {
|
|
return intersectsAboveOrBelow(successor(polygonPointIndex, nrOfPoints),
|
|
polygonPointIndex, polygon, nrOfPoints, c);
|
|
}
|
|
} else {
|
|
if (
|
|
(isGammaAngleBtw(angleGammaAndPoint, anglePointPredecessor, anglePointSuccessor)) ||
|
|
(
|
|
(isGammaAngleEqualTo(angleGammaAndPoint, anglePointPredecessor)) &&
|
|
(!isGammaAngleEqualTo(angleGammaAndPoint, angleFlushEdge))
|
|
) ||
|
|
(
|
|
(isGammaAngleEqualTo(angleGammaAndPoint, anglePointSuccessor)) &&
|
|
(!isGammaAngleEqualTo(angleGammaAndPoint, angleFlushEdge))
|
|
)
|
|
) {
|
|
return INTERSECTS_BELOW;
|
|
}
|
|
}
|
|
|
|
return INTERSECTS_CRITICAL;
|
|
}
|
|
|
|
//! If (gamma(x) x) intersects P between successorOrPredecessorIndex and pointIntex is it above/below?
|
|
/*!
|
|
* @param succPredIndex Index of the successor or predecessor
|
|
* @param pointIndex Index of the point x in the polygon
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static unsigned int intersectsAboveOrBelow(unsigned int succPredIndex, unsigned int pointIndex,
|
|
const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int c) {
|
|
if (height(succPredIndex, polygon, nrOfPoints, c) > height(pointIndex, polygon, nrOfPoints, c)) {
|
|
return INTERSECTS_ABOVE;
|
|
} else {
|
|
return INTERSECTS_BELOW;
|
|
}
|
|
}
|
|
|
|
//! Find gamma for a given point "p" specified by its index
|
|
/*!
|
|
* The function returns true if gamma exists i.e. if lines (a a-1) and (x y) intersect
|
|
* and false otherwise. In case the two lines intersect in point intersectionPoint, gamma is computed.
|
|
*
|
|
* Considering that line (x y) is a line parallel to (c c-1) and that the distance between the lines is equal
|
|
* to 2 * height(p), we can have two possible (x y) lines.
|
|
*
|
|
* Therefore, we will compute two intersection points between the lines (x y) and (a a-1) and take the
|
|
* point which is on the same side of line (c c-1) as the polygon.
|
|
*
|
|
* See paper [2] and formula for distance from point to a line for more details
|
|
*
|
|
* @param polygonPointIndex Index of the polygon point
|
|
* @param gammaPoint Point gamma(polygon[polygonPointIndex])
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param c Index c
|
|
*/
|
|
static bool gamma(unsigned int polygonPointIndex, cv::Point2f &gammaPoint,
|
|
const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int a, unsigned int c) {
|
|
cv::Point2f intersectionPoint1, intersectionPoint2;
|
|
|
|
// Get intersection points if they exist
|
|
if (!findGammaIntersectionPoints(polygon, nrOfPoints, c, polygonPointIndex,
|
|
polygon[a], polygon[predecessor(a, nrOfPoints)],
|
|
polygon[c], polygon[predecessor(c, nrOfPoints)],
|
|
intersectionPoint1, intersectionPoint2)) {
|
|
return false;
|
|
}
|
|
|
|
// Select the point which is on the same side of line C as the polygon
|
|
if (areOnTheSameSideOfLine(intersectionPoint1, polygon[successor(c, nrOfPoints)],
|
|
polygon[c], polygon[predecessor(c, nrOfPoints)])) {
|
|
gammaPoint = intersectionPoint1;
|
|
} else {
|
|
gammaPoint = intersectionPoint2;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//! Find vertex C which lies on side B at a distance = 2 * height(a-1) from side C
|
|
/*!
|
|
* Considering that line (x y) is a line parallel to (c c-1) and that the distance between the lines is equal
|
|
* to 2 * height(a-1), we can have two possible (x y) lines.
|
|
*
|
|
* Therefore, we will compute two intersection points between the lines (x y) and (b b-1) and take the
|
|
* point which is on the same side of line (c c-1) as the polygon.
|
|
*
|
|
* See paper [2] and formula for distance from point to a line for more details
|
|
*
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param a Index a
|
|
* @param c Index c
|
|
* @param sideBStartVertex Start vertex for defining side B
|
|
* @param sideBEndVertex End vertex for defining side B
|
|
* @param sideCStartVertex Start vertex for defining side C
|
|
* @param sideCEndVertex End vertex for defining side C
|
|
*/
|
|
static cv::Point2f findVertexCOnSideB(const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int a, unsigned int c,
|
|
const cv::Point2f &sideBStartVertex,
|
|
const cv::Point2f &sideBEndVertex,
|
|
const cv::Point2f &sideCStartVertex,
|
|
const cv::Point2f &sideCEndVertex) {
|
|
cv::Point2f intersectionPoint1, intersectionPoint2;
|
|
|
|
// Get intersection points if they exist
|
|
if (!findGammaIntersectionPoints(polygon, nrOfPoints, c, predecessor(a, nrOfPoints),
|
|
sideBStartVertex, sideBEndVertex,
|
|
sideCStartVertex, sideCEndVertex,
|
|
intersectionPoint1, intersectionPoint2)) {
|
|
CV_Error(cv::Error::StsInternal, ERR_VERTEX_C_ON_SIDE_B);
|
|
}
|
|
|
|
// Select the point which is on the same side of line C as the polygon
|
|
if (areOnTheSameSideOfLine(intersectionPoint1, polygon[successor(c, nrOfPoints)],
|
|
polygon[c], polygon[predecessor(c, nrOfPoints)])) {
|
|
return intersectionPoint1;
|
|
} else {
|
|
return intersectionPoint2;
|
|
}
|
|
}
|
|
|
|
//! Find the intersection points to compute gamma(point)
|
|
/*!
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
* @param polygonPointIndex Index of the polygon point for which the distance is known
|
|
* @param side1StartVertex Start vertex for side 1
|
|
* @param side1EndVertex End vertex for side 1
|
|
* @param side2StartVertex Start vertex for side 2
|
|
* @param side2EndVertex End vertex for side 2
|
|
* @param intersectionPoint1 First intersection point between one pair of lines
|
|
* @param intersectionPoint2 Second intersection point between other pair of lines
|
|
*/
|
|
static bool findGammaIntersectionPoints(const std::vector<cv::Point2f> &polygon, unsigned int nrOfPoints,
|
|
unsigned int c, unsigned int polygonPointIndex,
|
|
const cv::Point2f &side1StartVertex, const cv::Point2f &side1EndVertex,
|
|
const cv::Point2f &side2StartVertex, const cv::Point2f &side2EndVertex,
|
|
cv::Point2f &intersectionPoint1, cv::Point2f &intersectionPoint2) {
|
|
std::vector<double> side1Params = lineEquationParameters(side1StartVertex, side1EndVertex);
|
|
std::vector<double> side2Params = lineEquationParameters(side2StartVertex, side2EndVertex);
|
|
|
|
// Compute side C extra parameter using the formula for distance from a point to a line
|
|
double polygonPointHeight = height(polygonPointIndex, polygon, nrOfPoints, c);
|
|
double distFormulaDenom = sqrt((side2Params[0] * side2Params[0]) + (side2Params[1] * side2Params[1]));
|
|
double sideCExtraParam = 2 * polygonPointHeight * distFormulaDenom;
|
|
|
|
// Get intersection points if they exist or if lines are identical
|
|
if (!areIntersectingLines(side1Params, side2Params, sideCExtraParam, intersectionPoint1, intersectionPoint2)) {
|
|
return false;
|
|
} else if (areIdenticalLines(side1Params, side2Params, sideCExtraParam)) {
|
|
intersectionPoint1 = side1StartVertex;
|
|
intersectionPoint2 = side1EndVertex;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
//! Check if the given lines are identical or not
|
|
/*!
|
|
* The lines are specified as:
|
|
* ax + by + c = 0
|
|
* OR
|
|
* ax + by + c (+/-) sideCExtraParam = 0
|
|
*
|
|
* @param side1Params Vector containing the values of a, b and c for side 1
|
|
* @param side2Params Vector containing the values of a, b and c for side 2
|
|
* @param sideCExtraParam Extra parameter for the flush edge C
|
|
*/
|
|
static bool areIdenticalLines(const std::vector<double> &side1Params,
|
|
const std::vector<double> &side2Params, double sideCExtraParam) {
|
|
return (
|
|
(areIdenticalLines(side1Params[0], side1Params[1], -(side1Params[2]),
|
|
side2Params[0], side2Params[1], -(side2Params[2]) - sideCExtraParam)) ||
|
|
(areIdenticalLines(side1Params[0], side1Params[1], -(side1Params[2]),
|
|
side2Params[0], side2Params[1], -(side2Params[2]) + sideCExtraParam))
|
|
);
|
|
}
|
|
|
|
//! Check if the given lines intersect or not. If the lines intersect find their intersection points.
|
|
/*!
|
|
* The lines are specified as:
|
|
* ax + by + c = 0
|
|
* OR
|
|
* ax + by + c (+/-) sideCExtraParam = 0
|
|
*
|
|
* @param side1Params Vector containing the values of a, b and c for side 1
|
|
* @param side2Params Vector containing the values of a, b and c for side 2
|
|
* @param sideCExtraParam Extra parameter for the flush edge C
|
|
* @param intersectionPoint1 The first intersection point, if it exists
|
|
* @param intersectionPoint2 The second intersection point, if it exists
|
|
*/
|
|
static bool areIntersectingLines(const std::vector<double> &side1Params,
|
|
const std::vector<double> &side2Params,
|
|
double sideCExtraParam, cv::Point2f &intersectionPoint1,
|
|
cv::Point2f &intersectionPoint2) {
|
|
return (
|
|
(lineIntersection(side1Params[0], side1Params[1], -(side1Params[2]),
|
|
side2Params[0], side2Params[1], -(side2Params[2]) - sideCExtraParam,
|
|
intersectionPoint1)) &&
|
|
(lineIntersection(side1Params[0], side1Params[1], -(side1Params[2]),
|
|
side2Params[0], side2Params[1], -(side2Params[2]) + sideCExtraParam,
|
|
intersectionPoint2))
|
|
);
|
|
}
|
|
|
|
//! Get the line equation parameters "a", "b" and "c" for the line determined by points "p" and "q"
|
|
/*!
|
|
* The equation of the line is considered in the general form:
|
|
* ax + by + c = 0
|
|
*
|
|
* @param p One point for defining the equation of the line
|
|
* @param q Second point for defining the equation of the line
|
|
*/
|
|
static std::vector<double> lineEquationParameters(const cv::Point2f& p, const cv::Point2f &q) {
|
|
std::vector<double> lineEquationParameters;
|
|
double a, b, c;
|
|
|
|
lineEquationDeterminedByPoints(p, q, a, b, c);
|
|
|
|
lineEquationParameters.push_back(a);
|
|
lineEquationParameters.push_back(b);
|
|
lineEquationParameters.push_back(c);
|
|
|
|
return lineEquationParameters;
|
|
}
|
|
|
|
//! Compute the height of the point
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygonPoint Polygon point
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static double height(const cv::Point2f &polygonPoint, const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int c) {
|
|
cv::Point2f pointC = polygon[c];
|
|
cv::Point2f pointCPredecessor = polygon[predecessor(c, nrOfPoints)];
|
|
|
|
return distanceFromPointToLine(polygonPoint, pointC, pointCPredecessor);
|
|
}
|
|
|
|
//! Compute the height of the point specified by the given index
|
|
/*!
|
|
* See paper [2] for more details
|
|
*
|
|
* @param polygonPointIndex Index of the polygon point
|
|
* @param polygon The polygon representing the convex hull of the points
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
* @param c Index c
|
|
*/
|
|
static double height(unsigned int polygonPointIndex, const std::vector<cv::Point2f> &polygon,
|
|
unsigned int nrOfPoints, unsigned int c) {
|
|
cv::Point2f pointC = polygon[c];
|
|
cv::Point2f pointCPredecessor = polygon[predecessor(c, nrOfPoints)];
|
|
|
|
cv::Point2f polygonPoint = polygon[polygonPointIndex];
|
|
|
|
return distanceFromPointToLine(polygonPoint, pointC, pointCPredecessor);
|
|
}
|
|
|
|
//! Advance the given index with one position
|
|
/*!
|
|
* @param index Index of the point
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
*/
|
|
static void advance(unsigned int &index, unsigned int nrOfPoints) {
|
|
index = successor(index, nrOfPoints);
|
|
}
|
|
|
|
//! Return the succesor of the provided point index
|
|
/*!
|
|
* The succesor of the last polygon point is the first polygon point
|
|
* (circular referencing)
|
|
*
|
|
* @param index Index of the point
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
*/
|
|
static unsigned int successor(unsigned int index, unsigned int nrOfPoints) {
|
|
return ((index + 1) % nrOfPoints);
|
|
}
|
|
|
|
//! Return the predecessor of the provided point index
|
|
/*!
|
|
* The predecessor of the first polygon point is the last polygon point
|
|
* (circular referencing)
|
|
*
|
|
* @param index Index of the point
|
|
* @param nrOfPoints Number of points defining the convex polygon
|
|
*/
|
|
static unsigned int predecessor(unsigned int index, unsigned int nrOfPoints) {
|
|
return (index == 0) ? (nrOfPoints - 1)
|
|
: (index - 1);
|
|
}
|
|
|
|
//! Check if the flush edge angle/opposite angle lie between the predecessor and successor angle
|
|
/*!
|
|
* Check if the angle of the flush edge or its opposite angle lie between the angle of
|
|
* the predecessor and successor
|
|
*
|
|
* @param angleFlushEdge Angle of the flush edge
|
|
* @param anglePred Angle of the predecessor
|
|
* @param angleSucc Angle of the successor
|
|
*/
|
|
static bool isFlushAngleBtwPredAndSucc(double &angleFlushEdge, double anglePred, double angleSucc) {
|
|
if (isAngleBetweenNonReflex(angleFlushEdge, anglePred, angleSucc)) {
|
|
return true;
|
|
} else if (isOppositeAngleBetweenNonReflex(angleFlushEdge, anglePred, angleSucc)) {
|
|
angleFlushEdge = oppositeAngle(angleFlushEdge);
|
|
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
//! Check if the angle of the line (gamma(p) p) or its opposite angle is equal to the given angle
|
|
/*!
|
|
* @param gammaAngle Angle of the line (gamma(p) p)
|
|
* @param angle Angle to compare against
|
|
*/
|
|
static bool isGammaAngleEqualTo(double &gammaAngle, double angle) {
|
|
return (almostEqual(gammaAngle, angle));
|
|
}
|
|
|
|
//! Check if the angle of the line (gamma(p) p) or its opposite angle lie between angle1 and angle2
|
|
/*!
|
|
* @param gammaAngle Angle of the line (gamma(p) p)
|
|
* @param angle1 One of the boundary angles
|
|
* @param angle2 Another boundary angle
|
|
*/
|
|
static bool isGammaAngleBtw(double &gammaAngle, double angle1, double angle2) {
|
|
return (isAngleBetweenNonReflex(gammaAngle, angle1, angle2));
|
|
}
|
|
|
|
//! Get the angle of the line measured from the Ox axis in counterclockwise direction
|
|
/*!
|
|
* The line is specified by points "a" and "b". The value of the angle is expressed in degrees.
|
|
*
|
|
* @param a Point a
|
|
* @param b Point b
|
|
*/
|
|
static double angleOfLineWrtOxAxis(const cv::Point2f &a, const cv::Point2f &b) {
|
|
double y = b.y - a.y;
|
|
double x = b.x - a.x;
|
|
|
|
double angle = (std::atan2(y, x) * 180 / CV_PI);
|
|
|
|
return (angle < 0) ? (angle + 360)
|
|
: angle;
|
|
}
|
|
|
|
//! Check if angle1 lies between non reflex angle determined by angles 2 and 3
|
|
/*!
|
|
* @param angle1 The angle which lies between angle2 and angle3 or not
|
|
* @param angle2 One of the boundary angles
|
|
* @param angle3 The other boundary angle
|
|
*/
|
|
static bool isAngleBetweenNonReflex(double angle1, double angle2, double angle3) {
|
|
if (std::abs(angle2 - angle3) > 180) {
|
|
if (angle2 > angle3) {
|
|
return (((angle2 < angle1) && (lessOrEqual(angle1, 360))) ||
|
|
((lessOrEqual(0, angle1)) && (angle1 < angle3)));
|
|
} else {
|
|
return (((angle3 < angle1) && (lessOrEqual(angle1, 360))) ||
|
|
((lessOrEqual(0, angle1)) && (angle1 < angle2)));
|
|
}
|
|
} else {
|
|
return isAngleBetween(angle1, angle2, angle3);
|
|
}
|
|
}
|
|
|
|
//! Check if the opposite of angle1, ((angle1 + 180) % 360), lies between non reflex angle determined by angles 2 and 3
|
|
/*!
|
|
* @param angle1 The angle which lies between angle2 and angle3 or not
|
|
* @param angle2 One of the boundary angles
|
|
* @param angle3 The other boundary angle
|
|
*/
|
|
static bool isOppositeAngleBetweenNonReflex(double angle1, double angle2, double angle3) {
|
|
double angle1Opposite = oppositeAngle(angle1);
|
|
|
|
return (isAngleBetweenNonReflex(angle1Opposite, angle2, angle3));
|
|
}
|
|
|
|
//! Check if angle1 lies between angles 2 and 3
|
|
/*!
|
|
* @param angle1 The angle which lies between angle2 and angle3 or not
|
|
* @param angle2 One of the boundary angles
|
|
* @param angle3 The other boundary angle
|
|
*/
|
|
static bool isAngleBetween(double angle1, double angle2, double angle3) {
|
|
if ((((int)(angle2 - angle3)) % 180) > 0) {
|
|
return ((angle3 < angle1) && (angle1 < angle2));
|
|
} else {
|
|
return ((angle2 < angle1) && (angle1 < angle3));
|
|
}
|
|
}
|
|
|
|
//! Return the angle opposite to the given angle
|
|
/*!
|
|
* if (angle < 180) then
|
|
* return (angle + 180);
|
|
* else
|
|
* return (angle - 180);
|
|
* endif
|
|
*
|
|
* @param angle Angle
|
|
*/
|
|
static double oppositeAngle(double angle) {
|
|
return (angle > 180) ? (angle - 180)
|
|
: (angle + 180);
|
|
}
|
|
|
|
//! Compute the distance from a point "a" to a line specified by two points "B" and "C"
|
|
/*!
|
|
* Formula used:
|
|
*
|
|
* |(x_c - x_b) * (y_b - y_a) - (x_b - x_a) * (y_c - y_b)|
|
|
* d = -------------------------------------------------------
|
|
* sqrt(((x_c - x_b)^2) + ((y_c - y_b)^2))
|
|
*
|
|
* Reference: http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html
|
|
* (Last access: 15.09.2013)
|
|
*
|
|
* @param a Point from which the distance is measures
|
|
* @param linePointB One of the points determining the line
|
|
* @param linePointC One of the points determining the line
|
|
*/
|
|
static double distanceFromPointToLine(const cv::Point2f &a, const cv::Point2f &linePointB,
|
|
const cv::Point2f &linePointC) {
|
|
double term1 = linePointC.x - linePointB.x;
|
|
double term2 = linePointB.y - a.y;
|
|
double term3 = linePointB.x - a.x;
|
|
double term4 = linePointC.y - linePointB.y;
|
|
|
|
double nominator = std::abs((term1 * term2) - (term3 * term4));
|
|
double denominator = std::sqrt((term1 * term1) + (term4 * term4));
|
|
|
|
return (denominator != 0) ? (nominator / denominator)
|
|
: 0;
|
|
}
|
|
|
|
//! Compute the distance between two points
|
|
/*! Compute the Euclidean distance between two points
|
|
*
|
|
* @param a Point a
|
|
* @param b Point b
|
|
*/
|
|
static double distanceBtwPoints(const cv::Point2f &a, const cv::Point2f &b) {
|
|
double xDiff = a.x - b.x;
|
|
double yDiff = a.y - b.y;
|
|
|
|
return std::sqrt((xDiff * xDiff) + (yDiff * yDiff));
|
|
}
|
|
|
|
//! Compute the area of a triangle defined by three points
|
|
/*!
|
|
* The area is computed using the determinant method.
|
|
* An example is depicted at http://demonstrations.wolfram.com/TheAreaOfATriangleUsingADeterminant/
|
|
* (Last access: 15.09.2013)
|
|
*
|
|
* @param a Point a
|
|
* @param b Point b
|
|
* @param c Point c
|
|
*/
|
|
static double areaOfTriangle(const cv::Point2f &a, const cv::Point2f &b, const cv::Point2f &c) {
|
|
double posTerm = (a.x * b.y) + (a.y * c.x) + (b.x * c.y);
|
|
double negTerm = (b.y * c.x) + (a.x * c.y) + (a.y * b.x);
|
|
|
|
double determinant = posTerm - negTerm;
|
|
|
|
return std::abs(determinant) / 2;
|
|
}
|
|
|
|
//! Get the point in the middle of the segment determined by points "a" and "b"
|
|
/*!
|
|
* @param a Point a
|
|
* @param b Point b
|
|
*/
|
|
static cv::Point2f middlePoint(const cv::Point2f &a, const cv::Point2f &b) {
|
|
double middleX = static_cast<double>((a.x + b.x) / 2);
|
|
double middleY = static_cast<double>((a.y + b.y) / 2);
|
|
|
|
return cv::Point2f(static_cast<float>(middleX), static_cast<float>(middleY));
|
|
}
|
|
|
|
//! Determine the intersection point of two lines, if this point exists
|
|
/*! Two lines intersect if they are not parallel (Parallel lines intersect at
|
|
* +/- infinity, but we do not consider this case here).
|
|
*
|
|
* The lines are specified in the following form:
|
|
* A1x + B1x = C1
|
|
* A2x + B2x = C2
|
|
*
|
|
* If det (= A1*B2 - A2*B1) == 0, then lines are parallel
|
|
* else they intersect
|
|
*
|
|
* If they intersect, then let us denote the intersection point with P(x, y) where:
|
|
* x = (C1*B2 - C2*B1) / (det)
|
|
* y = (C2*A1 - C1*A2) / (det)
|
|
*
|
|
* @param a1 A1
|
|
* @param b1 B1
|
|
* @param c1 C1
|
|
* @param a2 A2
|
|
* @param b2 B2
|
|
* @param c2 C2
|
|
* @param intersection The intersection point, if this point exists
|
|
*/
|
|
static bool lineIntersection(double a1, double b1, double c1, double a2, double b2, double c2,
|
|
cv::Point2f &intersection) {
|
|
double det = (a1 * b2) - (a2 * b1);
|
|
|
|
if (!(almostEqual(det, 0))) {
|
|
intersection.x = static_cast<float>(((c1 * b2) - (c2 * b1)) / (det));
|
|
intersection.y = static_cast<float>(((c2 * a1) - (c1 * a2)) / (det));
|
|
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
//! Determine the intersection point of two lines, if this point exists
|
|
/*! Two lines intersect if they are not parallel (Parallel lines intersect at
|
|
* +/- infinity, but we do not consider this case here).
|
|
*
|
|
* The lines are specified by a pair of points each. If they intersect, then
|
|
* the function returns true, else it returns false.
|
|
*
|
|
* Lines can be specified in the following form:
|
|
* A1x + B1x = C1
|
|
* A2x + B2x = C2
|
|
*
|
|
* If det (= A1*B2 - A2*B1) == 0, then lines are parallel
|
|
* else they intersect
|
|
*
|
|
* If they intersect, then let us denote the intersection point with P(x, y) where:
|
|
* x = (C1*B2 - C2*B1) / (det)
|
|
* y = (C2*A1 - C1*A2) / (det)
|
|
*
|
|
* @param a1 First point for determining the first line
|
|
* @param b1 Second point for determining the first line
|
|
* @param a2 First point for determining the second line
|
|
* @param b2 Second point for determining the second line
|
|
* @param intersection The intersection point, if this point exists
|
|
*/
|
|
static bool lineIntersection(const cv::Point2f &a1, const cv::Point2f &b1, const cv::Point2f &a2,
|
|
const cv::Point2f &b2, cv::Point2f &intersection) {
|
|
double A1 = b1.y - a1.y;
|
|
double B1 = a1.x - b1.x;
|
|
double C1 = (a1.x * A1) + (a1.y * B1);
|
|
|
|
double A2 = b2.y - a2.y;
|
|
double B2 = a2.x - b2.x;
|
|
double C2 = (a2.x * A2) + (a2.y * B2);
|
|
|
|
double det = (A1 * B2) - (A2 * B1);
|
|
|
|
if (!almostEqual(det, 0)) {
|
|
intersection.x = static_cast<float>(((C1 * B2) - (C2 * B1)) / (det));
|
|
intersection.y = static_cast<float>(((C2 * A1) - (C1 * A2)) / (det));
|
|
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
//! Get the values of "a", "b" and "c" of the line equation ax + by + c = 0 knowing that point "p" and "q" are on the line
|
|
/*!
|
|
* a = q.y - p.y
|
|
* b = p.x - q.x
|
|
* c = - (p.x * a) - (p.y * b)
|
|
*
|
|
* @param p Point p
|
|
* @param q Point q
|
|
* @param a Parameter "a" from the line equation
|
|
* @param b Parameter "b" from the line equation
|
|
* @param c Parameter "c" from the line equation
|
|
*/
|
|
static void lineEquationDeterminedByPoints(const cv::Point2f &p, const cv::Point2f &q,
|
|
double &a, double &b, double &c) {
|
|
CV_Assert(areEqualPoints(p, q) == false);
|
|
|
|
a = q.y - p.y;
|
|
b = p.x - q.x;
|
|
c = ((-p.y) * b) - (p.x * a);
|
|
}
|
|
|
|
//! Check if p1 and p2 are on the same side of the line determined by points a and b
|
|
/*!
|
|
* @param p1 Point p1
|
|
* @param p2 Point p2
|
|
* @param a First point for determining line
|
|
* @param b Second point for determining line
|
|
*/
|
|
static bool areOnTheSameSideOfLine(const cv::Point2f &p1, const cv::Point2f &p2,
|
|
const cv::Point2f &a, const cv::Point2f &b) {
|
|
double a1, b1, c1;
|
|
|
|
lineEquationDeterminedByPoints(a, b, a1, b1, c1);
|
|
|
|
double p1OnLine = (a1 * p1.x) + (b1 * p1.y) + c1;
|
|
double p2OnLine = (a1 * p2.x) + (b1 * p2.y) + c1;
|
|
|
|
return (sign(p1OnLine) == sign(p2OnLine));
|
|
}
|
|
|
|
//! Check if one point lies between two other points
|
|
/*!
|
|
* @param point Point lying possibly outside the line segment
|
|
* @param lineSegmentStart First point determining the line segment
|
|
* @param lineSegmentEnd Second point determining the line segment
|
|
*/
|
|
static bool isPointOnLineSegment(const cv::Point2f &point, const cv::Point2f &lineSegmentStart,
|
|
const cv::Point2f &lineSegmentEnd) {
|
|
double d1 = distanceBtwPoints(point, lineSegmentStart);
|
|
double d2 = distanceBtwPoints(point, lineSegmentEnd);
|
|
double lineSegmentLength = distanceBtwPoints(lineSegmentStart, lineSegmentEnd);
|
|
|
|
return (almostEqual(d1 + d2, lineSegmentLength));
|
|
}
|
|
|
|
//! Check if two lines are identical
|
|
/*!
|
|
* Lines are be specified in the following form:
|
|
* A1x + B1x = C1
|
|
* A2x + B2x = C2
|
|
*
|
|
* If (A1/A2) == (B1/B2) == (C1/C2), then the lines are identical
|
|
* else they are not
|
|
*
|
|
* @param a1 A1
|
|
* @param b1 B1
|
|
* @param c1 C1
|
|
* @param a2 A2
|
|
* @param b2 B2
|
|
* @param c2 C2
|
|
*/
|
|
static bool areIdenticalLines(double a1, double b1, double c1, double a2, double b2, double c2) {
|
|
double a1B2 = a1 * b2;
|
|
double a2B1 = a2 * b1;
|
|
double a1C2 = a1 * c2;
|
|
double a2C1 = a2 * c1;
|
|
double b1C2 = b1 * c2;
|
|
double b2C1 = b2 * c1;
|
|
|
|
return ((almostEqual(a1B2, a2B1)) && (almostEqual(b1C2, b2C1)) && (almostEqual(a1C2, a2C1)));
|
|
}
|
|
|
|
//! Check if points point1 and point2 are equal or not
|
|
/*!
|
|
* @param point1 One point
|
|
* @param point2 The other point
|
|
*/
|
|
static bool areEqualPoints(const cv::Point2f &point1, const cv::Point2f &point2) {
|
|
return (almostEqual(point1.x, point2.x) && almostEqual(point1.y, point2.y));
|
|
}
|
|
|
|
//! Return the sign of the number
|
|
/*!
|
|
* The sign function returns:
|
|
* -1, if number < 0
|
|
* +1, if number > 0
|
|
* 0, otherwise
|
|
*/
|
|
static int sign(double number) {
|
|
return (number > 0) ? 1 : ((number < 0) ? -1 : 0);
|
|
}
|
|
|
|
//! Return the maximum of the provided numbers
|
|
static double maximum(double number1, double number2, double number3) {
|
|
return std::max(std::max(number1, number2), number3);
|
|
}
|
|
|
|
//! Check if the two numbers are equal (almost)
|
|
/*!
|
|
* The expression for determining if two real numbers are equal is:
|
|
* if (Abs(x - y) <= EPSILON * Max(1.0f, Abs(x), Abs(y))).
|
|
*
|
|
* @param number1 First number
|
|
* @param number2 Second number
|
|
*/
|
|
static bool almostEqual(double number1, double number2) {
|
|
return (std::abs(number1 - number2) <= (EPSILON * maximum(1.0, std::abs(number1), std::abs(number2))));
|
|
}
|
|
|
|
//! Check if the first number is greater than or equal to the second number
|
|
/*!
|
|
* @param number1 First number
|
|
* @param number2 Second number
|
|
*/
|
|
static bool greaterOrEqual(double number1, double number2) {
|
|
return ((number1 > number2) || (almostEqual(number1, number2)));
|
|
}
|
|
|
|
//! Check if the first number is less than or equal to the second number
|
|
/*!
|
|
* @param number1 First number
|
|
* @param number2 Second number
|
|
*/
|
|
static bool lessOrEqual(double number1, double number2) {
|
|
return ((number1 < number2) || (almostEqual(number1, number2)));
|
|
}
|
|
|
|
}
|