anki-3d-engine/AnKi/Math/Axisang.h

// Copyright (C) 2009-2021, Panagiotis Christopoulos Charitos and contributors.
// All rights reserved.
// Code licensed under the BSD License.
// http://www.anki3d.org/LICENSE

#pragma once

#include <AnKi/Math/Common.h>

namespace anki
{

/// @addtogroup math
/// @{

/// Axis angles. Used in rotations.
template<typename T>
class TAxisang
{
public:
	/// @name Constructors
	/// @{
	TAxisang()
	{
	}

	TAxisang(const TAxisang& b)
		: m_ang(b.m_ang)
		, m_axis(b.m_axis)
	{
	}

	TAxisang(const T rad, const TVec<T, 3>& axis)
		: m_ang(rad)
		, m_axis(axis)
	{
	}

	explicit TAxisang(const TQuat<T>& q)
	{
		m_ang = T(2) * acos<T>(q.w());
		T length = sqrt<T>(T(1) - q.w() * q.w());
		if(!isZero<T>(length))
		{
			length = T(1) / length;
			m_axis = TVec<T, 3>(q.x() * length, q.y() * length, q.z() * length);
		}
		else
		{
			m_axis = TVec<T, 3>(T(0));
		}
	}

	explicit TAxisang(const TMat<T, 3, 3>& m3)
	{
		if(isZero<T>(m3(0, 1) - m3(1, 0)) && isZero<T>(m3(0, 2) - m3(2, 0)) && isZero<T>(m3(1, 2) - m3(2, 1)))
		{

			if((absolute<T>(m3(0, 1) + m3(1, 0)) < T(0.1)) && (absolute<T>(m3(0, 2) + m3(2, 0)) < T(0.1))
			   && (absolute<T>(m3(1, 2) + m3(2, 1)) < T(0.1))
			   && (absolute<T>(m3(0, 0) + m3(1, 1) + m3(2, 2)) - 3) < T(0.1))
			{
				m_axis = TVec<T, 3>(T(1), T(0), T(0));
				m_ang = T(0);
				return;
			}

			m_ang = PI;
			m_axis.x() = (m3(0, 0) + T(1)) / T(2);
			if(m_axis.x() > T(0))
			{
				m_axis.x() = sqrt(m_axis.x());
			}
			else
			{
				m_axis.x() = T(0);
			}
			m_axis.y() = (m3(1, 1) + T(1)) / T(2);
			if(m_axis.y() > T(0))
			{
				m_axis.y() = sqrt(m_axis.y());
			}
			else
			{
				m_axis.y() = T(0);
			}

			m_axis.z() = (m3(2, 2) + T(1)) / T(2);
			if(m_axis.z() > T(0))
			{
				m_axis.z() = sqrt(m_axis.z());
			}
			else
			{
				m_axis.z() = T(0);
			}

			const Bool xZero = isZero<T>(m_axis.x());
			const Bool yZero = isZero<T>(m_axis.y());
			const Bool zZero = isZero<T>(m_axis.z());
			const Bool xyPositive = (m3(0, 1) > T(0));
			const Bool xzPositive = (m3(0, 2) > T(0));
			const Bool yzPositive = (m3(1, 2) > T(0));
			if(xZero && !yZero && !zZero)
			{
				if(!yzPositive)
				{
					m_axis.y() = -m_axis.y();
				}
			}
			else if(yZero && !zZero)
			{
				if(!xzPositive)
				{
					m_axis.z() = -m_axis.z();
				}
			}
			else if(zZero)
			{
				if(!xyPositive)
				{
					m_axis.x() = -m_axis.x();
				}
			}

			return;
		}

		T s = sqrt((m3(2, 1) - m3(1, 2)) * (m3(2, 1) - m3(1, 2)) + (m3(0, 2) - m3(2, 0)) * (m3(0, 2) - m3(2, 0))
				   + (m3(1, 0) - m3(0, 1)) * (m3(1, 0) - m3(0, 1)));

		if(absolute(s) < T(0.001))
		{
			s = T(1);
		}

		m_ang = acos<T>((m3(0, 0) + m3(1, 1) + m3(2, 2) - T(1)) / T(2));
		m_axis.x() = (m3(2, 1) - m3(1, 2)) / s;
		m_axis.y() = (m3(0, 2) - m3(2, 0)) / s;
		m_axis.z() = (m3(1, 0) - m3(0, 1)) / s;
	}
	/// @}

	/// @name Accessors
	/// @{
	T getAngle() const
	{
		return m_ang;
	}

	T& getAngle()
	{
		return m_ang;
	}

	void setAngle(const T a)
	{
		m_ang = a;
	}

	const TVec<T, 3>& getAxis() const
	{
		return m_axis;
	}

	TVec<T, 3>& getAxis()
	{
		return m_axis;
	}

	void setAxis(const TVec<T, 3>& a)
	{
		m_axis = a;
	}
	/// @}

	/// @name Operators with same type
	/// @{
	TAxisang& operator=(const TAxisang& b)
	{
		m_ang = b.m_ang;
		m_axis = b.m_axis;
		return *this;
	}
	/// @}

	/// @name Other
	/// @{
	ANKI_ENABLE_METHOD(std::is_floating_point<T>::value)
	void toString(StringAuto& str) const
	{
		str.sprintf("%f %f %f | %f", m_axis.x(), m_axis.y(), m_axis.z(), m_ang);
	}
	/// @}

private:
	/// @name Data
	/// @{
	T m_ang;
	TVec<T, 3> m_axis;
	/// @}
};

/// F32 Axisang
using Axisang = TAxisang<F32>;

/// F64 Axisang
using DAxisang = TAxisang<F64>;
/// @}

} // end namespace anki