From: Ovidiu Parvu Date: Wed, 11 Sep 2013 17:02:10 +0000 (+0100) Subject: - Added the minEnclosingTriangle function declaration to the imgproc header X-Git-Tag: submit/tizen_ivi/20141117.190038~2^2~910^2~17 X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=e6b58c4e79c4e57ac2b25919dc66c510ef0ad35c;p=profile%2Fivi%2Fopencv.git - Added the minEnclosingTriangle function declaration to the imgproc header - Added the source code for the function in the separate file min_enclosing_triangle.cpp --- diff --git a/modules/imgproc/include/opencv2/imgproc.hpp b/modules/imgproc/include/opencv2/imgproc.hpp index 55816cc..7011bb3 100644 --- a/modules/imgproc/include/opencv2/imgproc.hpp +++ b/modules/imgproc/include/opencv2/imgproc.hpp @@ -1451,6 +1451,10 @@ 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( const std::vector &convexPolygon, + CV_OUT std::vector &triangle, CV_OUT double& area ); + //! matches two contours using one of the available algorithms CV_EXPORTS_W double matchShapes( InputArray contour1, InputArray contour2, int method, double parameter ); diff --git a/modules/imgproc/src/min_enclosing_triangle.cpp b/modules/imgproc/src/min_enclosing_triangle.cpp new file mode 100644 index 0000000..cc6e96b --- /dev/null +++ b/modules/imgproc/src/min_enclosing_triangle.cpp @@ -0,0 +1,1209 @@ +/*M/////////////////////////////////////////////////////////////////////////////////////// +// +// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. +// +// By downloading, copying, installing or using the software you agree to this license. +// If you do not agree to this license, do not download, install, +// copy or use the software. +// +// INFORMATION REGARDING THE CONTRIBUTION: +// +// Author: Ovidiu Parvu +// Affiliation: Brunel University +// Created: 11.09.2013 +// E-mail: +// Web: http://people.brunel.ac.uk/~cspgoop +// +// These functions were implemented during Ovidiu Parvu's first year as a PhD student at +// Brunel University, London, UK. The PhD project is supervised by prof. David Gilbert (principal) +// and prof. Nigel Saunders (second). +// +// THE IMPLEMENTATION OF THE MODULES IS BASED ON THE FOLLOWING PAPERS: +// +// [1] V. Klee and M. C. Laskowski, “Finding the smallest triangles containing a given convex +// polygon,” Journal of Algorithms, vol. 6, no. 3, pp. 359–375, Sep. 1985. +// [2] J. O’Rourke, A. Aggarwal, S. Maddila, and M. Baldwin, “An optimal algorithm for finding +// minimal enclosing triangles,” Journal of Algorithms, vol. 7, no. 2, pp. 258–269, Jun. 1986. +// +// The overall complexity of the algorithm is theta(n) where "n" represents the number +// of vertices in the convex polygon. +// +// +// +// License Agreement +// For Open Source Computer Vision Library +// +// Copyright (C) 2000, Intel Corporation, all rights reserved. +// Copyright (C) 2013, OpenCV Foundation, all rights reserved. +// Third party copyrights are property of their respective owners. +// +// Redistribution and use in source and binary forms, with or without modification, +// are permitted provided that the following conditions are met: +// +// * Redistribution's of source code must retain the above copyright notice, +// this list of conditions and the following disclaimer. +// +// * Redistribution's in binary form must reproduce the above copyright notice, +// this list of conditions and the following disclaimer in the documentation +// and/or other materials provided with the distribution. +// +// * The name of the copyright holders may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// This software is provided by the copyright holders and contributors "as is" and +// any express or implied warranties, including, but not limited to, the implied +// warranties of merchantability and fitness for a particular purpose are disclaimed. +// In no event shall the Intel Corporation or contributors be liable for any direct, +// indirect, incidental, special, exemplary, or consequential damages +// (including, but not limited to, procurement of substitute goods or services; +// loss of use, data, or profits; or business interruption) however caused +// and on any theory of liability, whether in contract, strict liability, +// or tort (including negligence or otherwise) arising in any way out of +// the use of this software, even if advised of the possibility of such damage. +// +//M*/ + +#include "precomp.hpp" + +#include +#include +#include +#include + + +///////////////////////////////// Constants definitions ////////////////////////////////// + + +// Intersection of line and polygon + +#define INTERSECTS_BELOW 1 +#define INTERSECTS_ABOVE 2 +#define INTERSECTS_CRITICAL 3 +#define INTERSECTS_LIMIT 4 + +// Error messages + +#define ERR_MIDPOINT_SIDE_B "The position of the middle point of side B could not be determined." +#define ERR_SIDE_B_GAMMA "The position of side B could not be determined, because gamma(b) could not be computed." +#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." +#define ERR_TRIANGLE_VERTICES "The position of the triangle vertices could not be determined, because the sides of the triangle do not intersect." + +// Possible values for validation flag + +#define VALIDATION_SIDE_A_TANGENT 0 +#define VALIDATION_SIDE_B_TANGENT 1 +#define VALIDATION_SIDES_FLUSH 2 + +// Constant values + +#define PI 3.14159265358979323846264338327950288419716939937510 +#define EPSILON 1E-5 + + +/////////////////////////////////// Global variables ///////////////////////////////////// + + +static unsigned int validationFlag; + +static cv::Point2f vertexA; +static cv::Point2f vertexB; +static cv::Point2f vertexC; + +static cv::Point2f sideAStartVertex; +static cv::Point2f sideAEndVertex; + +static cv::Point2f sideBStartVertex; +static cv::Point2f sideBEndVertex; + +static cv::Point2f sideCStartVertex; +static cv::Point2f sideCEndVertex; + +static double triangleArea; + +static unsigned int a; +static unsigned int b; +static unsigned int c; + +static unsigned int nrOfPoints; + +static std::vector polygon; + + +////////////////////////////// Helper functions declarations ///////////////////////////// + + +static void advance(unsigned int &index); + +static void advanceBToRightChain(); + +static bool almostEqual(double number1, double number2); + +static double angleOfLineWrtOxAxis(const cv::Point2f &a, const cv::Point2f &b); + +static bool areEqualPoints(const cv::Point2f &point1, const cv::Point2f &point2); + +static bool areIdenticalLines(const std::vector &side1Params, + const std::vector &side2Params, double sideCExtraParam); + +static bool areIdenticalLines(double a1, double b1, double c1, double a2, double b2, double c2); + +static bool areIntersectingLines(const std::vector &side1Params, + const std::vector &side2Params, + double sideCExtraParam, cv::Point2f &intersectionPoint1, + cv::Point2f &intersectionPoint2); + +static bool areOnTheSameSideOfLine(const cv::Point2f &p1, const cv::Point2f &p2, + const cv::Point2f &a, const cv::Point2f &b); + +static double areaOfTriangle(const cv::Point2f &a, const cv::Point2f &b, const cv::Point2f &c); + +static double distanceBtwPoints(const cv::Point2f &a, const cv::Point2f &b); + +static double distanceFromPointToLine(const cv::Point2f &a, const cv::Point2f &linePointB, + const cv::Point2f &linePointC); + +static bool findGammaIntersectionPoints(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); + +static void findMinimumAreaEnclosingTriangle(std::vector &triangle, double &area); + +static cv::Point2f findVertexCOnSideB(); + +static bool gamma(unsigned int polygonPointIndex, cv::Point2f &gammaPoint); + +static bool greaterOrEqual(double number1, double number2); + +static double height(const cv::Point2f &polygonPoint); + +static double height(unsigned int polygonPointIndex); + +static void initialise(); + +static unsigned int intersects(double angleGammaAndPoint, unsigned int polygonPointIndex); + +static bool intersectsAbove(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex); + +static unsigned int intersectsAboveOrBelow(unsigned int succPredIndex, unsigned int pointIndex); + +static bool intersectsBelow(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex); + +static bool isAngleBetween(double angle1, double angle2, double angle3); + +static bool isAngleBetweenNonReflex(double angle1, double angle2, double angle3); + +static bool isFlushAngleBtwPredAndSucc(double &angleFlushEdge, double anglePred, double angleSucc); + +static bool isGammaAngleBtw(double &gammaAngle, double angle1, double angle2); + +static bool isGammaAngleEqualTo(double &gammaAngle, double angle); + +static bool isLocalMinimalTriangle(); + +static bool isNotBTangency(); + +static bool isOppositeAngleBetweenNonReflex(double angle1, double angle2, double angle3); + +static bool isPointOnLineSegment(const cv::Point2f &point, const cv::Point2f &lineSegmentStart, + const cv::Point2f &lineSegmentEnd); + +static bool isValidMinimalTriangle(); + +static bool lessOrEqual(double number1, double number2); + +static void lineEquationDeterminedByPoints(const cv::Point2f &p, const cv::Point2f &q, + double &a, double &b, double &c); + +static std::vector lineEquationParameters(const cv::Point2f& p, const cv::Point2f &q); + +static bool lineIntersection(const cv::Point2f &a1, const cv::Point2f &b1, const cv::Point2f &a2, + const cv::Point2f &b2, cv::Point2f &intersection); + +static bool lineIntersection(double a1, double b1, double c1, double a2, double b2, double c2, + cv::Point2f &intersection); + +static double maximum(double number1, double number2, double number3); + +static cv::Point2f middlePoint(const cv::Point2f &a, const cv::Point2f &b); + +static bool middlePointOfSideB(cv::Point2f& middlePointOfSideB); + +static void moveAIfLowAndBIfHigh(); + +static double oppositeAngle(double angle); + +static unsigned int predecessor(unsigned int index); + +static void searchForBTangency(); + +static int sign(double number); + +static unsigned int successor(unsigned int index); + +static void updateMinimumAreaEnclosingTriangle(std::vector &triangle, double &area); + +static void updateSideB(); + +static void updateSidesBA(); + +static void updateSidesCA(); + + +///////////////////////////////////// Main functions ///////////////////////////////////// + + +//! Find the minimum enclosing triangle and its area for the given polygon +/*! +* 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 +*/ +void cv::minEnclosingTriangle( const std::vector &convexPolygon, + CV_OUT std::vector &triangle, CV_OUT double& area ) { + // Check if the polygon is convex and is a k-gon with k > 3 + CV_Assert(isContourConvex(convexPolygon) && (convexPolygon.size() > 3)); + + polygon = convexPolygon; + area = std::numeric_limits::max(); + + // Clear all points previously stored in the vector + triangle.clear(); + + initialise(); + + findMinimumAreaEnclosingTriangle(triangle, area); +} + + +/////////////////////////////// Helper functions definition ////////////////////////////// + + +//! Initialisation function +static void initialise() { + nrOfPoints = static_cast(polygon.size()); + + a = 1; + b = 2; + c = 0; +} + +//! Find the minimum area enclosing triangle for the given polygon +/*! +* @param triangle Minimum area triangle enclosing the given polygon +* @param area Area of the minimum area enclosing triangle +*/ +static void findMinimumAreaEnclosingTriangle(std::vector &triangle, double &area) { + for (c = 0; c < nrOfPoints; c++) { + advanceBToRightChain(); + moveAIfLowAndBIfHigh(); + searchForBTangency(); + + updateSidesCA(); + + if (isNotBTangency()) { + updateSidesBA(); + } else { + updateSideB(); + } + + if (isLocalMinimalTriangle()) { + updateMinimumAreaEnclosingTriangle(triangle, area); + } + } +} + +//! Advance b to the right chain +/*! +* See paper [2] for more details +*/ +static void advanceBToRightChain() { + while (greaterOrEqual(height(successor(b)), height(b))) { + advance(b); + } +} + +//! Move "a" if it is low and "b" if it is high +/*! +* See paper [2] for more details +*/ +static void moveAIfLowAndBIfHigh() { + while(height(b) > height(a)) { + cv::Point2f gammaOfA; + + if ((gamma(a, gammaOfA)) && (intersectsBelow(gammaOfA, b))) { + advance(b); + } else { + advance(a); + } + } +} + +//! Search for the tangency of side B +/*! +* See paper [2] for more details +*/ +static void searchForBTangency() { + cv::Point2f gammaOfB; + + while (((gamma(b, gammaOfB)) && (intersectsBelow(gammaOfB, b))) && + (greaterOrEqual(height(b), height(predecessor(a))))) { + advance(b); + } +} + +//! Check if tangency for side B was not obtained +/*! +* See paper [2] for more details +*/ +static bool isNotBTangency() { + cv::Point2f gammaOfB; + + if (((gamma(b, gammaOfB)) && (intersectsAbove(gammaOfB, b))) || (height(b) < height(predecessor(a)))) { + 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" +*/ +static void updateSidesCA() { + sideCStartVertex = polygon[predecessor(c)]; + sideCEndVertex = polygon[c]; + + sideAStartVertex = polygon[predecessor(a)]; + sideAEndVertex = polygon[a]; +} + +//! Update sides B and possibly A if tangency for side B was not obtained +/*! +* See paper [2] for more details +*/ +static void updateSidesBA() { + // Side B is flush with edge [b, b-1] + sideBStartVertex = polygon[predecessor(b)]; + sideBEndVertex = polygon[b]; + + // Find middle point of side B + cv::Point2f sideBMiddlePoint; + + if ((middlePointOfSideB(sideBMiddlePoint)) && + (height(sideBMiddlePoint) < height(predecessor(a)))) { + sideAStartVertex = polygon[predecessor(a)]; + sideAEndVertex = findVertexCOnSideB(); + + 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 +*/ +static void updateSideB() { + if (!gamma(b, sideBStartVertex)) { + 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 +*/ +static bool isLocalMinimalTriangle() { + if ((!lineIntersection(sideAStartVertex, sideAEndVertex, sideBStartVertex, sideBEndVertex, vertexC)) || + (!lineIntersection(sideAStartVertex, sideAEndVertex, sideCStartVertex, sideCEndVertex, vertexB)) || + (!lineIntersection(sideBStartVertex, sideBEndVertex, sideCStartVertex, sideCEndVertex, vertexA))) { + return false; + } + + return isValidMinimalTriangle(); +} + +//! 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 +*/ +static bool isValidMinimalTriangle() { + 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)])) + : (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 minimumAreaEnclosingTriangle Minimum area triangle enclosing the given polygon +* @param minimumAreaEnclosingTriangleArea Area of the minimum area triangle enclosing the given polygon +*/ +static void updateMinimumAreaEnclosingTriangle(std::vector &triangle, double &area) { + 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 +static bool middlePointOfSideB(cv::Point2f& middlePointOfSideB) { + 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 +*/ +static bool intersectsBelow(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex) { + double angleOfGammaAndPoint = angleOfLineWrtOxAxis(polygon[polygonPointIndex], gammaPoint); + + return (intersects(angleOfGammaAndPoint, polygonPointIndex) == 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 +*/ +static bool intersectsAbove(const cv::Point2f &gammaPoint, unsigned int polygonPointIndex) { + double angleOfGammaAndPoint = angleOfLineWrtOxAxis(gammaPoint, polygon[polygonPointIndex]); + + return (intersects(angleOfGammaAndPoint, polygonPointIndex) == INTERSECTS_ABOVE); +} + +//! Check if/where the line determined by gammaPoint and polygon[polygonPointIndex] intersects the polygon +/*! +* @param angleGammaAndPoint Angle between gammaPoint and polygon[polygonPointIndex] +* @param polygonPointIndex Index of the polygon point which is considered when determining the line +*/ +static unsigned int intersects(double angleGammaAndPoint, unsigned int polygonPointIndex) { + double anglePointPredecessor = angleOfLineWrtOxAxis(polygon[predecessor(polygonPointIndex)], + polygon[polygonPointIndex]); + double anglePointSuccessor = angleOfLineWrtOxAxis(polygon[successor(polygonPointIndex)], + polygon[polygonPointIndex]); + double angleFlushEdge = angleOfLineWrtOxAxis(polygon[predecessor(c)], + polygon[c]); + + if (isFlushAngleBtwPredAndSucc(angleFlushEdge, anglePointPredecessor, anglePointSuccessor)) { + if ((isGammaAngleBtw(angleGammaAndPoint, anglePointPredecessor, angleFlushEdge)) || + (almostEqual(angleGammaAndPoint, anglePointPredecessor))) { + return intersectsAboveOrBelow(predecessor(polygonPointIndex), polygonPointIndex); + } else if ((isGammaAngleBtw(angleGammaAndPoint, anglePointSuccessor, angleFlushEdge)) || + (almostEqual(angleGammaAndPoint, anglePointSuccessor))) { + return intersectsAboveOrBelow(successor(polygonPointIndex), polygonPointIndex); + } + } 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 +*/ +static unsigned int intersectsAboveOrBelow(unsigned int succPredIndex, unsigned int pointIndex) { + if (height(succPredIndex) > height(pointIndex)) { + 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 closest to point polygon[a]. +* +* 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]) +*/ +static bool gamma(unsigned int polygonPointIndex, cv::Point2f &gammaPoint) { + cv::Point2f intersectionPoint1, intersectionPoint2; + + // Get intersection points if they exist + if (!findGammaIntersectionPoints(polygonPointIndex, polygon[a], polygon[predecessor(a)], polygon[c], + polygon[predecessor(c)], 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)], + polygon[c], polygon[predecessor(c)])) { + gammaPoint = intersectionPoint1; + } else { + gammaPoint = intersectionPoint2; + } + + return true; +} + +//! Find the intersection points to compute gamma(point) +/*! +* @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 another pair of lines +*/ +static bool findGammaIntersectionPoints(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 side1Params = lineEquationParameters(side1StartVertex, side1EndVertex); + std::vector side2Params = lineEquationParameters(side2StartVertex, side2EndVertex); + + // Compute side C extra parameter using the formula for distance from a point to a line + double polygonPointHeight = height(polygonPointIndex); + 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 &side1Params, + const std::vector &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 &side1Params, + const std::vector &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 lineEquationParameters(const cv::Point2f& p, const cv::Point2f &q) { + std::vector 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; +} + +//! 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 closest to point polygon[b]. +* +* See paper [2] and formula for distance from point to a line for more details +*/ +static cv::Point2f findVertexCOnSideB() { + cv::Point2f intersectionPoint1, intersectionPoint2; + + // Get intersection points if they exist + if (!findGammaIntersectionPoints(predecessor(a), 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)], + polygon[c], polygon[predecessor(c)])) { + return intersectionPoint1; + } else { + return intersectionPoint2; + } +} + +//! Compute the height of the point +/*! +* See paper [2] for more details +* +* @param polygonPoint Polygon point +*/ +static double height(const cv::Point2f &polygonPoint) { + cv::Point2f pointC = polygon[c]; + cv::Point2f pointCPredecessor = polygon[predecessor(c)]; + + 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 +*/ +static double height(unsigned int polygonPointIndex) { + cv::Point2f pointC = polygon[c]; + cv::Point2f pointCPredecessor = polygon[predecessor(c)]; + + cv::Point2f polygonPoint = polygon[polygonPointIndex]; + + return distanceFromPointToLine(polygonPoint, pointC, pointCPredecessor); +} + +//! Advance the given index with one position +/*! +* @param index Index of the point +*/ +static void advance(unsigned int &index) { + index = successor(index); +} + +//! 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 +*/ +static unsigned int successor(unsigned int index) { + 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 +*/ +static unsigned int predecessor(unsigned int index) { + 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 / 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 +* +* @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 (nominator / denominator); +} + +//! 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 presented at http://demonstrations.wolfram.com/TheAreaOfATriangleUsingADeterminant/ +* (Last access: 10.07.2013) +* +* @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 = (double)((a.x + b.x) / 2); + double middleY = (double)((a.y + b.y) / 2); + + return cv::Point2f((float) middleX, (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 (= A1xB2 - A2xB1) == 0, then lines are parallel +* else they intersect +* +* If they intersect, then let us denote the intersection point with P(x, y) where: +* x = (C1xB2 - C2xB1) / (det) +* y = (C2xA1 - C1xA2) / (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 = (float)(((c1 * b2) - (c2 * b1)) / (det)); + intersection.y = (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 (= A1xB2 - A2xB1) == 0, then lines are parallel +* else they intersect +* +* If they intersect, then let us denote the intersection point with P(x, y) where: +* x = (C1xB2 - C2xB1) / (det) +* y = (C2xA1 - C1xA2) / (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 = (float)(((C1 * B2) - (C2 * B1)) / (det)); + intersection.y = (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))); +} + + +/* End of file. */