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Diffstat (limited to 'src/system/Qt3DSCubicRootsImpl.h')
| -rw-r--r-- | src/system/Qt3DSCubicRootsImpl.h | 177 |
1 files changed, 177 insertions, 0 deletions
diff --git a/src/system/Qt3DSCubicRootsImpl.h b/src/system/Qt3DSCubicRootsImpl.h new file mode 100644 index 0000000..8cca59f --- /dev/null +++ b/src/system/Qt3DSCubicRootsImpl.h @@ -0,0 +1,177 @@ +/**************************************************************************** +** +** Copyright (C) 1993-2009 NVIDIA Corporation. +** Copyright (C) 2017 The Qt Company Ltd. +** Contact: https://www.qt.io/licensing/ +** +** This file is part of Qt 3D Studio. +** +** $QT_BEGIN_LICENSE:GPL$ +** Commercial License Usage +** Licensees holding valid commercial Qt licenses may use this file in +** accordance with the commercial license agreement provided with the +** Software or, alternatively, in accordance with the terms contained in +** a written agreement between you and The Qt Company. For licensing terms +** and conditions see https://www.qt.io/terms-conditions. For further +** information use the contact form at https://www.qt.io/contact-us. +** +** GNU General Public License Usage +** Alternatively, this file may be used under the terms of the GNU +** General Public License version 3 or (at your option) any later version +** approved by the KDE Free Qt Foundation. The licenses are as published by +** the Free Software Foundation and appearing in the file LICENSE.GPL3 +** included in the packaging of this file. Please review the following +** information to ensure the GNU General Public License requirements will +** be met: https://www.gnu.org/licenses/gpl-3.0.html. +** +** $QT_END_LICENSE$ +** +****************************************************************************/ + +//============================================================================== +// Namespace +//============================================================================== +namespace Q3DStudio { + +//============================================================================== +// Constants used by the functions +//============================================================================== +const FLOAT M_PHI = 3.14159265358979323846f; + +/* epsilon surrounding for near zero values */ +const FLOAT EQN_EPS = 1e-9f; + +#define ISZERO(x) ((x) > -EQN_EPS && (x) < EQN_EPS) + +// cube-root +#ifndef CUBEROOT +#define CUBEROOT(x) \ + ((x) > 0.0 ? static_cast<FLOAT>(pow((x), 1.0f / 3.0f)) \ + : ((x) < 0.0 ? -static_cast<FLOAT>(pow(-(x), 1.0f / 3.0f)) : 0.0f)) +#endif + +//============================================================================== +/** + * Find the root/s to a quadratic equation. + * + * The equation is of the form: c[2]*x^2 + c[1]*x + c[0] = 0 + * Note that this will fail if c[2] is zero, or this is a linear equation. + * + * @param inConstants The array of constants to the equation; see form above + * @param outSolutions The array of solutions to the equation + * @return the number of solutions for the equation + */ +INT32 CCubicRoots::SolveQuadric(FLOAT inConstants[3], FLOAT outSolutions[2]) +{ +#ifdef _PERF_LOG + PerfLogMathEvent1 thePerfLog(DATALOGGER_CUBICROOT); +#endif + FLOAT theP, theQ, theD; + INT32 theResult = 0; + + /* normal form: x^2 + px + theQ = 0 */ + + theP = inConstants[1] / (2 * inConstants[2]); + theQ = inConstants[0] / inConstants[2]; + + theD = theP * theP - theQ; + + if (ISZERO(theD)) { + outSolutions[0] = -theP; + theResult = 1; + } else if (theD < 0.0f) { + theResult = 0; + } else if (theD > 0.0f) { + FLOAT theSquareRootD = sqrtf(theD); + + outSolutions[0] = theSquareRootD - theP; + outSolutions[1] = -theSquareRootD - theP; + theResult = 2; + } + + return theResult; +} + +//============================================================================== +/** + * Find the root/s to a cubic equation. + * + * The equation is of the form: c[3]*x^3 + c[2]*x^2 + c[1]*x + c[0] = 0 + * Note that this will fail if c[3] is zero, or this is a quadratic equation. + * + * @param inConstants The array of constants to the equation; see form above + * @param outSolutions The array of solutions to the equation + * @return the number of solutions for the equation + */ +INT32 CCubicRoots::SolveCubic(FLOAT inConstants[4], FLOAT outSolutions[3]) +{ +#ifdef _PERF_LOG + PerfLogMathEvent1 thePerfLog(DATALOGGER_CUBICROOT); +#endif + + INT32 theResult; + FLOAT theSubstitute; + FLOAT theVariableA, theVariableB, theVariableC; + FLOAT theASquared, theVariableP, theVariableQ; + FLOAT thePCubed, theVariableD; + + /* normal form: x^3 + Ax^2 + Bx + C = 0 */ + + theVariableA = inConstants[2] / inConstants[3]; + theVariableB = inConstants[1] / inConstants[3]; + theVariableC = inConstants[0] / inConstants[3]; + + /* substitute x = y - A/3 to eliminate quadric term: + x^3 +px + q = 0 */ + + theASquared = theVariableA * theVariableA; + theVariableP = 1.0f / 3.0f * (-1.0f / 3.0f * theASquared + theVariableB); + theVariableQ = 1.0f / 2.0f * (2.0f / 27.0f * theVariableA * theASquared + - 1.0f / 3.0f * theVariableA * theVariableB + theVariableC); + + /* use Cardano's formula */ + + thePCubed = theVariableP * theVariableP * theVariableP; + theVariableD = theVariableQ * theVariableQ + thePCubed; + + if (ISZERO(theVariableD)) { + if (ISZERO(theVariableQ)) /* one triple solution */ + { + outSolutions[0] = 0; + theResult = 1; + } else /* one single and one double solution */ + { + FLOAT theVariableU = CUBEROOT(-theVariableQ); + outSolutions[0] = 2.0f * theVariableU; + outSolutions[1] = -theVariableU; + theResult = 2; + } + } else if (theVariableD < 0.0f) /* Casus irreducibilis: three real solutions */ + { + FLOAT thePhi = 1.0f / 3.0f * static_cast<FLOAT>(acos(-theVariableQ / sqrtf(-thePCubed))); + FLOAT theVariableT = 2.0f * sqrtf(-theVariableP); + + outSolutions[0] = theVariableT * static_cast<FLOAT>(cos(thePhi)); + outSolutions[1] = -theVariableT * static_cast<FLOAT>(cos(thePhi + M_PHI / 3.0f)); + outSolutions[2] = -theVariableT * static_cast<FLOAT>(cos(thePhi - M_PHI / 3.0f)); + theResult = 3; + } else /* one real solution */ + { + FLOAT theSquareRootD = sqrtf(theVariableD); + FLOAT theVariableU = CUBEROOT(theSquareRootD - theVariableQ); + FLOAT theVariableV = -CUBEROOT(theSquareRootD + theVariableQ); + + outSolutions[0] = theVariableU + theVariableV; + theResult = 1; + } + + /* resubstitute */ + theSubstitute = 1.0f / 3.0f * theVariableA; + + for (INT32 theIndex = 0; theIndex < theResult; ++theIndex) + outSolutions[theIndex] -= theSubstitute; + + return theResult; +} + +}; // namespace Q3DStudio |