Classes related to computer graphics and rendering process. More...

Classes
class	Bial::Vector3D
	The Vector3D class is a Geometric representation of a vector direction in 3D space. More...

class	Bial::Point3D
	The Point3D class is a Geometric representation of a point in 3D space. A point is a zerodimensional location in 3D space. More...

class	Bial::Normal
	The Normal class is the geometric representation of a Normal in 3D space. A surface normal (or just normal) is a vector that is perpendicular to a surface at a particular position. It can be defined as the cross product of any two nonparallel vectors that are tangent to the surface at a point. The implementations of Normal3D and Vector3D are very similar. Like vectors, normals are represented by three floats x, y, and z; they can be added and subtracted to compute new normals; and they can be scaled and normalized. However, a normal cannot be added to a point, and one cannot take the cross product of two normals. More...

class	Bial::Ray
	The Ray class is a mathematic representation of a light ray. A ray is a semiinfinite line specified by its origin and direction. More...

class	Bial::BBox
	The BBox class is a Bounding Box with 8 vertices, and can be represented by 2 points (6coordinates). More...

class	Bial::Transform3D
	The Transform3D class holds affine matrices and is used to apply geometric transformations over cartesian coordinates. The affine transformation multiplies the coordinates vector to the affine matrix. More...

class	Bial::DifferentialGeometry
	The DifferentialGeometry class is a parametric representation of the Shape geometry. More...

class	Bial::FastTransform

Functions
double	Bial::Lerp (double t, double v1, double v2)
	Simple linear interpolation. More...

Vector3D	Bial::operator* (double s, const Vector3D &vec)

Point3D	Bial::operator* (double s, const Point3D &p)

Normal	Bial::operator* (double s, const Normal &norm)

double	Bial::Dot (const Vector3D &v1, const Vector3D &v2)

double	Bial::Dot (const Normal &n1, const Normal &n2)

double	Bial::Dot (const Normal &n1, const Vector3D &v2)

double	Bial::Dot (const Vector3D &v1, const Normal &n2)

double	Bial::AbsDot (const Vector3D &v1, const Vector3D &v2)

double	Bial::AbsDot (const Normal &n1, const Normal &n2)

double	Bial::AbsDot (const Normal &n1, const Vector3D &v2)

double	Bial::AbsDot (const Vector3D &v1, const Normal &n2)

Vector3D	Bial::Cross (const Vector3D &v1, const Vector3D &v2)

void	Bial::CoordinateSystem (const Vector3D &v1, Vector3D v2, Vector3D v3)

double	Bial::Distance (const Point3D &p1, const Point3D &p2)

double	Bial::DistanceSquared (const Point3D &p1, const Point3D &p2)

Normal	Bial::FaceForward (const Normal &n, const Vector3D &v)

template<class O >
O &	Bial::operator<< (O &os, const Vector3D &vec)

template<class O >
O &	Bial::operator<< (O &os, const Point3D &pt)

template<class O >
O &	Bial::operator<< (O &os, const Normal &norm)

template<class O >
O &	Bial::operator<< (O &os, const Ray &ray)

template<class O >
O &	Bial::operator<< (O &os, const BBox &box)

template<class O >
O &	Bial::operator<< (O &os, const Transform3D &tr)

Detailed Description

Classes related to computer graphics and rendering process.

Class Documentation

class Bial::Vector3D

The Vector3D class is a Geometric representation of a vector direction in 3D space.

Date: 2015/Aug/21

Definition at line 44 of file Geometrics.hpp.

Collaboration diagram for Bial::Vector3D:

Public Member Functions
	Vector3D ()

	Vector3D (double xx, double yy, double zz)
	Vector3D constructor. More...

	Vector3D (const Normal &norm)
	Conversion from Normal to Vector3D. More...

bool	HasNaNs () const
	HasNaNs returns if the any of the components is'nt a valid number. return none. More...

bool	operator== (const Vector3D &vec) const
	Returns if the components match. More...

bool	operator!= (const Vector3D &vec) const
	Returns if the components do not match. More...

Vector3D	operator+ (const Vector3D &vec) const
	Add operation, the vector components are added. More...

Vector3D &	operator+= (const Vector3D &vec)
	Add operation, the vector components are added. More...

Vector3D	operator- (const Vector3D &vec) const
	Subtract operation, the vector components are subtracted. More...

Vector3D &	operator-= (const Vector3D &vec)
	Subtract operation, the vector components are subtracted. More...

Vector3D	operator* (double s) const
	Multiply operation, the vector components are multiplied to a scalar value. More...

Vector3D &	operator*= (double s)
	Multiply operation, the vector components are multiplied to a scalar value. More...

Vector3D	operator/ (double s) const
	Division operation, the vector components are divided by s. More...

Vector3D &	operator/= (double s)
	Division operation, the vector components are divided by s. More...

Vector3D	operator- () const
	Returns the vector inverse. More...

double	operator[] (int i) const
	Gives the option to loop over the components of a vector. More...

double &	operator[] (int i)
	Gives the option to loop over the components of a vector. More...

double	LengthSquared () const
	Returns the length of a vector. Given a vector $\vec{v} = (x,y,z)$ , this function returns $\|\|\vec{v}\|\| = \sqrt{xx+yy+z*z}$ . More...

double	Length () const
	Returns the squared length of a vector. Given a vector $\vec{v} = (x,y,z)$ , this function returns $\|\|\vec{v}\|\|^2 = {xx+yy+z*z}$ . More...

Vector3D	Normalized () const
	Returns the normalized vector. Given a vector $\vec{v} = (x,y,z)$ , this function returns $\frac{\vec{v}}{\|\|\vec{v}\|\|^2}$ . return none. More...

Point3D	toPoint () const
	Conversion from Vector3D to Point3D. More...

Static Public Member Functions
template<class D >
static Vector3D	fromVector (const Vector< D > vec)
	Conversion from Bial::Vector to Vector3D. More...

Public Attributes
double	x

double	y
	Vector direction in y. More...

double	z
	Vector direction in z. More...

Constructor & Destructor Documentation

Bial::Vector3D::Vector3D ( )

Bial::Vector3D::Vector3D	(	double	xx,
		double	yy,
		double	zz
	)

explicit

Vector3D constructor.

Date: 2015/Aug/21

Parameters

xx	Vector direction in x.
yy	Vector direction in y.
zz	Vector direction in z.

Warning: Throws if has NaN parameter.

Bial::Vector3D::Vector3D ( const Normal & norm )

explicit

Conversion from Normal to Vector3D.

Date: 2015/Aug/21

Parameters

norm	input normal.

Member Function Documentation

template<class D >

Vector3D Bial::Vector3D::fromVector ( const Vector< D > vec )

inlinestatic

Conversion from Bial::Vector to Vector3D.

Date: 2015/Aug/21

Parameters

Input vector.

Returns: Result vector.

Definition at line 976 of file Geometrics.hpp.

bool Bial::Vector3D::HasNaNs ( ) const

HasNaNs returns if the any of the components is'nt a valid number. return none.

Date: 2015/Aug/21

double Bial::Vector3D::Length ( ) const

Returns the squared length of a vector.
Given a vector $\vec{v} = (x,y,z)$ , this function returns $||\vec{v}||^2 = {x*x+y*y+z*z}$ .

Date: 2015/Aug/21

Returns: The squared length of a vector.

double Bial::Vector3D::LengthSquared ( ) const

Returns the length of a vector.
Given a vector $\vec{v} = (x,y,z)$ , this function returns $||\vec{v}|| = \sqrt{x*x+y*y+z*z}$ .

Date: 2015/Aug/21

Returns: The length of a vector.

Vector3D Bial::Vector3D::Normalized ( ) const

Returns the normalized vector.
Given a vector $\vec{v} = (x,y,z)$ , this function returns $\frac{\vec{v}}{||\vec{v}||^2}$ . return none.

Date: 2015/Aug/21

bool Bial::Vector3D::operator!= ( const Vector3D & vec ) const

Returns if the components do not match.

Date: 2015/Aug/21

Parameters

vec	Input vector to be compared. return none.

Vector3D Bial::Vector3D::operator* ( double s ) const

Multiply operation, the vector components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

s	A scalar value to be multiplied.

Returns: Result vector.

Vector3D& Bial::Vector3D::operator*= ( double s )

Multiply operation, the vector components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

s	A scalar value to be multiplied.

Returns: Reference to 'this' vector.

Vector3D Bial::Vector3D::operator+ ( const Vector3D & vec ) const

Add operation, the vector components are added.

Date: 2015/Aug/21

Parameters

vec	Input vector to be compared.

Warning: Throws if has NaNs.

Returns: Result vector.

Vector3D& Bial::Vector3D::operator+= ( const Vector3D & vec )

Add operation, the vector components are added.

Date: 2015/Aug/21

Parameters

vec	Input vector

Returns: Reference to 'this' vector.

Vector3D Bial::Vector3D::operator- ( const Vector3D & vec ) const

Subtract operation, the vector components are subtracted.

Date: 2015/Aug/21

Parameters

vec	Input vector

Returns: Result vector.

Vector3D Bial::Vector3D::operator- ( ) const

Returns the vector inverse.

Date: 2015/Aug/21

Returns: Result vector.

Vector3D& Bial::Vector3D::operator-= ( const Vector3D & vec )

Subtract operation, the vector components are subtracted.

Date: 2015/Aug/21

Parameters

vec	Input vector

Returns: Reference to 'this' vector.

Vector3D Bial::Vector3D::operator/ ( double s ) const

Division operation, the vector components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Result vector.

Vector3D& Bial::Vector3D::operator/= ( double s )

Division operation, the vector components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Reference to 'this' vector.

bool Bial::Vector3D::operator== ( const Vector3D & vec ) const

Returns if the components match.

Date: 2015/Aug/21

Parameters

vec	Input vector return none.

double Bial::Vector3D::operator[] ( int i ) const

Gives the option to loop over the components of a vector.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Vector component value at index i.

Warning: Throws if i < 0 or i > 2

double& Bial::Vector3D::operator[] ( int i )

Gives the option to loop over the components of a vector.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Vector component value at index i.

Warning: Throws if i < 0 or i > 2

Point3D Bial::Vector3D::toPoint ( ) const

Conversion from Vector3D to Point3D.

Date: 2015/Aug/21

Returns: Result point.

Member Data Documentation

double Bial::Vector3D::x

Definition at line 49 of file Geometrics.hpp.

double Bial::Vector3D::y

Vector direction in y.

Definition at line 51 of file Geometrics.hpp.

double Bial::Vector3D::z

Vector direction in z.

Definition at line 53 of file Geometrics.hpp.

class Bial::Point3D

The Point3D class is a Geometric representation of a point in 3D space.
A point is a zerodimensional location in 3D space.

Date: 2015/Aug/21

Definition at line 218 of file Geometrics.hpp.

Collaboration diagram for Bial::Point3D:

Public Member Functions
	Point3D ()

	Point3D (double xx, double yy, double zz)
	Point3D constructor. More...

bool	HasNaNs () const
	HasNaNs returns if the any of the components is'nt a valid number. return none. More...

bool	operator== (const Point3D &p) const
	Returns if the positions match. More...

bool	operator!= (const Point3D &p) const
	Returns if the positions do not match. More...

Point3D	operator+ (const Vector3D &vec) const
	Add operation, the point position is added to the vector components. More...

Point3D &	operator+= (const Vector3D &vec)
	Add operation, the point position is added to the vector components. More...

Vector3D	operator- (const Point3D &p) const
	Subtract operation, the point positions are subtracted, generating a Vector3D. More...

Vector3D	operator- (const Vector3D &vec) const
	Subtract operation, the point position is subtracted to the vector components, generating a Vector3D. More...

Point3D &	operator-= (const Vector3D &vec)
	Subtract operation, the point position is subtracted to the vector components. More...

Point3D &	operator+= (const Point3D &p)
	Add operation, the points positions are added. More...

Point3D	operator+ (const Point3D &p) const
	Add operation, the points positions are added. More...

Point3D	operator* (double f) const
	Multiply operation, the point position components are multiplied to a scalar value. More...

Point3D &	operator*= (double f)
	Multiply operation, the point position components are multiplied to a scalar value. More...

Point3D	operator/ (double f) const
	Division operation, the point position components are divided by s. More...

Point3D &	operator/= (double f)
	Division operation, the point position components are divided by s. More...

double	operator[] (int i) const
	Gives the option to loop over the components of the point position. More...

double &	operator[] (int i)
	Gives the option to loop over the components of the point position. More...

Vector3D	toVector () const
	Conversion from Point3D to Vector3D. More...

bool	operator< (const Point3D &p) const
	Simple function used in sorting algoritms. More...

bool	operator> (const Point3D &p) const
	Simple function used in sorting algoritms. More...

Public Attributes
double	x

double	y
	Point position in y. More...

double	z
	Point position in z. More...

Constructor & Destructor Documentation

Bial::Point3D::Point3D ( )

Bial::Point3D::Point3D	(	double	xx,
		double	yy,
		double	zz
	)

explicit

Point3D constructor.

Date: 2015/Aug/21

Parameters

xx	Point direction in x.
yy	Point direction in y.
zz	Point direction in z.

Warning: Throws if has NaNs.

Member Function Documentation

bool Bial::Point3D::HasNaNs ( ) const

HasNaNs returns if the any of the components is'nt a valid number. return none.

Date: 2015/Aug/21

bool Bial::Point3D::operator!= ( const Point3D & p ) const

Returns if the positions do not match.

Date: 2015/Aug/21

Parameters

p	Input point to be compared. return none.

Point3D Bial::Point3D::operator* ( double f ) const

Multiply operation, the point position components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

f	A scalar value to be multiplied.

Returns: Result point.

Point3D& Bial::Point3D::operator*= ( double f )

Multiply operation, the point position components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

f	A scalar value to be multiplied.

Returns: Reference to 'this' point.

Point3D Bial::Point3D::operator+ ( const Vector3D & vec ) const

Add operation, the point position is added to the vector components.

Date: 2015/Aug/21

Parameters

vec	Input vector.

Returns: Result point.

Point3D Bial::Point3D::operator+ ( const Point3D & p ) const

Add operation, the points positions are added.

Date: 2015/Aug/21

Parameters

p	Input point.

Returns: Result point.

Point3D& Bial::Point3D::operator+= ( const Vector3D & vec )

Add operation, the point position is added to the vector components.

Date: 2015/Aug/21

Parameters

vec	Input vector.

Returns: Reference to 'this' point.

Point3D& Bial::Point3D::operator+= ( const Point3D & p )

Add operation, the points positions are added.

Date: 2015/Aug/21

Parameters

p	Input point.

Returns: Reference to 'this' point.

Vector3D Bial::Point3D::operator- ( const Point3D & p ) const

Subtract operation, the point positions are subtracted, generating a Vector3D.

Date: 2015/Aug/21

Parameters

p	Input point.

Warning: Throws if has NaNs.

Returns: Result vector3D.

Vector3D Bial::Point3D::operator- ( const Vector3D & vec ) const

Subtract operation, the point position is subtracted to the vector components, generating a Vector3D.

Date: 2015/Aug/21

Parameters

vec	Input vector.

Warning: Throws if has NaNs.

Returns: Result point.

Point3D& Bial::Point3D::operator-= ( const Vector3D & vec )

Subtract operation, the point position is subtracted to the vector components.

Date: 2015/Aug/21

Parameters

vec	Input vector.

Returns: Reference to 'this' point.

Point3D Bial::Point3D::operator/ ( double f ) const

Division operation, the point position components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Result point.

Point3D& Bial::Point3D::operator/= ( double f )

Division operation, the point position components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Reference to 'this' point.

bool Bial::Point3D::operator< ( const Point3D & p ) const

inline

Simple function used in sorting algoritms.

Date: 2015/Aug/21

Parameters

p	Input point to be compared. return none.

Definition at line 374 of file Geometrics.hpp.

bool Bial::Point3D::operator== ( const Point3D & p ) const

Returns if the positions match.

Date: 2015/Aug/21

Parameters

p	Input point to be compared.

Warning: Throws if has NaNs. return none.

bool Bial::Point3D::operator> ( const Point3D & p ) const

inline

Simple function used in sorting algoritms.

Date: 2015/Aug/21

Parameters

p	Input point to be compared. return none.

Definition at line 385 of file Geometrics.hpp.

double Bial::Point3D::operator[] ( int i ) const

Gives the option to loop over the components of the point position.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Position component value at index i.

Warning: Throws if i < 0 or i > 2

double& Bial::Point3D::operator[] ( int i )

Gives the option to loop over the components of the point position.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Position component value at index i.

Warning: Throws if i < 0 or i > 2

Vector3D Bial::Point3D::toVector ( ) const

Conversion from Point3D to Vector3D.

Date: 2015/Aug/21

Returns: Result vector.

Warning: Throws if has NaNs.

Member Data Documentation

double Bial::Point3D::x

Definition at line 223 of file Geometrics.hpp.

double Bial::Point3D::y

Point position in y.

Definition at line 225 of file Geometrics.hpp.

double Bial::Point3D::z

Point position in z.

Definition at line 227 of file Geometrics.hpp.

class Bial::Normal

The Normal class is the geometric representation of a Normal in 3D space.
A surface normal (or just normal) is a vector that is perpendicular to a surface at a particular position.
It can be defined as the cross product of any two nonparallel vectors that are tangent to the surface at a point.
The implementations of Normal3D and Vector3D are very similar. Like vectors, normals are represented by three floats x, y, and z;
they can be added and subtracted to compute new normals; and they can be scaled and normalized.
However, a normal cannot be added to a point, and one cannot take the cross product of two normals.

Date: 2015/Aug/21

Definition at line 403 of file Geometrics.hpp.

Collaboration diagram for Bial::Normal:

Public Member Functions
	Normal ()

	Normal (double xx, double yy, double zz)
	Normal constructor. More...

	Normal (const Vector3D &vec)
	Conversion from Vector3D to Normal. More...

bool	HasNaNs () const
	HasNaNs returns if the any of the components is'nt a valid number. return none. More...

bool	operator== (const Normal &norm) const
	Returns if the components match. More...

bool	operator!= (const Normal &norm) const
	Returns if the components do not match. More...

Normal	operator+ (const Normal &norm) const
	Add operation, the normal components are added. More...

Normal &	operator+= (const Normal &norm)
	Add operation, the normal components are added. More...

Normal	operator- (const Normal &norm) const
	Subtract operation, the normal components are subtracted. More...

Normal &	operator-= (const Normal &norm)
	Subtract operation, the normal components are subtracted. More...

Normal	operator* (double s) const
	Multiply operation, the normal components are multiplied to a scalar value. More...

Normal &	operator*= (double s)
	Multiply operation, the normal components are multiplied to a scalar value. More...

Normal	operator/ (double s) const
	Division operation, the normal components are divided by s. More...

Normal &	operator/= (double s)
	Division operation, the normal components are divided by s. More...

Normal	operator- () const
	Returns the normal inverse. More...

double	operator[] (int i) const
	Gives the option to loop over the components of a normal. More...

double &	operator[] (int i)
	Gives the option to loop over the components of a normal. More...

double	LengthSquared () const
	Returns the length of a normal. Given a normal $\vec{v} = (x,y,z)$ , this function returns $\|\|\vec{v}\|\| = \sqrt{xx+yy+z*z}$ . More...

double	Length () const
	Returns the squared length of a normal. Given a normal $\vec{v} = (x,y,z)$ , this function returns $\|\|\vec{v}\|\|^2 = {xx+yy+z*z}$ . More...

Normal	Normalized () const
	Returns the normalized normal. Given a normal $\vec{v} = (x,y,z)$ , this function returns $\frac{\vec{v}}{\|\|\vec{v}\|\|^2}$ . return none. More...

Public Attributes
double	x

double	y
	Normal direction in y. More...

double	z
	Normal direction in z. More...

Constructor & Destructor Documentation

Bial::Normal::Normal ( )

Bial::Normal::Normal	(	double	xx,
		double	yy,
		double	zz
	)

explicit

Normal constructor.

Date: 2015/Aug/21

Parameters

xx	Normal direction in x.
yy	Normal direction in y.
zz	Normal direction in z.

Warning: Throws if has NaN parameter.

Bial::Normal::Normal ( const Vector3D & vec )

explicit

Conversion from Vector3D to Normal.

Date: 2015/Aug/21

Parameters

vec	input vector.

Member Function Documentation

bool Bial::Normal::HasNaNs ( ) const

HasNaNs returns if the any of the components is'nt a valid number. return none.

Date: 2015/Aug/21

double Bial::Normal::Length ( ) const

Returns the squared length of a normal.
Given a normal $\vec{v} = (x,y,z)$ , this function returns $||\vec{v}||^2 = {x*x+y*y+z*z}$ .

Date: 2015/Aug/21

Returns: The squared length of a normal.

double Bial::Normal::LengthSquared ( ) const

Returns the length of a normal.
Given a normal $\vec{v} = (x,y,z)$ , this function returns $||\vec{v}|| = \sqrt{x*x+y*y+z*z}$ .

Date: 2015/Aug/21

Returns: The length of a normal.

Normal Bial::Normal::Normalized ( ) const

Returns the normalized normal.
Given a normal $\vec{v} = (x,y,z)$ , this function returns $\frac{\vec{v}}{||\vec{v}||^2}$ . return none.

Date: 2015/Aug/21

bool Bial::Normal::operator!= ( const Normal & norm ) const

Returns if the components do not match.

Date: 2015/Aug/21

Parameters

norm	Input normal to be compared. return none.

Normal Bial::Normal::operator* ( double s ) const

Multiply operation, the normal components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

s	A scalar value to be multiplied.

Returns: Result normal.

Normal& Bial::Normal::operator*= ( double s )

Multiply operation, the normal components are multiplied to a scalar value.

Date: 2015/Aug/21

Parameters

s	A scalar value to be multiplied.

Returns: Reference to 'this' normal.

Normal Bial::Normal::operator+ ( const Normal & norm ) const

Add operation, the normal components are added.

Date: 2015/Aug/21

Parameters

norm	Input normal to be compared.

Warning: Throws if has NaNs.

Returns: Result normal.

Normal& Bial::Normal::operator+= ( const Normal & norm )

Add operation, the normal components are added.

Date: 2015/Aug/21

Parameters

norm	Input normal

Returns: Reference to 'this' normal.

Normal Bial::Normal::operator- ( const Normal & norm ) const

Subtract operation, the normal components are subtracted.

Date: 2015/Aug/21

Parameters

norm	Input normal

Returns: Result normal.

Normal Bial::Normal::operator- ( ) const

Returns the normal inverse.

Date: 2015/Aug/21

Returns: Result normal.

Normal& Bial::Normal::operator-= ( const Normal & norm )

Subtract operation, the normal components are subtracted.

Date: 2015/Aug/21

Parameters

norm	Input normal

Returns: Reference to 'this' normal.

Normal Bial::Normal::operator/ ( double s ) const

Division operation, the normal components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Result normal.

Normal& Bial::Normal::operator/= ( double s )

Division operation, the normal components are divided by s.

Date: 2015/Aug/21

Parameters

s	A scalar denominator.

Returns: Reference to 'this' normal.

bool Bial::Normal::operator== ( const Normal & norm ) const

Returns if the components match.

Date: 2015/Aug/21

Parameters

norm	Input normal return none.

double Bial::Normal::operator[] ( int i ) const

Gives the option to loop over the components of a normal.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Normal component value at index i.

Warning: Throws if i < 0 or i > 2

double& Bial::Normal::operator[] ( int i )

Gives the option to loop over the components of a normal.

Date: 2015/Aug/21

Parameters

i	is the component index ( 0 for x, 1 for y, and 2 for z )

Returns: Normal component value at index i.

Warning: Throws if i < 0 or i > 2

Member Data Documentation

double Bial::Normal::x

Definition at line 408 of file Geometrics.hpp.

double Bial::Normal::y

Normal direction in y.

Definition at line 410 of file Geometrics.hpp.

double Bial::Normal::z

Normal direction in z.

Definition at line 412 of file Geometrics.hpp.

class Bial::Ray

The Ray class is a mathematic representation of a light ray.
A ray is a semiinfinite line specified by its origin and direction.

Date: 2015/Aug/21

Definition at line 563 of file Geometrics.hpp.

Collaboration diagram for Bial::Ray:

Public Member Functions
	Ray ()

	Ray (const Point3D &origin, const Vector3D &direction, double start=0.f, double end=INFINITY, double t=0.f, int d=0)
	Ray constructor. More...

	Ray (const Point3D &origin, const Vector3D &direction, const Ray &parent, double start=0.f, double end=INFINITY)
	Ray constructor with "parent" ray. For convenience we also provide another ray constructor that takes a “parent” ray; the idea is that when additional rays are being spawned from an intersection, it’s useful to be able to copy the time value and set the depth value for the new ray based on the corresponding values from the previous ray. More...

Point3D	operator() (double t) const
	Operator that makes the ray be used as a parametric function and returns a Point3D at position t along the ray. Given a Ray with origin and direction $\vec{d}$ , this function returns $P = O + \vec{d} t$ . More...

Public Attributes
Point3D	o

Vector3D	d
	Ray direction vector. More...

double	mint
	Minimum value for parameter t. More...

double	maxt
	Maximum value for parameter t. More...

double	time
	Ray time counter used in animated objects simulation. More...

int	depth
	The ray depth member tracks how many times light has bounced along the current path. More...

Constructor & Destructor Documentation

Bial::Ray::Ray ( )

Bial::Ray::Ray	(	const Point3D &	origin,
		const Vector3D &	direction,
		double	start = `0.f`,
		double	end = `INFINITY`,
		double	t = `0.f`,
		int	d = `0`
	)

Ray constructor.

Parameters

origin	Ray origin point.
direction	Ray direction vector.
start	Minimum value for parameter t.
end	Maximum value for parameter t.
t	Ray time counter used in animated objects simulation.
d	The ray depth member tracks how many times light has bounced along the current path.

Bial::Ray::Ray	(	const Point3D &	origin,
		const Vector3D &	direction,
		const Ray &	parent,
		double	start = `0.f`,
		double	end = `INFINITY`
	)

Ray constructor with "parent" ray.
For convenience we also provide another ray constructor that takes a “parent” ray; the idea is that when additional rays are being spawned from an intersection, it’s useful to be able to copy the time value and set the depth value for the new ray based on the corresponding values from the previous ray.

Parameters

origin	Ray origin point.
direction	Ray direction vector.
parent	A parent Ray.
start	Minimum value for parameter t.
end	Maximum value for parameter t.

Member Function Documentation

Point3D Bial::Ray::operator() ( double t ) const

Operator that makes the ray be used as a parametric function and returns a Point3D at position t along the ray.
Given a Ray with origin $ O $ and direction $\vec{d}$ , this function returns $P = O + *\vec{d} * t$ .

Parameters

t	Input parameter .

Returns: The resulting point .

Member Data Documentation

Vector3D Bial::Ray::d

Ray direction vector.

Definition at line 573 of file Geometrics.hpp.

int Bial::Ray::depth

The ray depth member tracks how many times light has bounced along the current path.

Definition at line 589 of file Geometrics.hpp.

double Bial::Ray::maxt

mutable

Maximum value for parameter t.

Definition at line 581 of file Geometrics.hpp.

double Bial::Ray::mint

mutable

Minimum value for parameter t.

Definition at line 577 of file Geometrics.hpp.

Point3D Bial::Ray::o

Definition at line 569 of file Geometrics.hpp.

double Bial::Ray::time

Ray time counter used in animated objects simulation.

Definition at line 585 of file Geometrics.hpp.

class Bial::BBox

The BBox class is a Bounding Box with 8 vertices, and can be represented by 2 points (6coordinates).

Date: 2015/Aug/21

Definition at line 640 of file Geometrics.hpp.

Collaboration diagram for Bial::BBox:

Public Member Functions
	BBox ()

	BBox (const Point3D &p)

	BBox (const Point3D &p1, const Point3D &p2)

bool	operator== (const BBox &other) const

bool	operator!= (const BBox &other) const

BBox	Normalized () const

bool	Overlaps (const BBox &b) const

bool	Inside (const Point3D &pt) const

void	Expand (double delta)

double	SurfaceArea () const

double	Volume () const

int	MaximumExtent () const

const Point3D &	operator[] (int i) const

Point3D &	operator[] (int i)

Point3D	at (size_t vtx)

Point3D	Lerp (double tx, double ty, double tz) const

Vector3D	Offset (const Point3D &p) const

void	BoundingSphere (Point3D c, double rad) const

Public Attributes
Point3D	pMin

Point3D	pMax

Friends
BBox	Union (const BBox &b, const Point3D &p)

BBox	Union (const BBox &b, const BBox &b2)

Constructor & Destructor Documentation

Bial::BBox::BBox ( )

Bial::BBox::BBox ( const Point3D & p )

Bial::BBox::BBox	(	const Point3D &	p1,
		const Point3D &	p2
	)

Member Function Documentation

Point3D Bial::BBox::at ( size_t vtx )

void Bial::BBox::BoundingSphere	(	Point3D *	c,
		double *	rad
	)		const

void Bial::BBox::Expand ( double delta )

bool Bial::BBox::Inside ( const Point3D & pt ) const

Point3D Bial::BBox::Lerp	(	double	tx,
		double	ty,
		double	tz
	)		const

int Bial::BBox::MaximumExtent ( ) const

BBox Bial::BBox::Normalized ( ) const

inline

Definition at line 656 of file Geometrics.hpp.

Vector3D Bial::BBox::Offset ( const Point3D & p ) const

bool Bial::BBox::operator!= ( const BBox & other ) const

bool Bial::BBox::operator== ( const BBox & other ) const

const Point3D& Bial::BBox::operator[] ( int i ) const

Point3D& Bial::BBox::operator[] ( int i )

bool Bial::BBox::Overlaps ( const BBox & b ) const

double Bial::BBox::SurfaceArea ( ) const

double Bial::BBox::Volume ( ) const

Friends And Related Function Documentation

BBox Union	(	const BBox &	b,
		const Point3D &	p
	)

friend

BBox Union	(	const BBox &	b,
		const BBox &	b2
	)

friend

Member Data Documentation

Point3D Bial::BBox::pMax

Definition at line 643 of file Geometrics.hpp.

Point3D Bial::BBox::pMin

Definition at line 643 of file Geometrics.hpp.

class Bial::Transform3D

The Transform3D class holds affine matrices and is used to apply geometric transformations over cartesian coordinates.
The affine transformation multiplies the coordinates vector to the affine matrix.

Date: 2015/Aug/21

Definition at line 696 of file Geometrics.hpp.

Collaboration diagram for Bial::Transform3D:

Public Types
enum	: int { X = 0, Y, Z }

Public Member Functions
	Transform3D ()

	Transform3D (const Matrix< double > &mat)

	Transform3D (const Matrix< double > &mat, const Matrix< double > &inv)

Matrix< double >	getAffineMatrix () const

void	setAffineMatrix (const Matrix< double > &mat)

Matrix< double >	getInverseMatrix () const

void	setInverseMatrix (const Matrix< double > &value)

void	reset ()

Transform3D	copy ()

Transform3D	Inverse ()

bool	operator== (const Transform3D &other)

bool	operator!= (const Transform3D &other)

Transform3D	operator* (const Transform3D &other) const

Point3D	operator() (const Point3D &pt) const

void	operator() (const Point3D &pt, Point3D *res) const

Vector3D	operator() (const Vector3D &vec) const

void	operator() (const Vector3D &vec, Vector3D *res) const

Normal	operator() (const Normal &norm) const

void	operator() (const Normal &norm, Normal *res) const

Ray	operator() (const Ray &ray) const

void	operator() (const Ray &ray, Ray *res) const

BBox	operator() (const BBox &b) const

void	operator() (const BBox &b, BBox *res) const

Point3D	operator() (double x, double y, double z) const

Transform3D &	Translate (double dx, double dy, double dz=0.f)

Transform3D &	Scale (double sx, double sy, double sz=1.f)

Transform3D &	Scale (double factor)

bool	HasScale () const

Transform3D &	Rotate (double degrees, int dms)

Transform3D &	RotateRadians (double rad, int dms)

Transform3D &	Rotate (double degrees, const Vector3D &axis)

Transform3D &	RotateRadians (double rad, const Vector3D &axis)

Transform3D &	Shear (double s_xy, double s_yx, double s_xz, double s_yz, double s_zx, double s_zy)

Transform3D &	LookAt (const Point3D &pos, const Point3D &look, const Vector3D &up)

bool	SwapsHandedness () const

Member Enumeration Documentation

anonymous enum : int

Enumerator
X
Y
Z

Definition at line 699 of file Geometrics.hpp.

Constructor & Destructor Documentation

Bial::Transform3D::Transform3D ( )

Bial::Transform3D::Transform3D ( const Matrix< double > & mat )

Bial::Transform3D::Transform3D	(	const Matrix< double > &	mat,
		const Matrix< double > &	inv
	)

Member Function Documentation

Transform3D Bial::Transform3D::copy ( )

Matrix< double > Bial::Transform3D::getAffineMatrix ( ) const

Matrix< double > Bial::Transform3D::getInverseMatrix ( ) const

bool Bial::Transform3D::HasScale ( ) const

Transform3D Bial::Transform3D::Inverse ( )

Transform3D& Bial::Transform3D::LookAt	(	const Point3D &	pos,
		const Point3D &	look,
		const Vector3D &	up
	)

bool Bial::Transform3D::operator!= ( const Transform3D & other )

Point3D Bial::Transform3D::operator() ( const Point3D & pt ) const

void Bial::Transform3D::operator()	(	const Point3D &	pt,
		Point3D *	res
	)		const

Vector3D Bial::Transform3D::operator() ( const Vector3D & vec ) const

void Bial::Transform3D::operator()	(	const Vector3D &	vec,
		Vector3D *	res
	)		const

Normal Bial::Transform3D::operator() ( const Normal & norm ) const

void Bial::Transform3D::operator()	(	const Normal &	norm,
		Normal *	res
	)		const

Ray Bial::Transform3D::operator() ( const Ray & ray ) const

void Bial::Transform3D::operator()	(	const Ray &	ray,
		Ray *	res
	)		const

BBox Bial::Transform3D::operator() ( const BBox & b ) const

void Bial::Transform3D::operator()	(	const BBox &	b,
		BBox *	res
	)		const

Point3D Bial::Transform3D::operator()	(	double	x,
		double	y,
		double	z
	)		const

Transform3D Bial::Transform3D::operator* ( const Transform3D & other ) const

bool Bial::Transform3D::operator== ( const Transform3D & other )

void Bial::Transform3D::reset ( )

Transform3D& Bial::Transform3D::Rotate	(	double	degrees,
		int	dms
	)

Transform3D& Bial::Transform3D::Rotate	(	double	degrees,
		const Vector3D &	axis
	)

Transform3D& Bial::Transform3D::RotateRadians	(	double	rad,
		int	dms
	)

Transform3D& Bial::Transform3D::RotateRadians	(	double	rad,
		const Vector3D &	axis
	)

Transform3D& Bial::Transform3D::Scale	(	double	sx,
		double	sy,
		double	sz = `1.f`
	)

Transform3D& Bial::Transform3D::Scale ( double factor )

void Bial::Transform3D::setAffineMatrix ( const Matrix< double > & mat )

void Bial::Transform3D::setInverseMatrix ( const Matrix< double > & value )

Transform3D& Bial::Transform3D::Shear	(	double	s_xy,
		double	s_yx,
		double	s_xz,
		double	s_yz,
		double	s_zx,
		double	s_zy
	)

bool Bial::Transform3D::SwapsHandedness ( ) const

Transform3D& Bial::Transform3D::Translate	(	double	dx,
		double	dy,
		double	dz = `0.f`
	)

class Bial::DifferentialGeometry

The DifferentialGeometry class is a parametric representation of the Shape geometry.

Date: 2015/Aug/21

Definition at line 778 of file Geometrics.hpp.

Collaboration diagram for Bial::DifferentialGeometry:

Public Member Functions
	DifferentialGeometry ()
	DifferentialGeometry empty constructor. More...

	DifferentialGeometry (const Point3D &p, const Vector3D &dpdu, const Vector3D &dpdv, const Normal &dndu, const Normal &dndv, float u, float v, const Shape *sh)
	DifferentialGeometry constructor. More...

Public Attributes
Point3D	p
	p is the point of interest. More...

Normal	nn
	nn is the normalized version of the surface normal. It's obtained from the cross product between dpdu and dpdv. More...

Vector3D	dpdu
	dpdu is the partial derivative of the surface position in u. More...

Vector3D	dpdv
	dpdv is the partial derivative of the surface position in v. More...

Normal	dndu
	dndu is the partial derivative of the surface normal in u. The vectors dndu amd dndv record the differential change in surface normal along the surface. More...

Normal	dndv
	dndv is the partial derivative of the surface normal in u. The vectors dndu amd dndv record the differential change in surface normal along the surface. More...

float	u
	u is a parametric coordinate. More...

float	v
	v is a parametric coordinate. More...

const Shape *	shape
	shape is a reference to the Shape that the differential geometry lies on. More...

Constructor & Destructor Documentation

Bial::DifferentialGeometry::DifferentialGeometry ( )

DifferentialGeometry empty constructor.

Bial::DifferentialGeometry::DifferentialGeometry	(	const Point3D &	p,
		const Vector3D &	dpdu,
		const Vector3D &	dpdv,
		const Normal &	dndu,
		const Normal &	dndv,
		float	u,
		float	v,
		const Shape *	sh
	)

DifferentialGeometry constructor.

Parameters

p	is the point of interest.
dpdu	is the partial derivative of the surface position in u.
dpdv	is the partial derivative of the surface position in v.
dndu	is the partial derivative of the surface normal in u.
dndv	is the partial derivative of the surface normal in v.
u	is a parametric coordinate.
v	is a parametric coordinate.
sh	is a reference to the Shape that the differential geometry lies on.

Member Data Documentation

Normal Bial::DifferentialGeometry::dndu

dndu is the partial derivative of the surface normal in u. The vectors dndu amd dndv record the differential change in surface normal along the surface.

Definition at line 801 of file Geometrics.hpp.

Normal Bial::DifferentialGeometry::dndv

dndv is the partial derivative of the surface normal in u. The vectors dndu amd dndv record the differential change in surface normal along the surface.

Definition at line 806 of file Geometrics.hpp.

Vector3D Bial::DifferentialGeometry::dpdu

dpdu is the partial derivative of the surface position in u.

Definition at line 792 of file Geometrics.hpp.

Vector3D Bial::DifferentialGeometry::dpdv

dpdv is the partial derivative of the surface position in v.

Definition at line 796 of file Geometrics.hpp.

Normal Bial::DifferentialGeometry::nn

nn is the normalized version of the surface normal. It's obtained from the cross product between dpdu and dpdv.

Definition at line 788 of file Geometrics.hpp.

Point3D Bial::DifferentialGeometry::p

p is the point of interest.

Definition at line 783 of file Geometrics.hpp.

const Shape* Bial::DifferentialGeometry::shape

shape is a reference to the Shape that the differential geometry lies on.

Definition at line 818 of file Geometrics.hpp.

float Bial::DifferentialGeometry::u

u is a parametric coordinate.

Definition at line 810 of file Geometrics.hpp.

float Bial::DifferentialGeometry::v

v is a parametric coordinate.

Definition at line 814 of file Geometrics.hpp.

class Bial::FastTransform

Definition at line 844 of file Geometrics.hpp.

Collaboration diagram for Bial::FastTransform:

Public Types
enum	: int { X = 0, Y, Z }

Public Member Functions
	FastTransform ()

	FastTransform (const Matrix< int > &mat)

	FastTransform (const Matrix< int > &mat, const Matrix< int > &inv)

Matrix< int >	getAffineMatrix () const

void	setAffineMatrix (const Matrix< int > &mat)

Matrix< int >	getInverseMatrix () const

void	setInverseMatrix (const Matrix< int > &value)

void	reset ()

FastTransform	Inverse ()

FastTransform	copy ()

bool	operator== (const FastTransform &other)

bool	operator!= (const FastTransform &other)

FastTransform	operator* (const FastTransform &other) const

Point3D	operator() (double x, double y, double z) const

void	operator() (int x, int y, int z, int xx, int yy, int *zz) const

Point3D	operator() (const Point3D &pt) const

void	operator() (const Point3D &pt, Point3D *res) const

FastTransform &	Translate (int dx, int dy, int dz=0.f)

FastTransform &	Scale (int sx, int sy, int sz=1.f)

FastTransform &	Scale (int factor)

FastTransform &	Rotate (double degrees, int dms)

FastTransform &	RotateRadians (double rad, int dms)

FastTransform &	Shear (int s_xy, int s_yx, int s_xz, int s_yz, int s_zx, int s_zy)

Member Enumeration Documentation

anonymous enum : int

Enumerator
X
Y
Z

Definition at line 847 of file Geometrics.hpp.

Constructor & Destructor Documentation

Bial::FastTransform::FastTransform ( )

Bial::FastTransform::FastTransform ( const Matrix< int > & mat )

Bial::FastTransform::FastTransform	(	const Matrix< int > &	mat,
		const Matrix< int > &	inv
	)

Member Function Documentation

FastTransform Bial::FastTransform::copy ( )

Matrix< int > Bial::FastTransform::getAffineMatrix ( ) const

Matrix< int > Bial::FastTransform::getInverseMatrix ( ) const

FastTransform Bial::FastTransform::Inverse ( )

bool Bial::FastTransform::operator!= ( const FastTransform & other )

Point3D Bial::FastTransform::operator()	(	double	x,
		double	y,
		double	z
	)		const

void Bial::FastTransform::operator()	(	int	x,
		int	y,
		int	z,
		int *	xx,
		int *	yy,
		int *	zz
	)		const

Point3D Bial::FastTransform::operator() ( const Point3D & pt ) const

void Bial::FastTransform::operator()	(	const Point3D &	pt,
		Point3D *	res
	)		const

FastTransform Bial::FastTransform::operator* ( const FastTransform & other ) const

bool Bial::FastTransform::operator== ( const FastTransform & other )

void Bial::FastTransform::reset ( )

FastTransform& Bial::FastTransform::Rotate	(	double	degrees,
		int	dms
	)

FastTransform& Bial::FastTransform::RotateRadians	(	double	rad,
		int	dms
	)

FastTransform& Bial::FastTransform::Scale	(	int	sx,
		int	sy,
		int	sz = `1.f`
	)

FastTransform& Bial::FastTransform::Scale ( int factor )

void Bial::FastTransform::setAffineMatrix ( const Matrix< int > & mat )

void Bial::FastTransform::setInverseMatrix ( const Matrix< int > & value )

FastTransform& Bial::FastTransform::Shear	(	int	s_xy,
		int	s_yx,
		int	s_xz,
		int	s_yz,
		int	s_zx,
		int	s_zy
	)

FastTransform& Bial::FastTransform::Translate	(	int	dx,
		int	dy,
		int	dz = `0.f`
	)

Function Documentation

double Bial::AbsDot	(	const Vector3D &	v1,
		const Vector3D &	v2
	)

double Bial::AbsDot	(	const Normal &	n1,
		const Normal &	n2
	)

double Bial::AbsDot	(	const Normal &	n1,
		const Vector3D &	v2
	)

double Bial::AbsDot	(	const Vector3D &	v1,
		const Normal &	n2
	)

void Bial::CoordinateSystem	(	const Vector3D &	v1,
		Vector3D *	v2,
		Vector3D *	v3
	)

Vector3D Bial::Cross	(	const Vector3D &	v1,
		const Vector3D &	v2
	)

double Bial::Distance	(	const Point3D &	p1,
		const Point3D &	p2
	)

double Bial::DistanceSquared	(	const Point3D &	p1,
		const Point3D &	p2
	)

double Bial::Dot	(	const Vector3D &	v1,
		const Vector3D &	v2
	)

double Bial::Dot	(	const Normal &	n1,
		const Normal &	n2
	)

double Bial::Dot	(	const Normal &	n1,
		const Vector3D &	v2
	)

double Bial::Dot	(	const Vector3D &	v1,
		const Normal &	n2
	)

Normal Bial::FaceForward	(	const Normal &	n,
		const Vector3D &	v
	)

double Bial::Lerp	(	double	t,
		double	v1,
		double	v2
	)

Simple linear interpolation.

Date: 2015/Aug/21

Parameters

t	Factor
v1	value 1
v2	value 2 return none.

Vector3D Bial::operator*	(	double	s,
		const Vector3D &	vec
	)

Point3D Bial::operator*	(	double	s,
		const Point3D &	p
	)

Normal Bial::operator*	(	double	s,
		const Normal &	norm
	)

template<class O >

O& Bial::operator<<	(	O &	os,
		const Vector3D &	vec
	)

Definition at line 938 of file Geometrics.hpp.

template<class O >

O& Bial::operator<<	(	O &	os,
		const Point3D &	pt
	)

Definition at line 943 of file Geometrics.hpp.

template<class O >

O& Bial::operator<<	(	O &	os,
		const Normal &	norm
	)

Definition at line 948 of file Geometrics.hpp.

template<class O >

O& Bial::operator<<	(	O &	os,
		const Ray &	ray
	)

Definition at line 953 of file Geometrics.hpp.

template<class O >

O& Bial::operator<<	(	O &	os,
		const BBox &	box
	)

Definition at line 958 of file Geometrics.hpp.

template<class O >

O& Bial::operator<<	(	O &	os,
		const Transform3D &	tr
	)

Definition at line 963 of file Geometrics.hpp.

Classes

Functions

Detailed Description

Class Documentation

Public Member Functions

Static Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Public Member Functions

Public Attributes

Friends

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

Public Types

Public Member Functions

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Data Documentation

Public Types

Public Member Functions

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Function Documentation