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/* Copyright (c) 2007-2019 Juan Linietsky, Ariel Manzur.                 */
/* Copyright (c) 2014-2019 Godot Engine contributors (cf. AUTHORS.md)    */
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import "quat.h"
import "basis.h"
import "print_string.h"

// set_euler_xyz expects a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses XYZ convention (Z is the first rotation).
def Quat::set_euler_xyz(const Vector3 &p_euler):
	real_t half_a1 = p_euler.x * 0.5
	real_t half_a2 = p_euler.y * 0.5
	real_t half_a3 = p_euler.z * 0.5
	// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
	// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
	// a3 is the angle of the first rotation, following the notation in this reference.
	real_t cos_a1 = Math::cos(half_a1)
	real_t sin_a1 = Math::sin(half_a1)
	real_t cos_a2 = Math::cos(half_a2)
	real_t sin_a2 = Math::sin(half_a2)
	real_t cos_a3 = Math::cos(half_a3)
	real_t sin_a3 = Math::sin(half_a3)
	set(sin_a1 * cos_a2 * cos_a3 + sin_a2 * sin_a3 * cos_a1,
	-sin_a1 * sin_a3 * cos_a2 + sin_a2 * cos_a1 * cos_a3,
	sin_a1 * sin_a2 * cos_a3 + sin_a3 * cos_a1 * cos_a2,
	-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3)


// get_euler_xyz returns a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses XYZ convention (Z is the first rotation).
@const
def Quat::get_euler_xyz() ->Vector3:
	Basis m(*this)
	return m.get_euler_xyz()


// set_euler_yxz expects a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
def Quat::set_euler_yxz(const Vector3 &p_euler):
	real_t half_a1 = p_euler.y * 0.5
	real_t half_a2 = p_euler.x * 0.5
	real_t half_a3 = p_euler.z * 0.5
	// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
	// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
	// a3 is the angle of the first rotation, following the notation in this reference.
	real_t cos_a1 = Math::cos(half_a1)
	real_t sin_a1 = Math::sin(half_a1)
	real_t cos_a2 = Math::cos(half_a2)
	real_t sin_a2 = Math::sin(half_a2)
	real_t cos_a3 = Math::cos(half_a3)
	real_t sin_a3 = Math::sin(half_a3)
	set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
	sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
	-sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3,
	sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3)

// get_euler_yxz returns a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
@const
def Quat::get_euler_yxz() ->Vector3:
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND_V(!is_normalized(), Vector3(0, 0, 0))
	#endif
	Basis m(*this)
	return m.get_euler_yxz()


def Quat::operator*=(const Quat &q) ->void:
	set(w * q.x + x * q.w + y * q.z - z * q.y,
	w * q.y + y * q.w + z * q.x - x * q.z,
	w * q.z + z * q.w + x * q.y - y * q.x,
	w * q.w - x * q.x - y * q.y - z * q.z)


@const
def Quat::operator*(const Quat &q) ->Quat:
	Quat r = *this
	r *= q
	return r

@const
def Quat::length() ->real_t:
	return Math::sqrt(length_squared())


def Quat::normalize():
	*this /= length()

@const
def Quat::normalized() ->Quat:
	return *this / length()

@const
def Quat::is_normalized() ->bool:
	return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon

@const
def Quat::inverse() ->Quat:
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND_V(!is_normalized(), Quat())
	#endif
	return Quat(-x, -y, -z, w)

@const
def Quat::slerp(const Quat &q, const real_t &t) ->Quat:
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND_V(!is_normalized(), Quat())
	  ERR_FAIL_COND_V(!q.is_normalized(), Quat())
	#endif
	Quat to1
	real_t omega, cosom, sinom, scale0, scale1
	// calc cosine
	cosom = dot(q)
	// adjust signs (if necessary)
	if cosom < 0.0:
		cosom = -cosom
		to1.x = -q.x
		to1.y = -q.y
		to1.z = -q.z
		to1.w = -q.w
	else:
		to1.x = q.x
		to1.y = q.y
		to1.z = q.z
		to1.w = q.w
	// calculate coefficients
	if (1.0 - cosom) > CMP_EPSILON:
		// standard case (slerp)
		omega = Math::acos(cosom)
		sinom = Math::sin(omega)
		scale0 = Math::sin((1.0 - t) * omega) / sinom
		scale1 = Math::sin(t * omega) / sinom
	else:
		// "from" and "to" quaternions are very close
		//  ... so we can do a linear interpolation
		scale0 = 1.0 - t
		scale1 = t
	// calculate final values
	return Quat(scale0 * x + scale1 * to1.x, scale0 * y + scale1 * to1.y, scale0 * z + scale1 * to1.z, scale0 * w + scale1 * to1.w)

@const
def Quat::slerpni(const Quat &q, const real_t &t) ->Quat:
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND_V(!is_normalized(), Quat());
	  ERR_FAIL_COND_V(!q.is_normalized(), Quat());
	#endif
	const Quat &from = *this
	real_t dot = from.dot(q)
	if Math::absf(dot) > 0.9999:
		return from
	real_t theta = Math::acos(dot)
	real_t sinT = 1.0 / Math::sin(theta)
	real_t newFactor = Math::sin(t * theta) * sinT
	real_t invFactor = Math::sin((1.0 - t) * theta) * sinT
	return Quat(invFactor * from.x + newFactor * q.x, invFactor * from.y + newFactor * q.y, invFactor * from.z + newFactor * q.z, invFactor * from.w + newFactor * q.w)

@const
def Quat::cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) ->Quat:
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND_V(!is_normalized(), Quat());
	  ERR_FAIL_COND_V(!q.is_normalized(), Quat());
	#endif
	//the only way to do slerp :|
	real_t t2 = (1.0 - t) * t * 2
	Quat sp = this->slerp(q, t)
	Quat sq = prep.slerpni(postq, t)
	return sp.slerpni(sq, t2)


@const
def Quat::operator String():
	return String::num(x) + ", " + String::num(y) + ", " + String::num(z) + ", " + String::num(w)


def Quat::set_axis_angle(const Vector3 &axis, const real_t &angle):
	#ifdef MATH_CHECKS
	  ERR_FAIL_COND(!axis.is_normalized())
	#endif
	real_t d = axis.length()
	if d == 0:
		set(0, 0, 0, 0)
	else:
		real_t sin_angle = Math::sin(angle * 0.5)
		real_t cos_angle = Math::cos(angle * 0.5)
		real_t s = sin_angle / d
		set(axis.x * s, axis.y * s, axis.z * s,cos_angle)