bullet3

#pragma once


#include "Eigen/Dense"
#include "Eigen/StdVector"
#include "Eigen/Geometry"

#define _USE_MATH_DEFINES
#include "math.h"

const int gInvalidIdx = -1;

// for convenience define standard vector for rendering
typedef Eigen::Vector4d tVector;
typedef Eigen::Vector4d tVector3;
typedef Eigen::Matrix4d tMatrix;
typedef Eigen::Matrix3d tMatrix3;
typedef Eigen::Quaterniond tQuaternion;


const double gRadiansToDegrees = 57.2957795;
const double gDegreesToRadians = 1.0 / gRadiansToDegrees;
const tVector gGravity = tVector(0, -9.8, 0, 0);
const double gInchesToMeters = 0.0254;
const double gFeetToMeters = 0.3048;

class cMathUtil
{
public:
	enum eAxis
	{
		eAxisX,
		eAxisY,
		eAxisZ,
		eAxisMax
	};

	static int Clamp(int val, int min, int max);
	static void Clamp(const Eigen::VectorXd& min, const Eigen::VectorXd& max, Eigen::VectorXd& out_vec);
	static double Clamp(double val, double min, double max);
	static double Saturate(double val);
	static double Lerp(double t, double val0, double val1);

	static double NormalizeAngle(double theta);

	static double SmoothStep(double t);

	// matrices
	static tMatrix TranslateMat(const tVector& trans);
	static tMatrix ScaleMat(double scale);
	static tMatrix ScaleMat(const tVector& scale);
	static tMatrix RotateMat(const tVector& euler); // euler angles order rot(Z) * rot(Y) * rot(X)
	static tMatrix RotateMat(const tVector& axis, double theta);
	static tMatrix RotateMat(const tQuaternion& q);
	static tMatrix CrossMat(const tVector& a);
	// inverts a transformation consisting only of rotations and translations
	static tMatrix InvRigidMat(const tMatrix& mat);
	static tVector GetRigidTrans(const tMatrix& mat);
	static tVector InvEuler(const tVector& euler);
	static void RotMatToAxisAngle(const tMatrix& mat, tVector& out_axis, double& out_theta);
	static tVector RotMatToEuler(const tMatrix& mat);
	static tQuaternion RotMatToQuaternion(const tMatrix& mat);
	static void EulerToAxisAngle(const tVector& euler, tVector& out_axis, double& out_theta);
	
	static tMatrix DirToRotMat(const tVector& dir, const tVector& up);

	static void DeltaRot(const tVector& axis0, double theta0, const tVector& axis1, double theta1,
							tVector& out_axis, double& out_theta);
	static tMatrix DeltaRot(const tMatrix& R0, const tMatrix& R1);

	static tQuaternion EulerToQuaternion(const tVector& euler);
	
	static tQuaternion AxisAngleToQuaternion(const tVector& axis, double theta);
	static void QuaternionToAxisAngle(const tQuaternion& q, tVector& out_axis, double& out_theta);
	static tMatrix BuildQuaternionDiffMat(const tQuaternion& q);
	static tVector CalcQuaternionVel(const tQuaternion& q0, const tQuaternion& q1, double dt);
	static tVector CalcQuaternionVelRel(const tQuaternion& q0, const tQuaternion& q1, double dt);
	static tQuaternion VecToQuat(const tVector& v);
	static tVector QuatToVec(const tQuaternion& q);
	static tQuaternion QuatDiff(const tQuaternion& q0, const tQuaternion& q1);
	static double QuatDiffTheta(const tQuaternion& q0, const tQuaternion& q1);
	static double QuatTheta(const tQuaternion& dq);
	static tQuaternion VecDiffQuat(const tVector& v0, const tVector& v1);
	static tVector QuatRotVec(const tQuaternion& q, const tVector& dir);
	static tQuaternion MirrorQuaternion(const tQuaternion& q, eAxis axis);

	static double Sign(double val);
	static int Sign(int val);

	static double AddAverage(double avg0, int count0, double avg1, int count1);
	static tVector AddAverage(const tVector& avg0, int count0, const tVector& avg1, int count1);
	static void AddAverage(const Eigen::VectorXd& avg0, int count0, const Eigen::VectorXd& avg1, int count1, Eigen::VectorXd& out_result);
	static void CalcSoftmax(const Eigen::VectorXd& vals, double temp, Eigen::VectorXd& out_prob);
	static double EvalGaussian(const Eigen::VectorXd& mean, const Eigen::VectorXd& covar, const Eigen::VectorXd& sample);
	static double EvalGaussian(double mean, double covar, double sample);
	static double CalcGaussianPartition(const Eigen::VectorXd& covar);
	static double EvalGaussianLogp(double mean, double covar, double sample);
	static double EvalGaussianLogp(const Eigen::VectorXd& mean, const Eigen::VectorXd& covar, const Eigen::VectorXd& sample);
	static double Sigmoid(double x);
	static double Sigmoid(double x, double gamma, double bias);

	static tVector CalcBarycentric(const tVector& p, const tVector& a, const tVector& b, const tVector& c);

	static bool ContainsAABB(const tVector& pt, const tVector& aabb_min, const tVector& aabb_max);
	static bool ContainsAABB(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1);
	static bool ContainsAABBXZ(const tVector& pt, const tVector& aabb_min, const tVector& aabb_max);
	static bool ContainsAABBXZ(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1);
	static void CalcAABBIntersection(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1,
									tVector& out_min, tVector& out_max);
	static void CalcAABBUnion(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1,
								tVector& out_min, tVector& out_max);
	static bool IntersectAABB(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1);
	static bool IntersectAABBXZ(const tVector& aabb_min0, const tVector& aabb_max0, const tVector& aabb_min1, const tVector& aabb_max1);

	// check if curr_val and curr_val - delta belong to different intervals
	static bool CheckNextInterval(double delta, double curr_val, double int_size);

	
	static void QuatSwingTwistDecomposition(const tQuaternion& q, const tVector& dir, tQuaternion& out_swing, tQuaternion& out_twist);
	static tQuaternion ProjectQuat(const tQuaternion& q, const tVector& dir);

	static void ButterworthFilter(double dt, double cutoff, Eigen::VectorXd& out_x);
	
private:
	
	template <typename T>
	static T SignAux(T val)
	{
		return (T(0) < val) - (val < T(0));
	}
};