//Copyright 2013,2016 <>< C. N. Lohr.  This file licensed under the terms of the MIT license.

#include "linmath.h"
#include <math.h>
#include <float.h>

void cross3d( FLT * out, const FLT * a, const FLT * b )
{
	out[0] = a[1]*b[2] - a[2]*b[1];
	out[1] = a[2]*b[0] - a[0]*b[2];
	out[2] = a[0]*b[1] - a[1]*b[0];
}

void sub3d( FLT * out, const FLT * a, const FLT * b )
{
	out[0] = a[0] - b[0];
	out[1] = a[1] - b[1];
	out[2] = a[2] - b[2];
}

void add3d( FLT * out, const FLT * a, const FLT * b )
{
	out[0] = a[0] + b[0];
	out[1] = a[1] + b[1];
	out[2] = a[2] + b[2];
}

void scale3d( FLT * out, const FLT * a, FLT scalar )
{
	out[0] = a[0] * scalar;
	out[1] = a[1] * scalar;
	out[2] = a[2] * scalar;
}

void normalize3d( FLT * out, const FLT * in )
{
	FLT r = ((FLT)1.) / FLT_SQRT(in[0] * in[0] + in[1] * in[1] + in[2] * in[2]);
	out[0] = in[0] * r;
	out[1] = in[1] * r;
	out[2] = in[2] * r;
}

FLT dot3d( const FLT * a, const FLT * b )
{
	return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}

int compare3d( const FLT * a, const FLT * b, FLT epsilon )
{
	if( !a || !b ) return 0;
	if( a[2] - b[2] > epsilon ) return 1;
	if( b[2] - a[2] > epsilon ) return -1;
	if( a[1] - b[1] > epsilon ) return 1;
	if( b[1] - a[1] > epsilon ) return -1;
	if( a[0] - b[0] > epsilon ) return 1;
	if( b[0] - a[0] > epsilon ) return -1;
	return 0;
}

void copy3d( FLT * out, const FLT * in )
{
	out[0] = in[0];
	out[1] = in[1];
	out[2] = in[2];
}

FLT magnitude3d(const FLT * a )
{
	return FLT_SQRT(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
}

FLT anglebetween3d( FLT * a, FLT * b )
{
	FLT an[3];
	FLT bn[3];
	normalize3d( an, a );
	normalize3d( bn, b );
	FLT dot = dot3d( a, b );
	if( dot < -0.9999999 ) return LINMATHPI;
	if( dot >  0.9999999 ) return 0;
	return FLT_ACOS(dot);
}

/////////////////////////////////////QUATERNIONS//////////////////////////////////////////
//Originally from Mercury (Copyright (C) 2009 by Joshua Allen, Charles Lohr, Adam Lowman)
//Under the mit/X11 license.




void quatsetnone(FLT * q)
{
	q[0] = 1; q[1] = 0; q[2] = 0; q[3] = 0;
}

void quatsetidentity(FLT * q)
{
	q[0] = 1; q[1] = 0; q[2] = 0; q[3] = 1;
}

void quatcopy(FLT * qout, const FLT * qin)
{
	qout[0] = qin[0];
	qout[1] = qin[1];
	qout[2] = qin[2];
	qout[3] = qin[3];
}

void quatfromeuler( FLT * q, const FLT * euler )
{
	FLT X = euler[0]/2.0f; //roll
	FLT Y = euler[1]/2.0f; //pitch
	FLT Z = euler[2]/2.0f; //yaw

	FLT cx = FLT_COS(X);
	FLT sx = FLT_SIN(X);
	FLT cy = FLT_COS(Y);
	FLT sy = FLT_SIN(Y);
	FLT cz = FLT_COS(Z);
	FLT sz = FLT_SIN(Z);

	//Correct according to
	//http://en.wikipedia.org/wiki/Conversion_between_MQuaternions_and_Euler_angles
	q[0] = cx*cy*cz+sx*sy*sz;//q1
	q[1] = sx*cy*cz-cx*sy*sz;//q2
	q[2] = cx*sy*cz+sx*cy*sz;//q3
	q[3] = cx*cy*sz-sx*sy*cz;//q4
	quatnormalize( q, q );
}

void quattoeuler( FLT * euler, const FLT * q )
{
	//According to http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles (Oct 26, 2009)
	euler[0] = FLT_ATAN2(2 * (q[0] * q[1] + q[2] * q[3]), 1 - 2 * (q[1] * q[1] + q[2] * q[2]));
	euler[1] = FLT_ASIN(2 * (q[0] * q[2] - q[3] * q[1]));
	euler[2] = FLT_ATAN2(2 * (q[0] * q[3] + q[1] * q[2]), 1 - 2 * (q[2] * q[2] + q[3] * q[3]));
}

void quatfromaxisangle( FLT * q, const FLT * axis, FLT radians )
{
	FLT v[3];
	normalize3d( v, axis );
	
	FLT sn = FLT_SIN(radians / 2.0f);
	q[0] = FLT_COS(radians / 2.0f);
	q[1] = sn * v[0];
	q[2] = sn * v[1];
	q[3] = sn * v[2];

	quatnormalize( q, q );
}

FLT quatmagnitude( const FLT * q )
{
	return FLT_SQRT((q[0] * q[0]) + (q[1] * q[1]) + (q[2] * q[2]) + (q[3] * q[3]));
}

FLT quatinvsqmagnitude( const FLT * q )
{
	return ((FLT)1.)/((q[0]*q[0])+(q[1]*q[1])+(q[2]*q[2])+(q[3]*q[3]));
}


void quatnormalize( FLT * qout, const FLT * qin )
{
	FLT imag = quatinvsqmagnitude( qin );
	quatscale( qout, qin, imag );
}

void quattomatrix(FLT * matrix44, const FLT * qin)
{
	FLT q[4];
	quatnormalize(q, qin);

	//Reduced calulation for speed
	FLT xx = 2 * q[0] * q[0];
	FLT xy = 2 * q[0] * q[1];
	FLT xz = 2 * q[0] * q[2];
	FLT xw = 2 * q[0] * q[3];

	FLT yy = 2 * q[1] * q[1];
	FLT yz = 2 * q[1] * q[2];
	FLT yw = 2 * q[1] * q[3];

	FLT zz = 2 * q[2] * q[2];
	FLT zw = 2 * q[2] * q[3];

	//opengl major
	matrix44[0] = 1 - yy - zz;
	matrix44[1] = xy - zw;
	matrix44[2] = xz + yw;
	matrix44[3] = 0;

	matrix44[4] = xy + zw;
	matrix44[5] = 1 - xx - zz;
	matrix44[6] = yz - xw;
	matrix44[7] = 0;

	matrix44[8] = xz - yw;
	matrix44[9] = yz + xw;
	matrix44[10] = 1 - xx - yy;
	matrix44[11] = 0;

	matrix44[12] = 0;
	matrix44[13] = 0;
	matrix44[14] = 0;
	matrix44[15] = 1;
}

void quattomatrix33(FLT * matrix33, const FLT * qin)
{
	FLT q[4];
	quatnormalize(q, qin);

	//Reduced calulation for speed
	FLT xx = 2 * q[0] * q[0];
	FLT xy = 2 * q[0] * q[1];
	FLT xz = 2 * q[0] * q[2];
	FLT xw = 2 * q[0] * q[3];

	FLT yy = 2 * q[1] * q[1];
	FLT yz = 2 * q[1] * q[2];
	FLT yw = 2 * q[1] * q[3];

	FLT zz = 2 * q[2] * q[2];
	FLT zw = 2 * q[2] * q[3];

	//opengl major
	matrix33[0] = 1 - yy - zz;
	matrix33[1] = xy - zw;
	matrix33[2] = xz + yw;

	matrix33[3] = xy + zw;
	matrix33[4] = 1 - xx - zz;
	matrix33[5] = yz - xw;

	matrix33[6] = xz - yw;
	matrix33[7] = yz + xw;
	matrix33[8] = 1 - xx - yy;
}

void quatgetconjugate(FLT * qout, const FLT * qin)
{
	qout[0] = qin[0];
	qout[1] = -qin[1];
	qout[2] = -qin[2];
	qout[3] = -qin[3];
}

void quatgetreciprocal( FLT * qout, const FLT * qin )
{
	FLT m = quatinvsqmagnitude(qin);
	quatgetconjugate( qout, qin );
	quatscale( qout, qout, m );
}

void quatsub( FLT * qout, const FLT * a, const FLT * b )
{
	qout[0] = a[0] - b[0];
	qout[1] = a[1] - b[1];
	qout[2] = a[2] - b[2];
	qout[3] = a[3] - b[3];
}

void quatadd( FLT * qout, const FLT * a, const FLT * b )
{
	qout[0] = a[0] + b[0];
	qout[1] = a[1] + b[1];
	qout[2] = a[2] + b[2];
	qout[3] = a[3] + b[3];
}

void quatrotateabout( FLT * qout, const FLT * a, const FLT * b )
{
	FLT q1[4];
	FLT q2[4];

	quatnormalize( q1, a );
	quatnormalize( q2, b );

	qout[0] = (q1[0]*q2[0])-(q1[1]*q2[1])-(q1[2]*q2[2])-(q1[3]*q2[3]);
	qout[1] = (q1[0]*q2[1])+(q1[1]*q2[0])+(q1[2]*q2[3])-(q1[3]*q2[2]);
	qout[2] = (q1[0]*q2[2])-(q1[1]*q2[3])+(q1[2]*q2[0])+(q1[3]*q2[1]);
	qout[3] = (q1[0]*q2[3])+(q1[1]*q2[2])-(q1[2]*q2[1])+(q1[3]*q2[0]);
}

void quatscale( FLT * qout, const FLT * qin, FLT s )
{
	qout[0] = qin[0] * s;
	qout[1] = qin[1] * s;
	qout[2] = qin[2] * s;
	qout[3] = qin[3] * s;
}


FLT quatinnerproduct( const FLT * qa, const FLT * qb )
{
	return (qa[0]*qb[0])+(qa[1]*qb[1])+(qa[2]*qb[2])+(qa[3]*qb[3]);
}

void quatouterproduct( FLT * outvec3, FLT * qa, FLT * qb )
{
	outvec3[0] = (qa[0]*qb[1])-(qa[1]*qb[0])-(qa[2]*qb[3])+(qa[3]*qb[2]);
	outvec3[1] = (qa[0]*qb[2])+(qa[1]*qb[3])-(qa[2]*qb[0])-(qa[3]*qb[1]);
	outvec3[2] = (qa[0]*qb[3])-(qa[1]*qb[2])+(qa[2]*qb[1])-(qa[3]*qb[0]);
}

void quatevenproduct( FLT * q, FLT * qa, FLT * qb )
{
	q[0] = (qa[0]*qb[0])-(qa[1]*qb[1])-(qa[2]*qb[2])-(qa[3]*qb[3]);
	q[1] = (qa[0]*qb[1])+(qa[1]*qb[0]);
	q[2] = (qa[0]*qb[2])+(qa[2]*qb[0]);
	q[3] = (qa[0]*qb[3])+(qa[3]*qb[0]);
}

void quatoddproduct( FLT * outvec3, FLT * qa, FLT * qb )
{
	outvec3[0] = (qa[2]*qb[3])-(qa[3]*qb[2]);
	outvec3[1] = (qa[3]*qb[1])-(qa[1]*qb[3]);
	outvec3[2] = (qa[1]*qb[2])-(qa[2]*qb[1]);
}

void quatslerp( FLT * q, const FLT * qa, const FLT * qb, FLT t )
{
	FLT an[4];
	FLT bn[4];
	quatnormalize( an, qa );
	quatnormalize( bn, qb );
	FLT cosTheta = quatinnerproduct(an,bn);
	FLT sinTheta;

	//Careful: If cosTheta is exactly one, or even if it's infinitesimally over, it'll
	// cause SQRT to produce not a number, and screw everything up.
	if ( 1 - (cosTheta*cosTheta) <= 0 )
		sinTheta = 0;
	else
		sinTheta = FLT_SQRT(1 - (cosTheta*cosTheta));

	FLT Theta = FLT_ACOS(cosTheta); //Theta is half the angle between the 2 MQuaternions

	if (FLT_FABS(Theta) < DEFAULT_EPSILON)
		quatcopy( q, qa );
	else if (FLT_FABS(sinTheta) < DEFAULT_EPSILON)
	{
		quatadd( q, qa, qb );
		quatscale( q, q, 0.5 );
	}
	else
	{
		FLT aside[4];
		FLT bside[4];
		quatscale( bside, qb, FLT_SIN(t * Theta));
		quatscale( aside, qa, FLT_SIN((1 - t)*Theta));
		quatadd( q, aside, bside );
		quatscale( q, q, ((FLT)1.)/sinTheta );
	}
}

void quatrotatevector( FLT * vec3out, const FLT * quat, const FLT * vec3in )
{
	FLT tquat[4];
	FLT vquat[4];
	FLT qrecp[4];
	vquat[0] = 0;
	vquat[1] = vec3in[0];
	vquat[2] = vec3in[1];
	vquat[3] = vec3in[2];

	quatrotateabout( tquat, quat, vquat );
	quatgetreciprocal( qrecp, quat );
	quatrotateabout( vquat, tquat, qrecp );

	vec3out[0] = vquat[1];
	vec3out[1] = vquat[2];
	vec3out[2] = vquat[3];
}


// Matrix Stuff

Matrix3x3 inverseM33(const Matrix3x3 mat)
{
	Matrix3x3 newMat;
	for (int a = 0; a < 3; a++)
	{
		for (int b = 0; b < 3; b++)
		{
			newMat.val[a][b] = mat.val[a][b];
		}
	}

	for (int i = 0; i < 3; i++)
	{
		for (int j = i + 1; j < 3; j++)
		{
			FLT tmp = newMat.val[i][j];
			newMat.val[i][j] = newMat.val[j][i];
			newMat.val[j][i] = tmp;
		}
	}

	return newMat;
}

void rotation_between_vecs_to_m3(Matrix3x3 *m, const FLT v1[3], const FLT v2[3])
{
	FLT q[4];

	quatfrom2vectors(q, v1, v2);

	quattomatrix33(&(m->val[0][0]), q);
}

void rotate_vec(FLT *out, const FLT *in, Matrix3x3 rot)
{
	out[0] = rot.val[0][0] * in[0] + rot.val[1][0] * in[1] + rot.val[2][0] * in[2];
	out[1] = rot.val[0][1] * in[0] + rot.val[1][1] * in[1] + rot.val[2][1] * in[2];
	out[2] = rot.val[0][2] * in[0] + rot.val[1][2] * in[1] + rot.val[2][2] * in[2];

	return;
}


// This function based on code from Object-oriented Graphics Rendering Engine
// Copyright(c) 2000 - 2012 Torus Knot Software Ltd
// under MIT license
// http://www.ogre3d.org/docs/api/1.9/_ogre_vector3_8h_source.html

/** Gets the shortest arc quaternion to rotate this vector to the destination
vector.
@remarks
If you call this with a dest vector that is close to the inverse
of this vector, we will rotate 180 degrees around a generated axis if
since in this case ANY axis of rotation is valid.
*/
void quatfrom2vectors(FLT *q, const FLT *src, const FLT *dest)
{
	// Based on Stan Melax's article in Game Programming Gems

	// Copy, since cannot modify local
	FLT v0[3];
	FLT v1[3];
	normalize3d(v0, src);
	normalize3d(v1, dest);

	FLT d = dot3d(v0, v1);// v0.dotProduct(v1);
	// If dot == 1, vectors are the same
	if (d >= 1.0f)
	{
		quatsetidentity(q);
		return;
	}
	if (d < (1e-6f - 1.0f))
	{
		// Generate an axis
		FLT unitX[3] = { 1, 0, 0 };
		FLT unitY[3] = { 0, 1, 0 };
		
		FLT axis[3];
		cross3d(axis, unitX, src); // pick an angle
		if ((axis[0] < 1.0e-35f) &&
			(axis[1] < 1.0e-35f) &&
			(axis[2] < 1.0e-35f)) // pick another if colinear
		{
			cross3d(axis, unitY, src);
		}
		normalize3d(axis, axis);
		quatfromaxisangle(q, axis, LINMATHPI);
	}
	else
	{
		FLT s = FLT_SQRT((1 + d) * 2);
		FLT invs = 1 / s;

		FLT c[3];
		//cross3d(c, v0, v1);
		cross3d(c, v1, v0);

		q[0] = c[0] * invs;
		q[1] = c[1] * invs;
		q[2] = c[2] * invs;
		q[3] = s * 0.5f;

		quatnormalize(q, q);
	}

}

///////////////////////////////////////Matrix Rotations////////////////////////////////////
////Originally from Stack Overflow 
////Under cc by-sa 3.0
////  http://stackoverflow.com/questions/23166898/efficient-way-to-calculate-a-3x3-rotation-matrix-from-the-rotation-defined-by-tw
//// Copyright 2014 by Campbell Barton
//// Copyright 2017 by Michael Turvey
//
///**
//* Calculate a rotation matrix from 2 normalized vectors.
//*
//* v1 and v2 must be unit length.
//*/
//void rotation_between_vecs_to_mat3(FLT m[3][3], const FLT v1[3], const FLT v2[3])
//{
//	FLT axis[3];
//	/* avoid calculating the angle */
//	FLT angle_sin;
//	FLT angle_cos;
//
//	cross3d(axis, v1, v2);
//
//	angle_sin = normalize_v3(axis);
//	angle_cos = dot3d(v1, v2);
//
//	if (angle_sin > FLT_EPSILON) {
//	axis_calc:
//		axis_angle_normalized_to_mat3_ex(m, axis, angle_sin, angle_cos);
//	}
//	else {
//		/* Degenerate (co-linear) vectors */
//		if (angle_cos > 0.0f) {
//			/* Same vectors, zero rotation... */
//			unit_m3(m);
//		}
//		else {
//			/* Colinear but opposed vectors, 180 rotation... */
//			get_orthogonal_vector(axis, v1);
//			normalize_v3(axis);
//			angle_sin = 0.0f;  /* sin(M_PI) */
//			angle_cos = -1.0f;  /* cos(M_PI) */
//			goto axis_calc;
//		}
//	}
//}

//void get_orthogonal_vector(FLT out[3], const FLT in[3])
//{
//#ifdef USE_DOUBLE
//	const FLT x = fabs(in[0]);
//	const FLT y = fabs(in[1]);
//	const FLT z = fabs(in[2]);
//#else
//	const FLT x = fabsf(in[0]);
//	const FLT y = fabsf(in[1]);
//	const FLT z = fabsf(in[2]);
//#endif
//
//	if (x > y && x > z)
//	{
//		// x is dominant
//		out[0] = -in[1] - in[2];
//		out[1] = in[0];
//		out[2] = in[0];
//	}
//	else if (y > z)
//	{
//		// y is dominant
//		out[0] = in[1];
//		out[1] = -in[0] - in[2];
//		out[2] = in[1];
//	}
//	else
//	{
//		// z is dominant
//		out[0] = in[2];
//		out[1] = in[2];
//		out[2] = -in[0] - in[1];
//	}
//}
//
//void unit_m3(FLT mat[3][3])
//{
//	mat[0][0] = 1;
//	mat[0][1] = 0;
//	mat[0][2] = 0;
//	mat[1][0] = 0;
//	mat[1][1] = 1;
//	mat[1][2] = 0;
//	mat[2][0] = 0;
//	mat[2][1] = 0;
//	mat[2][2] = 1;
//}


//FLT normalize_v3(FLT vect[3])
//{
//	FLT distance = dot3d(vect, vect);
//
//	if (distance < 1.0e-35f)
//	{
//		// distance is too short, just go to zero.
//		vect[0] = 0;
//		vect[1] = 0;
//		vect[2] = 0;
//		distance = 0;
//	}
//	else
//	{
//		distance = FLT_SQRT((FLT)distance);
//		scale3d(vect, vect, 1.0f / distance);
//	}
//
//	return distance;
//}

///* axis must be unit length */
//void axis_angle_normalized_to_mat3_ex(
//	FLT mat[3][3], const FLT axis[3],
//	const FLT angle_sin, const FLT angle_cos)
//{
//	FLT nsi[3], ico;
//	FLT n_00, n_01, n_11, n_02, n_12, n_22;
//
//	ico = (1.0f - angle_cos);
//	nsi[0] = axis[0] * angle_sin;
//	nsi[1] = axis[1] * angle_sin;
//	nsi[2] = axis[2] * angle_sin;
//
//	n_00 = (axis[0] * axis[0]) * ico;
//	n_01 = (axis[0] * axis[1]) * ico;
//	n_11 = (axis[1] * axis[1]) * ico;
//	n_02 = (axis[0] * axis[2]) * ico;
//	n_12 = (axis[1] * axis[2]) * ico;
//	n_22 = (axis[2] * axis[2]) * ico;
//
//	mat[0][0] = n_00 + angle_cos;
//	mat[0][1] = n_01 + nsi[2];
//	mat[0][2] = n_02 - nsi[1];
//	mat[1][0] = n_01 - nsi[2];
//	mat[1][1] = n_11 + angle_cos;
//	mat[1][2] = n_12 + nsi[0];
//	mat[2][0] = n_02 + nsi[1];
//	mat[2][1] = n_12 - nsi[0];
//	mat[2][2] = n_22 + angle_cos;
//}