matrix4x3.h

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//
// 3D Math Primer for Games and Graphics Development
//
// Matrix4x3.h - Declarations for class Matrix4x3
//
// Visit gamemath.com for the latest version of this file.
//
// For more details, see Matrix4x3.cpp
//
/////////////////////////////////////////////////////////////////////////////

#ifndef __MATRIX4X3_H_INCLUDED__
#define __MATRIX4X3_H_INCLUDED__

class Vector3;
class EulerAngles;
class Quaternion;
class RotationMatrix;

//---------------------------------------------------------------------------
// class Matrix4x3
//
// Implement a 4x3 transformation matrix.  This class can represent
// any 3D affine transformation.

class Matrix4x3 {
public:

// Public data

	// The values of the matrix.  Basically the upper 3x3 portion
	// contains a linear transformation, and the last row is the
	// translation portion.  See the Matrix4x3.cpp for more
	// details.

	float	m11, m12, m13;
	float	m21, m22, m23;
	float	m31, m32, m33;
	float	tx,  ty,  tz;

// Public operations

	// Set to identity

	void	identity();

	// Access the translation portion of the matrix directly

	void	zeroTranslation();
	void	setTranslation(const Vector3 &d);
	void	setupTranslation(const Vector3 &d);

	// Setup the matrix to perform a specific transforms from parent <->
	// local space, assuming the local space is in the specified position
	// and orientation within the parent space.  The orientation may be
	// specified using either Euler angles, or a rotation matrix

	void	setupLocalToParent(const Vector3 &pos, const EulerAngles &orient);
	void	setupLocalToParent(const Vector3 &pos, const RotationMatrix &orient);
	void	setupParentToLocal(const Vector3 &pos, const EulerAngles &orient);
	void	setupParentToLocal(const Vector3 &pos, const RotationMatrix &orient);

	// Setup the matrix to perform a rotation about a cardinal axis

	void	setupRotate(int axis, float theta);

	// Setup the matrix to perform a rotation about an arbitrary axis

	void	setupRotate(const Vector3 &axis, float theta);

	// Setup the matrix to perform a rotation, given
	// the angular displacement in quaternion form

	void	fromQuaternion(const Quaternion &q);

	// Setup the matrix to perform scale on each axis

	void	setupScale(const Vector3 &s);

	// Setup the matrix to perform scale along an arbitrary axis

	void	setupScaleAlongAxis(const Vector3 &axis, float k);

	// Setup the matrix to perform a shear

	void	setupShear(int axis, float s, float t);

	// Setup the matrix to perform a projection onto a plane passing
	// through the origin

	void	setupProject(const Vector3 &n);

	// Setup the matrix to perform a reflection about a plane parallel
	// to a cardinal plane

	void	setupReflect(int axis, float k = 0.0f);

	// Setup the matrix to perform a reflection about an arbitrary plane
	// through the origin

	void	setupReflect(const Vector3 &n);
};

// Operator* is used to transforms a point, and also concatonate matrices.
// The order of multiplications from left to right is the same as
// the order of transformations

Vector3		operator*(const Vector3 &p, const Matrix4x3 &m);
Matrix4x3	operator*(const Matrix4x3 &a, const Matrix4x3 &b);

// Operator *= for conformance to C++ standards

Vector3		&operator*=(Vector3 &p, const Matrix4x3 &m);
Matrix4x3	&operator*=(const Matrix4x3 &a, const Matrix4x3 &m);

// Compute the determinant of the 3x3 portion of the matrix

float	determinant(const Matrix4x3 &m);

// Compute the inverse of a matrix

Matrix4x3 inverse(const Matrix4x3 &m);

// Extract the translation portion of the matrix

Vector3	getTranslation(const Matrix4x3 &m);

// Extract the position/orientation from a local->parent matrix,
// or a parent->local matrix

Vector3	getPositionFromParentToLocalMatrix(const Matrix4x3 &m);
Vector3	getPositionFromLocalToParentMatrix(const Matrix4x3 &m);

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#endif // #ifndef __ROTATIONMATRIX_H_INCLUDED__