Math functions namespace. More...

Functions
3-Components Vectors
GLvoid	Cross3 (GLfloat result[3], const GLfloat vector0[3], const GLfloat vector1[3])
	Computes the cross product of two 3-components vectors.
GLfloat	Dot3 (const GLfloat vector0[3], const GLfloat vector1[3])
	Computes the dot product of two 3-components vectors.
GLfloat	EuclideanNorm3 (const GLfloat vector[3])
	Computes the euclidean norm of a 3-components vector.
GLfloat	EuclideanNorm3 (const GLfloat x, const GLfloat y, const GLfloat z)
	Computes the euclidean norm of a 3-components vector.
GLvoid	Normalize3 (GLfloat vector[3])
	Normalizes a 3-components vector.
4x4 Matrices
GLfloat	Determinant4x4 (const GLfloat m[16])
	Computes the determinant of a 4x4 matrix.
GLboolean	InvertMatrix4x4 (GLfloat result[16], const GLfloat m[16])
	Inverts a 4x4 matrix.
GLvoid	MultMatrix4x4 (GLfloat matrix[16], const GLfloat matrix0[16], const GLfloat matrix1[16])
	Multiplies two 4x4 matrices.
GLvoid	LoadIdentity4x4 (GLfloat matrix[16])
	Loads an identity 4x4 matrix.
GLvoid	Rotate4x4 (GLfloat matrix[16], GLfloat angle, GLfloat x, GLfloat y, GLfloat z)
	Combines a rototranslation matrix with a new rotation obtained using and angle and an axis.
GLvoid	RotateAngles4x4 (GLfloat matrix[16], GLfloat ax, GLfloat ay, GLfloat az)
	Combines a rototranslation matrix with a new rotation obtained using three angles.
GLvoid	Translate4x4 (GLfloat matrix[16], GLfloat x, GLfloat y, GLfloat z)
	Combines a rototranslation matrix with a new translation matrix.
GLvoid	Scale4x4 (GLfloat matrix[16], GLfloat x, GLfloat y, GLfloat z)
	Combines a rototranslation matrix with a new scale matrix.
GLvoid	LookAt4x4 (GLfloat result[16], GLfloat eyeX, GLfloat eyeY, GLfloat eyeZ, GLfloat centerX, GLfloat centerY, GLfloat centerZ, GLfloat upX, GLfloat upY, GLfloat upZ)
	Initializes a rototranslation matrix to look at a specified point.
GLvoid	Ortho4x4 (GLfloat result[16], GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearVal, GLfloat farVal)
	Sets up an orthogonal projection matrix.
GLvoid	Perspective4x4 (GLfloat result[16], GLfloat fovy, GLfloat aspect, GLfloat zNear, GLfloat zFar)
	Sets up a perspective projection matrix.
GLvoid	Frustum4x4 (GLfloat result[16], GLfloat left, GLfloat right, GLfloat bottom, GLfloat top, GLfloat nearVal, GLfloat farVal)
	Prepare perspective matrix that produces a perspective projection.
Matrices and vectors
GLvoid	MultMat4x4Vector3 (GLfloat result[3], const GLfloat matrix[16], const GLfloat vector[3])
	Multiplies a transformation matrix to a 3-components vector.
GLvoid	MultMat4x4Vector4 (GLfloat result[4], const GLfloat matrix[16], const GLfloat vector[4])
	Multiplies a transformation matrix to a 4-components vector.
void	TriangleNormal (const GLfloat vertex1, const GLfloat vertex2, const GLfloat vertex3, GLfloat normal)
	Computes the normal vector for a given triangle.

Detailed Description

Math functions namespace.

Function Documentation

GLvoid VR3Math::Cross3	(	GLfloat	result[3],
		const GLfloat	vector0[3],
		const GLfloat	vector1[3]
	)

Computes the cross product of two 3-components vectors.

The product is written in the result out parameter, no strange behaviour will arise if the vector used to store the result is also one of the operands.

Parameters:

[out]	result	The result vector
[in]	vector0	The first vector
[in]	vector1	The second vector

GLfloat VR3Math::Determinant4x4 ( const GLfloat m[16] )

Computes the determinant of a 4x4 matrix.

Parameters:

[in] m 4x4 GLfloat matrix

GLfloat VR3Math::Dot3	(	const GLfloat	vector0[3],
		const GLfloat	vector1[3]
	)

Computes the dot product of two 3-components vectors.

The product is returned by this function.

Parameters:

[in]	vector0	The first vector
[in]	vector1	The second vector

GLfloat VR3Math::EuclideanNorm3	(	const GLfloat	x,
		const GLfloat	y,
		const GLfloat	z
	)

Computes the euclidean norm of a 3-components vector.

Parameters:

[in] x,y,z The 3 components of the given vector

GLfloat VR3Math::EuclideanNorm3 ( const GLfloat vector[3] )

Computes the euclidean norm of a 3-components vector.

Parameters:

[in] vector The given 3-components vector

GLvoid VR3Math::Frustum4x4	(	GLfloat	result[16],
		GLfloat	left,
		GLfloat	right,
		GLfloat	bottom,
		GLfloat	top,
		GLfloat	nearVal,
		GLfloat	farVal
	)

Prepare perspective matrix that produces a perspective projection.

Sets up a projection matrix according to the specified parameters.

Parameters:

[out]	result	Resulting projection matrix
[in]	left,right	The coordinates for the left and right vertical clipping planes
[in]	bottom,top	The coordinates for the bottom and top horizontal clipping planes
[in]	nearVal,farVal	The distances to the near and far depth clipping planes

GLboolean VR3Math::InvertMatrix4x4	(	GLfloat	result[16],
		const GLfloat	m[16]
	)

Inverts a 4x4 matrix.

Computes the invert matrix of a 4x4 GLfloat matrix. The operation is not always possible, if the inversion is impossible the return value states the failure. Please note that if the result matrix and the input matrix are the same, the operation will work as expected.

Parameters:

[in]	m	The matrix to invert
[out]	result	The result matrix

Returns:: GL_TRUE on success, GL_FALSE on failure

GLvoid VR3Math::LoadIdentity4x4 ( GLfloat matrix[16] )

Loads an identity 4x4 matrix.

Loads a 4x4 identity matrix into the matrix out parameter.

Parameters:

[in,out] matrix The matrix where to load identity matrix

GLvoid VR3Math::LookAt4x4	(	GLfloat	result[16],
		GLfloat	eyeX,
		GLfloat	eyeY,
		GLfloat	eyeZ,
		GLfloat	centerX,
		GLfloat	centerY,
		GLfloat	centerZ,
		GLfloat	upX,
		GLfloat	upY,
		GLfloat	upZ
	)

Initializes a rototranslation matrix to look at a specified point.

The resulting matrix is stored in the result GLfloat array, the eye position may be specified using the eye parameters while the target center is expressed using the center parameters. The up vector is used to understand the camera orientation.

Parameters:

[out]	result	The resulting rototranslation matrix
[in]	eyeX,eyeY,eyeZ	The eye (camera) position
[in]	centerX,centerY,centerZ	The target center position
[in]	upX,upY,upZ	The camera up vector

GLvoid VR3Math::MultMat4x4Vector3	(	GLfloat	result[3],
		const GLfloat	matrix[16],
		const GLfloat	vector[3]
	)

Multiplies a transformation matrix to a 3-components vector.

No strange behaviour will arise if the vector used to store the result is also one of the operands. We assume that the 3 component vector is the first part of a homogenous coordinate vector (x,y,z,w) and that w is 1.0f, we do not compute the last component of the resulting 4 components vector assuming that it will be 1.0f (this means that this operation is only useful for modeling and viewing transformation but not with perspective projection matrices).

Parameters:

[in]	matrix	The 4x4 matrix
[in]	vector	The 3-components vector
[out]	result	The resulting vector = matrix*vector

GLvoid VR3Math::MultMat4x4Vector4	(	GLfloat	result[4],
		const GLfloat	matrix[16],
		const GLfloat	vector[4]
	)

Multiplies a transformation matrix to a 4-components vector.

No strange behaviour will arise if the vector used to store the result is also one of the operands.

Parameters:

[in]	matrix	The 4x4 matrix
[in]	vector	The 4-components vector
[out]	result	The resulting vector = matrix*vector

GLvoid VR3Math::MultMatrix4x4	(	GLfloat	matrix[16],
		const GLfloat	matrix0[16],
		const GLfloat	matrix1[16]
	)

Multiplies two 4x4 matrices.

Two matrices are multiplied and the result is copied in a new GLfloat vector. Please note that if one of the matrices or both are used as input matrix AND output matrix the operation will work as expected.

Parameters:

[in]	matrix0	The first matrix
[in]	matrix1	The second matrix
[out]	matrix	The resulting matrix (matrix0*matrix1)

GLvoid VR3Math::Normalize3 ( GLfloat vector[3] )

Normalizes a 3-components vector.

Parameters:

[in,out] vector The given 3-components vector

GLvoid VR3Math::Ortho4x4	(	GLfloat	result[16],
		GLfloat	left,
		GLfloat	right,
		GLfloat	bottom,
		GLfloat	top,
		GLfloat	nearVal,
		GLfloat	farVal
	)

Sets up an orthogonal projection matrix.

Sets up a projection matrix according to the specified parameters.

Parameters:

[out]	result	Resulting projection matrix
[in]	left,right	Coordinates for the left and right vertical clipping planes
[in]	bottom,top	Coordinates for the bottom and top horizontal clipping planes
[in]	nearVal,farVal	Distances to the nearer and farther depth clipping planes, these values are negative if the plane is to be behind the viewer

GLvoid VR3Math::Perspective4x4	(	GLfloat	result[16],
		GLfloat	fovy,
		GLfloat	aspect,
		GLfloat	zNear,
		GLfloat	zFar
	)

Sets up a perspective projection matrix.

Sets up a projection matrix according to the specified parameters.

Parameters:

[out]	result	Resulting projection matrix
[in]	fovy	The field of view angle in the y direction (degrees)
[in]	aspect	The aspect ratio that determines the field of view in the x direction (width/height)
[in]	zNear	The distance from the viewer to the near clipping plane (always positive)
[in]	zFar	The distance from the viewer to the far clipping plane (always positive)

GLvoid VR3Math::Rotate4x4	(	GLfloat	matrix[16],
		GLfloat	angle,
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Combines a rototranslation matrix with a new rotation obtained using and angle and an axis.

Post-multiplies the given matrix with the rotation matrix obtained by rotating angle degrees around the (x,y,z) axis.

Parameters:

[in,out]	matrix	The resulting altered matrix
[in]	angle	The rotation angle
[in]	x,y,z	The rotation axis components

GLvoid VR3Math::RotateAngles4x4	(	GLfloat	matrix[16],
		GLfloat	ax,
		GLfloat	ay,
		GLfloat	az
	)

Combines a rototranslation matrix with a new rotation obtained using three angles.

Post-multiplies the given matrix with the rotation matrix obtained by rotating according to the angles in the following order:

rotate ax degrees around the X axis (roll)
rotate ay degrees around the Y axis (pitch)
rotate az degrees around the Z axis (yaw)

Parameters:

[in,out]	matrix	The resulting altered matrix
[in]	ax,ay,az	The rotation angles

GLvoid VR3Math::Scale4x4	(	GLfloat	matrix[16],
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Combines a rototranslation matrix with a new scale matrix.

Post-multiplies the given matrix with the scale matrix obtained by scaling by (x,y,z) on the three axis.

Parameters:

[in,out]	matrix	The resulting altered matrix
[in]	x,y,z	The scaling factors

GLvoid VR3Math::Translate4x4	(	GLfloat	matrix[16],
		GLfloat	x,
		GLfloat	y,
		GLfloat	z
	)

Combines a rototranslation matrix with a new translation matrix.

Post-multiplies the given matrix with the translation matrix obtained by translating by the (x,y,z) vector.

Parameters:

[in,out]	matrix	The resulting altered matrix
[in]	x,y,z	The translation vector components

void VR3Math::TriangleNormal	(	const GLfloat *	vertex1,
		const GLfloat *	vertex2,
		const GLfloat *	vertex3,
		GLfloat *	normal
	)

Computes the normal vector for a given triangle.

Parameters:

[in]	vertex1,vertex2,vertex3	Triangle vertices
[out]	normal	The normal vector

VR3Math Namespace Reference

Functions

Detailed Description

Function Documentation