// This code is in the public domain -- castanyo@yahoo.es

#ifndef NV_MATH_BASIS_H
#define NV_MATH_BASIS_H

#include <nvmath/nvmath.h>
#include <nvmath/Vector.h>
#include <nvmath/Matrix.h>

namespace nv
{

	/// Basis class to compute tangent space basis, ortogonalizations and to
	/// transform vectors from one space to another.
	class Basis
	{
	public:

		/// Create a null basis.
		Basis() : tangent(0, 0, 0), bitangent(0, 0, 0), normal(0, 0, 0) {}

		/// Create a basis given three vectors.
		Basis(Vector3::Arg n, Vector3::Arg t, Vector3::Arg b) : tangent(t), bitangent(b), normal(n) {}

		/// Create a basis with the given tangent vectors and the handness.
		Basis(Vector3::Arg n, Vector3::Arg t, float sign)
		{
			build(n, t, sign);
		}

		NVMATH_API void normalize(float epsilon = NV_EPSILON);
		NVMATH_API void orthonormalize(float epsilon = NV_EPSILON);
		NVMATH_API void robustOrthonormalize(float epsilon = NV_EPSILON);
		NVMATH_API void buildFrameForDirection(Vector3::Arg d);

		/// Calculate the determinant [ F G N ] to obtain the handness of the basis. 
		float handness() const
		{
			return determinant() > 0.0f ? 1.0f : -1.0f;
		}

		/// Build a basis from 2 vectors and a handness flag.
		void build(Vector3::Arg n, Vector3::Arg t, float sign)
		{
			normal = n;
			tangent = t;
			bitangent = sign * cross(t, n);
		}

		/// Compute the determinant of this basis.
		float determinant() const
		{
			return 
				tangent.x() * bitangent.y() * normal.z() - tangent.z() * bitangent.y() * normal.x() +
				tangent.y() * bitangent.z() * normal.x() - tangent.y() * bitangent.x() * normal.z() + 
				tangent.z() * bitangent.x() * normal.y() - tangent.x() * bitangent.z() * normal.y();
		}
		
		bool isValid() const;
		
		// Get transform matrix for this basis.
		NVMATH_API Matrix matrix() const;
		
		// Transform by this basis. (From this basis to object space).
		NVMATH_API Vector3 transform(Vector3::Arg v) const;

		// Transform by the transpose. (From object space to this basis).
		NVMATH_API Vector3 transformT(Vector3::Arg v);

		// Transform by the inverse. (From object space to this basis).
		NVMATH_API Vector3 transformI(Vector3::Arg v) const;

		
		Vector3 tangent;
		Vector3 bitangent;
		Vector3 normal;
	};

} // nv namespace

#endif // NV_MATH_BASIS_H