text: /********************************************************************************
  * ReactPhysics3D physics library, http://www.reactphysics3d.com                 *
  * Copyright (c) 2010-2019 Daniel Chappuis                                       *
  *********************************************************************************
  *                                                                               *
  * This software is provided 'as-is', without any express or implied warranty.   *
  * In no event will the authors be held liable for any damages arising from the  *
  * use of this software.                                                         *
  *                                                                               *
  * Permission is granted to anyone to use this software for any purpose,         *
  * including commercial applications, and to alter it and redistribute it        *
  * freely, subject to the following restrictions:                                *
  *                                                                               *
  * 1. The origin of this software must not be misrepresented; you must not claim *
  *    that you wrote the original software. If you use this software in a        *
  *    product, an acknowledgment in the product documentation would be           *
  *    appreciated but is not required.                                           *
  *                                                                               *
  * 2. Altered source versions must be plainly marked as such, and must not be    *
  *    misrepresented as being the original software.                             *
  *                                                                               *
  * 3. This notice may not be removed or altered from any source distribution.    *
  *                                                                               *
  ********************************************************************************/
  
  #ifndef REACTPHYSICS3D_MATHEMATICS_FUNCTIONS_H
  #define REACTPHYSICS3D_MATHEMATICS_FUNCTIONS_H
  
  // Libraries
  #include "configuration.h"
  #include "decimal.h"
  #include <algorithm>
  #include <cassert>
  #include <cmath>
  #include "containers/List.h"
  
  /// ReactPhysics3D namespace
  namespace reactphysics3d {
  
  struct Vector3;
  struct Vector2;
  
  // ---------- Mathematics functions ---------- //
  
  /// Function to test if two real numbers are (almost) equal
  /// We test if two numbers a and b are such that (a-b) are in [-EPSILON; EPSILON]
  inline bool approxEqual(decimal a, decimal b, decimal epsilon = MACHINE_EPSILON) {
      return (std::fabs(a - b) < epsilon);
  }
  
  /// Function to test if two vectors are (almost) equal
  bool approxEqual(const Vector3& vec1, const Vector3& vec2, decimal epsilon = MACHINE_EPSILON);
  
  /// Function to test if two vectors are (almost) equal
  bool approxEqual(const Vector2& vec1, const Vector2& vec2, decimal epsilon = MACHINE_EPSILON);
  
  /// Function that returns the result of the "value" clamped by
  /// two others values "lowerLimit" and "upperLimit"
  inline int clamp(int value, int lowerLimit, int upperLimit) {
      assert(lowerLimit <= upperLimit);
      return std::min(std::max(value, lowerLimit), upperLimit);
  }
  
  /// Function that returns the result of the "value" clamped by
  /// two others values "lowerLimit" and "upperLimit"
  inline decimal clamp(decimal value, decimal lowerLimit, decimal upperLimit) {
      assert(lowerLimit <= upperLimit);
      return std::min(std::max(value, lowerLimit), upperLimit);
  }
  
  /// Return the minimum value among three values
  inline decimal min3(decimal a, decimal b, decimal c) {
      return std::min(std::min(a, b), c);
  }
  
  /// Return the maximum value among three values
  inline decimal max3(decimal a, decimal b, decimal c) {
      return std::max(std::max(a, b), c);
  }
  
  /// Return true if two values have the same sign
  inline bool sameSign(decimal a, decimal b) {
      return a * b >= decimal(0.0);
  }
  
  /// Return true if two vectors are parallel
  bool areParallelVectors(const Vector3& vector1, const Vector3& vector2);
  
  /// Return true if two vectors are orthogonal
  bool areOrthogonalVectors(const Vector3& vector1, const Vector3& vector2);
  
  /// Clamp a vector such that it is no longer than a given maximum length
  Vector3 clamp(const Vector3& vector, decimal maxLength);
  
  // Compute and return a point on segment from "segPointA" and "segPointB" that is closest to point "pointC"
  Vector3 computeClosestPointOnSegment(const Vector3& segPointA, const Vector3& segPointB, const Vector3& pointC);
  
  // Compute the closest points between two segments
  void computeClosestPointBetweenTwoSegments(const Vector3& seg1PointA, const Vector3& seg1PointB,
  										   const Vector3& seg2PointA, const Vector3& seg2PointB,
  										   Vector3& closestPointSeg1, Vector3& closestPointSeg2);
  
  /// Compute the barycentric coordinates u, v, w of a point p inside the triangle (a, b, c)
  void computeBarycentricCoordinatesInTriangle(const Vector3& a, const Vector3& b, const Vector3& c,
                                               const Vector3& p, decimal& u, decimal& v, decimal& w);
  
  /// Compute the intersection between a plane and a segment
  decimal computePlaneSegmentIntersection(const Vector3& segA, const Vector3& segB, const decimal planeD, const Vector3& planeNormal);
  
  /// Compute the distance between a point and a line
  decimal computePointToLineDistance(const Vector3& linePointA, const Vector3& linePointB, const Vector3& point);
  
  /// Clip a segment against multiple planes and return the clipped segment vertices
  List<Vector3> clipSegmentWithPlanes(const Vector3& segA, const Vector3& segB,
                                                             const List<Vector3>& planesPoints,
                                                             const List<Vector3>& planesNormals,
                                                             MemoryAllocator& allocator);
  
  /// Clip a polygon against multiple planes and return the clipped polygon vertices
  List<Vector3> clipPolygonWithPlanes(const List<Vector3>& polygonVertices, const List<Vector3>& planesPoints,
                                      const List<Vector3>& planesNormals, MemoryAllocator& allocator);
  
  /// Project a point onto a plane that is given by a point and its unit length normal
  Vector3 projectPointOntoPlane(const Vector3& point, const Vector3& planeNormal, const Vector3& planePoint);
  
  /// Return the distance between a point and a plane (the plane normal must be normalized)
  decimal computePointToPlaneDistance(const Vector3& point, const Vector3& planeNormal, const Vector3& planePoint);
  
  /// Return true if the given number is prime
  bool isPrimeNumber(int number);
  
  }
  
  
  #endif
  