/**************************************************************************** ** ** This file is part of the LibreCAD project, a 2D CAD program ** ** Copyright (C) 2010 R. van Twisk (librecad@rvt.dds.nl) ** Copyright (C) 2001-2003 RibbonSoft. All rights reserved. ** ** ** This file may be distributed and/or modified under the terms of the ** GNU General Public License version 2 as published by the Free Software ** Foundation and appearing in the file gpl-2.0.txt included in the ** packaging of this file. ** ** This program is distributed in the hope that it will be useful, ** but WITHOUT ANY WARRANTY; without even the implied warranty of ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ** GNU General Public License for more details. ** ** You should have received a copy of the GNU General Public License ** along with this program; if not, write to the Free Software ** Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA ** ** This copyright notice MUST APPEAR in all copies of the script! ** **********************************************************************/ #ifndef RS_MATH_H #define RS_MATH_H #include #include #include class QString; class QRegularExpressionMatch; class RS_Vector; class RS_VectorSolutions; /** * Math functions. */ namespace RS_Math { int round(double v); double round(double v, double precision); double pow(double x, double y); RS_Vector pow(const RS_Vector& x, int y); /** * @brief equal test whether two floating points are equal * @param d1 number 1 * @param d2 number 2 * @param tolerance tolerance to use, if the value is smaller than ulp of d1/d2, double of the ulp is used * @return true if the floating points are considered equal */ bool equal(double d1, double d2, double tolerance = 0.); bool notEqual(double d1, double d2, double tolerance = 0.); double rad2deg(double a); double deg2rad(double a); double rad2gra(double a); double gra2rad(double a); double gra2deg(double a); unsigned findGCD(unsigned a, unsigned b); /** * Tests if angle a is between a1 and a2. * All angles in radians. * * @param a - an angle * @param amin - the start angle * @param amax - the end angle * @param reversed - whether the range is reversed, default to false * reversed=true for clockwise testing. false for ccw testing. * @return true if the angle a is between amin and amax. */ bool isAngleBetween(double a, double amin, double amax, bool reversed = false); //! \brief correct angle to be within [0, +PI*2.0) double correctAngle(double a); //! \brief correct angle to be within [-PI, +PI) double correctAnglePlusMinusPi(double a); //! \brief correct angle to be unsigned [0, +PI) double correctAngle0ToPi(double a); void calculateAngles(double &angle, double &complementary, double &supplementary, double &alt); //! \brief angular difference double getAngleDifference(double a1, double a2, bool reversed = false); /** * @brief getAngleDifferenceU abs of minimum angular difference, unsigned version of angular difference * @param a1,a2 angles * @return the minimum of angular difference a1-a2 and a2-a1 */ double getAngleDifferenceU(double a1, double a2); double makeAngleReadable(double angle, bool readable = true, bool* corrected = nullptr); bool isAngleReadable(double angle); bool isSameDirection(double dir1, double dir2, double tol); //! \convert measurement strings with rationals or unit symbols to current unit double convert_unit(const QRegularExpressionMatch&, const QString&, double, double); QString derationalize(const QString& expr); //! \{ \brief evaluate a math string double eval(const QString& expr, double def = 0.0); double eval(const QString& expr, bool* ok); //! \} std::vector quadraticSolver(const std::vector& ce); std::vector cubicSolver(const std::vector& ce); /** quartic solver * x^4 + ce[0] x^3 + ce[1] x^2 + ce[2] x + ce[3] = 0 @ce, a vector of size 4 contains the coefficient in order @return, a vector contains real roots **/ std::vector quarticSolver(const std::vector& ce); /** quartic solver * ce[4] x^4 + ce[3] x^3 + ce[2] x^2 + ce[1] x + ce[0] = 0 @ce, a vector of size 5 contains the coefficient in order @return, a vector contains real roots **/ std::vector quarticSolverFull(const std::vector& ce); //solver for linear equation set /** * Solve linear equation set *@param mt holds the augmented matrix *@param sn holds the solution *@param return true, if the equation set has a unique solution, return false otherwise * *@author: Dongxu Li */ bool linearSolver(const std::vector>& m, std::vector& sn); /** solver quadratic simultaneous equations of a set of two **/ /* solve the following quadratic simultaneous equations, * ma000 x^2 + ma011 y^2 - 1 =0 * ma100 x^2 + 2 ma101 xy + ma111 y^2 + mb10 x + mb11 y +mc1 =0 * *@m, a vector of size 8 contains coefficients in the strict order of: ma000 ma011 ma100 ma101 ma111 mb10 mb11 mc1 *@return a RS_VectorSolutions contains real roots (x,y) */ RS_VectorSolutions simultaneousQuadraticSolver(const std::vector& m); /** solver quadratic simultaneous equations of a set of two **/ /** solve the following quadratic simultaneous equations, * ma000 x^2 + ma001 xy + ma011 y^2 + mb00 x + mb01 y + mc0 =0 * ma100 x^2 + ma101 xy + ma111 y^2 + mb10 x + mb11 y + mc1 =0 * *@param m a vector of size 2 each contains a vector of size 6 coefficients in the strict order of: ma000 ma001 ma011 mb00 mb01 mc0 ma100 ma101 ma111 mb10 mb11 mc1 *@return a RS_VectorSolutions contains real roots (x,y) */ RS_VectorSolutions simultaneousQuadraticSolverFull(const std::vector>& m); RS_VectorSolutions simultaneousQuadraticSolverMixed(const std::vector>& m); /** \brief verify simultaneousQuadraticVerify a solution for simultaneousQuadratic *@param m the coefficient matrix *@param v a candidate to verify *@return true, for a valid solution **/ bool simultaneousQuadraticVerify(const std::vector>& m, RS_Vector& v); /** wrapper for elliptic integral **/ /** * wrapper of elliptic integral of the second type, Legendre form *@k the elliptic modulus or eccentricity *@phi elliptic angle, must be within range of [0, M_PI] * *@\author: Dongxu Li */ double ellipticIntegral_2(const double& k, const double& phi); // The ULP (Unit at Last Place) for a floating point /** * @brief ulp - the ULP (Unit at Last Place) for a floating point * @param x - a floating point * @return - the ULP of the given floating point * @author: Dongxu Li */ template std::enable_if_t, FT> ulp(FT x) { if (std::signbit(x)) return x - std::nexttoward(x, -std::numeric_limits::infinity()); else return std::nexttoward(x, std::numeric_limits::infinity()) - x; } /** * @brief less - compare two floating points using ULP as tolerance * @param a - a floating point * @param b - a floating point * @return bool - true, if a is less or equal within twice of the ULP of b * @author: Dongxu Li */ template std::enable_if_t, bool> less(FT a, FT b) { return a <= b + 2 * RS_Math::ulp(b); } /** * @brief inBetween - whether a floating point is between two given floating points * @param x - a floating to determine whether in range * @param a - one bound of the range * @param b - one bound of the range * @return bool - true, if the floating point x is within the range defined by * a and b, with floating point ULP used as tolerance in comparison * @author: Dongxu Li */ template std::enable_if_t, bool> inBetween(FT x, FT a, FT b) { return RS_Math::less(x, std::max(a, b)) && RS_Math::less(std::min(a, b), x); } QString doubleToString(double value, double prec); QString doubleToString(double value, int prec); void test(); int getPeriodsCount(double a1, double a2, bool reversed); }; // namespace RS_Math #endif